MECHANISMS OPERATING METALS AT ELEVATED …

PROCEEDINGS

of

THE EIGHTH SAGAMORE ORDNANCE MATERIALS RESEARCH C O N F E R E N C E

MECHANISMS OPERATING IN METALS AT ELEVATED TEMPERATURES

Conducted at

Sagamore Conference Center

Rocquette Lake, N e w Jork

August 22, 23, 24, and 25, 1961

Contract No. DA-30-069-ORD-3298

Sponsored by

THE ORDNANCE M A T E R I A L S RESEARCH O F F I C E

of the

U. S. ARMY

A r r a n g e m e n t s by

SYRACUSE UNIVERSITY R E S E A R C H INSTITUTE

T A B L E OF C O N T E N T S

... P R E F A C E , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , , . . . . .~ .m 111

T E C H N I C A L P R O G R A M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

SESSION I: "THE S T R U C T U R A L A S P E C T S O F METALS", Dr. Volker Weiss a n d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mr. G. T . Schaeffer 1

I v SESSION 11: "THE R O L E O F IMPERFECTIONS IN DIFFUSION'*, Dr. C. E.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $i

Birchenall 61

i P r e p r e d D i s c u s s i o n - "DISLOCATIONS AND DIFFUSION IN ............................. SILICON", Dr. H. J. Q u e i s s e r 75

SESSION 111: "RECRYSTALLIZATION AND P H A S E TRANSFORMATION", Dr. John N e w k i r k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

P r e p a r e d D i s c u s s i o n - '''THE R O L E O F E L E C T R O N CONFIGURATION . . . . . . . . . ON RECRYSTALLIZATION", Dr. E. P. Abrahamson, I1 107

. . . . . . . . . . . . . SESSION IV: "SOLID-GAS REACTIONS", Dr. E. A. Gu lb ransen 113

SESSION V: "GRAIN BOUNDARY BEHAVIOR IN HIGH T E M P E R A T U R E DEFORMATION AND FRACTURE", Dr. Arthur W. Mullendore and . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dr. N i c h o l a s J. Gran t 151

L I S T O F A T T E N D E E S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

P R E F A C E

T h e papers assembled in t h i s report were presented a t the Eighth Sagamore Ordnance Materials Research Conference held a t Syracuse University 's Sagamore Conference Center near Racquet te Lake , New York from August 22nd to the 25th, 1961. Syracuse University 's Department of Chemical Engineer ing and Metallurgy made the arrangements for conducting t h i s conference with the a s s i s t a n c e of the Adirondack Conference Center staff , under Contract No. DA-30-O6PORD-3298. T h e conference was sponsored by the Ordnance Materials R e s e a r c h Office, Watertown, Mass. T h e general planning and operations were t ransacted through a conference committee comyosed of representat ives of the Army and Syracuse University with N. L, Reed of the Ordnance Materials Research Office a s chairman.

This conference, which was the eighth of a s e r i e s devoted t o various a s p e c t s of mater ia ls r esea rch of in tereet t o the U. S. Army Ordnance Corps, w a s intended t o provide Government and associated Non-Government groups with information on the present s t a t u s of research on the sub jec t of mechanisms operating in metals a t e levated temperaturae, principally to investi- g a t e and evaluate the phys' ical metallurgical f ac to r s involved. T h e scope of th i s conference included the s t ructural a s p k c t s of metals , the role of irnperfectiona in diffusion and mechanical properties, ~ h a s e transformlation, and solid-gas reactions. T h e l ec tu res and d i scuss ions defined, more expl ic i t ly , the ;ole played by the factors evaluated and indicated a r e a s where information i s lacking or inconclusive. Out of th is , i t i s hoped that future research programs may be developed which wil l r e su l t in more complete knowledge in th i s extremely important f i e ld of metallurgy. I

A to ta l of 70 persons a s s o c i a t e d with research in the a r e a of the conference s u b j e c t a t tended and contributed from their knowledge and exper iences with talke, comments, and dis- cuseions . T h i s group w a s made up primarily of representat ives from government agenc ies , univers i t ies , and industr ia l research organizations.

T h e Committee is * r e d l y indebted to those who contributed t o the s u c c e s s of th i s conference , e spec ia l ly t o the spe 'akers including the dinner speaker , Dr. Bruce Inverasity, Director of the Adirondack Museum ht Blue Mountain Lake, New York, whose ta lk on Adirondnek Lore i s not included in t h e s e prdceedings.

T h e a t t endees were welcomed by N. L. Reed, Chairman of the Conference and A s s i s t a n t Director of the Ordnance he rials R e ~ e a r c h Office and by Dr. R. A. Galbraith, Dean of Engineering a t Syracuse University.

by the Conference Committee

N. L. REED

J. J. BURKE

J* L. MARTIN k F. JONES ~ P. R. KOSTING C. R. CORNTHWAITE V* WEISS , J. V. LATORRE

Chairman Ordnance Materials Research Office Secret my Ordnance Materials Research Office Ordnance Materials Research Office Ordnance Materials Research Office Army Research Office Durham Office, Chief of Ordnance

Symcuse University Research Insti tute

Syracuse University Research Institute

TECHNICAL PROGRAM

Tuesday, August 22, 1961

7 : ) s P.M. SESSION I

Wednesday, August 23, 1961

9:00 A.M.

"THE STRUCTURAL ASPECTS O F METALS"

Moderator: Mr. John Burke, Ordnance Materials Resea rch Office, Watertown, Mass.

Speaker: Dr. Volker Weiss, Syracuse University Resea rch Ins t i tu te , Syracuse , New York

"THE ROLE OF IMPERFECTIONS IN DIFFUSION"

Moderator: Dr. W. B. Robertson, Ya le University, New Haven, Connect icut

Speaker: Dr. C. E. Birchenal l , Univers i ty of Delaware, Newark, Delaware

Wednesday, August 23, 7963

7:00 P.M.

Propared Discussion: "DISLOCATIONS AND DIFFUSION IN SILICON", Dr. H. J. Queisser, Shockley Transistor, Palo Alto, California

SESSION 111

Moderator: Dr. E. P. Abrahameon, 11, Watertown Arsena l Labora- toriea, Watertown, Maesachueet ts

Speaker: Dr. John Newkirk, Cornel l University, I thica, New York

Prepared Discussion; "THE ROLE O F ELECTRON CONFIGURATION ON RECRYSTALLIZATION", Dr. E. P. Abrahamson, I1

T h u r s d a y , August 24, 1961

9:00 A.M. SESSION I V

"SOLID-GAS REACTIONS"

Moderator: Dr. J a m e s Bechtold, Westinghouse Reaearch Labora- tory, Pittsburgh 35, Pennsylvania

Speaker : Dr. E. A. Galbransen, Westinghouse Reeearch Labora-

I

i tories, Monroeville, Pennsylvania

3:30 P.M. SESSION V

"GRAIN BOUNDARY BEHAVIOR IN HIGH TEMPERATURE DEFORMATION ANDFRACTURE"

I

F r i d a y , August 25, 1961

Moderator: Dr. Klaus Zwi l sky , New England Materials Laboratory, Medford, Massachusetts

Speaker: Dr. N . J. Grant, Massachusetts Institute of Technology, Cambridge, Masaachusetta

8:30 A.M. I SESSION V I I

I "PANEL DISCUSSION" !

I Chai rman: Mr. N. L. Reed, Ordnance Materials Research Office, Watertown Arsenal, Watertown, Maaaachusetta

THE STRUCTURAL ASPECTS OF METALS

Dr. Volker Weiss

and

Mr. G. T. Schaeffdr

A B S T R A C T

Thi s introductory lecture represents an up-to-date review of the structural aspec.ts of metals with epecial reference to the behavior of metals a t elevated temparetures. The proper- t i e s of metale a t elevated temperature may also, according to Smekal, be classified a s atructure sensi t ive and atructure insensitive properties. Among the latter are the thermal - -

expansion, the electrical and thermal conductivity, the compressibility and the specific heat. Here relatively simple aesumptiona concerning the makeup of a solid lead to good agreement between theory and experiment. Examples are the relationships of Wiedemann and Franz, Ilulong and Pet i t , and the Grueneisen Rules. No such simple relationships have not been found for structure seneitive properties such a s most mechanical properties of solids. Aa these properties are often strongly affected by not "visible" growth defects of crystals or not epectroscopically determinable impurities one cannot expect to predict them, Defect theory i s therefore primarily concernred with an analysis in retrospect, i.e. with the deduction of the types and arrangements of etructural defects from the experimental evidence.

After a brief review of the ideal crystal structure and i t s consequences with respect to propertiee the c l a s s e s of lattice defects with respect to their geometrical order are discussed. These are point defecta (zero order) such am vacancies and interstitiale, line defecte (first order) i,e. dielocations, and area defects (second order) such a s grain boundaries. The various interactions between these defects as well a s their motion under external and internal forces are discuesed. Microscopically observed deformation characteristics are explained in terms of the motion and interaction of these defecta. Modern experimental techniques yielding some direct evidence of the existence of the various defects postulated are briefly reviewed.

Finally the modes of failure of metals a t elevated temperatures will be discussed. They are evaporation, creep and fracture. No final and generally applicable laws have been found to date which would allow a prediction of these technically s o important and scientifically s o baffling events, but many facets have become clarified through careful consideration of the defect etructures of metals,

1.0 I N T R O D U C T I O N

I t is the object ive of th i s conference t o d i s c u s s the various mechanisms known to b e uperalive in me ta l s at e levated temperature and t o pinpoint the a r e a s tha t are in need of c lar i f ica t ion through future research efforte. Although this is an "elevated temperaturev conference the primary emphas i s is on mechanisms ra ther than on the behavior of me ta l s above a certain temperature. I t i s therefore quite conceivable tha t room temperature proper t ies of certain low mel t ing meta l s wi l l be d i s c u s s e d a s cha rac te r i s t i c examples of e l eva ted temper- a ture mechanisms. ~ h u s , i f we wanted to define a n e leva ted temperature range in terms of operative mechanisms, i t hould have a s the lower l imit some fraction of t h e abso lu te melting point, T h i s i s borne out by s u c h simple a property a s the maximum se rv ice temperatures for which meta l s can be used; T h e y a re around 4 5 6 3 % of the absolute melting point (W-45%, Mo-59%, Ti-46%, S tee l , 8-63%, AI-60%), s e e F igure 1.

I

T h i s introductory lectLre i s intended t o present a review of the s t ructura l a s p e c t s of me ta l s with emphas i s on the e l eva ted temperature mechanisms and properties. I t should a l s o provide the background foi the more deta i led s e s s i o n s on diffusion, transformation a n d re- crys ta l l iza t ion, sol id-gas r eac t ions and imperfections and mechanical properties tha t a re to follow. I t is therefore nothing more than a n up-dated review of the sub jec t presented to fi t in the top ica l frame of the cAnference. A s quite recent ly severa l excel lent reviews and symposia have been given on t h i s sub jec t (1-10) the effort is mainly one of res ta tement with a different frame of reference.

When a metal lurgis t mentions the word s t ructure , one e x p e c t s him to talk about c rys ta l structure; and when we a l s o know that h e is primarily in teres ted in deformation and fracture, we expec t to hea r a great deal about d is locat ions . However, before deal ing with t h e s e a s p e c t s a few comments concerning the atomic and e lect ronic s t ruc tu res of me ta l s a re in order. F ina l - ly the modes of failure will be d i s c u s s e d briefly.

1.1 ELECTRONIC STRUCTUf?E

Modern theory of so l ide t e l l s u s that we have to t r ea t and "understand" the elementary par t ic les , thei r motion and in teract ions by w a y of thei r wave functions and the l a w s of quantum mechanics (11-18). T h u s from a n atomic point of view the s t ructure of me ta l s is character ized by regular arrangements of posi t ive ions with more or l e a s free e lect rons between them (19). In cer ta in ins tances , among them under e l eva ted temperature conditions, these free e l ec t rons can to a fairly good approximation b e t rea ted a s an e lect ron g a s (20).

With the help of t h i s c l a s s i c a l free e lect ron theory of me ta l s i t w a s poss ib le to exp la in e l ec t r i ca l conductivity and i t s re la t ionship to thermal conductivity by the Wiedemann-Franz law. Sommerfeld's quantum mechanical treatment (21) of the e lect ron g a s w a s able t o accoun t for the electron's contribuhon t o the h e a t capaci ty , the e lect rochemical potent ia l , t he P e l t i e r and Thomson e f fec t s and the Hall effect.

Bloch (22) and ~ r i l l o u h (23) a l s o accounted for the motion of an e lect ron in a per iodical ly changing potent ia l and havie thereby generated the e lect ron band theory of metals . According to t h i s theory the e lect rons are energet ica l ly separa ted into energy banda. There a re forbidden energy regions for e lect rons . An e lect ron can only move in a band tha t is incompletely f i l led as e lec t rons nea r the top o:f a band have infinite inert ia. T h i s band model is i l lus t ra ted in F igure 2 (12). A s t he interatomic d i s t ance d e c r e a s e s bands may overlap which can give in- c reased e lec t r i ca l conductivity s ince a not completely fi l led band may overlap a f i l l ed band. B e c a u s e of the tendency tci ach ieve the lowes t energy s t a t e the band theory a l s o a l l o w s for a n interpretation of of metals and a l loys as the band s t ructure is dependent upon

the crys ta l s t ructure (14). From that point of view i t i s important to know how the band s t ructure changes with temperature and i f a t some temperature there ia a different c rys ta l s t ructure which wi l l l e a d t o a lower energy s t a t e .

With the excep t ion of the transit ion metals the e lec trons have l i t t l e measurable contribution to the heat c a p a c i t y (14). In the transit ion metals the contribution i s to the abso - lu te temperature T according to:

Equat ion 1

where no i s the number of free e lec trons per atom, R the g a s constant and T, t h e degeneracy temperature. (To: Ni = 3470 OK, To: P d = 1,750 OK). T o go further into de ta i l of the f ree e lect ron theory would go beyond the s c o p e of the conference.

One a s p e c t worth mentioning here, however, i s the ques t ion of w h y the free e lec trons do not l e a v e the c ry s ta l , and together w i t h answering th i s ques t ion to exp la in the working of the field emis s ion microscope (24). T h e dens i ty and-potential in a crys ta l vary periodically, i.e. t he potent ia l a t a nuc leus becomes negatively infinite. A t larger d i s t a n c e s the ions a t t r ac t the e lect rons with a potent ia l V = -e/gx. T h e average potent ia l within a c rys ta l i s therefore negative, s e e F igure 3. Here Em is the maximum kinet ic energy, 1 the work function and Ef the Fermi energy. Thus , in order to remove e lect rons from a c rys ta l we must apply a very high f ie ld a s i l lus t ra ted in Figure 4.

The etronger the f i e ld the greater i e the l ikelihood of an e lect ron tunneling through the narrow triangular potent ia l barrier. An es t imate of the field e t rength required a t room or lower temperatures can be obta ined from the work function (Ww = 4.5 eV) and y ie lds 20-30MV/cm. T h i s is achieved by having a very smal l t ip radius of the material (cathode) to be investigated. T h e e lect rons wi l l l eave perpendicularly to the su r face and form an image on a f luorescent s c r e e n tha t r ep resen t s a r ep l i ca of the electron dens i ty on the t ip surface , s e e Figure 5. T h e ecat ter ing, which is due t o thermal motion of the atornos and rad ia l veloci ty components of the e l ec t rons y ie lds a resolut ion of approximately 10-20 A .

T h e ion emiss ion microscope (25) works on a s l ight ly different principle. Here a low pressure g a s is introduced ( p z lop) which is ionized in the vic ini ty of the tip (now anodic). A s the locus of the ionization is again a function of the atomic arrangement a t the surface the posi t ive gas i ons a re acce le ra ted towards the sc reen where an image of the tip su r face i s formed. T h i s method, employing a field of approximately 500 MV/cm, h a s a n even higher resolut ion because of the low deSBrogl ie w a v e length of the ions. P ro fessor Newkirk wi l l p resen t some ~ h o t o ~ r a p h s obtained with th i s technique and demonstrate their interpretation.

So much for the e lect ronic s t ructure of metals. Can we t a lk about de fec t s in th i s s t ructure? T h e answer must be y e s , however, these de fec t s are r e spons ib le for the particular e l ec t r i ca l , magnetic and chemical characteristic^ of an e lement but have l i t t le ef fect on the mechanical properties. T h e y can a l s o be ~ r e d i c t e d a prior; from quantum mechanics and a minimum energy condition. A typical example of s u c h a defect atructure is the electron configurations of the t ransi t ion metals and the rare ea r th elements. T h e band s t ructure i t se l f can be considered a de fec t s t ructure imposed by the periodic potent ia l of a crys ta l . Similar arguments can be made, e.g., for overlapping banda as a function of the l a t t i ce spac ing , for impurity bands in semiconductors, for F-centers , e t c .

1.2 ATOMIC STRUCTURE

Most metals in the so l id s t a t e have a close-packed or nearly c l o s e - ~ a c k e d s t ructure (fcc, cph), s e e F igure 6. T h i s means that the atoms can be thought of as spheres touching e a c h other in a close-packed arrangement. An exception is the bcc structure which is not a c lose-

s t ructure (Li, Na , W , Fe). While in a close-packed structure the coordination number (number of nea res t neighbors) is 12, the coordination number for the bcc la t t ice is 8 . There are a l s o some meta l s with a coordination number 4 (Ge, Sn) where covalent bonds are present and others (Ga, Hg, Bi) where other inf luences a re active. The Hurne-Rothery 8-N rule app l ies to moat e lements in the B subgroup. T h e number of nea res t neighbors i s 8-N where N is the number of the group to which the element belongs.

Mie sugges ted (26) to express the mutual potential of two atoms or ions by the binomial express ion: 1

Such a otential , i l lus t ra ted i n Figure 7, cona i s t s of an attractive part -+ a n d a repuls ive I! part +-. Since for a smal l but f in i te n, 4 depends very l i t t le on the digtance between r " I

atoms, t t is evident that second neares t neighbors, etc. may have an effect on the l a t t i ce energy. T h i s explains tb some degree the s tabi l i ty of the b c c la t t ice ( m z n).

Mie's equation for t h i potential a l lows the derivation of the two G r B n e i ~ e n Rules . T h e f i rs t rule pe r ta ins to the bulk modulus K of a so l id which i s given by;

where Vo is the equilibrium volume and 4 the equilibrium la t t ice energy. F o r the change in compressibil i ty as a function of pressure one obtains :

which y ie lds approximately the right r e s u l t s for the a lka l i hal ides (27) with m = l , n=9, i.e. 5.33. Some alkali metala show low va lues (Li: 2.6, N a : 2.8. K: 2.8, Rb: 5.22, Cs: 5.20) while other meta l s show much higher values. Bridgman (28) concludes that in these c a s e s the compressibil i ty of thh ions themselves may be responsible ,

Grilneisen's second rule per ta ins to the thermal expansion to the melting point. Here the assumption is made that melting occurs a s the atomic separat ion reaches the inflection point of the curve. T h e volume expansion a t the melting point, 3emelt, is given by:

I

I 1 I "melt = - Equat ion 5

8Y

where y (m + n + 3)/6 the Grdneisen number. Some y va lues for metals are shown i n the table below. ,

TABLE I

Body-Centered Cubic

Metal Li N a K Rb Ca W Fe Mo Ta

1.17 1.25 1.34 1.48 1.29 1.62 1.60 1.57 1.75 L

Face-Centered Cubic

Metal A1 Co Ni Cu Pd Ag P t Au Pb

Thus for y = constant we should observe the relationship:

a T, = constant Equation 6

where a is the expansion coefficient, a s i s indeed the case, s e e Figure 8. For metals Snd ionic compounds the middle curve with 3 a Tm = 6% appliesb

The specif ic heat of al l sol ids should be, according to Dulong and Pet i t , 3R. This is due to the 1/2 kT of kinetic and potential energy per degree of freedom. Each atom with 3 degrees of freedom hae therefore an average energy of 3kT, each ram-atom-3Nkt = 3RT and the specific heat, C = (aE,/aT) b = = 3R = 5.96 cal. deg.-krnol.-l. Thi., however i s

P not obecrved a t lower temperatures where c * ( T / $ ) ~ where i s the Debye characteristic

v temperature, cf Figure 1. At room and elevated temperaturea the specific heat i s close t o the 3R value or higher. The increaee can be, according to Born and Brody (29), due to the anharmonic terms in the vibration spectrum or in transition metals due to the electronic contribution (30) a e mentioned before. Some values are presented in Table 11.

Although the free electrons are responsible for the conductivity of metals the crystal ~ t r a c t u r e and i t s defects (+ thermal vibration) determine i t s temperature dependence. A perfect latt ice (O°K) would have infinite conductivity s ince the electron w a v e s could pass through i t unscattered. As roon ae thermal vibrations and defects are introduced the amount of scattering determines the conductivity. Calculations show i t to be proportional to T-' for TmBD and to T~~ for T<<~'JJ. In one can e r p r e ~ s the resistivity (Cu, Au) by the formula:

R = A + BT + C T ~ + D. exp{-Q/kT) Equation 7

where the l a s t term may be attributed to scattering due to Schottky defects (see below).

If we accept Smekals classification of the properties of aolida into structure sensi t ive and structure ineensitive properties (31) the above discueaed properties belong to the latter category. They can be deducted from the electron theory of metale with the assumption of a periodic atructure of the atoms and a binomial expression for the potential between two atoms. The agreement with experimental data i s eurprisingly good. In the following chapters the structure sensi t ive properties will be discussed in terms of the defects responsible for them. A division into defect-een~it ive and defectinasnsitive properties would be more appropriate (1, 2) as the properties in question are often affected by minute impurities or defects of

atomic dimensions. It should be pointed out, that the defect s t ructures themse lves were obta ined in re t rospect from an a n a l y s i s of t h e s e s t ructure sens i t ive properties. However, for the s a k e of obtaining a lqgical sequence , the order of d i scuss ion will be reversed, i.e. a dis- cuss ion of the failure modes w i l l follow the d i scuss ion of the various la t t ice defects .

TABLE I

0bserVed specific H e a t s , C,, in cal-degml per gm-atom

An idea l crysta l is defined as one whose atoms are uniquely posi t ioned in accordance with the l a w s of crystallography, Ear ly experimental evidence, e spec ia l ly x-ray diffraction s t u d i e s were certainly i n s u p p o r t of the theory that there is not much difference between real and idea l crysta ls . However, a careful examination of a l l the consequences of a n ideal crysta l structure made i t obvious that the real crysta l differs from the idea l c rys ta l in that i t contain^ defec t s which destroy the un iqueness of the p s t u l a t e d arrangement. Although these de fec te generally elude conventional x-ray or optical examinations b e c a u s e of their smal l dimensions, they are primarily responsible for a number of phys ica l and mechanical properties with which we a re familiar and which are generally referred to as material charac- t e r i s t i c s .

Some of the consequences that led t o the conclusion that r ea l c r y ~ t a l s are far from perfect a re l i s t ed below:

1. X-ray extinction: 'The diffraction intensi ty from a perfect cryata l would b e considerably lower than the observed one due to primary extinction, ibe. double reflection in the direction of the incident beam (32).

2. E lec t r i ca l conductivity: At O°K the e lec t r i ca l conductivity of a perfect crysta l should be infinite except when the Bragg conditions a re fulfilled.

3. Theoret ical sheLr h e n & : T h e e l a s t i c s h e a r s t ra in should be 2 0.25 while obaerved values are near 10'~ t o (10).

4. Theoretical fracture strength: Should be commensurate with theoretical shear strength, e.g. ,0.1E (33).

5. Activation energy for aelf diffusion: The only mechanism for self diffusion in a perfect crystal would be atomic exchange. The activation energy for such an exchange. The activation energy for such an exchange in C u is according to Huntington and Seitz (34) ~ 1 0 . 3 e V while the experimental determinations lead to an activation energy of 2.09 cV (35).

A s it is extremely difficult to obtain direct "photographic" type evidence of the defects within a crystal, defect theory i s primarily concerned with an accounting for the experimentally observed phenomena with the help of models. Nevertheless, subsequent critical and very refined experimentation has yielded a significant amount of direct irrefutable evidence of a good share of these defects s o that their e x i ~ t e n c e i s now generally accepted with confidence.

Several systematic schemes for defects have been given by various authors. Seitz (36) proposes s i r primary types of imperfectione, 1) ~ h o n o n s 2) electrons and holes, 3) excitons, 4) foreign atoms (interstitial of substitutional), 5) vacant lattice s i tes , 6) dislocations; plua three transient types of imperfections, I ) light quanta 2) charged radiation and 3) uncharged radiation. P ick (37) proposes a system consisting of a.) chemical imperfections (impurity concentration) b.) structural imperfections and c.) electrical imperfections.

The following discussion will be limited to structural defects in "nearly perfect crystale" s ince they are primarily responsible for the mechanical behavior of metals, According to Seeger (1) they can be claesified very logically in terms of their geometrical extent, i.e.:

Q - order defects or atomic defects such aa vacancies, interstit ials, atoms a t wrong positions (in compounds), etc.

I - order defects such a s a dislocation line and

I1 - order defects such a s grain or twin boundaries.

2.2 0-ORDER DEFECTS

Frenkel (38), Wagner and Schottky (39) and Jos t (40) have postulated that a t elevated temperature there are alwaye some vacancies and often a l so atoms in interstitial locations. The two bas ic for such defects are known a s Frenkel defects and Schottky defects, i l l u~ t r a t ed schematically in Figure 9. In the former, atoms are removed from their regular lattice s i t e s and placed interstitially. In the latter the removed atoms are removed to the crystal surface. The creation of Schottky defects caueea a l o s s in crystal density. The creation of Frenkel defects can a l so cause d e ~ s i t p c h a n ~ e s a s the expansion due to the interstit ials i s often overcompensated for by the lattice contraction due to the vacancies. Thermodynamical calculations (1) show that for both casee the number of defects increases exponentially with the temperature according to:

Frenkel: Schottky:

Equation 8

where:

n = number of defects

N = ndmber of atoms in crystal

~1 = number of available interetitial bositions

= for the creation of a Frenkel or Sbottky defect ='s

Thus the activation e n e r ' ~ for the thermal of Frenkel defects is 1:/2 the defect energy while that for tbecreat ion of a Scbottky defect i s equal to the defect energy. Mott and Gurney (41) have shown that the number of defects in thermal equilibrium ia Larger than the above indicated; for Schottky defects by a factor of lo3 -lo4, for Frenkel defects by a considerably smaller factor.

a In the derivation of the above equation i t wae aleo assumed, that the activation energy

for the formation of a defect ia known. A simple relationship for this activation energy exista, bowever, only for Schottky defects in monatomic solids.

At absolute zero temperature this energy i s eqnal to the binding energy per atom as:

U = - 2 p r k ) binding energy 2

I k

u l = -1 removal energy -

i k 1

U 2 = 4-U1 energy gain by putting I#? atom on nurface ,

Equation 9

The most exact theoreticall procedure for tbe calculation of activation energies of Schottky defects i s due to Fumi (42) who reports for the noble metals

There i s no simple way of estimating the activation energy for the formation of Frenkel defects, or interstitial atoms in general, as the energy for the interstitials dependa upon the available volume. Since the activation energies for the various processes are of the order of a few electron volts, even small differences cause tbe dominance of a particular type of defect. Thus i t is justified jo assume that in a certaiu lattice strncture Freakel, Scbottky or anti-Schottky defects are dominant.

I

One group of experimental obaervations for wbich these point defects can account is in the field of diffusion in metals, which ie intimately related to the motion of the point defects, z

For the motion of interatitials in Cu Huntington and Seitz (34) and Huntington (43) estimated

for the activation energy between 0.25 and 0.5 eV while the experimental value i s approximately 0.7 eV. The activation energy for the motion of a vacancy i s estimated by Hintington (44) somewhat above 1 eV. Two additional mechanisms for self diffusion have been proposed by Zener (45, 46):

a. direct exchange of atoms and

b. exchange by a ring mechanism

Huntington and Seitz (34) have calculated the activation energy for direct exchange in Cu a s 10.3 eV. Zener's ring-mechanism requires an activation energy (in Cu) of 4 eV. The experimental value for the activation energy of self diffusion in Cu ie 2.09 eV (25) which i s c loses t to that predicted for the vacancy diffusion mechanism.

Fo r the production of these point defects there are three basic mechanisms:

1. Thermal vibrations

2. Radiation damage

3, Plas t ic deformation

The equilibrium concentration for thermally created defects was discussed early in this chapter. Measurements of the electrical conductivity on Cu and Au ~ i e l d a defect concentration of approximately 1,/400 and 1./200 respectively a t their respective melting points (47).

Neutron bombardment of a metal c ause s primarily Freeks l defects along the high energy position of the neutron path. A s the neutron s lows down w e obtain a zone of local melting- displacement spike where the defect concentration is that which corresponds t o the melting temperature. In addition we may find dislocation rings, microcryetals, etc. Thia i e illustrated in Figure 10.

T h e creation of point defects a s a reeult of p las t ic deformation will be diacuosed in the next chapter on line defecta. In this caae the motion of dislocation l ines containing jogs represents the most likely mechaniam for the formation of interstit iale and vacanciee.

F ina l ly we should d i scuss some experimental evidence for the existence of point defects a s discussed. In addition to measurements of the activation energy for diffueion, changes in the re sietivity can be used to estimate the defect concentration. Foreign atoms, interstit ials, vacancies and any other irregularity in a crystal la t t ice cauee an increaae of the resis t ivi ty due to their additional ecattering effects of the electrons. T h i s change i s generally propor tional to the defect concentration. Jongenburger (48) eatimated for vacanciee in Cu

A p = 1.25 p cmfi vacancies Equation 10

For the case of vacancy paira th i s value increases to about 2,u !2 cm/% vacancy paira. In- t e r s t i t i a l ~ in Cu cause an increase of the resistivity:

A p- , 0.5 p R cm/% iinterstitials Equation 11

With these relationshipe one can check the predictions made for thermal defects and the activation energies asmociated with them. On quenching to very low temperature the elevated

temperature defect structure can be "frozen in". From the increase of the res i s t iv i ty as

compared to i t s equilibrium value and subsequent changes with temperature one can obtain both the energy of formaqion and migration of t h e s e defects. T h u s Kauffman and Koehler (49) observed for gold a n activation energy of 0.4 eV which i s most l ikely due to the migration of

vacancy p a i r s as the activation energy for se l f d i f fus ion i s between 1.9 and 2.0 eV, that for the formation of vacanciks 0.6 to 0.8 eV and that for the migration of simple v a c a n c i e s between 1.4 and 1.7 eV. I

Additional d a t a exis; for a l loys showing long range and shor t range order. F o r the former i t could be concluded that the ordering p rocess i s due to the migration of vacancies . In a l loys with shor t range order the ordering p rocess is too f a s t t o obtain useab le diffusion measurements. According to Zener (50) the different s i z e a toms cause a s t r e s s system which in turn l ea& to a n ordered s t a t e that minimizes the s t r e s s s ta te . T h i s i s observed from internal friction experiments where increased damping is obtained during t h i s recovery period.

A summary of recovery da ta on Cu i s presented in Figure 11 where the res i s t iv i ty changes for quenched, irradiated, deformed polycrysta ls and deformed s ingle c rys ta l s are plotted a s a function of temperature. We observe five d i s t inc t s t e p s of recovery:

I Stage: between 3 5 O K and 4S°K ~ c t i v a t i o n e n e r g y 0.1 eV. This s t a g e is only observed a s a resul t of neutron bombardment and probably due to the changes occurring in the microcrystals of the displacement spikes .

I1 Stage : between 100°K and 200°K Activation e n e r g y 0.2-0.5 eV. Occurs in irradiated as wel;l as deformed speci-

w mens and i s probably caused by the migration of vacancy pairs , vacancy complexes or in ters t i t ia ls , most l ikely pairs.

I

111 Stage: between 220°K and 270°K Activation energy 0.72 eV occurs in irradiated and deformed samples . Most l ikely due to the migration and annili lation of intersti t ials.

IV Stage: At about 370°K and 570°K Activation energy 1.2 eV, occurs in quenched, irradiated and deformed epeci- rnens. Most l ikely due to the migration of vacanc ies and their d isappearance a t d i s loca t ions or grain boutldariea.

V Stage: between 500°K and 610°K Activation energy 2 2.1 eV. Coinc ides in Cu with ha rdness recovery due to recrystalization. The activation energy is close to that for self diffusion.

In summary i t can be s a i d that :

1. P o i n t d e f e c t s are present in metals as a resu l t of the various manufacturing techniques , i .e. solidification and plas t ic deformation. T h e equilibrium concentration near the melting point i s somewhere below 1%. They a re a l s o produced a s a resu l t of neutron bombardment.

The mechanism for the motion of point defects are, in order of increaainp, activation energies: migration of vacancy complexes, m'igratioa of vacancy pairs, migration of single vacancies and self diffusion. With the exception of self diffusion the annihi- - lation and migration of these defects do not seem to affect the mechanical properties of a material but are responsible for increased damping and resistivity changes. Self diffusion and recrystallization lead a l so to a recovery in hardness.

The peced ing remarks pertain p imar i ly to noble and alkali metals. In alloys additional events connected with the interaction of vacancies and phase transformation complicate the scheme of events. Both Ni and P t (transition metals) show recmery phenomena commensurate with that of Stage IV, i.e. migration of single vacancies.

2.3 LINE DEFECTS

These defects have a linear extent and are called dislocations. They were postulated independently by Taylor (511, Orowan (52) and Polanyi (53) a s a mechanism t o explain the plast ic behavior of metale. considerable experimental evidence has s ince been gathered (54), (1,2) which proves their existence beyond any doubt.

2.31 GEOMETRICAL CONFlGURATlONS

The two baaic types of dislocations are the edge dislocation and the screw dislocation ~ -

whose configurations for a simple cubic lat t ice are shown inFigure 12. T h e characteristic entity which describes a dislocation i s the Burgers vector, b defined a s indicated in Figure 12 from the Burgers circuit. A dislocation line may be defined a s the line separating the d i p p e d from the anslipped region, Figure 13. It can be curved or straight. The portions of the d& location line that are parallel to b are made up of s c r e w dielocations, the ones normal t o b are made up of edge dislocations the composite being called a Y dialscation. Dicllocations can combine or separate according to the vector equation:

Equation 12

The atability of euch a reaction i s determined by the energy dissipation or consumption of the reaction. The latter i s to g a although i t i s d m influenced to a minor degree by the elast ic anistropy of the crystals. Thus:

where Q is the reection energy of the process which i s positive (attractive force) if the Burgera vectors of two parallel dislocation lines include an angle larger than 90°, zero if this angle is 90' and negative (repulsive force) if this angle ia l ee s than 90'. The a-hove equation for Q can be utilized a s a criterion for stability of a dimkca-tion. If the product bl.b2 of the co-onents i s positive, the dislocation b, i s stable, if bl .b2 i s zero i t is undecided and if A

b l + b 2 is negative it i s unatable. This can be applied to the determination of the poasible Burgers vector of the four basic metallic crystal structures.

1. Simple cubic: (CsC1) b = a<100> shortest. Stability of b = a f i < l 1 0 > and b = a &<111> in two or three b = a<100> undecided. All others unstable.

2. Body Centered Cubic: b = 'X a 6<111> ehortest, b = a <loo> next shortest. Both vectors are stable; This is the only ca se of i t s kind where two Burgers vectors having different ldngths are stable. A l l others are unstable. ~

3. F a c e Centered cubic : b = '/2 a 4 < 110> shortest. Stability of b = a <loo> undecided.

4. Close Packed ~ e i a p n a l : b = 1/3 a < 1 l i 0 > shortest, stable. b = C <0001> next shortest, stable. Stability of b = 1 /3 <1123> with respect

> > to dissociation in a or c vectors undecided.

The second characterlistic of a dislocation i s i t s slip plane. Since the ene rm of a dislocation depends indirechy on i t s slip plane by way of anisotrony of the e las t ic constants i t i s hard to predict theoretically. In general the s l ip planes are those with densest packing, i.e. (111) in fcc and (0001) in cph. However, in many materials having the same crystal structure different crystallographic planes are observed as slip planes, i.e. (110), (112) and (123) in bcc. (10).

I

Dislocations with different Burgers vectors can meet a t a single point. Such triple or quadruple points or nodes cannot exist in simple cubic systems a s there a l l <loo> vectors are either orthogonal or ~nt ipara l le l . The same is true for the dislocations in the cph system. However, the a dislocations within themselves can form stable triple pointe. In the fcc lattice we can expect stable triple points and stable quadruple points. Generally these dislocation l ines will have different slip planes. If three dislocation l ines have three different s l ip planes their of intersection ia immobile. Such immobile nodes are important a s sources of dislocation lines.

A s we sha l l s e e later, the thermal generation of dislocation l ines i s a very unlikely event, except at very high temperatures. Similarily we shal l find that s t r e s se s of the order of the theoretical yield strength 2 0.1 G would be required for the generation of a dislocation line in a perfect crystal. However, since yielding and fracture and therefore the motion of a considerable number of dislocation linea takes place a t s t reseea of: to lov4 G, another mechanism for the gener&ion a t very much lower s t r e s se s and temperatures must be active. T h i s mechanism was first pointed out by Frank and Read (55, 56). It assumee an anchored dislocation line which bulges out under the influence of an applied s t ress , reaches the crystal surface where it causes a step, continues (backwards) to p a s s over the remainder of the slip plane, where finally the 4wo short pieces of the dislocation line join up again and the process can be repeated, Figure 13. The anchor points required for this mechanism are provided among others by the above disc?ssed nodes. However, gliding much below the theoretical ehear strength i s a l so obaerved in eystems where such immobile intersection@ do not exiet, One may therefore assume that anchor points can a l so be formed through dislocations in other than the microscopically observed glide planes which have a very low mobility.

T h i s mechanism for a dislocation source has the consequence that all dislocation l ines are in one particular s l i p plane. During their motion, however, i t might happen that a particular dislocation line jumps from one s l ip plane to a parallel s l ip plane causing a dislocation jog as illustrated in Figure 14. The motion of such a jog may be conservative or nonconservative,

i.e. cause a change in volume (vacancies or interatitials) or not. Even for most general crystal etrnctures such joge contain always some edge-component and are never pure acrew dielocations. Jogs in dislocation l ines that have predominantly edge character are able to move along with the dislocation line through the absorption of vacancies or the creation of interstitiale. T h i s caueea a lifting or climbing of the dislocation line, a process which occum' durinR recovery and elevated temperature creep. Even if a thermal production of joge - . -

i e impossible due to a very high activation energy, a c dislocation ring containing joge may climb if the resulting Burgere vector has a component normal to the plane of the dislocation ring (57). Figure 15 illustrates the process for dislocation l ines having predominantly acrew character. A s the line bulge out between the jogs l ines of predominantly screw character will meet behind the joge caueing either interst i t ia ls or vacancies,

Final ly we have to concern ourselves with partial dielocationa, i.e. dislocations whose Burgers vector is not a vector in the Bravais lattice. The most important casem are the stacking faolts in close-packed systems, namely fcc and cph. These are il lustrated in Figure 16 for the fce and the cph lattice. A reaction between partial dislocations is schematically illuetrated in Figure 17. Th i s dislocation 1:/6 (110, i s a lso called a Cottrell dislocation and the reaction i s called the Cottrell-Lorner reaction. Th i s dislocation ia completely immobile, can neithet climb nor glide, and playa a role in the s train hardening of fcc metals.

2.32 THEORETICAL CONSIDERATIONS

From the preceading geometrical coneiderations i t is evident that the presence of a dislocation line causes a stress field in the crystal. Since the distortions have atomic dimeneions it is not feaeible to u s e continuum mtchanica, that is, theory of elasticity, for the description of the etreee field in the immediate vicinity of the dislocation line, however, ench calculations are extremely helpful in understanding the long range etreee field of the dislocation. The equationa describing thia long range s t r e s s field of a eingle dialocation are given below:

Equation 14

The geometrical orientation to which thie equation pertains i s illtiatrated in Figure 18. In general one can eee that the s t r e s s cauaed by a dialocation decrease8 to the inverse power of the distance from the dislocation, i.e. L/r. The above equations pertain to the s treee field of an edge dislocation. A similar dependence of the streea on the distance from the dielocation i s obtained for the etrees field of a acrew dislocation as indicated by the equations below:

Eqna tion 15

The reaction force betweed two screw dialocations i s repulsive if they are parallel and attractive if they are anti-barallel, Seeger (1) has proven that one can obtain a atable network of ecrew dislocations if thqee ecrew dislocations are arranged much that the d,irection of one of them disec ts the angle between the two remaining into two equal parts.

Stable arrangements of edge dislocations on two parallel s l ip planes are i l lustrated in Figure 19. Thus edge dialoeationa of equal sign will line up one above the other while edge dislocatione of opposite sign will line up under 45'.

Of special importance i s the so called pile up of dislocations in a glide plane. Consider- ing the Frank-Read mechanism for the creation of dislocations in one glide plane a number of dislocations of the same sign will be generated in this glide plane and move in the same direction. A s soon as the first dialocation of this group h i t s an obstacle, e.g. the grain boundary or a dialocation in another s l ip plane, i t will b e blocked and exert a repulsive force on the following dialocations. Such a dislocation pile up i s illustrated in Figure 20. The equations that determine the equilibrium position of snch a dimlocation pile-up have been derived by Eshelby, Frank and Nabarro* and are in agreement with experimental observations**.

Continuum mechanics a l so allows u s to d i s cus s the energy of a dislocation. I t i s defined by the work which i~ necessary to create the dislocation in question in an otherwiee perfect crystal. I t i s obvious t ha t this energy depends upon the length of the didocat ion line and therefore energy values fog dislocations are given in terms of their energy per unit length. The energy of a single dislocation line in a crystal of infinite extent is therefore infinity if we assume the dis locat ion line to be straight, Thae we a lso have a dependence of, the energy of the dislocation on the &e of the crystal, If we consider a statistical arrangement of an equal number of positive and negative parallel dislocations, the energy of the dislocatione remains finite. An order-of-magnitude estimate of snch an arrangement givee an energy of 3.9 eV for aluminum and 4.5 eV for copper. These energies are in the order of magnitude of the energies required for the creation of interstit ial atoms but considerably higher than those required for the formation of vacancies.

The discussion of the energy of a dislocation ge ts further complicated by the fac t that dislocation l ines need not be straight, but can carve, bow oat around an obstacle, etc. and have various geometrical shapes. Straieht dielocation l ines made up of edge dielocations have an energy per unit length approximately equal to b2.G and ecrew dielocations approximately 2/3 of this value. Thus these energiee muet be furnished in order to increase the length of the dislocation line by the unit length. A s a dislocation line assumes a curved shape, part of the dislocations will be screw type and part will be edge type eo that the l ine t endon of a dislocation i e not conetant along the dialocation line. According to Stroh (58) one can give a line tension of a dislocation ring of radius R in the form':

Gb2 R E, 2 C log -

87~ Equation 16

*Phil Mag. v 42 (1951) p 951.

**Gould, J.R., M.S. Thos i s 1959, Syracuaa Univarsity

where ro is the unelas t ic region tha t had t o be eliminated from continuum mechanical con- s iderat ion, R , the radius of curvature of the dislocation and C a constant of the order of unity. With the help of th i s equation the activation energy of a Frank-Read source can be es t imated as:

Equation 17

With the help of continuum mechanics i t i s a l s o poss ib le to make some thermodynamic e tud ies concerning the s t ab i l i ty df the dislocation. F o r plausible va lues of r. one obtains a shear s t r e e s of 0.02 G to be required to produce euch a dis locat ion source. S t r e s s e s of that magnitude cannot be applied to a s ing le crysta l of macroscopic dimensions and s ince the plaet ic deformation of a s ingle crysta l occurs a,t s t r e s a e s which are lower by a factor of about loa i t must be assumed, that d is locat ions are present in the as-received crysta l which have been generated by some other mechanism, probably occurring during the-growth of these crysta ls . Once a crysta l contains a dis locat ion i t i s poss ib le that the local s t r e s s concentration in the immediate vic ini ty of the dielocation is sufficient to c a u s e the thermodynamic or spontaneous generation of new dis locat ions . T h i s mode of generation of new dis locat ions from a n exis t ing dis locat ion has , however, to date not been es tab l i shed experimentally.

Another in teres t ing a s p e c t of the continuum mechanics treatment of the s t r e s s field of dis locat ions concerns the interaction between dis locat ions and point defects . In general the energy of the formation of a point defect a t an edge dis locat ion i s considerably below that for the generation of the same point de fec t in a perfect part of the crystal . T h e interaction between dis locat ions and impurit ies will a l ao c a u s e a migration of the impurit ies in the neighborhood of the dis locat ion in order to relieve the s t r e s s field of the dielocation. Fur ther motion of dialocatione which are surrounded by an impurity atmosphere i s determined by the diffusion rate of the impurities.

In order to get some bet ter insight into the motion of dis locat ions i t i s n e c e s s a r y to con- s ide r the s t r e s s field in the immediate vicinity of the dis locat ion. Two bas ic models have been proposed: 1) the Frenke l model which i e a n arrangement of m a s s points coupled through spr ings (59) and 2) the P e i e r l s model which is an extension of the continuum e las t i c i ty approach where the nonlinearity of the e l a s t i c dis tor t ions ia considered only in the s l i p plane (60). In both c a s e a the d i s loca t ions move in a field of a periodically changing potential . The most important r esu l t of the calcula t ions with the help of the P e i e r l s model is the determination of the P e i e r l s s t r e s s t which i s defined a s the s t r e s s required to move a dis locat ion a t

P a temperature T with a given mean velocity. T h e s e P e i e r l s s t r e s s e s a re given for aluminum in the table below:

TABLE Ill

Peier l s Stresses in Aluminum

Comparison with the critical shear s t resses indicates that the r e s ~ l t s l is ted in the above table are in disagreement with the experimental resul ts by a factor of approximately 50. Th i s disagreement i s probably due to the fact that in the calculation for Pe ier l s s t reas there are two parameters which are not clearly defined. These parameters both enter in the eqna- tion a s negative exponentials and one might expect that both parameters were chosen too low. A e the temperature increases the Pe ier l s s t r e s s i s reduced. T h i s reduction i s caused by two events: 1. With increasing temperature an increasing number of dislocations of higher order are formed. (These disloc'ations are caused by the fact that the dislocation line becomes wavy aa i t progresses across a crystal. The waves may move sidewaye and thereby r e h c e the Pe ier l s etreee) and 2. The thermal motion of the lattice. The latter causes an increase in the width of the dislocation line which again cauees a decreaee in the Peierle etreea.

Peier ls Strese

0.1.10'~ G 5. 10'~ G 1.2 10'' G

(111)

(111)

(111)

The split-up of complete dislocations into partial dislocatione can a l so be treated with the help of a Pe ier l s mode,l. The elast ic interaction between the dislocatione tend to increase the separation while the aurface energy of a stacking fault tends to hold them to- ge the r . One finds, according to Seeger (1) with the help of a Pe ier l s model that the close- ~ a c k e d metals can be clansified in two groupe with respect to the strength of the separation of the partial dislocations, Namely one group with high stacking fault energy whereY>1w2 G b 2 / c in which case the beparation i s only dependent on the length of the Burgers vector and not on the value of 7. The metals aluminum and probably magnesium, zinc and cadmium belong to this group. If Y Y ~ O - ~ G b2/c the partial dialocations are clearly separated. This separation i s relatively sensi t ive to the etacking fault energy and varies a s Y". The metals cobalt, copper and probably nickel, eilver and gold belong to this group.

Dislocation Width

0.50 a

0.76 a

0.92 c

Slip Plane

(010)

(01 0)

(111)

120° half dislocation

90° dislocation

30' dislocation

It was already indicated in the diacuesion of the pometr ica l aepec ts of dislocations that plast ic deformation will be associated with climbing of the dialocation line that i s the formation of jogs. If man, of the dielocatione are present in the form of extended dislocatione, i.e. dislocations spl i t up into partial dislocations, the jog formation will only be possible if the partial die location^ show a constriction. With the help of Peierle ' model i t i s again ~ o s s i b l e to determine the energy required for the constriction of a dislocation and bring i t in relation to the activation energy for the formation of the jog. The resul ts of thia calculation are shown below:

Dislocation Type -.-

90° dislocation 0

0 dislocation

00 half dielocation

ACTIVATION ENERGIES FOR JOG FORMATION

Metal

Intersection jog Diffusion jog

Intereection jog Diffision jog

Activation Energy

T h i s explains the difference in mechanical behavior of otherwise similar materials such ae aluminum end copper. A a aluminum haa a high stacking fault energy, the energy for the conetriction of an extended dialocation i s very much lower compared to copper wh ich h a s a much lower stacking fault energy.

2.33 EVIDENCE O F THE EXISTENCE OF DlSLOCATlONS

Because of their smallnese one must not expect to s e e dialocationa except those in crystals with large lattice constant6 compared to atomic dimensions. The majority of the evidence in support of the existence of dislocations is indirect evidence. In this group fall the examination of etch p i t s which are caused by preferential chemical attack of a metal in the region disturbed by the s t r e s s field of a dislocation. Other methods are the coloring of dislocations or the etudy of dislocations in photo sensitive crystals. One very elegant and convincing piece of evidence ie the observation of the motion of a low angle boundry which is shown in Figure 2 1 (61). One of the most striking experimental pieces of evidence that ha s been obtained is the observation of the motion of the dislocations in very thin films under the electron microscope.

The following film warn made by P. Hirech and associates. It shows the motion of dislocation linea in a very thin s ta in less s tee l foil a s photographed through the electron microscope. The effect that allows u s to s e e the dielocation linen and the location over which they have paesed (which will show up a s either a dark or a lighter region) i s the so-called Moire effect, i.e. 'the interference phenomena obtained when one looks through two slightly misaligned screens. T h i s picture is chosen here because i t not only allows us to observe the preeence, motion and generation of dislocation linee, but a l so gives a very good insight into the complexity of the proceases occurrina as the result of the motion of these dislocations much as the annihilation of a grain boundary, the interaction betweea partial dislocations, the formation of extended dislocations, and the creation of dislocations near the edge of the foil,

After seing this picture you will probably agree with me that any mathema tical attempt for an accounting of the phenomena occurring in a r e a l crystal will lead to tremendous difficulties. Nevertheless it i s a l so obvious that these phenomena do occur and that we have to find some sort of a scheme to account for them if we want to be able to understand and predict the phenomena occnring in eolids.

3.0 A R E A DEFECTS

T h e l a s t type of de fec t s that we have to d i s c u s s , are the de fec t s of second order, tha t ia the de fec t s having a two dimensional extent. T h e s e de fec t s a re the s tacking fau l t s which we have a l ready d i scussed , the low angle boundaries, high angle boundaries and twin boundaries. We sha l l s e e that the good majority of them can be generated in terms of a more or l e a s system- a t i c arrangement of the de fec t s of 0 and 1 s t order. We s h a l l limit the following d i scuss ion to low angle boundaries, which can be generated by a ver t ical array of evenly spaced edge dis- locat ions , high angle boundaries, which cannot be descr ibed crystallographically, and p h a s e boundaries, e spec ia l ly thosk tha t can be generated through dis locat ion l ines.

3.1 LOW ANGLE BOUNDARIES

A low angle boundary ie schemat ical ly i l lustrated in Figure 22. T h e spec i f i c energy of a grain boundary can be defined as the additional energy that the boundary h a s per unit a rea as compared to the s ingle cryskal. Read and Shockley (62) have shown that the difference between free energy and internal energy of a grain boundary i s small and i s primarily affected by the angular dependence of the e l a s t i c constants . T h e energy of a grain boundary made up of such dis locat ions is given below::

$ E ( ; 5 ) = E o . $ ( I - log-) Equation 18

+ma,

and i l lus t ra ted in Figure 22 as a function of the angle $. T h e c o n ~ t a n t s E. and$,,, depend on the crystallographic orie~ntation of the grain boundaries and d e t a i l s of d is locat ion model. T h e ~ a r a m e t e r 4 ~ ~ ~ cannot be obtained theoretically from e las t i c i ty and i t is therefore not poss ible t o obtain the absolute value of the grain boundary energy, and therefore of the con- s t a n t Eo. However, in a of E/qb vs. + we should, in accordance with equation 18, obtain a s t ra ight line. T h i s is i l l i s t r a t e d in Figure 23. T h e fac t tha t the geometrical build-up of such a low angle boundary i s completely feas ible and indeed often occurs is i l lus t ra ted by the fac t tha t the motion of 40w angle boundaries under a n applied s h e a r s t r e s s proceeds exact ly a s predicted by d i s loca t ion theory (61).

3.2 HIGH ANGLE BOUNP'ARlES

I t i s surpr is ing that thei above equation for the free energy for low angle boundaries a l e o app l ies to grain boundar ies having much higher angle. T h i s is espec ia l ly true for s i l icon iron as i l lus t ra ted in F igure 23. However, in z inc and l ead no decrease with increasing angular difference is observed. N o dependence of the grain boundary energy on the orientation differ- e n c e w a s a l s o observed for' high orientation difference6 in si lver. T h i s w a s analyzed by R e a d (63) who showed t h a t i n a high angle boundary the dis locat ion packing would be extremely dense. C a v i t i e s will therefore be p resen t in the region of the grain boundary. In order to generate such a grain boundary a preesure p must be appl ied to create these cavi t ies . T h e npecific energy of the g r a i i boundary c a n be es t imated from pAV = M (b.p). In other words, the energy of a high angle %rain boundary becomes independent of the orientation difference.

S tud ies of internal friction, the relaxation of the s h e a r modulus, and s t r e s s relaxation in polycrysta ls have shown that the mobility of high angle boundar ies can be expressed (64) in terms of i t s apparent v isco$i ty where the activation energy i e a t l e a s t approximately eqnal to the activation energy for se l f diffusion. From thia Ke (65) concluded tha t the grain boundariee

are made up of small regione of misaligned atoma which are more or leee equivalent to a diffneed vacancy. A compat i~on of the activation energy values for volume diffusion and those for grain boundary relaxation shows that this is not always the case (see table below) especial ly not for copper.

TABLE IV

Comparison of Activation Energies for Self Diffueion and Grainboundary Relaxation

Metal-Alloy

a - Brass (29% Zn) a - Iron Aluminum Copper

However, as the impurity concentration increases the degree of agreement i s aleo improved. Mott (66) ham euggeeted a ao called ialand model of the grain boundariea which aaaumes that a grain boundaty ia made up of island8 of n atoms which have a good f i t with the neighboring graine. The velocity v of the motion of eueh a grain boundary under a ehear s t r e s s i s given by the equation:

Self Diffueion k cal

41.7 78.0 33.0 48.0

1 nL v = C.- exp (- -) .7 Eqdation 19

kT kT L = Heat of fueion per atom

Grainboundary Relaxation k cal

41.0 85.0 34.5 32 .O

F o r n 14 good agreement i s reached with experimental r e m l t s on aluminum. Recent Russian work* on the background intensity of polycryetalline Cu and Ag led these authors to the conclusion, that grain boundaries in these metals have an apparent thickness of several hundred A. Thie value decreases with increasing purity. The motion of a high angle boundary i s illustrated in comparison to that of a low angle boundary in Figure 22. This type of grain boundary sliding was indeed observed and will be diecussed later during this conference in greater detail.

I t may a l so be possible to have high angle boundaries made up of a number of parallel dislocation wall@.** Although the energy increases, they might he stable due to the absorption of impurities.

3.3 PHASE BOUNDARIES

Little i e known about the make-up of a phaee boundary and the growth of a new crystalline phase a t the expense of a second phaee. Thie problem, however, i s of extreme importance to the practical metallurgiet. The driving force for a traneformation to occur i s a1way.e a lower free energy of the new growing pheee, We can dietinguiah between transformations that require

*hkharoo, V.I., Botieov, B.5. and Vaagongsim, Phra. Motdo md Metallagr~~hy v 10/3, (1960) p. 58. ,

**Cklov. A.N. and Sbvarte, I.A.. P h p . Metals and Mstnllographp v 10/3 (1960) p. 175.

diffusion and those that occur without the diffusion. Thc Martensite transformation belongy to the latter group. Here we can generally speak of two stages namely: a) microscopically homogenous shearing which might a l so cause a s l ight change in volume and b) subsequent arranging of the atoms to their final lattice location. Both phases occur in the austenite- martensite transformation, however, only the first phase in cobalt. The shear angle in cobalt i s approximately 20° and one might assume (1) that a dislocation mechanism is co-operative. Figure 24 shows a mechani~m whereby the required shear s tage of the transformation i s accomplished by means of a &ha1 source, that i s a third dislocation climbs around a polar dislocation made up of two dislocations. In order for this mechanism to work it is necessary to have three dislocations with Burgers vectors bl , b2 and b which are energetically feasible a and indeed present, Th i s topic of phase transformations wil be discussed in very much greater detail by ProfessorNewkirk later during th is conference.

4.4 FA ILURE MECHANISMS

In this chapter an attempt will be made to survey the mechanisms of failure in metal parts with special consideration ;of their behavior at elevated temperatures. The discussion will be limited to four modes of failure and their explanation in terms of the defect reactions disensaed previously. They are: 1) Deformation under increasing loads, in other words the phenomena occuring during a tensile test. 2) The deformation under constant load or s t ress , i.e. the various creep phenomena. 3) The occurrence of fracture and 4) Evaporation.

4.1 DEFORMATION UNDGR INCREASING LOAD

The discussion centers on the shape of the s treae etrain curve and the mechanisms which can account for the s t r e s s strain curve. Although materials showing complete brittlenese, that i s no plast ic deformation prior to fracture, are of considerable theoretical interest, the technical ueage of such materials is rather rare. In general the materials employed for technical applicationa show some degree of plaeticity or ductility. For th i s reason the discussion will primarily dea lwi th the phenomena occurring above the yield strength, that i s crystal plasticity.

The plast ic deformatiods of crystals ha s been shown to take place in the form of sliding of crystallographic planes i n top of each other. T h i s s l ip mechani~m can be described in terms of the s l ip direction and the s l ip plane, Figure 25. Evidence w a s a l so presented that th i s s l ip i s accomplished by the motion of dislocations through a crystal. The s l ip direction is that direction having the shortest Burgerye vector and therefore i t i s given by the direction of the shortest lattice vector in the Bravais lattice. This i s indeed the case.* The only exceptions are the intermetallic compounds PbTe, AgMg and the ordered phase of b1 - CuZn. Th i s may be explained in terms of the ordering process occurring in these crystals. A complete dislocation in the unordered phase having a smaller Bravais lattice than the ordered phase, may sp l i t up into two partial dislocations in the ordered phase between which w e have a stacking fault. These stacking faul ts conetitute the boundaries between the ordered and the anti-phase regions. Th i s applies to the s l ip direction of PbTe, AgMg, and the ordered phase of ,@ - CuZn. I t should aleo be noted that during the motion of these partial dislocations the order of the intermetallic compounds i s destroyed. Cottrell (67) and Rachinaer (68) have explained th is in terms of a var; low energy of ordering. Seeger (2) h a s pointid out that in a l l alloys where the ordering takes place below the melting point one might expect the presence of partial dielocationa in the ordered structure. It will a l so be extremely unlikely, even if

the energies of ordering are high, that these dislocations will combine to complete dialocations s o that one can alwaya expect the s l ip direction to be determined by the incomplete dislocations.

A s already indicated, i t ia much more difficult to define the slip plane in terms of dislocations mechanics. The energy and the Pe ier l s s t r e s s of a dislocation determines whether a lattice plane can function a s slip plane or not. However, the density of packing has a considerable effect a s i s illustrated by the low temperature results on hexagonal metals. There i t can be shown that slip plane is the basal plane if c / a > 6 and i t i s one of the prism planes if c / a < 6. Thi s pertains to metals having a high stacking fault energy. In metals having a low atacking fault energy one muat consider the action of partial dislocations and thus i t may be possible that even in metals having a strongly subnormal c/a ratio such a s osmium and rhenium the basal plane might be the preferred s l ip plane.

The deformation of single crystals under increasing load i s beat diecuased on the bas i s of the shear s t r e s s shear strain diagram illustrated in Figure 26. The definition of the critical shear s t r e s s i s a l so indicated in Figure 26. A s the shear s t ress is increased above the critical shear s t r e s s we have a strain hardening portion of the strese-strain diagram which again, a t l eas t in fcc metals, can be subdivided into three s tages.

The critical shear s t r e s s for metal single crystal a t room temperature i s in the neighborhood of 20-50 gm/mm2, Schmid (69) has shown that the critical shear s t r e s s for a given sl ip system i s independent of the crystal orientation. T h i ~ statement has become known under the name "Schmid's Shear Stress Law". In terms of dislocation mechanics i t can be s tated that "the force acting on the dislocations i s responsible for the initiation of slip". It should be noted, however, that there are deviations from this law and that an orientation dependence becomes marked if the crystallographic orientation l ies somewhere near the edge of the stereo- graphic orientation triangle. At low temperatures the critical shear s t r e s s generally decreases with increaeing temperature while a t higher temperaturea this quantity becomes nearly temperature independent. An increase in the deformation rate i s equivalent to a decrease in the test temperature. Here, too, the velocity dependence of the critical shear s t r e s s i s very small. Examples of the critical shear streaa a s a function of the absolute temperature are given in Figure 27.

In alloys having low concentrations of second elements we generally find an increase of the critical shear s t r e a ~ with increasing alloy concentration. The critical shear s t r e s s a t low temperatures becomes now quite temperature dependent. In the high temperature region where the critical shear s t r e s s again becomes almost independent of the testing temperature a serrated s t r e s s strain diagram i s observed (cf. Figure 27) indicating that the deformation occurs in form of jumps.

The existence and temperature dependence of the critical shear s t r e s s may be interpreted a s follows. Assuming (70) that the mean distance between dislocations in annealed single crystals is between lom4 and cm, there i s in a crystal a very large number of long dislocation sources and the generation of dislocatione can occur under very low stresaea. This dislocation network causes an internal s t r e s s field in the crystal whose periodicity i?,, i s given by the apacing of the immobile dislocations.

Figure 28 shows such an arrangement schematically. The shear s t r e s s neceseary to move the dislocations in the glide plane i s given by:

for edge dislocations and: ~

Equation 20

Equation 21

I

for screw dislocations. Th i s mechanism is independent of the temperature with the exception of the temperature dependence of the shear modulus G. Another contribution to the critical shear s t r e s s comes from the process where dislocations have to intersect each other. Thie process i s associated with the formation of dislocation jogs and the creation of atomic defects. Cottrell (71) and Mott (72)have shown that the activation energy for such a process i s decreased under the presence of a shear s t ress . The ahear s t ress required for such a climbing i s given by: I

I vo Uo - kT log (NIF. b. -

N - = number of dislocations per unit volume

F = area per dislocation per activation

v; = Debye frequency (- 8.4.1012 C ~ S )

2 = strain rate

v = activation volume

T = temperature

Ui = activation energy

Equation 22

The first part of this equation i s the previously discussed component il lustrated in Figure 28. The above equation i s only valid a s long a s t > t ~ . The temperature To (t = tG) which may be interpreted a s the temperature above which the critical shear s t r e s s ia temperature independent i s given by:

To 5 k log (N.F.b. - vo !

i Equation 23

Thus a t absolute zero the critical shear s t ress ia independent of the deformation velocity a and i s given by:

I

u 0

r~ = COK =rG +-

Equation 24 I v

The above comments primarily to metals having a high etacking faul t energy. In metale having a low stacking fault energy we need the additional mechanism of constriction before a climbing process can takeplace . Th i s i s a contribution to the energy of the climbing process

which i s considerably higher than that required for the formation of the jog. While in metals having a high stacking fault energy one may conclude that edge dislocations move faster than the ecrew dislocations which causes an elliptical shape of the dislocation lines. The same statement cannot be made for metals having a low stacking fault energy. Here several processes may be active which could be characterized by their activation etreas, their tempep ature and their activation energy. Thue the critical ahear s t r e s s versus tes t temperature curve ia obtained from the sum of these individual contributions a s illustrated in Figure 29. Th i s schematic illustration represents the actual case present in deformed copper single crystals.

The remainder of the s t r e s s strain diagram i s characterized by the fact that the shear s t ress increaeee with increasing ahear strain. The oldest ptoponal for an explanation for this phenomenon i s due to Taylor (51) who explains strain hardening in terms of a reduction of the movement of dislocations which is due to the streea fielde created by the i n c r e a s i n ~ number of dislocations. A ~ e c o n d model for the explanation of strain hardening i s called the strain exhaustion hypothesis. Thi s model atatee that the flow s t r e s s i s determined by the number of dislocation sources which have the lowest activation s tress . These sources are generally the longeet sources. Strain hardening i s caused by a blocking of a number of these eources eo that with increasing strain more and more sources having a higher critical flow streaa must be activated. Theae two hypotheses can be combined by making the assumption that the atrain hardening i s due to a number of dislocations becoming blocked inside the cryetal during the deformation proceas.

Latent strain hardening i s the type of strain hardening which takes place in a non-active s l ip syatem, if i t i s euddenly called upon through a change of the loading on the crystal. The Bauschinger effect ie a special caee of such latent strain hardening. Here i t i e observed that after a certain degree of strain hardening has been reached in one direction the atart of plast ic flow in the opposite direction occurs under a much lower s tress . T h i s i s illustrated in Figure 30 which i s taken from Sachs and Shoji (73). The reduction in the shear streaa a t which plaatic f low is initiated in the opposite direction is due to an unstreaaing of piled-up dislocations. The general case of latent strain hardening i s illustrated in Figure 30 (74) which shows the strees-strain curves for Zn single crystals first loaded in one direction in the basal plane and then in the directions inclined a t angles of 60' and 120' to the first, again in the basal plane.

Often the primary slip syetem i s relieved by i t s conugate slip system or double slip. This cauaea a gradual change of the orientation of the s l ip plane with respect to the specimen axis. If the latent atrain hardening of the conjugate s l ip eystem i s larger than that of the primary s l ip system, the specimen ax i s rotates beyond the symmetry axis of the two d i p eyatems. If the latent etrain hardening i s smaller in the conujugate s l ip system, the specimen axis never reaches the symmetry axis but bends towards the (211) pole lying on that a r ia .

The flow curves of the hexagonal metals which deform primarily in basal $lide can be postulated from the above equations. One finds, that the slope of the s t ress etrain curve in the etrain hardening region muat be given by:

Equation 25

and does not depend upon the tes t temperature. Thia i s due to the fact that the temperature dependent term becomes zero after differentiation, since the activation volume v(a) does not

change with the strain, s e e equation 24. (As long a s the s l ip system i s limited to the basal plane, the density of the dislocation forest does not change). The theory thus predicts a temperature independent slope of the s t rese straih curve a t low temperatures. The resul ts on Cd and Mg confirm these predictions, s e e Figure 27. At higher temperatures the strain hardening coefficient decreases markedly. It a lso becomes rate sensitive. Polanyi and Schmid (75) have connected this softening with the s tar t of the s tat ic recovery in Cd. Similar evidence was obtained for Zm (76).

Some data are ale0 a v h a b l e on the effect of alloying. Figure 31 shows the effect of A 1 and Zn additions to Mg. In the former ca se the s lope $ first increases, but for concentrations in exces s of 6.856, decreases. Small additions of Zn to Mg seem to have lit t le effect an the slope of the curve, s e e Figure 31. In Zn-Cd crystals the strain hardening coefficient a t room temperature decreases with increasing Cd concentration (10) a phenomenon generally observed in fcc alloy crystals. The critical shear s t ress increases in a l l cases , aa discussed above.

By far the largest amiunt of data is available for fcc single crystals. The flow curves of these crystals fall a l l in the general pattern illustrated in Figure 32 which shows the presence of three distihct regions (identified a s I, 11, 111). These regions are characterized by three distinctly different strain hardening coefficients.

Region I, a lso called easy glide region, i s characterized by a very low strain hardening coefficient, (+/G = 1.4.10m4) which, however, depends on the crystal orientation with respect to the direction of s t r e s s and the thickness of the specimen. I t can increase to about 1 0 times that of region 11. ~ J z u k i , Ikeda und Takeuchi (77) have shown that thie orientation dependence disappears a s t4e specimen diameter i s below 0.4 mm. Seeger (2) concludes that two basic mechanisms must be active to account for the observed behavior. One of them i s identical to that operative in hexagonal metals, discussed above, equation 20. No barriers are created during this process. The second mechanism which is needed to explain the thickness and orientation effect is believed (2) to be the formation of dielocation barriere in the form of Cottrell-Lomer dislocations. Such a model leads to a strain hardening coefficient of approximately ( $ / G = 6.10m4 which ia in general agreement with the experimental result*. The conditions necessaryfor the creation of Cottrell-Lomer dislocations and their effect on moving dislocation lines explain the observed orientation and thickness dependence.

In the transition from region I to region Ll a second group of Cottrell-Lomer dislocations i s added which limits the bot ion of the dielocations in the primary s l ip plane in al l directions.

Region I1 i s characterized by a very high strain hardening coefficient. The motion of dislocations in the (111) plane i s now limited in al l directions by the Cottrell-Lamer barriere ( a s shown in Figure 33). The strain hdrdening coefficient i s nearly temperature independent. The length of the dislocation line decreases linearly with increasing strain (78). Temperature cycling experiments (79) have shown that the high strain hardening coefficient i s not due to an increase in the density of dislocation forest, but rather that the slip in the secondary system has a catalytic action on the formation of additional Cottrell-Lomer dislocations, The fact that alloying additions have lit t le influence on the strain hardening coefficient in this region i s not in conflict with the above model a s the strain hardening exponent depende on nb/l where 1 is a model constant related to the length of the dislocation line. The metal surface in renion - I1 may, according to ~ a d e r (78) be termid structured microslip. Recent measurements have shown that the dislocation density in Cu and A 1 single crystals increase8 from 2 1oB/cm2 in the annealed s tate to 2 lo1" - 1011/cm2 if s t ressed beyond the easy glide region, a > lo9.

In region 111 of the flow curve an irreversible temperature dependence i s observed, s e e Figure 32. Here then, the mechanism responsible for the high strain hardening coefficient of region I1 is partially eliminated by thermally activated processes (2). T h i s recovery, a typical example of dynamical recovery, i s strongly s t r e s s dependent. The process responsible for this recovery ie thermally activated croes s l ip of screw dislocations (80, 81, 79). Such cross d i p again depends on the stacking fault energy and occurs easi ly in A 1 and Pb a t room temperature, while not in Cu and other fcc metals. On the surface $lide bands and fragmented glide bands are observed.

The energy of stacking faults i s a dominant factor governing the deformation modes of alloy crystals. In Cu-Ge and Cu-Ga alloy crystals i t decreases rapidly with increaeing concentrations of Ge or Ga from : 105-165erg/cm2 to 2 10erg/cm2 a s a function of the electron- concentration. (1.15 to 1.2, phaee boundary 1.40) Th i s causes an increase in tl11 (cross s l ip) and the formation of deformation twins, independent of temperature but dependent on the concentration.**

4.2 DEFORMATION UNDER A CONSTANT LOAD OR STRESS

Since the las t lecture of this conference by Professor Grant i s primarily concerned with the phenomena occuring under a s teady applied s t r e s s or load, they will not be covered here. . ..

I t might only be mentioned that the beta-creep portion of transient creep in fcc metals appears to be related to the region 111 of the flow curve (82).

4.3 F R A C T U R E

A description of the occurrence of fracture in terms of the crystal defects h a s been pre- eented by Petch (83) and Cottrett (84). Here we are mainly concerned with the creation of cracke within a grain. From there on the engineering fracture concepts for polycrystalline materidcp such a s fracture mechanics developed by Irwin and assoc ia tes or the Nenber concept developed a t Syracuse University (85) can be applied with more or l ee s success. Froti a defect structure point of view the question a r i ses a s to what mechanisms are responsible for the formation of a crack across a single grain.

The problem i s how the conversion from glide dislocations to cavity dislocations takes place. Four possible models are shown in Figure 34 taken from Cottrell (86). The mechanisms illustrated are: 1) pile-up of edge dislocations, 2) pile-up in a slip band of edge dislocations against a grain boundary, 3) ehear on two intersecting slip bands and 4) sl ip band crossing a ti l t boundary. In order for any of these systems to work i t i s necessary that the elast ic energy which the dislocations bring with them i s not rapidly dispersed through plast ic flow in the nearby material. In materials having only one or two easy s l ip systems the mechanisms are feasible-the britt leness of h.exagonal metals can be explained on this basis , cf. Figure 4. For cubic crystals with good sl ip systems in several directions, Mott (87) and Stroh (88) pointed out that a yield drop i s required for the mechanism to work. Such a phenomenon gives rise to dislocation avalanches which run together and form a crack before nearby didocat ion sources can star t working. With the help of these micromechanisms for crack formation, and the Griffith concept, Cottrell (83) and Petch (84) were able to define fracture in terms of the yield strength, the dislocation pinning strength and the eurface tension by the well known equation.

*Hordoa, M.J. and Avsrbsch, B.L. Actn Met. v 9 (1961) No. 3, p. 237.

**Haasen. P. and King. A.Zeit. Metallhnde v 51/12 (1960) p. 722.

= yield strength Y 1 d = grain s ize I

Y = surface tension

uD = unpinning s t r e s s for dislocation

8 = spacing of sources

Equation 26

Th i s equation gives information on both brittle and ductile fracture. When the left hand side exceeds the right hand aide, the yield s t r e s s i s more than sufficient to propagate the micro- creeks. On the other bar&, w h e n the right hand side i n larger than the left hand .ids, the yield s t r e s s does not suffice to propagate the microcracks. T h e equality eign defines the condition for fracture transition. It i s interesting to note, that the surface energy finds i t s way into the above equation via the Griffith concept. Thus far, there was no direct information available concerning the effect of surface tension. Recent experiments on the effect of liquid metals on the fracture of solid metals (89) illustrate the predicted role of surface t endon rather drastically.

The final failure mechanism mentioned before is that of evaporation. Quantum mechanics gives the following formula for the vapor pressure (90).

15k = force energy of lattice vibration

M = molar mass

E b = binding energy

Fo r high temperature this reduces to:

The evaporation rate itself* i s governed by the composition of the surrounding atmosphere. If we assume that none of the evaporated atoms return w e obtain the curvm shown .in Figure 35 (91). An indication concerning the relative evaporation rate of two elements constituting a dilute solid aolution of orie of them can be obtained with the help of Raoult's law which s ta tes

I I I

1 *With the help of the Claueius-Clapryron equstion one can calculate the heat of sv~porstian per atom p(T) = Eb -- k T as a function of the temperatura. 1 2

Equation 29

that the vapor pressure of a component A of a dilute solution i s reduced approximately by the mole fraction of A present. However, i t has been repeatedly pointed out that this is only a very rough approximation and may not apply a t all. If the law applied strictly, no disturbance of a chemical makeup of the eolid in queation would occur. It i s well known that the evaporation rate also depends on the crystallographic orientation. This i s the underlying effect made use of in thermal etching.

5.0 SUMMARY

The properties of so l ids that can be derived from the electron theory of metalm or similar aeeumptiona fall in the group of structure ineeneitive properties. Here the agreement between theoretical prediction and experimental evidence i s satisfactory. An application of the s a m e principlee to mechanical properties of materials, moat of which are structure sensitive, leads to disagreement between theory and experiment to the order of 10'' or more. This i s due to the fac t that the mechanical properties are extremely sensi t ive to etructural defects. Such defects are introduced both in the manufacture a s well a s during the service life of metal parts.

These defects can be classified according to their geometrical order into point defecte (vacancies and interatitials) line defects (dislocations) and area defecte (low and high angle boundaries). By far the most experimental evidence ex is t s for fcc metals. Generally the mechanism of interaction between like and unlike defects and the motion of these defects contain temperature dependent and temperature independent terme. The temperature dependence i s ueually exponential and mechaniame have been deduced whose activation energies are in agreement with the experimentally observed activation energies. Most of the defect reactione were arrived a t in retrospect, however, there existe now considerable quasi-direct experimental evidence for the existence of these defecte and eome of their reactions. The stress-strain curve for face centered cubic single crystals can be almost completely defined in term4 of the various dislocation reactions. An application of these mechanisms to materials in the polycrystal s ta te cannot be expected a t the present time in any quantitative sense , however, eome qualitative considerations are possible.

For an accounting of the varioua modem of failure namely deformation under increasing load, creep, fracture, and evaporation, the defect concepts developed can a l so be applied. This i s eapecially true for the three mechanical failure modes which are extremely structure sensitive. To a first approximation, evaporation may be considered a structure insensitive property of material and thermodynamical treatmente of the phenomena are ueually adequate.

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I

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32. R. W. J ames , The Opt ical P r inc ip lea of the Diffraction of X-Rays, G. Bel l , London (1948).

33. A. A. Griffith, Phi l . Trans . Roy. Soc., Ser ies A., Vol. 221 (1921) p. 163.

34. H. B. Huntington and F. Sei tz , Phya. Rev., Vol. 76 (1949) p. 1728.

35. J. E. Dorn, Symposium on Creep and Fracture of Metals a t High Temperatures , Teddington (1954).

36. F. Sei tz , Imperfections in Nearly P e r f e c t Crys ta l s , John Wiley, New York (1952) p. 3.

37. H. P i c k , Naturwiss, Vol. 14 (1954) p. 346.

38. J. Frenkel , Zeit . Phye., Vol. 35 (1926) p. 652.

39. C. Wagner and W. Schottky, Zeit . Phys . Chem. Sect ion B;Vol. 11 (1930) p. 163.

40. W. Jost , J. Chern. Phys . , Vol. 1 (1933) p. 466.

41, N. F. Mot t and R , W. Gurney, Elect ronic P r o c e e s e s in Ionic Crystals, Oxford (1948).

42. F. G. Fnmi, Phi l . Mag., Vol. 46 (1955) p. 1007.

43. H. B. Huntington, Phys . Rev., Vol. 91 (1953) p. 1092.

44. H . B. Huntington, Phys . Rev., Vol. 61 (1942) p. 325.

45. S e e reference (36) p. 289.

46. C, Zener, Acta Cryet., Vol. 3 (1950) p. 346.

47. A , D. L e Claire, ~ c t a Met., Vol. 1 (1953) p. 438.

48. P, Jongenburger, Appl. Sci. Res. B., Vol. 3 (1953) p. 237.

49. J. W. Kauffmen and $. S. Koehler, Phy. Rev., Vol. 88 (1952) p. 149.

50. C. Zener, Elasticity, and Anelasticity of Metals, University of Chicago Press , Chicago (1948) p. l l l f f . ~

51. G. I. Taylor, Proc. doy. Soc. A., Vol. 145 (1934) p. 362.

52. E. Orowan, Zeit. ~ h y s . , Vol. 89 (1934) p. 634.

53. M. Polanyi, Zeit. pqye., Val. 89 (1934) p. 660. ~

54. A. H. Cottrell, ~ i s l & a t i o n a and Plas t ic Flow in Crystals, Oxford (1953).

55. F, C. Frank and W. T. Read, Phya. Rev., Vol. 79 (1950) p. 722.

56. W. T. Read, ~ i e l o c a t i o n s in Crystals, McGraw-Hill (1953) p. 70.

57. A. Seeger, Report of the Briatol Conference on Defects in Crystalline Solids, The Physical Society, ind don (1955) p. 391.

58. A. N. Stroh, Proc. Phys. Soc. Lond., Ser. B, Vol. 67 (1954) p. 427.

59. J. Frenkel and T. Kontorova, J. Phys. U. S. 5. R., Vol. 1 (1939) p. 137.

60. R. Peierls, Proc. Phys. Soc. Lond., Vol. 52 (1940) p. 34.

61. J. Washburn and E. R. Parker, J . Metals, Vol. 4 (1952) p. 1076.

I 62. See reference (36) pd 352.

63. W. T. Read, Conference on Mechanical Effects of Dislocations in Crystale, Birmingham (1954) - s e e also reference (56) p. 172.

64. K. Lucke, Zeit. Metallkunde, Vol. 44 (1953) p. 370, 418.

65. T'ing Sui Ke", J. ~ ~ ~ 1 . Phya., Vol. 19 (1948) p. 285.

66. N. F. Mott, Proc. p h i s . Soc. Lond., Vol, 60 (1948) p. 391.

67. A. H. Cottrell, ~ e f o r m s t i o n and Flow of Solids, Madrid Colloquim, Springer-Vedag (1956).

68. W. A. Rachinger and:^. H. Coteel l , Acta Met., Val. 4 (1956) p. 109.

69. E. Schmid, Proc. Int. Cong. Appl. Mech. Delft. (1924) p. 342.

70. A. Seeger, Zeit. Natorforsch, Vol. 9a (1954) p. 758.

71. A. H. Cottrell, L'Etat Solide (Bericht Vom 9. Solvay-Kongrees fur Phyeik) Bruseel: R. Stoops, (1952) p. 421.

72. N. F. Mott, Phil. Mag., Vol. 44 (1953) p. 742.

73. G. Sacha and H. Shoji, Ziet. Physik, Vol. 45 (1927) p. 776.

74. E. H. Edwards and J. Washbnm, Trans. A. I. M. E., Vol. 200 (1954) p. 1239.

75. M. Polanji and E. Schmid, Naturwise, Vol. 17 (1929) p. 301 - see also reference (10).

76. R. Drouard, J. Washburn and E. R. Parker, Trans., A. I. M. E., Vol. 197 (1953) p. 1226.

77. H. Suxnki, S. Ikeda and S. Takenchi, J. Phys. Soc. Japan, Vol. 11 (1956) p. 382.

78. S. Mader, Zeit. Phymik, Vol. 149 (1957) p. 73.

79. A. Seeger, J. Diehl, S. Mader and H. Rebatock, Phil. Mag., Vol. 2 (1957) p. 323.

80. J. Diehl, S. Mader and A. Seeger, Zeit. Metallkunde, Vol. 46 (1955) p. 650.

81. See reference (67) p. 90.

82. A. Seegcr, Zeit. Naturforsch, Vol l l a (1956) p. 958.

83. N. J. Peteh, Phil. Mag., Vol. 3 (1958) p. 1089 - eee also J. Heslop and N. J. Petch, Phil. Mag. Vol. 3 (1958) p. 1128,

84. A. H. Cottrell, Trans. Met. Soc. A.I . M. E., Vol. 212 (1958) p. 192.

85. V. Weiee, Proc. Seventh Sagamore Ord. Mat. Rca. Conf. (1960).

86. A. H. Cottrell, Fracture, Technology Press and John Wiley (1960) p. 20.

87. N. I?. Mott, J. Iron Steel Inet., Vol. 183 (1956) p. 233.

88. A. N. Stroh, Advances in Physics, Vol. 6 (1957) p. 418.

89. W. Rostoker, J. M. McCaughey and H. Markns, Embrittlement by Liquid Metals, Reinhold Publ. Corp. New York (1960).

90. G. Leibfried, Encyclopedia of Phyeice, Vol. VII/I Springer-Verlag, (1955) p. 316.

91. G. F. Vanderechmidt, Proc. Fifth Sagamore Ord. Mat. Rss. Conf. (1958) p. 78.

The authors tuould like to express their p t i t u d e to the personnel

of the Metallurgical Research Laboratory for their help in the prepara-

tion of this ma+uscript. Special thanks are due to the following members

of the staff: ~ Mr. K . S. Grewal Mr. J. 4. McKeon Mr. J. F. Schell

Mrs. D. A. Anderson Miss C. L. Swaneon

TE

MP

ER

AT

UR

E-D

EG

. K

EL

VIN

~ FIGURE 2

ENERGY BANDS IN COPPER AS A FUNCTION OF INTERNUCLEAR SEPARATION. [AFTER H. M. KRUTTER, PHYS. REV. 48, 664 (193511

FIGURE 3

MEAN POTENTIAL INSIDE AND OUTSIDE THE CRYSTAL

FIGURES 2 & 3

t Potential Energy of on Elmctron

(a) No Extrmol F i d d (b) Moderotm External F l d d

( c ) Vwy Strong Extornol F i d d

POTENTIAL ENERGY OF AN ELECTRON AS A FUNCTION OF ITS DISTANCE X FROM THE SURFACE OF A METAL

FIGURE 4

SCHEMATIC DIAGRAM ILLUSTRATING MECHANISM OF IMAGE FORMATION

FIGURE 5

CRYSTAL STRUCTURES OF THE ELEMENTS

c. - CUBtC h. - HEXAGONAL t - TETRAGONAL

* METALS

rho. - RHOMBOHEDRAL orh. - ORTHORHOMBIC

+ *-METALS t- GROUP I METALS B-METALS 1

METALLOIDS -a

Be h.12

3 2

Zn h.

c . I2 ,6 (12)

Cd h. 6(12)

Hg h.6

L1 e.8 h. 12

Na c. 8

K c.8

Rb c.8

Cs c.8

B h.3 c.12

At , c.12

Go orth.

In t.12

T 1 c.12 h.12

C c 4 h.3

Si c.4

G a c.4

Sn t.6 c.4

Pb c.12

Cu

A 3 2

Au c.12

Br 1

I 1

As rho. 3(6)

Sb rho. 3(6)

- TRANSlTlON METALS -

B i rho. 3(6)

Se 2(6)

Ts 2Ib)

Ni c.12

Pd c . 1 2 ,

P t c.12

Ca c.12 h.12

Rh c.12

I r c.12

Mn c.8 c.12

Tc h.12

R e h.12

V c.8

Nb c.8

Ta c.8

T i c8 h.12

Zr c.8 h.12

Hf h.12

Ca h.12 c.12

Sr c.12

Ba c.0

Fe c.12 c.8

RU h.12

0 s h.12

Cr c.12 c.8

Mo c.8

W c.8

Sc c.12 h.12

-

Yt h.12

L a e.8 c.12

ME'S POTENTIAL FOR TWO ATOMS

I FIGURE 8

RELATION BETWEEN EXPANSION COEFFICIENT AND MELTING POINT. (ZWIKKER)

FIGURES 7 & 8

SCHOTTKY AND FRENKEL DEFECTS IN A CRYSTAL* THE ARROWS IHDICATE THE DIRECTION OF DISPLACEMENT OF THE ATOMS.

FIGURE 9

FIFTH SAGAMORE ORD. MATS. RES. CONFERENCE (19581, p. 2061 , I

I

I I I I 111 IV v

1 FIGURE 11

SCHEMATIC REPRESENTATION OF THE- RECWERY OF THE RESISTIVITY OF COPPER, (SEEGER).

FIGURES 10 8 11

(a) SCREW DISLOCATION L

(b) EDGE DISLOCATION

SCREW AND EDGE DISLOCATIONS WITH THEIR R~SPECTIVE BURGERS CIRCUITS

FIGURE 12

I THE OPERATION OF A FRANK-READ SOURCE

FIGURE 13

SCHEMATIC ILLUSTRATION OF A JOG

FIGURE 14

SCHEMATIC ILLUSTRATION O F A JOB

F I G U R E 15

FORMATION OF VACANCIES AT JOGS OF DISLOCATION LINES HAVING PREDOMINANTLY SCREW CHARACTER

FIGURES 14 & 15

o b a b a b a b o b a b o b a b

I F I G U R E 16

COMPLETE DISLOCATION EXTENDED TO FORM A STACKING F A U L T I N FCC AND CPH CRYSTALS (100) AND (2110) PLANES RESPECTIVELY

FIGURE 17

LOMER-COTTRELL REACTION

FIGURES 16 & 17

Screw Dl sloeation

FIGURE 18

THE LONG RANGE STRESS F IELD OF DISLOCATIONS

FIGURE 19

STABLE ARRANGEMENTS OF EDGE DlSLOCITlONS OF EQUAL AND.OPPOSITE SIGNS

FIGURES 18 & 19

FIGURE 20

PILE-UP OF EDGE DISLOCATIONS AGAINST A BARRIER (SCHEMATIC)

FIGURE 21

MOTION OF A LOW IMGLf DOUNDIRY UNDER STRSSS

FIGURES 20 & 21

MOTION AND ENERGY OF A LOW ANGLE BOUNDARY IN WITH T H A T - O F A NONCRYSTALLOGRAPHIC BOUNDARY

COMPARISON

FIGURE 22

THE EFFECT OF 6 ON THE RELATIVE GRAlN BOUNDARY ENERGY IN SILICON-IRON

FIGURE 23

I

FIGURE 24

NODE IN PHASE BOUNDARY E BEIWEEN PHASES P AND Q. BOUNDARY MOVES IN DIRECTION k.

FIGURE 25

SLIP MODEL

FIGURES 24 & 25

Sheor Strain a

SHEAR STRESS-STRAIN DIAGRAM, SCHEMATIC

FIGURE 26

TEMPERATURE OK

CRITICAL SHEAR STRESS OF Mg, Bi, Mo m d Zn PLUS 1% Cd AS A FUNCTION OF TEMPERATURE

FIGURE 27

blSLbCATlONS IN A SLIP PLANE PASSING BETWEEN TWO SEZSILE DISLOCATIONS, MOD& PQR THE DERIVATION OF EQUATION 20

I

FIGURE 28

CRITICAL SHEAR STRESS OF ,METALS HAVING A LOW STACKING FAULT ENERGY AS A FUNCTION OF TEMPERATURE

FIGURE 29

BAUSCHIN6ER EFFECT IN BRASS AND LATENT STRAIN H A R P ENlNG I N ZN SINGLE CRYSTALS.

FIGURE 30

THE EFFECT OF ALLOYING ADDITIONS ON THE SHEAR STRESSSTRAIN CURVE OF MG CRYSTALS WITH A1 AND Z N ADDITIONS

FIGURE 31

SCHEMATIC ILLUSTRATION OF THE SHEAR STRESS- STRAIN CURVE AND ITS TEMPERATURE DEPENDENCE POR FCC METAL CRYSTALS.

FIGURE 32

COTTRLLL-LOMER BARRIERS LIMITING THE DISLOCATION PATH. SCHEMATIC

FIGURE 33

-- --

DISLOCATIONS AND CRACKS (a) ELASTIC CRACK REGARED AS PILE- UP OF EDGE DISLOCATIONS (b) CRACK FORMED FROM PILE-UP AGAINST A BOUNDARY (e) CRACK RESULTING FROM SHEAR ON TWO BANDS (d) CRACK FORMED AT A T I L T BOUNDARY

FIGURE 34

RATE OF LOSS OF VARIOUS METALS AS A FUNCTION OF TEMPER- ATURE. (THE MELTING POINT (OC) I S SHOWN BELOW EACH METAL)

FIGURE 35

ACKNOWLEDGMENT

The authors would l ike to express their gratitude to the personnel of the Metallurgical Research Laboratory for their help in the preparation of thig manuscript. Special thanks .are due to the following members of the staff:

Mr. K. S. Grewal Mrm. D, A* Andemon Mr. J. J. McKeon Miss C. L, Swanson Mr. J, F. Schell

THE ROLE OF IMPERFECTIONS IN DIFFUSION

by

Dr. C. E. Birchenall

A B S T R A C T

The identification, description and determination of the concentrations of point defecta in cryetala lie a t the core of the problem of diffusion in solids. The identification of the important defects has been accomplished and their concentration h a s been meaeured in certain c a m e , but the theoretical description of the defecta has been only approximate. Neverthelees, kinetic and phenomenological theories have been developed which seem to describe many as- pecte of sol id atate diffnsion adequately, but the underlying assumptions of these theories continue to be explored. Experimental teehniquee have improved greatly in recent years, allowing improved precision of measurement. Paral lel improvements in the electron theory of sol ide and computational methods may lead to comparable improvemente in the theory of diffueion eventually.

Some of the current active aspec ts of the study of volume diffueion which eeem likely to continue in a fruitful way are: (1) the drift effect imposed on the random motions of atoms as a result of the variation of the thermodynamic activity coefficients of the elements with change in compoaition in a molution, (2) correlation effects in the motion of ieotopic tracers, (3) the effects of small concentrations of aolute atoms on the diffusivities of both solute and solvent atome, (4) the interactions of point defects with dielocatione and the influence of strain rate on diffusivity, (5) the Curie point anomaly. In view of the existence of many recent reviews eeveral important and active aspec ts of volume diffueion are not discussed.

Boundary and surface diffusion aeem likely t o be the subjec ts of more frequent and more careful investigation than they have in the past. The very narrow boundary region assumed to apply to very pure metals h a s been shown not to be applicable to a t l eas t some eolid so- lutiona. In alloys i t ie neceaaary to establ ish how the boundary etructure dependa upon compoeition and variations in composition as well aa on relative orientations of neighboring grains. In the etudy of surface diffusion careful correlations of the detailed structure of the expoeed eurface, the symmetries of the planem lying in the real ~ n r f a c e and the presence and concentration of adsorbed impurities are required. Only the first hesitant s teps have been taken in these directions and much more remaiaa to be done.

Paper for the Eighth Sagmare [Mamcs Materialm Remuch Confatonce. "Meehmimmm Dpermting in Metdo at Elpvnted Tempemtnmd8, A u w t 22 -26. 1%1.

INTRODUCTION

A major purpose of this conference i s to attempt to distinguish the important problems of the immedieta future within the subject area under discussion. In the case of diffusion in metals i t i s necessary to note that a t l e a s t one review has been undertaken recently for just this purporsel. There are other review articlesabprepared recebtly that aerve to identify some of the problems that might otherwise be given greater prominence here. Thus the relative emphasis on topics in this report should not be taken as the only evidence of their relative importance.

The frequency of the apecial review art icles and the number of references accruing between annual reviews6 should be an accurate indicator of the $enera1 importance of diffusion in materials problems. It seems likely that research activity on diffusion in sol ids will intensify rather than abate, and that i t s value a s a tool for studying the structure and binding of erolids will increase a t the same time that i t s relevance to the underatanding and control of teehnolo- gical processes a l so increases.

VOLUME DIFFUSION

THE EQUILIBRIUM DEFECTS

Diffusion in crystals ia the result of the motion of point imperfections. It i s necessary and desirable to have evidence which i s a s direct and unambiguous as poslaible about the nature and concentrationa of the point imperfections. Until a few years ego evidence about the nature of the dominant imperfections was exclusively theoretical for metals, derived from the calculations of Huntington and Seitz7and Zeners, later followed by Brooks9, Fumiloand others. These calculations involve finding the s m a l l reeidue, the energy of defect formation, from a number of large positive and negative contributione, some of which have uncertainties of the laame order an the magnitude of the remainder, as pointed oat by ~ o m e r ' l and Amarl*. Amar ca l l s attention to the uncertainties arieing from the use of the mams of the free electron in calculating the Fermi energy and correlation energy and the assumption of a uniform distribution of electron density within the Wigner-Seitz ce l l in calculating the electronic aelf-energy instead of the experimentally observed effective electron mass and a more realietic radial electron distribution function.

Experimental s tudies like the Kirkendall shift of markers and quenching-in of high temperature defect demonstrate the need for a defect-type explanation for diffusion rather then a description in terms of rotating rings of atom@. The quenching experiments give reasonable values for the defect concentratione, but, apart from the theoretical bas i s cited, the explanations of these effects are virtually symmetrical with respect to vacancy or interstitial-type defects.

Therefore, it irs reasenring that high precision direct meaeurementa of x-ray and gravime.tric densi t ies by Simmons and ~ a l l u f f i l ~ have shown that vacancies are really preeent and that they are present in the expected concentrations, The fact that similar measarementr have been done much earlier on nonstoichiometric ionic crystals1' should not detract from the recognition of the importance and diffic,ulty of-demonstrating these effects in metals.

I t is desirable to extend these comparative density measurements to the highest poseible precision and to apply them to a wide range of systems. With these expectations concerning the nature and concentratione confirmed, the quenching methods may be pursued with a new degree of confidence, a s l a t g a s i t ia recognized that the technique requiree great care in

performance and interpretation. For axample, note the wire s ize effect atudied by Tahmun" . Aleo the aeaociation of vacanciea into pairs or larger aggregate6 complicatee the low temper atnre behavior.

The comparieon of x-ray and gravimetric densitiea does not give direct evidence about the effective volume of a vacancy, or the configuration of atom8 about a vacancy. This ~roblern can be approached through theoretical calculatione of the type mentioned above or by fitting more empirical interaction potentiale and minimizing the energy of the syetem with reapeet to variation of the positions of a group of atoma around a vacant eite. Both types of calculation benefit gteatly from the growth of large capacity and high speed cornputera. One activity of this sort is mentioned below.

Information about defect volume can aleo be obtained from the effects of preeaara in diffueion. However, thie measurement mixes the defect volume and the volume increase required for the defect to make a diffueion jump* A more desirable meaeurement is the effect of pressure on defect concentration a t conetant temperature, a meaenrement which may only be possible in the near future by one of the indirect methode.

EXPERIMENTAL METHODS

Zener slid Wert 14. proposed an adaptation of reaction rate theory to diffusion which gave tbe equation

where aim a geometrical factor determined by the crystal strncture and diffusion mechanism, f i e the Bardeen-Herring correlation coefficient which was omitted from the original theory, Y in the vibration frequency of the diffusing atom, a i s the lattice parameter, R ie the gas conetant, T is the abeolute temperature, AS ia the aum of the entropy of formation and activation entropy for motion per mole of defect and AH is the sum of the enthalpy of formation and activation energy for motion per mole of defect. The equation hae the empirically observed Arrhenias form.

Aosnming that the activation energy for motion i s used to strain the lattice and that the macroscopically obeerved temperature coefficient applies, Zener1& hae been very successful in explaining the magnitude of AS and conmequently of the frequency factor a e a whole. This eucceee has prompted too mach concern about the mijpificance o( frequency factor. which do not conform readily to the Zener model. It eeemm appropriate to reiterate Zener's initial saggeetion - if the experiment does not fit, repeat the experiment. On at least two recent occaeionel"* 17b the canees of the theoretical excitement have evsporated when the experimental meaeurements were repeated belatedly. And in a t least one of these instances the more interesting problem that remaine, the probable need for several type8 of jump in P tin, seems to have made no strong impreasion on the theoriete. Evaluation of the correlation factor f for competing jnmpe in anieotropic cryatale hae not been carried through.

Although a great deal of the real progrees that has been made in diffusion ~ t u d i s e in the paet decade ie the reealt of improvements in experimental precieion of meaaurement, i t is un- wise to take i t for granted that optimum precision ie obtained in every experiment and on every conceivable eymtsm, Dioerspanciee etill remain, rome large, some emall, some of unknown magnitude. However, i t would be profitable for new gtoupe entering the field to check out their

techniques on some material other than pure silver, which might be described justly a a done to death.

Improvemsnte, in prsci*ion have been confined m a i d y to the measurements of self-diffuaion in metals and al loys using radioactive tracers. With reasonable care in the counting procedures most of the errors ar ise from temperature measarementa and sectioning of the specimens. Precision grinding techniipes3* l8 have lead to the greatest share of improvement recently.

I t appears that the development of the electron microprobs x-ray analyrer19 h a s greatly improved the precision of chemical interdiffusion meaeurements. In addition, and a s important, it reduces the time of making such measnrements which previously depended on multitudes of preciare quantitative analyses by conventional methods on very small samplee. The extension of chemical interdiffusion peasurements to a wide variety of casee, accompanied by the study of marker shif ts and self-diffasion measurements, im an obvioue, challenging, but tedious f ield for study.

INTERSTITIAL DEFECTS

The fac t that interstit iala ~ robab ly , do not contribute significantly to self-diffusion in pure metals does not eliminate them from interest. Interstit ials are produced a s a part of radiation damage and muat diffuse during annealing-out of the damage. The elaborate calculation by Vineyard e t a l W offers an example of the application of modern computer technique6 to the investigation of the theoriea of physical procemsee in aolide which may make it eas ie r to improve those aspec ts of the theories which bear on diffnsion. In this particular case, the stability of the interstit ial pair in the form of a dumbbell with i t s ax i s normal to a cube face and bisected by the face is shown to be etable relative t o a single interstit ial in the body- center of a face-centered aubic crystal within the limitations imposed by the model.

In the study of interstit ial alloys inveetigatore should continued to remain aler t for thoee instances in which solute atoms are distributed over both snbatitutional and interstit ial poaitione. Becaume the s ike factor should lie in the range where it i s favorable for neither type of solubility, the total solubility in a metallic solvent should be small and preference for boundary and dislocation~jdiffusion should be high.

THEORY OF VOLUME DIFFUSION

There are four main diiections in which the theory of volume d i f fn~ ion h a s advanced recently.

(1) ~ e C l a i r e ~ l ham examined the c lass ica l theory of diffusion in the presence of a cbn- centration gradient. He predicts that the chanee in barrier height for a diffusion jump which varies along the concentration gradient imposee a general drift on the otherwise random motion of the diffusing atoms. These drift effects have been observed in d g C d al loys by ManningE and in eCuZn al loys by c&rnagmi, Pavallini and Shuttlewortha%. The part of the drift that a r i ses from the variation in the elf-diffusion coefficient or mobility with concentration may be more important than the drift that a r i ses from the nonideality of the solution, The latter ir responeible for the Kirkendall effect. The theory of Darken i s not complete because i t omits the former effect,

(2) Although isolated defects in eal ids may diffume by random jumps the resulting displacements of the atoms may not be random. In particular, the displacements of tracer atoms,

which are observed in self-diffusion, may be highly correlated because of the high ~robabi l i t ; that an atom which has juet exchanged p laces with a vacancy will jump back. Once Bardeen and Herring recognized the need for a correlation correction, the theory for self-diffusion in la t t ices of high symmetry was advanced rapidly by Compaan and Haven25 and by Lidiard and LeClairea6. An excellent account of the theory i s given by Lidiard, s o there i s no need to repeat i t here.

(3) LeClaire and Lidiard aleo examined the correlation problem for solute diffusion by a vacancy mechanism in a face-centered cubic lattice. Manning2' pointed out that the various jump probabilities that"contribute to the diffueion coefficient (see Equation 5 below) may not have the rame temperature dependence, rro that the correlation factor a s a whole i e expected to have a temperature coefficient in $enera1 which may not be exactly exponential.

Also in the ca se of alloy diffusion the trend i s away from attempts to e.xplain the concentration dependence of diffusivities in concentrated alloys toward high precision s tudies in very dilate alloys. The theory of self-diffusion of solvent atoms in dilute solution was developed by R e i e e a . The difficulty in expanding thie type of treatment to even modestly concentrated eolutionr hap been discussed in detail by Lararus4.

In the case of a solute atom that diffuees by a vacancy mechanism in a face-centered cubic eolvent lattice the correlation coefficient f can be calculated approximately, according to Lidiard and LeClairea6, when only jumpe involving the nearest neighbor s i tea of the solute atom are considered. They find

, w 2 and kl are respectively the probabilities per second that a vacancy in a s i t e where nearest wlh t e solute atom exchange6 with one of the four solvent atoms that are simultaneouely nearest neighbors of solute and vacancy, with the aolute atom itself, or with one ~f the other solvent atoms which are neareat neighbors of the vacancy. The las t type of jump i s s a id to diesociate the vacancy and solute pair and further correlation in their motion i s n e g l e c t u in this approximation.

On the other hand for eelf-diffusion by the vacancy mechanism in a pure substance, if the jump direction h a s two-fold aymmetry or higher the correlation factor i s given exactly by

1 + cos e f 5

1 - coe 8

where 6 ia the angle between the direction8 of two consecutive jumps of the tracer atom and the bar over coe 9 indicates that the average value is taken.

F o r two different isotopes of the same element with masses ml > m2, diffusing in the same material with diffneivitiee Dl and D2, ~ c h o e n ~ ' defines the strength of the isotope effect, S, by the equation

If the diffusivity were invereely proportional to the aquare root of the isotope m a e s S would have a value of unity. This behavior is consistent with the observations in a number of systems, but Schoen observed that Cd iaotopea diffueing in Ag and Cu gave diffusivities ~ u b s t a n t i a l l ~ independent of their mass corresponding to S 0. The diffusivity of a solute atom i s proportional to the correlation factor times w2, the probability of exchange per unit time with a vacancy, or

7 If wz >> WI +-k the diffusivity i s independent of w2. That is, the rate controlling jump of the vacancy i s % i h the soJvent atoms. In this caae the maas df the aolutc atom should be immaterial and the strength of the ieotope effect ~ h o u l d be small. However, if x2<< w + 1 k

1 2 1 the diffusivity i s proportional to wg. In thin case, end in the ca se of self-diffusion in a pure metal, i t is deeirable to establieh aa precisely as possible the etrength of the isotope effect.

Th i s technique appears to be very useful for exploring the association between solute atoms and defects and a s a test for detailed theories of vacancy jump mechanisms. It ia doubtful that the full range of possibi l i t ies is clear at the present time. This field may be one of the moet popular aapects of diffusion in the near future.

(4) One of the most noteworthy of recent trends is the probing of the underlying aaeump- tions of reaction rate theory as it relates to diffusion by Rice and his coworkersm. T h i ~ endeavor tends to sharpen the understanding of dynamical contribntiona to the diffusion jump which are treated very superficially in earlier models, The necessi ty for correlated displacc- ments of atoms around the saddle point i s shown to restrict the configurations leading to a diffusion jump to only a fraction of the configurations having energy in exces s of the activation energy. These considerations lend general support to Zener's proposal that the activation energy is the energy necessary to strain the lattice to produce the saddle point configuration and remain consistent with the form of the relations employed in the eimpler theories. The jump frequency ia found to be relatively inaenaitive to changes i n the normal modes of vibration resulting from the introduction of a vacancy as a neighbor. Appreciable relaxation about a vacancy is predicted, and the activation volume AV is given approximately by

where Va is the atomic volume and y is the Gruneisen conatant. Since y is often a b o ~ t 2 to 3, the activation volume ehould be roughly half the atomic volume, a s is sometimes reported.

EFFECTS OF STRAIN

There i s $enera1 agreement that prior strain has relatively lit t le effect on diffusion coef- f ic ients measured in conve~ t iona l experiments which invariably required enough t i m e a t the diffusion temperature to anneal out the effects of m a i n . However, Cohan and hie have reported that the continuous deformation of iron in compreseion during diffusion increased the meaaured self-diffusion coefficients in direct proportion to the rate of straining. Similar resulte have been obtained for silver in torsion by Lee and Maddinw. They attribute the decrease in activation energy aasociated with diffusion during deformation to the farmation of exces s vacancies through dislocation interactiona, thus eliminating the contribution of the hea t of formation of vacancies from the activation energy for diffueion. It hae been suggested

a lso that maintaining a higher than normal dislocation concentration may account for the enhanced diffusivity, with a heat of motion equivalent to that expected in low angle grain boundades (see below). Foreetieri and ~ i r i f a l c o * found similar strain rate effects in silver, noting that the magnitude of the effects diminishes with rising temperature.

Using conditions that overlap those of the other groups working with silver, Darby, Tomizulca and Balluffia8 fail to find significant atrain rate effects which clearly exceed the experimental uncertainties. Here lies the most important, unresolved, flat contradiction in experimental resul ts in the current diffusion literature. The resul ts on both e ides are plentiful. Only a more careful s e t of investigations under varied conditions seems likely to resolve this contradiction.

EFFECT OF PRESSURE

High hydrostatic pressure decreases the rate of diffnsion in crystals, According to Zener's mods1 the activation volume im given by

Many o i the high pressure s tudies on diffnsion in metale have been done by Nachtrieb and his coworkers34. Although there i s l e s s optimism about predicting mechanisms from measurements of activation volume than formerly, i t i s probably too early to give up the attempt. In any case, if vacancies are present there must be appreciable relaxation of the neighboring atoms to be consistent with the observed activation volumes which, a e s tated above, are da the order of one-half the atomic volume for self-diffusion in pure crystals of the elementa.

Measurements of eelf-diffueion in lead by Hudnon and offm man^ up to 4 x 10' k&cm2 presenre suggest that the activation volume ia about two thirds of the atomic volume up 40 half the maximum preaaure and then decrease8 aa the pressure increases.

Fo r nitrogen diffusing i n t e r ~ t i t i a l l ~ in iron, where the activation volume ia almost entirely the volume change produced by the atom jump, the activation volume was found by Bosman, Brommer and Rathenaua6 to be only about 4 pct. of the volume of a nitrogen atom.

A s the techniquea improve for producing and measuring high temperatures and pressures arimultaneoualy i t i s probable that work in this field will become increasingly valuable.

THE CURIE POINT ANOMALY

Birchenall and Mehls7 obeerved that their self-diffusion measuremente in alpha iron did not obey the A d e n i n e equation, but the precision of measurement was too low to associate definitely the deviatione from the usual behavior with the presence of the Curie temperature within the range of rneibqrement. After better sectioning techniques were developed Borg and B i r ~ h e n a l l ~ ehowed that an abnormal decrease in d i f fu s iv i t~ occurred while cooling through the Curie point range. Cohen and coworkerssg confirmed this result and found similar behavior for Nia diffuaing in very dilute solution in alpha iron. Stanley and wertq0find a similar effect in aFe-18% V alloys. On the other hand, Borg and ~ a i ' ' have been unable to find any deviation from the Arrhenius equation for Co60 diffudng in dilute solution in alpha iron, and there appears to be no large anomaly near the Curie temperature in pure cobaltd2.

in del ta iron consist of a single point by C o h e n ' ~ ~ ~ group, and new experiments have been made covering a range o f temperature by Staffansson and Birchenallc(and by Borg and Laiqo. The measurements do not agree very well in absolute value, but the activation energy in delta iron appears to be much lower than i t i s above the Curie point in the alpha range. Although Cohen'sg9 line in the alpha range extrapolates into the region covered by the experimental points in the delta range, the line i s based on points with rather large scatter. The Borg and Birchenallaa line requires a continuous curvature of the Arrhenius plot above the Curie temper ature in order to extrapolate to the delta range values smoothly.

Because of the extra ehergy required to remove a vacancy from a eystem with well-ordered spins, i t seems that a thermodynamic effect leading to an abnormal decrease in equilibrium vacancy concentration i s necessary when cooling through the Curie point range. If the energy of motion were unaffected, the diffusivity should reflect directly the decreaee in vacancy concentration. However, the decrease in diffusivity in alpha iron seems to be too large to be accounted for by this source alone, while in cobalt a much larger effect should be observed than even the present scat ter of data allow. Some other effect must be present, probably connected with the activation energy for motion. Two experiments are in progress which may help to elucidate thia effect. Borg and Lai are diffusing gold, which has no magnetic moment., into alpha iron. Staffansson and Birchenall are measuring self-diffusion in alpha iron parallel and perpendicular to the ax is of a magnetic field saturating the sample. Additional experimental and theoretical studies are likely to be required before thia phenomenon i~ understood.

GRAIN BOUNDARY AND DISLOCATION

Burgers model of a low angle grain boundary as a parallel array of edge dislocations leads to the expectatiohs that, if atom mobilities are greater along dislocatione than in the undisturbed volume of the crystal, (1) the self-diffusion coefficient averaged over a l l directions in a low angle grain boundary should increase a s the misorientation of neighboring grains increases, (2) diffueivity should be anisotropic within the boundary plane, preferring the direction parallel to the dislocation lines, and (3) the region about the boundary participating in enhanced boundary diffusion should be very narrow for self-diffuaion in a pure metal. Furthermore, for high angle grain boundariea variation of diffusivity with misorientation angle should be relatively small and anisotropy should be small.

These expectations have been confirmed by experiment. Using first the simple boundary conditions for grain boundary diffusion* of Fishera6 and later more exact solutions by Whipple4' - - and Vorisov, ~ i o l i k o v and LynbovQB, a l l for constant surface concentration, grain boundary diffuaivities have been obtained for polycrystalline pure Numeroue measurements have a l so been made in alloys50.

Hoffman and urnb bull^^ showed that the diffusivity in low angle boundaries i s proportional to the dislocation density, or that the mobility of atomn along the p ipes is independant of boundary angle for a Burgeh-type boundary. The mobility along dislocations in silver boundaries was found to a&ee well with the value measured in isolated dislocations by Hendrickson and Mach1i1.1~~. Hoffman5a showed that diffusion within low angle boundariee is anisotropic and that the anisotropy extended to higher angles than was anticipated.

*These calculetiona assume isotropic diffusion within the boundm. Therefore. they are mod &table for use with high angle boundariea which predominate in polycrystallins earnplea.

Usually the aqtivation energies for grain boundary diffusion are found to be about half those for volume diffusion in the s a m e material. HartM proposed that apparently low activation energies for volume diffusion obtained from relatively low temperature measurements are the resul ts of contributions from rapid diffnsion along dislocation networks. Rather extreme examples of this type of behavior are pobably contained in the work of Jaumot and Smith5= on zinc single crystals.

In the study of diffusion of sulfur in alpha iron Ainslie e t a lM found that sulfur diffuses a t a rate characteristic of substitutional diffnsion, that there was a large grain boundary preference and that sulfur in the grain boundaries could exceed the normal solubility of sulfur in iron single crystals. It was shown that the sulfur was highly concentrated in the grain boundary region. The volume for some microns on either aide of the boundary was dense with dislocations induced by the diffusion of sulfur. In a s ense the diffusing atoms plough their own furrow. The structure i s probably a transient one if the temperature i s high enough, but for a considerable t i m e the amount of solute held may greatly exceed the true solubility. In- man and TiplerS7 may have observed similar behavior earlier for phosphorus in alpha iron, but their o b e e ~ a t i o n s were obscured by precipitation effects.

I t i s obvious from these s tudies that grain boundary diffusion in alloys can be very complex. The need for s tudies on systems in which grain boundary adsorption can be controlled'is evident. I t i s important to determine whether anch phenomena remain sensi t ive to the history of treatment or whether etationary boundary structurela can be made in which diffuaivitiea may be measured without changing the etructure. The numerous Ruasian studies58 on diffusion in ternary and higher eysteme may be a s tep in this direction, although there i s no indication that they are combining etruc ture observations with their diffusion -measurements,

SURFACE DIFFUSION45

With the great improvements recently made in the techniques for observing the configurations and changes in configurations of atoms on crystal surfaces i t would seem that the study of uurface diffusion might advance rapidly in the immediate future. There seem to be basically three kinda of techniques available a t th i s time.

F ie ld emieeion and field-ion microecopy permit high resolution obaervation of the surfacea of a limited range of metals. The technique has been applied recently to the surface self- diffusion of tungsten by Barbour e t a159, Gomer and ~ u l r n ~ ~ had studied oxygen diffusion on tungsten surfaces earlier. Similar resu l t s may be obtained, although with lower d i r te t resolution, from the study by means of electron microecopy of part icles nucleating and growing on surfaced1. Low energy electron diffraction as applied by F a ~ n s w o r t h ~ ~ and by Germera yields information about groupings of amall concentrations of atoms on surfaces and a h o n ~ d be adaptable to mobility studies.

Grooves form a t the intersection of a grain boundary with a free surface when a riretal i s heated to reaeonably high temperature. The thermal grooving may take place by volume diffusion, surface diffueion or evaporation or some combination of these processes. ~ u l l i n s ~ has deduced the kinetics of grooving for the contributing proceaaea, and Mullins and S h e ~ r n o n ~ ~ and Gjoatein and R h i n e ~ ~ ~ have measured aurface diffusion coefficients under conditions for which the kinetics favor this type of control, assuming that the diffuoivity i s constant of the range of orientations on the surface defining the groove. These investigators obtain values for surface self-diffusion of copper in agreement with each other but not with the tracer i e ~ s u r e m e n t e of Hackerman auu Si1n~son6~.

The third type of measurement based on the apreading of radioactive tracere differs in an essent ia l way from the other two methods* Surface diffusion i s observed only for those tracer etoms which remain on the aurface. The tracer i s no longer contributing to the measurement when it has taken a volumle diffusion jump although the counting procedure may et i l l record its presence. I n t h e methods that depend on surface contour, a l l atoms on the surface are observed in principle and their average motion i n v e ~ i i ~ a t e d . On the other hand the tracer method offers a selectivity which permite i t s extension beyond the aelf-diffusion case more fruitfully.

The average number of jumps an atom can take before being trapped into the specimen is given approximately by the ratio of the surface diffusivity DS to the volume diffusivity Dv. The bes t methods of resolution, probably autoradiogaphy, nnder the most favorable conditions

5 (weak beta radiation) cannot resolve l e s s that 1 0 jumps in the same direction. It is substantially impossible by this method to measure surface diffusion unlees DS/DV is greater than lo6, Consequently, the diffusion coefficients for surface migration are likely to be more significant the lower the temperature of measurement.

All sor t s of surface s tudies show the great care that i s needed to produce clean, or even reproducibly dirty, surfaces, to characteriie those surfaces, and to ascertain that they remain unchanged topographically during the measurement. Surface diffusion measurements at 7S0°C. on various copper p lanes :'show an,.unerpected anisotropy on the {loo) faces. Since isotropic diffusion i s to be expected if the face i s normal to an ax is of three-fold or higher symmetry some effect of faceting or adsorption might be suspected. It was mentioned above that the average of these measurements does not agree with growing measurements.

Similarly surface self-diffusion coefficients by the tracer method on polycryetalline s i lver by Nickerson and parker68 disagree with grooving kinet ics measurements of Winegard and C h a l m e r ~ ~ ~ . Unpublished experiments with refined methods by Drew and pye@ on (321) faces of silver single crystals yield values which lie between, but not especial ly close to, the earlier measurements. The tentative results up to 500°C. obey the equation

D ~ g ( s ) = lom4 exp (-8700/RT) cm2 per eecond

but deviations become pronounced far DS = lo6 Dv. NO an i~o t ropy has been observed on th is surface. Its detailed topography has not yet been ~ t u d i e d , Diffusion under oxygen pressure is appreciably faster than it is under vacuum, but i t i s uncertain whether the surface rearranges, I t should be recalled that the surface energy of s i lver i s markedly affected by adsorbed oxygen.

S U M M A R Y

The understanding of almost every aspect of solid s ta te diffusion i s incomplete in sp i te of the fact that many advynces have been made in recent years. I t appears that the opportunity to apply improved t e c h n i q ~ e s to more carefully controlled materials ham never been better. Theoretical advances, esgecial ly those related to correlation effects, have opened up new approaches to the study of mechanism, that all-too-often ambiguoua pursuit that l i es a t the core of the problem. However, the obvious theoretical problems are a l so very formidable and progress on some of them may depend on the development of new experimenlal data.

Of all the aepecte of diffusion none eeems to offer greater challenge and prorniee of re- ward than the study of ~ u r f a c e diffusion which plays an important role in many phenomena - catalyris , nucleation of surface reactions, condensation, thermal etching - to liet a few. I t appears that the toale are a t hand. All that is needed is the skill , the determination and the infinite patience required to u se them properly,

R E F E R E N C E S

1. "Diffusion and Mass Trans ort", a report dated Nov. l 5 , 1959, pre ared for the NASNRC Committee on Perspectives in Meterials l f eeauch by a panel under ihe chairman& of D. Lazarus, to be publilished.

2. C. E. Birchenall, Met. Rev. 9, 225 (1958).

3. C. T. Tomieuka, in "Methods in Experimental Physics," Vol. 5, Academic Press , New Yotk. 1959.

4. D. Lazarus, in "Advances in Solid State Physics," Vol. 10, Academic Press , New York, 1960.

5. C. E. Birchenall in the Proceedings of the Fourth International Conference on Reaction of Solids, Amsterdam, 1960, to be published.

6. a P. G. Shewmon, Ind. Eng. Chern. 51, 402 (1959). b. P. G. Shewrnon and T. R. Winslow, Ind. Eng. Chern. 52, 343 (1%0). c. P. G. Shewmon and G. R. Love, Ind. Eng. Chem. $3, 325 (1961).

7. H. B. Huntin on end F. Seira, Phys. Rev. 61, 315 (1942), 76, 1728 (1949); H. B. Buntington, Phys. Rev. 61, 325 (194$ 8. B. Hintiagton, P h y ~ . Rev. 91, 1092 (19531.

8. C. Zener, Acta Cryst. 3, 346 (1950).

9. H. Brooks in "Impurities and Imperfections," pp. Iff, Am. Soc. for Metals, Clevelaad, 1955.

10. F. G. Fumi, Phil. h;ag. 46, 1007 (1955).

11. W. M. Lamer, in Prog. in Metal Physics, 8, 255 (1959).

12. H. b a r , AEC Report NYO-2565, November, 1960.

13. R. 0. Simmons and R. W. Balluffi, Phya. Rev. 117, 52 (1960), 119, 980 (1960).

14. E. 8. je t te and F. Foote, J. Chern. Phye. 1, 29 (1933). but see d ~ o W. L. l o t h , J. Appl. phym. b p p l . 30, 3 0 1 (1959); H. Pick and H. Weber, Z. Physik. 128, 409 (1950).

15. J. Takamura, Acta. Met. 9, 547 (1961).

16. a. C. Wert and C. Zener, Phys. Rev. 76, 1169 (1949). b. C. Zener, Chap. -11 in "Imperfections in Nearly Perfect Crystals, Wiley, N.Y. 1952.

17. a P. J. Fensham Auetralian J. Sci. Res. 3A, 9 1 (1950); 4, 229 (1951). J. D. Meakin and E. Klokholm, Trans. AI.M.E!- 21 8, 463 (1950).

b. H. W. Paxton and E. G. Condolf, Arch. Eisenhuttenw, 30, 55 (1959). W. C. Hagel, submitted to A1.M.E. 1961.

18. F. H. Eisen and C. &. Birchna l l , Acta. Met. 5, 265, (1957).

19. R. Castain . Publ. O.N.E.R.A. No. 55 (1951); Y. M d a , J. Philibert, C. Mairy and P. Bouchert, Rept. C.E.A. No. 880 (1f58); Y. Adda and k Kirimenko, 3. Nucl. Met. 2, 120 (1959).

20. J. i3. Gibson, k N. Goland, M. Milgram and G. H. Vineyard, Phys. Rev. 120, 1229 (1960). See ale0 k Seeger and E. Mann, J. Phys. Chem. Solids, 12, 326 (1960).

21. k D. LeClaire, in Colloquesur L a Diffu~ion a lPEtat Solids, p. 1, Antre d'Etude, Nucleaires de Saclay, France, 1959.

22. J. R. Manning, Phys. Rev. 116, 69 (1959).

23. P. Camagni, Pavallini and $. Shnttleworth, quoted in Ref. 21.

24. J. R. Bardeen and C. Herring, Chapter 10 in "Imperfections in Nearly Perfect Wiley, N.Y.,. 1952.

25. K. Cornpaan and Y. Haven, Trana. Fatad. Soc. 52, 786 (1956); 54, 1498 (1958).

26. A 3. Lidiard, Pbil. Mag. 46, 1218 (1955);. kg. LeClaire and A. B. Lidiard, Phil. Mag. 1, 518 (1956); A B. Lidiard. Chapter in Encyclopedm of Physlcs. Vol. 20, Springer-Verlag, Berlin, 1957.

27. J. R. Manning, Phys. Rev. Lett. 3, 365 (1958)

28. .H. Reism, Phys. Rev. 91 3, 1445 (1959).

29. .k H. Schoen, Phya. Rev. Lett. I , 140 (1958). See a lso Univ. Microfolms, L.C. Card No. Mic 58-5492.

30. .S. k Rice, Phys. Rev. 112 004 (1958) ; . k Rice and N. H. Nachtrieb, J. Chem. Phya. 31. 135 (1959); A. W. Lawson, S. A. Rice, k. D. Cornellussea and N. H. Neehtrieb, J. Chem. Phye. 92, 447 (1960); 0. P. Manley and 5. A. Rice, Phys. Rev. 117. 632 (1960); S. A.Rice and H. L. Friach, J. Chern. P h p . 32, 1026 (1960); O.P. Manley, J. Phya. Chem. Solide, 13, 244 (1960). See also, D. Lazwus. Solid State Physics, lo, 71 (1960).

31. F. S. Buffington and M. Cohen, Trana. A1.M.E. 194, 859 (1952). -U. U J ~ e, B. L. Averbach, M. Cohen tad V. Cliffithe, Acta Hot. 6, 68 (1958). See also I. Ya, Dektyr aud'V. S'&khdenkov, Ubain. F. Z. j i (1958).

32. C. H. Lee and R. Maddin, Trans. A.I.M.E. 215, 397 (1959), A. F. Foraetieri and L. A. Girifalco, J. Phys. Chem. Solids 10, 99 (1959).

33. J. B. Oarby, Jr.,,C. T. Tomizuka and R. W. Balluffi, J. - 1. Phye. 30, U)4 (19591, 32, 840 (1961). See also A. V. Savitzkii, Fir . Metall. i Lbtalloved, Atad Nauk, S&, Ural. Filial 10, 564 (1960). and P. Chollet, I. Grosse and J. Philiben, Compt. rend. 252. 728 (1961).

34. N. EI. Nachtrieb, H. k Redng and S. A. Rice. J. Chem. Phye. 31, 135 (1959).

35. J. B. Hudaon and R. E. Hoffman, Ph i l a Meeting of A.I.M.E., Oct.. 1960.

36. k J. Bornan, P. E. Brammer a d G. W. Rathenan, Physica, 23, 1001 (1957).

37. C. E. Biichenall and R. F. Mehl, Trane. A.I.M.E. 188, 144 (1950).

38. R. J. Borg and C. E. Birchenall, Trans. A.I.M.E. 218, 980 (1960).

39. F. S. Buffi ton, K. Hirano and M. Cohen, Acta Met. 9, 434 (1961), K. Hirano, M. Cohen and B. L. Averbach, Acta Met 9 3 4 0 (1961).

40. J. Stanley and C. Wert, J. Appl. Phys. 32, 267 (1%1).

41. R. J. Borg and D. Lei, unpublished research, Lawrence Radiation Laboratory, Livermore, Calif.

42. H. W. Mead and C. E. Birchenall, Trane. kI;M.E, 203, 994 (1955).

43. F. S. Buffington, I.D. Bakdar and M. Cohen, Trans. A.1;M.E. 188, 1374 (1950).

44. L. I. Staffansson and C. E. Birchenall, Report from the University of Dolaware, AFOSR-733, 1%1,

45. For a review of this field ~ s e G. L e p o n b , "Lee Ttaceurs Radioctifs en Metallurgie Physiqae, Dunod, Paris, 1960, pp. 8&115.

46. J. C. Fiehw,- J. Appl. Phys. 22, 74 (1951).

47. R. T. P. Whipple, Phil. Meg. 45, 1225 (1954).

48. V. T. Vorieov V. M. Kzolikov and B. Ya Lpbov, Izvest. Alred. Nauk. S.S.S.R., Otdel. Tekh. Nauk, 10, 37 (1956). See d a o a. 5. Levine and C. J. MacCallum, J. Appl. Phys. 51, 833 (1960) for a criticism of Refa. 46,47,48.

49. For exam le see R. E. Hoffman ad D. Turabull, J. Appl. Phys. 22, 634, 984 (1951) and B. Ikkeree, Acta Met. 2, 5 f l (l954).

50. For example, s ee 5.R.L. Coding and R. Smoluchoweki, J. Appl. Phya 25, 1538 (1954) and S. Yukawa and M. J. Sinnott, Ttan~. A.I.M.E. 203, 9% (1955).

51, D. Turnbull and R. E. Hoffman, Acta Met, 2, 419 (1953). See also B. Okkerse, T. Tiedema and W. Burgers, Acta Met. 3, 300 (1955).

52. A. k Elendrickeon and E. S. Mechlin. Tr-. k1.M.E. 200, 1035 (1954).

53. R. E, Hoffman, Acta Met. 4, 97 (1956).

54. E. W. Hart, Acta Met. 5, 597 (1957).

55. F. E. Jaumot, Jr. d R. L. Smith, Trans. k1.M.E. 206, 164 (1956).

56. N. G. Ainslie and A. U. Seybolt, J. Iron and Steel Inst. (London) 194, 341 (19601, N. G. Ainslie, R. E. Hoffman and A U. Seybolt, Acta Met. 8, 523 (19601, N.G. Aindie, V. A. Phillipe and D. Turnbull, Acta Met. 8. 528 (1960).

57. M. C. Inmm md H. R. Tipler, Acta Met. 6, 73 (1958).

58. For example, see V. I. Arkharov, S. M. Klotsman, and k N. Timfeev, Phya Metals Metallog. 5, No. 2, 152 (19571, 6, 255 (19581, and k A. Pentina, Phys. Metals Metallog. 4, No. 3, 122 (1957).

59. J. P. Barbour, et. al. Phym. Rev. 117, 1452 (1960).

60. R. Gomer and J. K. Hulm, J.Chem. Phys. 27, 1363 (1957).

61. For exam le see P.. B. Kehoe; R. C. ~ e w m u n a d D. W. Paahley, Phil. Mag. I , 783 (19561, Brit. J. Appl. Phys. 7, E9 t1956).

62. R. E. Schlier and H. 3. Farmworth in Adv-em in Catal sia 9, 434 (1957). H. E. Faneworth and H. 3. Madden, in "Structure a d Properties of Thin Filmq'* wirey, 1959, p p Sltff .

63. L. H. Germer and C. D. Hartman, J. Appl. Phye. 31, 2085 (1960).

64. W. W. Mulline. J. Apply. Phye. 28, 333 (1957).

65. W. W. Mullins and P. G. Shewmon, Acta Met. 7, 163 (1959).

66. N. k Gjostein and F. N. Rhinee, Acta Met. 74 224 (1959).

67. N. Hackerman errd N. Simpeon, Trans. Farad. 4oc. 52, 638 (1956).

68. R. A. Nickerson and E. R. Parker, Trans. ~ ~ ~ 1 4 2 , 376 (1950).

69. W. C. W i n e p d and B. Chalmers, Canadian J. Phys. 30, 422 (1952); W. C. Winegerd, Acta Met. 1, 230 (1953).

70. J, B. Drew and J. Pye, unpublished research, Franklin Institute Laboratories for Research and Development, Phi ldelphia , Fa.

Prepared Discussion

DISLOCATIONS AND DIFFUSION I N SILICON

by

Dr. H. J . .Queisser

INTRODUCTION

In th i s note two comments are made about interrelations of impurity diffusion and dislocations in silicon. There will first be a discussion of impurity diffusion along the dislocations of a small angle grain bonndary in silicon. Theoretical descriptions and physical interpretations for the observed diffusion enhancement are reviewed. Secondly, the generation of dislocations by diffusion of large concentrations of undermired impurities will be discussed. Regular patterns are observed on boron-doped silicon surfaces. These patterns are attributed to s l ip caused by the s t ress in the diffused layer.

A. DIFFUSION ALONG DISLOCATIONS IN SILICON

Diffusion experiments were carried out with silicon bicrystals having grain boundaries with a misfit of lo0 or smaller. These erperimenta are described in detail elsewhere1 and sha l l only be summarized here.

Figure 1 shows a beveled and - stained section of a p-type silicon bicrystal into which phosphorus was diffused. The p-n junction, as revealed by the staining, i s an isoconcentration line. It i s seen that the enhanced diffusion a t the bonndary gives a spike-shaped diffusion front.

Three reasons may be given for the higher grain boundary diffusivity: the concentration enhancement due to the Cottrell attraction2, a possible

Figure 1. BEVELED AND STAtWED IECTLW OF A PHOSPHORUS The first contribution may be DIFFUSED SIUCOM ~ICRYSTAL. PHOSPHORUS* estimated theoretically1. It follows

DOPED (H-TTPE) UTERIAL APPEARS WHITE, P-TTPE that the higher the misfit of an impmity, DARK. DIFFUSION "SPIKE" AT GRAIN BOUNDARY.

the more enhanced should be the

'1. Hubner m d W. Shockley in "Shucture m d Properties of Thin Films", ed. by Neugebauer et d. p. 302 (John Wiley m d Sons. New York, 1959); EL J. Qudsser, K. Hubner, and W. Shockley. Phys. Rev. 123, 1245 (1961). This work was supported by U.S. Air Force C.mhri&e Reseuch Lmboratov.

2~~ Cottroll, *'Dislocations m d Plastic Flow in C~).st.ls*@ p. 56 Cluendon Press, Oxford 1953.

the diffusion a t the grain boundary versos bolk diffusion. Recent, unpublished measurements with different donors and acceptors verify this prediction.

A new mathematical treatment of g a i n boundary diffusionldescribes the diffusion behavior in terms of the individual dislocations of the small angle boundary. A relation between the tip angle of the spike, the velocit of s ike advance and two parameters i s theoretically predicted by the so-called "spike-ve~ocityP* method. This prediction i s fulfilled by the experiments. One dislocation carries about 400,000 times as much phosphorus diffusion flux a t 1050°C a s does an area of one Burgers vector square.of good silicon.

Studies of three layer structures2 showed interesting interactions between the two impurities that were diffused subsequently into the silicon. It was possible to obtain two diffusion spikes within each other. However, boron diffusiotrs reveeled uncxptcted anornalice. There a peared t o be no prefcreo~ial a i n boundary diffusion into previous1 y phos borum-doped materiar. On 'r g t h e other h a n d , phosp orus diffusions caused wide short-circuits t rouRh boron-diffused layers at tbe grain boundary. This indicates some strong interustionrr with "third atoms" a t g a i n bou~dar iea , as pointed ou t in Prof. Birchenall'sa talk.

8. DlFFUSlON - INDUCED DISLOCATIONS IN Si

' : I

I I Further roof for tbc existence of disloca- . " 1 ,

-,-A t ions in .PC boron-doped silicon samples hen ! - *i 3. \

1 - recently been found by Schwuttka6, using X-raf methods. Orientations and Burgere-vectora for

Figun 2. SLIP PATTERNS ON HIGHLY BOROW-DOPgD the dislocations on the different difhsed (100) SURFACE O F A SlLlCOH BICRYSTAL WITH GRAIN 6OUNOARI in A (110) PLANE surfaces have been obtained.

Diffusion of sufficiently high concentrations of underaited substitutional atoms, such as boron in silicon, causes s t r e s s which i s relieved by the formation of dislocatians4. The presence of these dislocations has been made apparent by etching of highly boron-doped silicon surfaces4 or by etchiag cleavage lanes perpendicular to the exposed surface6.

. , , , , , , Figure 2 shows a typical example of a surface

Theoretical estimates of strain a n d dielocatioa encrqy arc need to predict a minimum amount of boron impurities necessary to favor tbc formatlo f d ia loca t~ons o e r a .trained 5 lattice"'. This minimum amount is estimated to be 3 x i&%omn atoms/cm S i sadace . Ex- periments with different amounts of doping a g e s with this prediction.

, , . . !, :

- .,.. :;, i j ' .' - .. . ,. . .. .;? ..: --,. . , , . , .; t. ' : ' ) I f ':?g;; ~ .

, : ;I. ' , s

, . . . . m , ,- .a< ' - , . , .

'K. Hubnw and W. Shockley in Yhucture mud Properties of Tkin Film.". ad, d. Nelyebsuer et d. p. 802 (John Wiloy r d Son. New Yo&. 1959); H.J. Queimmer, K. Hubnw and W. Shockley, Phy- Rev. 123, 1245 (1961. This d w u apported by U.S. Air Force Cambridge Reseuch Laboratory.

. , 3. . . . , s l ip p a t e . A bicrystal s l ice was used in ' * < . ; j , . . , this experiment, which i s of course not necessa .

t . , 1 , - 1 The dark center line is the boundary, a s reveale 7 .,. , / L . ~ : ,..*;!.i;! .! . ._a - , , I - . _ : ! . . by etching. Both ~ r a i n n show s e t s of l ines along , , . . . . : - ...... --- (110) - dircctiona. A l l observed patterns on -

. ~ different crya tallographic surfaces can be inter reted as intersectione of (111) - type planes

I .- wit the surface. This is consistent with the i "i'ir fact that the s l ip planes in silicon are the

, (111) - planes.

2 ~ . J. Qude.sr. "Diffused Three Layer Shacrtwe Along Smdl Ande Gmin Boonduin in Silicon*' IRE C o d oa Solid State Device Remeuch. Stmabod 1%1.

3 ~ . Bkehead. pro^ Eighth Sag- Coat 'H. J. Queiuer BulL Am. Phym. Soc. 6. 106 (1961) and J. Appl. Phys. (September 1961); work mponmored by Air Force Cambridge

Reseuch Lmboratoriem 5 5. Yiu8rin J. Appl. PAT.. (Sept. 1Yol) 6 ~ . ~ ~chwmnte. brirate communication) . .

'w. Shockley, manuscript in preparation

RECRYSTALLIZATION AND PHASE TRANSFORMATION

by

Dr. J o b n Newkirk

INTRODUCTION

Most commercially practical materials, high temperature alloys in particular, do not lend themselves well to study by the fundamental approach which most solid s ta te scient is ts prefer. There are too many components and too many concurrent, overlapping and often competing processes i n action a t once to allow theoriea and experiments to be devised which are sat is- fyingly unambiguous and complete. One school, consisting mostly of the practical alloy de- velopers, has boldly met nature head-on and largely by the "next elemlent in the periodic table" approach have in l e s s than ten years improved oxidation resis tance of service alloys by rno.re than two orders of magnitude and increased their strength a t 2000°F. by about one order and yet a t a production cos t of l e s s than half an order hi&er. This i s very respectable progress.

Nevertheless, the weight of evidence indicatea that returns, by the empirical approach, must decline seriously before long. Empiricism must therefore be replaced by basic under- tand din^ of the effects of common variables on procesaes related to the manufacture and service of refractory materiala. Alloy research and development by the fundamental approach has coneequently become the objective of increasing numbers of basic physical scient is ts . Mostly their work i s highly specialized, through the intense study of some single or process (such a s grain boundary mobility) which contributes to the over-all behavior of an alloy in service. After all of the sub-processes are well-understood, there will remain the problem of how one process will influence the others a s a l l a c t together.

At present we are s t i l l a t the s tage where sc ien t i s t s are hard a t work trying to identify and solve problems connected with the unit procesees making up recrystallization, grain growth, phase traneformations and other long range reactions in crystalline materials. Usually they work with simple syatems and study phenomena, hoping that their resul ts can be applied, in principle a t leaet , to more complex metal mixtures. Consequently the literature i s full of new information about phenomena, which are more or l e s s related to problems of high temperature metallurgy. Much of this information i s illustrated by experiments with materials like lead, silver, lithium fluoride, etc., not particularly inspiring to practicing refractory metals men. A s basic understanding develops, we can expect to reap the due rewards in more sophisticated and more effective alloy design. The work of Beattie and Hagle, described later in this paper, proves that Home of the practical rewards of baaic underatanding have already arrived.

With the foregoing paragraphs a s my defense I shall now describe what appears to be the highlights of the current s t a tu s in the fields of recrystallization and phase transformations in metals, accenting and de-emphasizing materials. I have picked out those areas in which there has recently been especially significant activity, and in which there appears to be above normal promise of further gain through further effort. The significance of the cited work i s pointed out and where possible 1 have suggested what further s t eps might be taken to extend our knowledge of recrystallization and phase transition phenomena.

RECRY STALLlZATlON

T h e most recent survey of the s t a t u s of the field of recrysta l l izat ion appeared a s a s e r i e s of papers b y Liicke, Beck, Burgers, Deter t , Stuwe and Dehlinger (1) ear l ier th is year. W . C. L e s l i e i s now preparing a n extensive survey on recrysta l l izat ion, to be presented a t the 19611 Metals Congress and published soon thereafter. Also, there is in preparation, and due for publication early in 1962, a survey on a c losely re la ted subject , viz., grain boundary migration by K . Liicke (2). Surveys on phase transformations are mentioned in a l a te r sec t ion of th i s paper.

Within the s c o p e of t h i s conference, recrysta l l izat ion is understood to be an irreversible p r o c e s s of atom rearrangement which occurs by grain boundary motion during annealing, in which n o true phase change is involved and in which diffusion d i s t a n c e s for matrix so lven t a toms a re of the order of only a few la t t i ce dimensions. New c rys ta l s grow a t the expense of the original ones. There i s no long range composition change-and the driving energy der ives from some eource other than the difference in the chemical f ree energ ies of the recrysta l l ized and the unrecrystall ized materials.

Pr ior to and during tota l recrysta l l izat ion, the p r o c e s s of recovery occure wherein la t t ice : s t r a i n s which may be p r e s e i t in the matrix, are re l ieved with only s l igh t changes in the g ross microstructure. Recovery is a re la t ively brief procese and i s usua l ly accompanied by changes in cer ta in physical and other properties. Atoms a re espec ia l ly mobile during recovery due to the presence of many la t t ice imperfections. Therefore, they can e a s i l y move, generating a re la t ively unstra ined la t t ice through a n unorganized crystallographic relaxation. T h i s loca l rearrangement sometimes r e s u l t s in the migration of dis locat ions , v a c a n c i e s and impurity atoms to pos i t ions of alignment, thereby forming subgrain boundaries. T h e rearrangement polygonizes and re laxes the original s t ra ined structure.

Concurrently, th is atom rearrangement may lead t o the generation of smal l misoriented regions having l i t t l e or no mechanical s t ra in and low energy. T h e s e re la t ively s t ab le regions a c t a s the nucle i of a subsgquent recrysta l l izat ion s tage. They continue to grow a t the expense of their unstable neidhbors unt i l the recrysta l l izat ion p rocese is completed or the neces - sary free energy for drivinglthe reaction h a s been diss ipated. I t fo l lows tha t whatever t ends t o promote strain 'recovery by p ~ l y ~ o n i z a t i o n will diminish the generation and growth of true recrystall ization nuclei . One might in that c a s e expec t a larger final recrysta l l ized grain s i z e because of the few ini t ia l nuclei .

Usual ly the more an unrecrysta l l ized material i s p las t ical ly s t ra ined, the smal ler i s the recrysta l l ized grain s i ze . Heavy cold working therefore can be s a i d to increase the amount of recovery by nucleus formati~on relative to the ra te of subsequen t growth of the nuclei .

I t i s clearly apprecia ted by now tha t the enlargement of recrysta l l izat ion nucle i is a highly - - complex process . Consequent ly severa l workers have recent ly been concentrating on s t u d i e s of the nature of recrystall izlation boundaries and their migration character is t ics . The i r work i s d i s c u s s e d in more de ta i l i n a following sect ion, I t is enough t o s a y a t thin point t h a t the contact interface between the recrysta l l ized and unrecrysta l l ized material i e the focus of nearly a l l of the factors which affect the k ine t i cs of the recrysta l l izat ion reaction. Anything which a l t e r s that in terface affects the k ine t i cs of recrystall ization.

A s ye t the mechanisms c a u s i n g many of the recrysta l l izat ion kinet ic e f fec t s a re p i t e imperfectly understood. Fuf the r s t u d i e s of the nature and behavior of grain boundaries in

single phase materials are therefore badly needed. However, new techniques and special materials (for example, ultra high purity metals) for such studies are becoming increasingly available s o that the probability of succes s in work of this type appears to be high. There- fore most of what follows in this section concerns grain boundariee, their structure, their properties, how they move, and how they can be observed.

I , GRAIN BOUNDARY STRUCTURE AND RECRYSTALLIZATION

A point on a grain-boundary can in general be described by specifying angular degreea of t i l t and degreea of twiat of the adjoining crystale a t that point. The ~ t ruc tu re and placement of atoms a t small angle boundaries (ca. radians) i s now fairly well underatood in these terms, a s i s exemplified by well known experimental work of Vogel in 1955 and more recently of Hirsch and co-workers.

Fo r large angle boundariee however, the picture i s not neatly s o clear. Several models have been proposed which will be briefly outlined here.

1. The "island" of group-process model, euggested by Mott (3), describes zones or islanda of more or l e s s close crystallogrphic registry between the adjoining crystallites, with corresponding regione of poor fit, which are some times described as disordered or melted. It i s proposed that the cohesion of two adjoining crystals a r i ses mainly through their interaction a t the is lands of good fit. The movement of the boundary would require groups of atoms on one s ide of the regions of misfit to "melt," i.e., to leave their positions of crystalline regularity as the disordered interface pasaee through. The theory has recently been tested using the 4 6 group meltingg' criterion. Th i s i s described later.

2. The "undercooled liquid" model described by Ke (4) assumes that a cryatallographically disordered region of 2 to 3 atom distances in thickness ex is t s between adjoining grains. T h i s region i s eupposed to have a quasicrystalline structure aimilar to that usually associated with the glaesy state. Boundary motion in thia model would involve individual and unorganized atom removal from original lattice positions to other crystallographic positions on the new grain across the boundary.

3. Kronberg and Wilson (5) have shown geometrically that there may be "special" orientations of high angle boundaries for which the lat t ice a i tes of the undistorted crystals on both s ides of the boundary are coincident a t the boundary. They proposed that these spec ia l positions of adjoining crystals should be associated with a lower boundary energy and higher boundary mobility than that of positions a few degrees away in any direction. Considerable support has been found for their ideas. This a l so will be discussed in more detail later.

4. Read and Shockley (6) proposed that a grain boundary can be described in terms of arrays of screw and edge dislocations. Boundary movement could then be explained by allowing the dislocations to move according to standard rules for their glide in the s l ip lane and for climb normal to the s l ip plane.

Conaiderable work has been done to clarify the true nature of recrystallization boundaries, mostly in terms of the preceding four concepts. Unfortunately the experimental work has not resolved completely the role of impurity atoms which reaide a t or near the boundary itself. Recently. with the increased application of zone refining m e thods, more definite resul ts have been reached, notably by Aust and Rutter (7). Theae authors reduced the impurity level in eeveral metals, probably to a few parts per million, and then added very small amounts of

known impurities to specimens of controlled crystalline orientation. They could then study ra tes of boundary motion under more closely controlled conditions then have ever before been possible.

The recent resul ts of Leveral investigators on the rates of grain boundary motion will now be discussed relative to the various models of grain boundaries which have been outlined above.

T H E "ISLAND" THEORY

According to Mott'a model a boundary must move by the disordering or melting of a group of atoms on one aide of the boundary and reordering them a s a part of the newly forming lat t ice on the other side. I Aust and Rutter (8) have tested the group aepect of the theory by comparing the entropies of activation predicted by Mott with their observed activation entropy for boundary motion in pure lead. Figure 1 shows that a consistent diaagreement of about 15 cal. per degree per gram atom exists between Mott's theory and their experiments. The theory a l so predicts the rate of boundary migration in terms of controllable variables and reasonable assumptions. However, the experimentally determined rates , even with the purest zone refined lead are from 100 to 1000 times l e s s than those predicted.

The apparent f a i l u r e ~ o f the Mott theory do not necessarily deny h is phyaical picture of the grain boundary. They only indicate that boundary motion does not proceed by the process of disordering (melting) groups of "n" atoma each, which are presumed to occur a t intervals along the boundary.

UNDERCOOLED L IQUID,

Recent evidence ham been found which indicates that boundary motion occum by single atom jumps. Assuming that the elementary procems in moving a boundary consis ts of activat- ing not a group of atoms a s in the Mott theory, but rather a single atom, one can neglect the entropy term in the-boundbry velocity expreesion:

where K includes the atom vibration frequency and P l a n c k ' ~ conetant. This allows a calculation which can be compared with measured boundary mobility rates. A comparison of this type was made for refined lead by Aust and Rutter and good agreement was found for spec ia l Kronberg-Wilson boundaries, but not for those of crystals in random large-angle orientation relationship. These results may be qualitatively explained in terms of residual impurities, the effects of which are not taken into account by the theory but which effects are l ea s t in the ca se of the spec ia l bmundaries. It seema to be justified to take this work a s further evidence that boundary mobility occurs not by group processes but by unorganized activation of single atoms. F o r the : ca se of lead the activation energy for grain boundary migration was measured by Aust and Rutter to be approximately 6 Kcal per gram atom, which, a s Turnbull (9) points out, might be e ~ ~ e c t e d to be the same a s for grain boundary self-diffusion. An approach to this comparison can be made using the data summarized in Table I. The close agreement among the activation energies implies that grain boundary diffusion and grain boundary migration occurby similar basic processes. Even more to the point would be a comparison of boundary motion with selfdiffusion a t grain boundaries. Unfortunately such data are not available for highly pure lead.

TABLE I

FREE ENERGIES OF ACTIVATION FOR LEAD, 300°C

FA Kcal per G Atom Source

Grain boundary .migration A 5.2 i 0.5 Aust and Rutter (1958)

Grain growth

I Grain boundary diffusion 9

6.2 i 0.7 Boiling and Winegard (1958)

Okkerse (1954) Turnbull and Treaftis (1958)

About 12 years ago Kronberg and Wilson suggested that special grain boundaries may exiet which should have high mobility. These boundaries are characterized by a high d e n ~ i t y of atomic s i te* which are c&mnon to-the unetrained la t t ices on both s ide& of the interface. An example of this arrangement ie given in Figure 2. T h i s diagram shows a (111) plane of two face-centered cubic crystals which have been rotated 22 or 38 degrees about their common < I l l ) crystallographic axee. One in eeven of the atomic s i t e s in one crystal coincide with those in the other. The coincident atoms are shown a s white areas. As the boundary moves, theee special atoms need not move a t all. Also, s ince these epecial boundaries have relatively good lat t ice matching between the adjoining crystals, one might expect that foreign atome will have leee tendency to eegregate there than a t the higher energy random boundaries. I t follows that the properties of epecial boundaries should be l e s s influenced by the presence of impuritiee than are random boundaries where the degree of misfit i s higher and the tendency for erolute segtegation ia therefore greater. Again, mopporting evidence for this concept i e found in the fact that the activation energy for boundary motion of lead i s highly dependent upon impurity (Sn) concentration whm the boundariee are of the random type but ia very small for Kronberg-Wilson boundariee and practically independent of concentration in the dilute range studied by Anet and Rutter (see Figure 3). Energy cuspe of the Kronberg-Wilaon type were observed by Aust and Rutter in lead. In copper however they have not been detected though they were specifically sought by Gjostein and Rhines (10). The reason for this i s not clear.

A basic feature of the Kronberg-Wilson model i s i t s inaenaitivity to the curvature of the boundary. One can s e e from Figure 2 that the pattern of the s e t of coincident atoms is unchanged whether or not the boundary ia curved. T h i s geometrical circumstance i s favorable for the development of the curvature which i s often neceeeary'for boundary migration and aharply diatinguishea the K-W special boundariea from twin boundaries. In twinning the atomic matching is even better but no curvature is possible. Since twin boundaries move relatively elowly 6 i s c lear that boundary coherency d o n e doee not govern the migration rate.

THE LUCKE*DETERT THEORY (13 )

The retarding effect of substitutional impurity atoms on recryatallation kinetics has been known by empirical experience for a long time. In the refractory metals the varying potency of different aolute elements for retarding recrystallization i s eepecially striking though there appear to be aome curioua and lit t le understood exceptions. For example in molybdenum a few elementm actually deprese the one hour recryetallization temperature, though most elements have the normal elevating influence. (See Figure 4).

In tungsten interstit ial impurities appear to have lit t le effect on the recrystallization temperature, while minute increases of trace substitutional metallic elements can increase the recrystallization temperature by amounts up to 900°F (12).

T h e Liicke-Detert (L-D)I theory i s an attempt to account for the effects of impurities on the migration behavior of rahdom grain boundaries. In this theory i t i s assumed that interaction forces exist. between foreign atoms in solid solution and the boundary, acting to increase the - -

concentrations (or low temperatures) of impurities a t the boundary (see Figure 5). At high conce~t ra t ionn the moving boundaries are held back by the foreign atoms, and the speed of the boundary i s controlled by the rate of transfer of the foreign atoms diffusing behind it. At low concentrations (or h igh temperatures) the boundary i s not held up by the foreign atoms and breakaway occurs, allowing the boundary to move faster. I t i s predicted that below the critical concentration for breakaway, the recrystallization temperature would drop much faster with decreasing concentration than i t does above this concentration. Bes ides this effect, the total amount of solute accumulating a t the boundary a t ateady s ta te should be temperature dependent, thereby causing a more potent inhibiting effect on migration rate a t lower temperatures. There- fore the migration rate in an impure material would be influenced by a t l e a s t two temperatnre- dependent processes, viz. a ) solvent atom transfer ac ros s the boundary and b) solute aegre- gation to the boundary. The preaence.of impurities would thus be expected to increaae the temperature dependence of migration rate and to give a measured activation energy for migration which is larger than that corresponding to the simple transfer of solvent atoms across the interface. Many qualitative obeervations support these ideas.

To explain quantitative meaanrements, Liicke and Detert propose that the speed of a boundary i s controlled by the rate of bulk diffusion of the foreign atoms in the newly formed lattice behind the boundary. If this propoeition were true, the activation energy for grain boundary migration should equal that for bulk diffusion of the solute in the matrix lattice. In fact, however, recent qnantitive measurements of the effect of tin in lead (see Figure 6) do not support the idea that bulk diffusion controls the boundary migration rate. However, Turnbull (9 ) h a s pointed out that experimentally determined activation energies may be abnormally high due to the influence of inclusions in retarding grain boundary motion. Fo r the case of silver and gold in l=ad, Aust and Rutter found that the apparent activation energies for grain boundary motion were lower than those predicted by several orders of magnitude. Les l ie and co-workers(l5) Gave recently shown that the effect of manganese on boundary motion in iron i s about 1000 times larger than predicted by the LEcke-Dietert theory. The lat ter work (Fe) covered a relatively broad concentration range and s o constitutes a better t e s t of the theory than d o e s the cited work on lead.

An evident weakness of the L-D theory i s that i t t akes no account of the now recognized orientation dependence of the kinetics of grain boundary migration. Also, only elast ic interactions are considered; possible chemical and electronic effects are ignored. Furthermore, in molybdenum (16) the presence of Ni , Co and Fe actually increase8 the recrystallization rate, an effect which i s not easi ly explained in terms of the L-D model. See Fignre 4,

Incoherent boundaries ake believed by some (42) to be governed by a diffusion coefficient which may be identified with the grain boundary diffusion coefficient, presuming that such a single valued quantity exists. Turnbull points out (9) that there i e no theoretical justification for this assumption and thai other controlling factors must be identified before complete understanding of incoherent grain bonndary motion is reached. It ia clear that much more will have to be learned about the interaction of different solute atoms with various types of grain boundaries before a satisfying picture of grain bonndary migration can be had.

DRIVING ENERGY

The three most probable sources of driving energy for recrystallation are: 1 ) The difference in bulk free energy of the recrystallized and unrecrystallized material, 2) the difference in aub-grain boundary free energies and 3) the difference in free surface energies. Creep, polygonization and other local thermally activated local atomic adjustments reduce the difference in bulk free energy during the early s tages of annealing, thereby leesening the probability of total recrystallization. Semmel and Machlin (17) feel that a t l eas t in silver the energy of dislocations in the ~ n r e c r ~ s t a l l i z e d material play only a small part in driving the reaction and that exces s point defects, eapecially vacancies produced by the applied plastic deformation provide the major source of driving energy. They propose that internal vacancy s inks are not infinite and that the long vacancy degradation time which they observed ia a measure of the time required for the exces s vacancies to diffuse to the specimen aurface. Their views could be checked more directly if some technique could be applied for observing the number and distribution of point imperfections.

Walter and Dunn (18) ahowed by an ingenious but simple experiment that under suitable conditions surface impurity atoms can effect an actual reversal of the growth of auitably oriented adjoining silicon-iron crya tah . They ahow that surface impurities can be an important factor in and aometimes control, the competitive growth of crystals in an aggregate. Eaeen- tially their method consis ted in observing the position of the boundary between two crystals which preaentsd respectively their (100) and (110) planea to the free surface of the specimen. When held a t 1200°C in a good vacuum the boundary advanced into the (100) grain, i.e., the - -

grain which had a low density plane a t the surface. However, when impure argon was admitted to the atmosphere the boundary retreated into the (110) grain. These authors conclude that one effect of surface impurities is to reduce the free energy of the (100) surface below that of the higher density (110) surface and that this difference i s enough to control the direction of grain growth. Walter and Dunn's work i s wholly qualitative but i s a strong indicator that aurface effects must not be neglected in considering the mechanism and kinetics of recrystal- l ization and grain growth, especial ly in shee t materials. T h i s i s further evidence that more

- -

study of the surface structure and energy of crystals is needed to complete our understanding of their bulk behavior. Rea l and formerly unexpected benefit might be gained through the application of surface energy aourcea in driving metal reactions.

In another s e r i e s of experirne nta (19) Aust and Rutter showed that the driving energy for grain boundary motion could derive from the aub-grain boundaries which existed id as-solidified cryetals of high purity lead. They found that migration of a recrystallized grain bounaary into a striated grain removes the striations a s i t sweeps ahead, suggesting that the energy of the relatively disordered atriation structure provides the driving energy for the boundary migration. One may also offer the suggestion, on the basie of Semmel and Machlin's ideas, that point defects, instead of striation boundariee, provide the energy for the boundary movement. How- ever the likelihood of this i s slight mince, in the experiments with lead, new grains would not grow in a direction normal to the direction of the striations and grew most rapidly when the interface waa s o oriented that i t intersected a maximum number of the striation boundaries.

EFFECTS OF THERMAL GROOVING

Another influence on boundary migration kinetics i s the groove which constantly tends to form along the line where the boundary intersects the specimen aurface. Mullins (20) and others have advanced a theory to expreas this effect quantitatively. Evidence to support the Mullins concept is given in Figure 7 in which success ive positions of a boundary are seen aa

a n organized pattern of grooves. Th i s effect i s s a id to resul t from spasmodic movement of the intersection of the boundary with the surface. The spasmodic motion i s explained as follows: A migrating boundary becomes stuck a t the surface due to the lower energy at a groove in the surface. Meanwhile the boundary belew the surface can continue to migrate s o far that the portion close to the surface becomes nearly parallel with the surface. Th i s con- s t i tu tes a very unstable situation s o that the edge a t the surface pops out of i t s old thermal groove and moves along the surface very rapidly until i t catches up with the interior boundary. There i t moves s o slowly that surface forces and thermal atomic motion can again cause the formation of a groove which p ins the boundary edge and the cycle i e repeated. Whether surface boundaries will always move in a spasmodic manner or follow a steady s ta te behavior probably depends upon many factors which are not yet evaluated. Very recent unpublished studies of G. V. Smith show that spasmodic recrystal l izat ion'b~undar~ movement can occur without the influence of a thermal surface groove.

EFFECTS OF INCLUSIONS

I t i s well establ ished that foreign particles can retard the motion of grain boundaries. For example the relatively small amount of recrystallization and consequent sustained high elevated temperature strength in the refractory alloy F48 (Mo 5, W 15, Zr 1, C.03, N .01, Ox .03) i s probably due to the presence of s table compound inclueions. See Figure 8. Also the pdwer of finely dispersed thoria to inhibit grain powth in tungsten i s well known. Most of the recent basic work in this area h a s been done on silicon-iron eheet because of the commercial importance of this soft magnetic material. The preaence of certain sulfides in Si-Fe i s known to be necessary for the successful development of the desired secondary recrystallization texture. Apparently the function of the sulfide inclnsions i s to retard primary recrystallization s o that secondary recrystallization can proceed. Th i s retarding effect of minor impurities i s not thoroughly understood, nor i s i t always recognized when experimental observations of boundary migration r a t e s are interpreted. I t was mentioned earlier that activation energies measured in recrystallixation experiments may sometimes appear to be abnormally high as a result of the unrecognized retarding influence of inclusions. This effect i s eepecially marked when there are many different degrees of dispersions of the inclusions. The measured activation energy then would be the resul t of the operation of a t l eas t two thermally activated procekses, one of which would be the interaction of the moving boundary with the array of inclueions. Any work which i s done on the kinetics of boundary movement should not neglect the inclusion effects.

T h e foregoing ~ a r a g r a p h s illustrate that with different materiale and under different experimental conditions i t i s apparently possible for the main driving energy for recrystallization to come from one of several sources. No one has attempted to generalize on the subject, though a complete theory would be u ~ e f u l . More experimental work following the methods of Aust and Rntter and of Les l ie and co-workers, where experimental conditions are carefully controlled, should pave the way to a more thorough description of the proceas of grain boundary migration. I

E F F E C T OF ELECTROMIC STRUCTURE

Some empirical observations by Abrahameon and co-workers (21) have indicated that there may be a direct and fundamental relationship between the rate of change of the recryatallitation temperature of a metal and the electronic structure of added solute elements. On the hypotheaio that recrystallization is an atomic bonding phenomenon they reasoned that the outer she l l electrons might be directly involved .in the recrystallization or boundary motion process.

Their first experiments consisted of adding small amounts of e o l o b metals to 99.95+ P c t iron and observing the temperature a t which a cold rolled specimen softened (i.e. recrystal- l ized) during a one hour anneal. A s expected, a l l of the transition element6 raised the recrystallization temperature, with the greatest effect occurring a t or l e s s than 0.10 a t .% solute. Of more interest i s their finding that a linear correlation sxiets , when the number of outer s she l l electrons in the solute i s constant, such that the logarithm of the rate of change of recry~ta l l iza t ion temperature with atomic per cent solute i s a linear function of the number of outer d shel l electrons of the solute atom. Figure 9 i l lustrates their resul ts and shows that the cuwee for solutes having 0, 1 and 2 outer s ehell electrons are parallel and that 1 and 2 have a definite minimum effect at seven d electrons. Aleo, in iron, for eolnte atoms having a like number of outer d she l l electrons, the fewer outer s she l l electrons there are the greater i s the magnitude of rate of change of recrystallization temperature. These experimental resu l t s are a s yet not supported by any detailed theory. More recent work which I hope Dr. Abrahameon will describe to u s during the discussion period, has provided tpalitative confirmation of h i s earlier findings. These observations are most interesting, and a satisfying interpretation in fundamental terma would be very welcome. To my knowledge no one except Abrahameon and his immediate co-workers are studying recrystallization from th is point of view.

INFLUENCE O F GRAIN BOUNDARY MOBILITY ON PREFERRED ORENTATION

The origin of recrystallization textures in cold worked, then heat treated metals i s s t i l l not clearly identified. In an attempt to explain the origin of textures in recrystallized polycryetalline rhee t copper and silicon-iron, Hibbard and Tully (22) performed a very ingenioue experiment. They coldrolled single crystale of copper and Si-Fe .in orientatia.ne epecifically chosen to produce individually the major known components of the polycrystalline deformation texture. The orientation dependence of the recrystallization kinetice was then observed with reepect to the primary recrystallization textures of these specimens. Surpri~ingly, they found that in both copper and Si-Fe the orientation eomponenta which recrystallized the fas tes t in the rolled single crystal specimens are not those which are present in the normal recrystallized textures of initially polycrystalline material. Therefore they could not rationalize or synthesize polycrystalline behavior on the bas is of their single crystal experiment. Their resul ts auggeat that the interaction of adjoining grains during the deformation of polycrystalline aggregates plays an important role in determining not only the rolling texture but the final re- eryatallized texture aa well.

Auet and Rutter have had aome very recent resul ts (unpublished) which in part support the oriented nucleation-growth theory of Burgers (23). In t h i s theory the growth selectivity could be due to differences in large angle boundary mobility by virtue of randomly occurring Kronberg-Wilson boundaries. Also, Burgers suggested that these spec ia l orientation relation- s h i p ~ might be associated with the low energy cusps in the curve of interfacial energy VE.

angular miaorientation derived by Read and Shockley (6). In the ir s tudies of grain boundary mobility in pure lead Aust and Rutter found that the temperature dependence of the grain boundary migration rate i s smaller for large angle coincidence-type boundaries than for large angle random boundaries. In Figure 1 0 the upper curve referer to a coincidence-type boundary of the sor t discussed by Kronberg and Wilson. The mobilities of these two types of boundaries are similar a t 300°C, but a t 175OC the coincidence-type ham a greater mobility by a factor of four. This observation suggested a n experiment by which the authors could show tha t competitive of randomly oriented recrystallized grains into a striated mono-crystal of zone-refined lead produced a multi-crystalline aggregate with preferred orientations of the

coincidence type during annealing a t 175OC but not a t 300°C. Thie preferred orientation clearly resulted from the higher mobility and lower energy of large-angle coincidence boundaries compared to large angle non-coincidence boundaries.

These resul ts are in outright disagreement with any theory of annealing textures which presumes that textures are determined by oriented nucleation alone. The oriented growth theory of Beck (24) s t a t e s that the orientation dependence of grain boundary mobility alone i s sufficient to account for bbserved .annealing textures and that grains in preferred relative orientations can grow most succesefully in competition with their randomly oriented neighbors. Aust and Rutter's resul ts do demonstrate the importance of grain boundary mobil.ity .in determining whether preferred orientation relationships are introduced by a twinning process in which relative grain boundary energy i s the decisive factor. However, in beck'^ oriented growth theory i t i e assumedtha t the highest mobi1,ity boundariee are only those of maximum misfit and consequently of maximum relative en-ergy without regard to the coincidence s i t e boundaries of lower relative energy. T h i s aasumption is not in accord with the experimental findings on lead.

It ia possible that the experimental work of Aust and Flutter, supporting the oriented nucleation-growth selectivity theory of Burgers (23) for the origin of recrystallization texture, may initiate a break-through in our understanding of the subject, Continued experiments of the Aust-Rutter type in other systemb including refractory alloys would be most ueeful.

PHASE TRANSFORMATIONS

Excellent and recent reviews of the fundamental aspec ts of this subject ere included in 6 6 Perspect ives in Materials Research" (25). Also, s t i l l useful are the proceedings of the Institute of Metals Symposium on the Mechanism of Phase Transformations in Metals (26). A review of the theory of diffusional growth in solid-eolid transformatione ha^ been made by J. S. Kirkaldy and will soon be p b l i s h e d a s part of an AIME monograph (27). H, T. Aaroneon a l so h a s in preparation a review of phase transformation proeesaea in which he gives spec ia l attention to the morphology of the product phase. Thie review i r due late thie year. Therefore only those parts of the subject wherein critical probleme are well recognized, eopecially those concerned with refractory mqtals and alloys, are discussed here. I shal l attempt to define the problems and to indicate, where possible, the most promising approach to their solution.

A large amount of effort h a s been spent ey ing to apply the quantum mechanical theory of cohesion to the calculation pf the differences in thermodynamic propertiee of phaeee (62). I n spi te of these attempts i t i s not yet possible to calculate the stability of one phaae relative to another from fundamental principles. What succese there h a s been in this a rea has come mainly from the u s e of empirical crystal chemical correlations, and at this point it appsam that the empirical approach will probably continue to be the most fruitful.

I

A solid s tate system may undergo a phase change by a discontinuous (aometimee called first order) or a continuous (second order) transition. In the former came the process is by nucleation and growth of small domains of the new phase and a l l reaction occure a t the .interface between i t and the emrounding matrix. In the ca se of the continuous transition there is a continuum of intermediate s t a t e s between the initial and final s t a t e s without a sharp phase interface, i.e., the process occurs homogeneouely throughout the eyatem.

Continuous phase changes arc not uncommon in metal syetems. Fo r example orderdisorder transitions are aometimea but not alwaye of the second order type. There ex is t a t present a

few theories about the order of phase t r a n e i t i ~ n e . ~ * ~ Some of these are in part conaistent with observation. For example in systeme having a close-packed structure there i s apparently a strong tendency for an ordelcdisorder reaction to be first order. But a s yet no theory ex i s t s by which the transition type can be predicted from 1 s t principles.

A defect in theories of continuous transitions ie that they treat those transitions a s homo- geneoue firet order processes which are governed from s ta r t to finish by a single relaxation time. This cannot be an accurate assumption because the many small coherent antiphase domains which form initially must be structurally isolated from one another and will presumably grow according to one relaxation time constant. Later in the process competitive intersection e e t s in and the more s table domains (largest, l eas t strained, etc.) grow a t the expense of the others. The latter proceee i s distinctly different from the first and a s far a s I know no theory takes this two s tage mechanism into account.

Diecontinuoue changes in general occur by nucleation and growth, a s do the primary and secondary r e ~ r ~ e t a l l i z a t i o n processes. The overhll rate of the reaction i e specified by the frequency of nucleation and the rate of motion of th,e new phase boundaries. Both of these parametera are now fairly well underatood in simple systems and i t only remains to apply them to the useful interpretation of phase transitione in practical materials. Recent analytical resul ts of Ham (30) on diffusion-limited precipitation procbeses show that unfortunately no conclueion about the morphology of the precipitate can be drawn from the time exponent of the transformation law. More will be said about the problem of precipitate morphology in a later section.

An appreciation of the effects of high specific eurface energy of very small in discontinuous phase transitions has resulted from a rigorous theoretical treatment of Lifshi ts e t a1 (31). These authors recognized that, because of the small s ize of precipitate particles during early s t ages of nucleation, the solute concentration s t i l l greatly exceeds that corre- eponding to equilibrium in the presence of large crystals of precipitate. They arrived a t the conclusion that in general a characteristic aize dietribution should be approached aaymp- totically with time.

A very serious problem in the field of solid s ta te transformation kinetics i s our poor un- deretanding of the structure of solid-solid interfaces, their interaction with impurities and their influence on the growth of a new and different phase. The interface may separate domains which differ in crystalline orientation, structure, composition or al l three. A limiting ca se is that of the coherent interface which aeparates domains which are nearly cont.inuoua crystallographically but which differ in composition. Recent theoretical work of Cahn and Hilliard (32) hae indicated that across a coherent boundary the free energy associated with the boundary will be leas t if the composition change occurs over eeveral layers, i.e. i f the composition boundary i s somewhat diffuee. Experimental confirmation of their reaults remains to be done. This i s technically difficult eince observations must be made on an atomic scale .

Boundaries separating domaine which differ only in crystallographic orientation (single phaee aggregate) can in many casee be represented a s dislocation -arrays. Those aeparating two different crystalline phases can eornetimee be represented a s a single phase grain boundary with an equivalent array of dielocatione, though their energy appears to be slightly lesa than that of the equivalent grain boundary. Thie eimilarity has been applied in a few casee (33) but the riak of oversimplification i s great and caution i s needed.

It was pointed out in an earlier section that no satisfactory model ex is t s for large angle incoherent grain boundaries or between phases which differ greatly in structure. That such boundaries need not 'be completely isotropic has been shown by Hoffman (34) who found that in silver a t non-special t i l t boundaries as large a s 4S0 the rate of diffusion i s clearly anisotropic. T h i s i s apparently the result of second order crystallographic influences which are quite imperfectly understood. Broadly speaking, i t i s expected that a t r u c t u r ~ l differences will contribute much more to the boundary energy than composition differences. Thus the energy of a semi- or incoherent boundary i s likely to be much greater than that of a coherent one, regardless of composition effects.

New techniques may very w e l l be successful ly applied to the observation and character- ization of grain boundariea, Individual dislocations can now be rendered visible by a variety of methods including electron microscopy, X-ray diffraction microscopy, etch pitting techniques, ion emission microscopy add Borrmann micro-radiography (35). It seems that the solution of some of the grain boundaryproblems may soon be reached by the application of these new techniques. I

INTERFACE MOTION AND MORPHOLOGY

The motion of boundaries in phase changee is related to that occurring during recryetallization, with the important additional requirement that where composition changes are involved a continued supply of solute atoms by diffusion to and across the interface is essential. Measurements of growth rates in precipitation systems have indicated that the kine t ics i s determined by the volume diffusion of solute to the interface (also sometimes by diffusion along a grain boundary) rather than the process of crossing the boundary. The morphology of the precipitated particles however i s often different from that expected on the baeia of diffusion alone. In theae c a s e s the interfacial characteristic@, diffusion ra tes or some other kinetic or thermodynamic ptoperty may control the shape of the product.

The morphology of trayformation products has been considered recently by several authors. Dub&, Aaronson and Mehl (36) propose that in the ca se of decomposition of auetenite in hypoeutectoid ateel , the proeutectoid ferrite morphology can be classified according to the following terms:

1. Grain boundary allo~riomorphs

2. Grain boundary idiohorphs

3. Widmanstatten sideplates, sometimes called Widmanstatten sawteeth

5. Intra-granular Widmanstatten

These morphological forms 'are sketched in Figure 11.

Aaronson in particular, haa been looking a t a number of t ran~formations with spec ia l attention given to the morphology of tranefonnation products. He h a s found that the Dnbe' system of morphological c lassif icat ions often applies. Good examples of the various ehapes, aa seen by section polishing, are given in h is recent study of a hypoeutsctoid T i 4 r alloy (37). Many other examples can be found (for example, Figure 12 in the preeent paper) of structures which seem to f i t the Dub6system. The general applicability of the system and, more important,

the understanding of the factors which determine what morphology will be taken by a transformation product, are important areaa for future study. Evidently such properties a s grain boundary energy and structure are important a s well a s bulk and boundary diffusion rates, dislocation climb and other motion behavior, la t t ice strain energy and bulk free energy re- lationsbipa between the matrix and transformation product. A few generalities about reaction product morphologies appear to be emerging from the work of Aaronaon and olners. For example when the crystal structure of a cubic lattice precipitate i s very close, both in lat t ice type and parame ter, to the parent matrix, the precipitate usually takes the form of intragranular equiaxed idiomorph~, which are cubic in shape and are aometimes orthogonically s l iced through the cube center (38,391.

Kirkaldy hae concluded that most of the unsolved morphology problema in eolid-solid trans forme tione are those of complexity rather than principle. He recognizes that the problems of morphological growth may not be soluble through a theory which ia limited to macroscopic eituations and in which therefore c lass ica l thermo-dynamics can be freely applied. Actual situations, involving the kinetic nucleation of very small units of a new .crystalline spec i e s and their diffusional growth may requite sequence9 of atrnctural and thermodynamic metasta- bility analogous to some chemical and bio-chemical processes. The nucleation processes, requiring the cooperative action of small numbere of atome, may not lend themselves, to the standard thermodynamic treatment. To meet this poasibility'he advances "variational principles" on which he bases theories to explain obsewed morphological growth for eteady and non-steady s t a t e proceeaes. These theories are too involved for diacuseion here but have evoked considerable interest and remain to be thoroughly tested experimentally.

The drastic effects which high energy boundaries may have on transformation kinetic8 h a s not been much exploited, though some of them are a t l e a s t qualitatively recognized. For example i t h a s been shown that tin can precipitate from a lead-tin solid solution at an appreciable rate a t temperatures a s low a s -70°C. I t i s now fairly well established that the abnormal rate of this reaction occurs by virtue of very rapid diffueion along the moving incoherent boundary between both the precipitate lamellae and the reoriented lattice of the solute (40). Another mechanism of abnormally rapid diffuaion reactions, for example in A l h g , A1-Cut Al-Zn alloya, a t temperaturea a s low aa -60°C involves the influence of a high concentration of vacenciea a t the reaction temperature which were retained by rapid quenching (41). T h e

- - - scientific and technological impact of these high diffusion rate phenomena are probably not yet fully appreciated.

MARTENSlTIC REACTIONS

All the traneformations discueeed above involve the movement of a so-called non-glissile interface, i.e., one which requires thermal activation for the interface to move. The other main c lase of transformations, including most twinning and martensitic tranaitiona, involve the rapid organized movement of atoms without thermal activation. Such interface motion i s called glissile. The dislocation motions by which glisaile interfaces move has been theoretically propoeed in a recent high quality review (25). The verification of the theoretical details, however, i s yet to be done.

Another problem concerning the martensite reaction i s the anomalous combination of effects of some elements. Chromium for example, i s know to favor the formation of the ~ l r ~ h a s e of iron (Cr former a closed -loop in the Fe-Cr ayetem); on the other hand Cr i s found to lower the Ms temperature. Alternative explanations for these apparently inconsistent effects are offered by Zener (magnetic specific heat effect) (43) and by Kaufman (regular solution thermodynamic effects) (44). The question i s apparently still not settled.

NUCLEATION

Although c a s e s a re occas iona l ly reported (45) in which homogeneous nucleation is thought to have occurred, dear ly a l l a c t u a l meta l c r y s t a l s conta in ubiqui tous nucleat ion s i t e s s u c h a s impurity particle ' su r faces , Rrain boundar ies and d i s loca t ions where nucleat ion c a t a l y s i s occurs - before true homogeneous nucleat ion can b e achieved. Furthermore, the most re l iable nucleat ion theory predic ts that the frequency of homogeneous nucleat ion shou ld be a strongly dec reas ing function of the degree of l a t t i ce misfi t between the two structures. Consequent ly the condi t ions necessa ry for developing a irery high motivating f ree energy, i.e. high supersatura t ion (low temperature), a r e usua l ly s u c h that atomic mobili ty in the bulk c rys ta l is t m low to a l low the react ion to proceed a t a s e n s i b l e rate. Quant i ta t ive observat ion of nucleat ion frequency in s o l i d s i s experimentally qui te d i f f icul t and more definit ive exper iments on the s u b j e c t are badly needed t o clarify the theory, What l i t t le qual i ta t ive information is avai lable s e e m s to support the theoret ica l descr ip t ion by Brooks (46). In c a s e s where very high par t ic le d e n s i t i e e (from 1015 t o 1018 per cm3) are observed, e i the r the s t ructura l misf i t h a s been very smal l , e.g. C o from Cu-Co, Zn from ~ 1 - ~ n , F e from Cu-Fe, or the supersatura t ion (driving energy) h a s been very large, e.g., Cu from A1-Cu, Cu from Si-Cu and Sn from Pb-Sn.

I I

T h e inoculation treatment used b y Saulnier (47) in s t u d i e s of precipitation in A1-Si a l loys h a s p o v i d e d a s t imulus to the understanding of nucleation. H e found that by rapidly quenching di lu te alloy of Si in A 1 from the homogenizing temperature and holding i t for a su i t ab le time a t room temperature or below, the number of s i l i con precipi ta te formed during aging a t 200°C w a s of the order of 1016 per cm3 i n s t e a d of about l o 6 which form during ordinary ag ing a t 200'. Saulnier be l i eves :hat t h i s inoculation treatment l e a d s to the formation of vacancy c lus te r s (dislocation loops) which might se rve a s nucleat ion c a t a l y s t s or that, because of the high supersatura t ion and the high s i l i con mobility due t o the e x c e s s v a c a n c i e s p resen t af ter the rapid quench, a c t u a l homogeneous nucleation occurred a t room temperature. T h e l a t t e r interpretation i s apparently favored s i n c e the number of s i l i con s e e n during ag ing a f t e r inoculation is much larger than the number of d is locat ion loops which formed, as observed by e lect ron microscopy. No doubt commercial appl ica t ion h a s often, perhaps unknowingly, been made of the inoculation principle. A sound unders tanding of the and i t s in- f luence upon t r ans fo rmat ionk ine t i c s however, is much to be des i red s o that the phenomenon can intell igently be put to more effect ive use.

T h e interaction of va r iohs types of precipi ta tes i n complex high temperature a l loys often l e a d s to their phys ica l beha:vior which is quite difficult to understand, F o r example in iron or n icke l b a s e a l l o y s (12000F to l80O0F se rv ice ) which a re hardened by precipitation of Ti-and Al-containing phases , the hardening h a s been attr ibuted mostly to the p h a s e (hcp NigTi) by Craver e t a1 (481, t he Y' p h a s e ( fcc Ni3A1) by Bea t t i e and Hagel (49) and to both by L e n a (50). T h e picture is made unclear b y the reported a b s e n c e of y' in the p h a s e diagram of Tay lo r and Floyd (51) a t low aluminum contents and by the cha rac te r i s t i ca l ly coa r se dispers ion of which would not be expected to contribute much to hardening. A further complication in Fe-Ni b a s e a l l o y s h a s been the appearance of a gra in boundary transformation, notably after cold working, which s ignif icant ly r educes ' the notched stress-rupture properties. Attempting to resolve t h e s e problems Mihalisin and Decker (52) s tudied the transformations in Ni-base a l loys conta ining T i and A l , with s p e c i a l emphas i s g iven to mutual so lub i l i t i e s of p h a s e s and to non-equilibrium t ransi t ion s t ructures . T h e y conc luded that under non-equilibrium condi t ions during aging the y' s t ructure which forms by cont inuous precipitation c a n have any composit ion between fcc Ni3A1 and Ni jTi and that the non-equilibrium Ti-rich y' phase decomposes on overaging t o the equilibrium 7 p h a s e by an i n t r a g a n u l a r a s we l l a s a grain boundary reaction. T h e y conclude that hardening is due mainly t o the y' phase , thereby confirming B e a t t y and Hagel. Boron

additions retard the grain boundary converslion to but have no effect on the intragranular reaction. Replacing T i by A1 retards the Y +r] conversion, both at and away from grain boundaries. The micro-structures of the Y , Y' and r] phases which they found at various s t ages of precipitation are reproduced in Figure 12.

T h i s type of study illustrates the empirical approach by which useful information can be obtained about complex phenomena and systems commonly found in high temperature alloys. Contihued study of fundamental processes are much needed; but in most practical materiale the compositione and treatments which have been found empirically to give the bes t properties a re anything but simple. The most effective approach to their understanding hae been through intelligent though s t i l l empirical methods.

Pursuing this problem in a systematic way, Beattie and Hagel (53) have recently had succes s in characterizing multicomponent austenitic al loys by certain features of their transformation processes. They found that certain groups of elements a c t a s one, and that the relationships among some precipitation processes are relatively simple. Reporting on extensive

- aging studies of seven complex cobalt or nickel-base austenitic alloys, they propose that the precipitation reactions in a l l seven alloys could be grouped into one of two c lasses , depending on the base composition. They point out that their findings are largely consistent with earlier l i t t le known work of Laves and Wallbaum (54) and constitute a recognition of important

about the transformation behavior of many auatenitic refractory alloys.

According to Laves and Wallbaum (confirmed by Beattie and Hagel) elements in the central portion of the periodic table can be divided into groups A and B, a s shown in Figure 13, with respect to their precipitation behavior in binary A-B alloys. They found a consistent change in cryatal chemistry for the B-rich intermetallic a s the B-member pas se s to the right from cobalt and i t s homologues to nickel and i t s homologues. The vertical line dividing the chart separates element groups of clearly different crystal chemistry B-elements to the left of the line combine with A-elements t o form the complicated structures of Laves (AB2) or o (unstoichiometric) adding molybdenum and tungsten to the A-group introduces p phase . .

(A&) a s well a s more examples of Laves and 6 phases. B-element8 form ordered close packed structures of the formula AB3. This .general behavior has been confirmed several times, (55) although a s Beatty and Hagel point out, there are indications that the dividing line should be moved to the left to bisect the cobalt group, s ince several examplea of ordered AB3 cobalt compounds are known, as well a a l a v e s , T and p phases of cobalt. T h e Lavea- Wallbaum dividing line apparently a l so separates B members that seek minimum interstitial space (Kaeper polyhedrn) (56) from those that seek crystal structures of high symmetry.

The Lavee-Wallbaum correlation i s a useful aid in interpreting structures in precipitation alloys. Using, for example, a etudy of the Ni-base alloy known a s Rend 41 by Hagel and Beattie, i t i s seen that a t first the nickel-rich matrix favors the precipitation of y' over the p phase. After enough y ' h a s been precipitated, the matrix i s depleted in nickel and i s left relatively rich in cobalt. Therefore, by the Laves-Wallbaum criteria, the precipitation of a structure with Kasper polyhedra i s favored. This i s the Co7M06 phase which w a s in fact found to occur in Rend 41. Here i s a ca se in which the change in matrix which i s necessary to promote the precipitation of a different phase automatically and conveniently provides the proper delay for further strengthening after the effects of the f i rs t strengthening reactions have been fully exploited. Th i s sequence illustrates a promising possibility for introducing true and sophisticated metallurgical deeign into the development of high temperature alloys. Further examination of these ideae i s certainly justified.

Important parts of the field of transformation which I sha l l only mention are a) the effects of high s ta t ic pressure on phase stability and transformation kinetics, and b) the effects of high energy mechanical shock on the structure of solids. High pressure phenomena have been treated in a recent volume (63) which contains the proceedings of an international conference on the subject. Dynamic shock treatment has also been the subject of a major conference, the proceedings of which are available in book form (64). These a reas are s t i l l unexploited and undoubtedly s t i l l contain undiscovered branches raving scientific a s well as technological importance. !

NEW TECHNIQUES FOR OBSERVlNG STRUCTURES DURING RECRYSTALLIZATION AND PHASE TRANSFORMATIONS

During the las t annual Pdecting of the American Institute of Mining, Metallurgical and Petroleum Engineem a conference was held on the subject "Direct Observation of Imperfee- -

t ions in Crystals." The proceedings of the conference are to be published a@ a hard cover volume by Interscience Publications, Inc.., recently acquired by John Wiley and Sons, Inc. The volume i s due for public release in November, 1961

Among the items presented a t the conference were several new techniques by which transformations and recrystalliza'zion can be observed. Some techniques are outlined here s ince they will probably find useful application in future experimental atudiee. For detailed description and application examples, I refer you to the Proceedings of the cited conference.

X-RAY DETECTION OF T H E ONSET OF RECRYSTALLlZATlON

C. S. Barrett ham found that the progress of recrystallization in a cold worked or fine grained metal can be conveniently and accurately followed by the growth of sharp spota in Debye-Sherrer diffraction patterns observed by means of a counter diffractometer instead of the usual ~ h o t o ~ r a p h i c film. The counter, with large detector aperture, i s s e t in a stationary position on one of the strong Debye rings and the specimen is then rotated or o ~ c i l l a t e d a few degrees. The diffracted intensity i s recorded on a chart in the ueual way. The f i rs t presence of recrystallized grains ia recognized by the sudden appearance of definite intensity peaka from the recrystallized graine in place of the relatively smooth record from the cold worked matrix. Recrystallization i s a l so indicated by a drop in the intenaity of the background between the peaks. Barrett found that the temperature a t which recrystallization s tar ted in similar cold worked sprcimens was remarkably independent of heating rate. The method i s apparently rapid, relatively convenient and gives quite reproducible results.

THERMlONlC EMISSION MCCROSCOPY

When a conducting surface i s heated to a high enough temperature, electroner are emitted from the surface at a rate which i s characterized by the electron emisaion work function of the surface. The emitted electrons may be electrically drawn from the surface in etraight l i m e which are normal to the macroscopic surface. By a suitable electron optical eystem, the electrons can be focused and projected as an enlarged image of the emitting ~ u r f a c e upon a fluorescent screen (57). Since different surfaces (material, topography and cryetallographic orientation) emit at different rates, the projected image represents the surface features of the emitting specimen. Any change of the specimen surface i s seen as a region of contrast on the image. Thus, recrystallization and phase transformatione can be directly observed at magnifi- cat ions roughly equivalent to those attainable by optical microscopy, Without special treatment a surface must be heated to about 600°C S O that enough thermal electrons will be emitted to

provide a useful image. Fo r lower temperature emiesion a very thin layer of thorium pr barium i s vapor depoeited onto the specimen eudace , thereby lowering the electronic work fhnction. The practical upper temperatnre limit i s about 1300°C, above which aerioue instrumental de- terioration sets in.

Although the motion of grain boundariee at high temperature i s dramatically shown by thie technique, the limitation remains that only the specimen surface i s visible. Therefore the interpretation of the pbaerved transformation kinetica ie not simple with reepect to the three dimensional process which ie actually occurring.

F I E L D ION MICROSCOPY

Thie technique, developed and exploited moat actively in th i s country by E. W. Mfiller (58), dependm upon abnormal electron tunneling a t minute s u d a c e projections of a fine tip. T h e tip i e maintaiued a t a poeitive elec.tro-Potential with reapect to a surrounding atmosphere of ga13 (helium) a t low pressure. According to a simplified picture of the process, the g a s atoms are ionized in a region close to the epecimen murface and then are repelled in a direction a t right anglee to that part of the enrface where ionization occurred. The ions are accelerated as they move radially from the ,epecimen tip to a concentric fluorescent screen. In practice the screen coneiate of the walls of the glaee container on which has been deposited a sui table fluoreeeent material. Since the number of ione emitted at a given point on the jip depends upon the etructure of the tip material, the pattern formed on the fluoreecent ecreeb repreeente the actual aurface topography of the point. Under beet conditions, individual atom e i tee can be observed and ~ r y e t a l l o g a ~ h i c planea can be identified.

Pound and Moaaed have ueed field electron emieaion microscopy for observing the fundamental kinetice of nucleation of metal vapor on tungsten t ips (59). The method of field ion microecopy hae potential applications of more direct intereat to high temperature materials, i n that the er~ain recovery process a t the tip can be viewed directly on an atomic scale. Pre- liminary obeervations of thie type have been made very recently by Mfiller (35).

X-RAY OIFFRACTION MICROSCOPY

Several variatione of X-ray diffraction microecopy have recently been developed (60). All depend upon forming a topographical image horn a single crystal epecimen by the Bragg diffraction of white or characteristic X-rays. Image contrast may be due to differences in primary extinction from point to point on the specimen, surface topography, regions of strain, or other internal defecta of varioue aorta. Most of the methods are very sensi t ive to deviations in crystallographic orientation eo the position of a phase or intercryetalline boundary can be clearly eeen. The Lang and the Berg-Barrett methods are eepecially sensi t ive to strain gradientm. They are therefore appropriate for studying straine around precipitatee or other foreign particlee in a matrix crystal. T h e linear msolution however i s only about three microns. The method of Bonse u ses a highly collimated beam of monochromatic X-rays and therefore features great senaitivity to small orientation differences.

Theee diffraction methoda are capable of producing topographical pictures of h e defects including individual dielocations and ehould therefore be useful for etudying the structures of grain boundariee. Figure 14 showr, a light micrograph and three X-ray diffraction mierograph~ of the eame aurface of a lithium fluoride cryetal which had been slightly diatorted by horizontal compreeeion. T h e d i p lines and a l l aub-grain boundaries have been made vieible by etching am eeen in (a). The alip linee are visible in some diffraction photomicrographs and not others,

depending on the relative orientation of the Burgers vector of s l ip and the diffracting lanes (details described in reference 61). The grain boundaries appear in different contrast in b, c and d, depending on factors which are not yet resolved. Very l i t t le application has s o far been made of these new and powerful techniques, although they are inrtrumentally much simpler than electron microscopy,

ELECTRON MICROSCOPY

Thi s method i s now well recognized as a powerful tool for watching r e ~ r ~ a t a l l i r a t i o n and other processee in thin film specimens on a nearly atomic scale , The increaeed application of high accelerating voltage makee i t possible to examine relatively thick epecimena. How- ever, the application of thin film behavior t o the bulk behavior of the material can s t i l l be misleading. Most of the effort in electron microscopy of crystalline eolids i s directed at an understanding of the behavior of point and line defects and therefore ha@ been more useful in the study of such processCs aa recrystallization and sl ip than the transformation behavior of high temperature alloys, ,

RECAPITULATION

In this brief review of current knowledge in the field of recrystallization and phase transformations a few points stand out as being especially attractive for future work. There ie no question that other important and appropriate research areas now exist or will be developed in these fields. Nevertheless, for what value they may be, I submit these euggeations for future research consideration. ,

I

Subject Discussod on page

Study the effects of impurity atom (subetitutional and interstit ial) 85, 87, 88 in high-purity base met& to clarify and generalize recent experimental observaticms on !boundary mobility.

2) Gather reliable thermodynamic data on grain boundary self-diffusion 81 to help develop a model of structure of grain boundaries, their mobilities and other properties.

3) Apply new diffraction and other techniques to study the nature of 79, 87, 88, 92 grain boundaries and of, intra-grain imperfections and of their effects in crystallographic transitions.

4) Develop a method for topographic observations of point defecta 82, 83

5) Rationalize and evaluate quantitatively the var.ious sources of- the 82, 84 controlling driving energies of recrystallization.

6) Explain and extend the empirical observationa of the effects of 84, 85 electronic structure on recrystallization.

7) Define the controlling 6rocessee in recrystallization to a point where 85 recrystallization textur+ can be predicted and synthesized.

8) Develop a theory by which one can predict from first principlee whether a transformation will be one of first or second order.

9) Exploit the known ultra-high rate diffusion which ie known to occur under some circumstances.

10) Investigate' experimentally the propoeed mechanirams for the motion of a martensite boundary.

11) Rationalize the now anomalous effects of some elements on the behavior of martensite..

12) Explore the phenomenon of inoculation in phase transformatione and apply it t o practical use.

13) Develop an u n d e r ~ t a n d i n ~ of the factors which control the mop phology of transformation products.

14) Look for further validity of the Laves-Wallbaum rule and apply the principle in the design of complex alloy transformations.

15) Apply modem techniques to the direct observation of atom positions, grain boundary motion, lattice strains, appearance of new ctyatals, etc.

AKNOWLEDGMENTS

D i s c u r n ~ d on page

86

8 9

89

89

9 0

88

91

92

Thi s brief review was prepared while the author was partially muppotted by the Cornell Materials Science Center, under contract to the Advanced Reaearch Projects Agency of the Department of Defense. Discuesions with other members of the Center and stenographic aaeis tance i s gratefully acknowledged.

REFERENCES

1. K. Lucke, e t al, Z. F. Metalkunde, 52 (1961) 1-46

2. K. Lucke, to be published I

3. N. F. Mott, Proc. Roy. Soc., 60 (1948) 391

4. T. S. Ke, Phys, ~ e v . , 72 (1947) 41

5. M. L. Kronberg and F. H, Wilson, Tr. AIME, 185 (1949) 501 I

6. W. T. Read and W. Sihockley, Phye. Rev., 78 (1950) 275

7. See for examples K. T. Aost and J. 1. Ratter, Tr. AIME, 1961 and earlier

K. T. Auat and J. W! Rutter, Tr;-AIME, 215 (1959) 820

0. Turnbull, Tr. A ~ E , 191 (1951) 3

N. A. Gjoetoin and F. N. Rhines, Acta Met., 7 (1959) 319

R. H. Atkinson e t al, Westinghouse Lamp Div., WADD Tr. 60-37 on contract A F 33 (61 O)-5632, May 196P

K. Lucke end K. ~ e t e r t , Acta Met. 5 (1957) 628 !

J. W. Ruttet and K. F. Aust, Tr. AIME, 218 (1960) 682

W. C. Lesl ie , F. Pleci ty and J. T. Michalek, to be published

L. P. Jahnke, AIME conference on High Temperature Materials, 1461. Proceedings, Interscience ~ublieikt ions, Inc.

J. W. Semmel and EJ S. Machlin, Aeta Met., 5 (1957) 582

J. L. Walter and C. b. Dunn, Aeta Met., 8 (1960) 497

K. T. Auat and J. W I Rutter, Tr. AIME, 215 (1959) 119

W. W. Mullina, ~ c t a ~ e t . , 6 (1958) 414 1

E. P. Abrahamaon, and B. S. Blaksney, Jr., Tr. AIME, 218 (1960) 1101

W. R. Hibbard and d . R. Tully, Tr. AIME, 221 (1961) 337

W. G. Burgers, L'E$~ Solide, B r u s s e l ~ , (1952) 73 I

P+ A. Beck, Acta Mht., 1 (1953) 230 1

eepor ts of Panela sbonsored and distributed by ONR, Waahington, D. C. -Editor, It. Himmel 1 Mechanism of ~ h a s d Transformations in Solids, Inst, of Metals Monograph and Report Series 18, 1955 I J. S. Kirkaldy, ~ ~ r n d o e i u m on " D s c ~ m ~ o ~ i t i o n of A.uAhnite by ~ u c l e a t i o n and Diffmional Growth,'' AIME, Monograph, 1961

To Muto and Y. Takagi, solid s ta te physics, 1 (1955) 193, Academic P r e s s

L. Guttman, ibid, 3 (1956) 145

F. S. Ham, J. Phys. and chemistry of aolids, 6 (1958) 335

I. M. Lifshitz and V. V. Slezov, Soc. Phys., JETP. 8 (1959) 331

J. W. Cahn and J. E. Hilliard, J. Chem. Phys., 31 (1959) 688

L. H. van Vlack, Tr. AIME, 191 (1951) 251

R. E. Hoffman, Acta Met. 4 (1956) 97

AIME aymposium on "Direct Observation of Imperfertione in Cryatale," edited by J. B. Newkirk and J. H. Wetnick, Interscience Publications, Inc., New York, 1961

A. Dube, H. I. Aaroneon and R. F. Mehl, Rev. de Met., 55 (1958) 201

H. I. Aaronaon, Tr. AIME, 218 (1%0) 331

J. HI Westbrook, 2. Krist, 110 (1958) 21

J. B. Newkirk, Tr. AIME, 209 (1957) 1214

D. Turnbull, Acta Met., 3 (1955) 55

D. Turnbull, Acta Met., 8 (1960) 277

P. A. Beck e t al, J. Appl. Phye., 21 (1950) 420

U. Roesler, H. Sato, C. Zener, "Theory of Alloy Phaeea" ASM (1956) 255

L. Kaufman, Tr. AIME, 215 (1959) 218

R. C. Williams, Tr. AIME, 215 (1959) 1026

H . Brooke, unpublished. See D. Turnbull, Solid State Phyeice, 3 (1956) 225, Academic P r e s s

A. Saulnier, Comptes rendue, 251 (1960) 2160

C. B. Craver s t al, unpubliehad. See Reference 52

H. J. Beattie and W. C. Hagel, Tr. AIME, 209 (1957) 911

A. J. Lena, "Precipitation f rc7 Solid Solutions," ASM (1959) 244

A. Taylor and R. W. Floyd, J L Inst. Metals, 81 (1952) 25

J. R. Mihaliain and R. F. Decker, Tr. AIME, 218 (1960) 507

H . J. Beattie and W. C. Hagel, Tr. AIME, 221 (1961) 28

F . Laves and H. J. Wallbaum, Naturwiee, 27 (1939) 674

A. E. Dwight and P. A. Beck, 215 (1959) 976

F. C. Frank and J. S. Kasper, Acta Cryet., 12 (1959) 483

57. W. L. Grabe, to be

58. E. W. Muller, JL. ~&d. Phys., 28 (1957) 1

59. G. M. Pound and K. L. Moazed, to be publiehed 1

60. W. W. Webb, in Reference 35

61. J. B. Newkirk, Tr. dIME, 215 (1959) 483

62. D. Turnbull, unpubli~shed report to the NATO Committee on Solid State Sciences, Paris, 1961

63. "Progress in Ve y High Preesure Research," F. P. Bundy, W. R. Hibbard, Jr., A. M. Strong, Ed.., 4 . Wiley and Son., 1961

I

64. "Response of Metale to High Velocity Deformation," P. G, Shewrnan end V. F. Zackay, Interscience Publ,, 1961

/ PREDICTED BI

//THEORY OF NOT1

/ /

/

/

I I I I 1 1 1 eo

1 40 6 0 8 0

AS: CAL PER DEGREE PER OAIY ATOM

FIGURE 1

COMPARISON OF EHTAOPIES OF ActlvAnw PW WIN BOUNDARY MIGRATION PREDICTED BY MOTT WJTH THOSE DERIVED EXPERE. MENTALLY BY AUST AND ElOlTER SHOWS A CWSTAHT DIFFERENCE OF ABOUT 15 CAL PER DEGREE

FIGURES 1 & 2

" RANDOM" BOUNDARIES,

Id /

/

" S P E C I A L ' BOUNDARIES

- I 0 L -

0.0001 0.0005 0.0010 0.0015 0.0020 0.0025 TIN CONCENTRATION (WT PCT)

FIGURE 3

EXPERIMENTALLY DETERMINED ACTUATION ENERGIES OF "SPECIAL" OR COINCIDENCE BOUNDARIES A R E SMALL W ~ T H ~ E S P E C T T O THOSE OF "RANDOM" HIGH ANGLE BOUNDARIES AND ARE PRACTICALLY INDE- PENDENT O F lMPURlTY CONCENTRATION. (AUST-RUTTER)

ALLOY, WEIGHT-PERCENT F I G U R E 4

DIFFERENT ALLOYING ELEMENTS HAVE WIDELY DIFFERENT EFFECTS ON THE RECRYSTALLIZATION TEMPERATURE OF MOLYBDENUM. (JAHNKE)

FIGURES 3 & 4

FIGURE 5

LUCKE'S PICTURE OF 1 HE BOUNDARY BETWEEN DISTORTED AND RECRYSTALLIZED MATERIAL. IMPURITY ATOMS ARE DRAGGED ALONG WITH W E BOUNDARY AND MUST DIFFUSE THROUGH THE R ECRYSTALLITEb LATTICE BEHIND THE INTERFACE.

0 l l 4 I 0 1 I0 I0 0 100

1

XXUTE CONCENTRATION ( ATOMS PER I0 ' I FlQURE 6

ORAIH IK)UNWRY MIORAT ION RATES OBSERVED BY AUST-RUTTER W NOT AGREE WRL WITH THOSE CALCULATED ON THE BASIS OF THE LUCKE-DETERT THEORY.

FIGURES 5 h 6

FIGURE 7

MfA -GE

.5 I 10 100 HOURS

FIGURE 8

'TNE HlOBlUM W E ALLOY FSll IS HIGHLY RESISTENT TO RE- GRYSTALUZAT~ e v w AT m o o F. TEN-HOUR RUPTURE STRENGTH IS GIVEN AS ABSCISSA. (JAHNK E)

FIGURES 7 & 8

LOG

RA

TE

Rh

TE

OF

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OF

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TA

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TEM

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8

Du b6 Classification o f Morphology

Grain Boutidary Allotriornorph Int.ragronulor Plate

Widmonstdtten Sideplote Id iomorph

MORPHOLOGIES OF PHASE TRANSFORMATION PRODUCTS ACCORDING T O THE CLASSIFICATION PROPOSED BY DUBE.

F IGURE 11

TIME- HOURS

FIGURE 12

TYPICAL MICROSTRUCTURES FOUND I N NI-12 T I ALLOY ILLUSTRATE MANY O F THE DuBE M o R p H o L o G ~ c f L CLASSES. (MIHALISIN)

FIGURE 13

ACCORDING TO LAVES AND WALLBAUM ELEMENTS IN THIS PART OF THE PERIODIC TABLE CAN BE DIVIDED BY THE VERTICAL LINE INTO TWO DlSTlHCTLY DIFFERENT CLASSES WITH RESPECT TO THEIR PRECIPITATION BEHAVIOR.

FIGURES 12 & 13

Prepored Discussion

THE ROLE OF ELECTRON CONFIGURATION ON RECRYSTALLIZATION

Dr. E . P. Abrahamson, I!

As Dr. Newkirk pointed out in the .molybdenum recrysta l l izat ion ve rsus so lu te curve, there a re both posi t ive and negat ive changes in recrysta l l izat ion temperature with so lu te additions. We have examined titanium1, zirconium2, vanadium3, columbium4, irons*6 and nickel7 base sya tems alloyed with dilute binary additions of the t ransi t ion elements. Figure 1 ind ica tes aome typical recrysta l l izat ion curvea. I t will be noted that there is an ini t ia l posi t ive or negative l ine or change followed by a break, or l imit of l inearity, and another l inear portion.

In s tud ies of the effect of time on recrystall ization, c.f. Figure 2, i t w a s noted t h a t a variation in time from 20 t o 4000 minutes did not change the in i t ia l slope. The only variation noted w a s beyond the limit of l inear i ty where the curve changed from a negative t o a s l igh t ly posi t ive slope.

Ae s e e n in Figure 9 of Dr. Newkirk's paper, there i s a definite correlation between the number of ground s t a t e outer d and s elect rons in the so lu te and the init ial ra te of recrysta l - l ixation temperature change by the solute . In a s imilar manner, e tudies on iron have a l s o ehown that the l imit of l inear i ty ia a l s o a function of e lect ron configuration, c.f. Figure 3.

Figure 4 indicates , in a periodic manner, the s l o p e correlations to date. I t will be noted that the curvea are in the form of V'e - inverse for titanium, zirconium and vanadium, normal for columbium, iron and nickel. The curver are similar in tha t the apex of the a = 2 electron curve a lways occurm a t one d e lect ron more than the solvent ' s configuration. The brittle-to- ductile t r ami t ion temperature correlation for chromium base a l loys8 is presented to indicate that the correlation holds for other properties. It should be further noted that the role of the solvent'^ configuration can be s e e n in the change in the apex, the dieplacement of apexes in the c a s e of so lven te having one d electron, and in the s imilar i ty between correlation curves of so lven t s with the same outer electron configuration.

Pr ior t o the determination of recrystall ization in nickel base a l loys , a n empirical relation- ehip waa es tab l i shed between the other curves. T h i s allowed the prediction of the nickel ,correlation curve wel l within experimental error.

At the moment i t i e difficult to present a model to explain t h e s e correlations. I t is known tha t s imilar correlations can be ahown for other phyeical a n d mechanical properties. There- fore, i t will be necessa ry t o construct a model which a p p l i e s t o more than one case .

ATO

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66-8

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lOOMin

ATOMIC PERCENT COLUMBIUM

IRON RECRYSTALLIZATION TEMPERATURE AS AFFECTED BY COLUMBIUM FOR A VARIETY OF TIMES, COLD WORK CONSTANT AT 75%

FIGURE 2

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-61

SOLID-GAS REACTIONS

by

Dr. E . A . Gul bransen

MICROTOPOLOGY OF THE SURFACE REACTIONS OF OXYGEN AND WATER VAPOR WITH METALS

A B S T R A C T

Current theoriee of metal oxidation assume the formation of a uniform oxide film separating the reacting gaa from the metal. According to the Wagner theory of oxidation reaction occurs by the diffuaion of metal or oxygen ions through interstit ial s i tee or through cation and anion defects in the oxide film. Much work has been directed toward checking the predictions of the theory and to extending the theory to complex systems.

T h e microtopological point of view i s a n attempt to observe changes in surface structure a e a reeult of oxidation. It i s assumed that metal structure, dislocation, inclusions, s t r e s s and other factors play an important pert in the oxidation process. Two particular problems are eoneidered in thie paper. F i re t what i s the nature of the f i rs t s t ages in oxidation? Second, what is the nature of the localized growths which occur during oxidation?

In the early 1950's, Bardnlle and Benard, and Gulbransen, McMillan,and Andrew used low preesure oxidation methods to study the initial s tep in the oxidation of iron. At temperatures of 650°C to 850°C and low oxygen pressures, amall oxide nuclei were formed on iron during the firet s t ages of reaction.

The resul te suggest that the initial a tage of oxidation involves the formation of a thin uniform layer of small oxide crystallites. Th i s was rapidly followed by the formation of much larger oxide cryetala along certain and regularly spaced lines on the metal grain. As oxidation continues, the oxide crystals grow, and new cryetale form filling the remaining area of the metal. This results in the formation of a uniform moeaic of large oxide cryetala.

Recent electron optical s tudies are presented on the effects of environment, s t r e s ~ and metal etructure on the formation of localized oxide growths on iron. Three types of localized growths were found when pure iron waR reacted with oxygen and water vapor atmospheree a t 450°C. Thin oxide whiskera 100-150 1 in diameter form when w e annealed iron was reacted in dry oxygen.o These whisken grow to lcngtha up to 500,000 f1.11~. Thin blade shaped platelets 100 A thick, 300 to 13,000 X wide and 80,000 A long formed when iron w a s eacted with water vapor containing t races of oxygen. Thin, rounded latel lets of oxide 100 A thick, 75,000 8 high and wide formed when cold worked iron was reacted with dry oxygen.

The environmental conditions for forming these localized growths has revealed many new ideas on the corrosion of iron and the oxidation of metals. The relation of these growthe to the metal mhucture and to the oxide i s now being studied a s i s the problem of whether theee growths lead to pitting and trenching of the metal itself. Although i t is too early to draw any definite conc lu~ ione i t appeara that electron optical studies of the microtopology of the localized oxide growths offer a new method for observing the e f fec t of crystal imperfections on the chemical reactivity of metals and alao fo r s tudy of metal structure.

Another area of interest i s the mechanical properties of these new oxide growths. Calcu- lations show that these crystals have very high e las t ic strain limits. If these oxide whiakem and platelets have high strengths w e may ha re new structural materials which not only have high melting points, low vapor pressure, high e las t ic yield limite and high strengths but a l so are non-reactive in oxygen environments.

In recent years the science and technology of raurface reactione has become a field of critical importance in modelm technology. As a resul t a great deal of work i s being directed a t understanding the mechanisms of surface reactions. Real progress ham been made due to two developments. Sensitive methods have been devised for the study of the kinetica and crystal structure factors h isur face reactions. Theoretical developmgnte have been made to correlate and interpret the mechanisms of gawmetal reaction^.

Aa recently a s 10 y e m i ago much work in the field of metal oxidation was directed at testing the Wagner1 theory bf oxidation. During the pas t decade work has been directed along more practical lines. The development of nuclear reactors hew focussed attention on the reactive metals, zirconium and uranium and their a l loys while the dsvelopment of miesiles and space vehicles has directed work to the refractory metals such aa tungaten, niobium, tantalum and molybdenum. Interest in molecular electronics has led t o oxidation s tudies of metals and semiconductors where the material i s in the form of an evaporated or sputtered film.

This paper will diecusd another new direction in metal oxidation; namely, the role of metal structure in the initiation and growth of oxide films on metals. The approach is. that of t he observer school and emphasizes the microtopological structure of the oxide. The paper con- a i s t s of two parts. The first part is concerned with the initial a tages of the oxidation proceea, while the second part is concerned with the nature of oxide growths occurring during oxidation.

Due t o space and time limitations we will limit our discussionsl to the oxidation and corrosion of iron and s ta in less steel.

In contrast to other papera no attempt will be made to coven the complete field of oxidation.

I / . PRESENT PICTURE OF OXlDATlON

The Wagner1 theory of tbe oxidation of metals i s accepted by most rc iea t i s t r . The theory is based on the diffusion of metal ions or atoms or oxygen ions or a t o m through an oxide film. Diffusion occurs through interstit ial s i t e s or through cation and anion defects in the oxide. A uniform oxide film is assumed and the metal i s assumed to be structureless over a given metal grain. Wagner'a theory can only be applied under conditions where a coherent oxide film ie formed and where the oxides are not soluble in the metal,

Figure 1 shows a schematic picture of two alternative mechanisms for oxidation. The first involves the diffneion of metal ions through vacancies in the oxide while the eecond involves the diffusion of oxygen ions or atoms through the oxide. Equatione A and B Figure 1 show detai ls of the two mechanisms.

One of the difficulties id the Wagner theory i s that complex oxidation and corrosion problema cannot be handled. Thus, how can one apply the theory to the complex localized reactions

involved in s t r e s s corrosion cracking of 304 s ta in less s tee l or to the complex influence of water on the corrosion of iron? These probleme inevitably go back to the selective oxidation or corrosion of localized structures in the metal. Recent developments in metal physics have shown that crystal orientation, dislocations, precipitates, impurities and other defects determine the mechanical properties of the metal. We feel these factors may determine a l so the chemical reactions of metal surfaces.

111. THERMOCHEMICAL EVALUATION OF THE OXIDATION REACTIONS

Before presenting experiments on the nucleation of oxide films or the formation of localized oxide growths i t i s essent ial to consider the thermochemical equilibrium involved. Thermo- chemical equilibrium does not exist for a system undergoing reaction; for example, iron reacting with oxygen. However, thermochemical calculations may be useful in choosing one of several posaible reaction mechanisms. The reactions which do occur are those that are feasible both thermochemically and kinetically.

In a more limited eenee, an approximation to equilibrium may exist a t certain planes in a metal Byetem undergoing reaction after the initial period. Thus, the concentration of iron in ferrous oxide a t the FeO-Fe interface and a t the FeO-Fe304 interface may be estimated from the iron-oxygen diagram2, although the concentrations within the several phases may be far from equilibrium.

From a chemical point of view five types of reactions may occur during the reaction of iron with oxygen:

Formation or decompoeition of the several oxides by direct oxidation.

Reaction with HZO.

Solid phaee reactions with iron or oxygen occurring a t the several internal interfaces.

Phariie transformation of FegOq to FeO a t 570°C.

Formation of the spinel FeaOg from FeO and Fe203.

Thermochemical calculatione are made for the five equilibria involved in the reaction of iron with oxygen, using the deta given by Chipman and Murphys on the free energy of formation of ferrous oxide, ferriferrous oxide, and ferric oxide. The equilibrium data are expressed in terms of Iog lO~ , where K i s the equilibrium constant, or loglop, where P i s the pressure of oxygen g a s in atmospheres.

Table 1 shows a listing of the reactions of internet together with the resul ts of the calculations, Each of the oxides i s s table to direct decompoe.itions over the temperature range considered and in vacua of loe5 m m of Hg. The reactions of iron with water vapor are possible a t 400°C but not above 600°C. The reaction to form Fe2o3 i s the leas t favorable of the water vapor teactiona. Feg03 can form only if hydrogen i s removed.

The reduction of F e O w-ith F e to form Fe304 i s favorable a s i s the oxidation of Fe304 2 3. to form Fe203. The oxidat~on of Fe304 with water vapor i s not favorable except a t low temper-

atures.

TABLE I

EQUILIBRIA CALCULATIONS ON IRON-OXYGEN REACTIONS

TABLE I (Continued)

Reaults on Above Equations

- -

log K log K

-7.32

-5.57

-5.24

-5.44

-5.91

-6.56

log K

-50 1

-2.2

-0.63

+0.09

+0.43

+0.49

B1

log K *

0.60

0.19

0.20

B3

log K

8.9

3.2

0.45

-0.94

-1.75

-2.29

log K

15.4

10.0

8.1

7.7

8.0

8.70

OF& not .table with rmmpect to Fasol and Fc below 570°C.

Fea04 can be reduced by Fe to form FeO only below 570°C while FeO can be oxidized to form Feg04 at all temperatures. The reaction of FeO with water vapor ie favorable a t low temperature but not at the highest temperaturee in Tnble I. Care must be uaed in interpreting the reactions of iron between 400' and 600°C. This is the temperature range of interest in th i s work.

The formation of the spinel Feg04 from FeO and Fe203 is poseible at all temperaturee in the absence of iron and oxygen.

IV . STUDIES ON OXIDE NUCLEATION

A. Thin Fi lm Range

The fac t that metals react with oxygen to h r m a non-uniform oxide film is not new. Phelps, Gulbransen and Hickman4 reviewed the evidence in 1946 for a granular etrncture in oxide films. These authors, in addition studied the crystalline nature of thin oxide filme formed on a wide variety of metals including iron and iron based alloys. Samples of m e t a l s were carefully oxidized and the oxide film removed electrochemically.

Figures 2 and 3 shaw the resul ts of en electron microscope study of the oxide filme formed on 44Puron"* aud Pire nickel. Electron diffraction show. the iron oxide film to be Fe304 and Fe203 while the nickel oxide film was NiO. The iron specimen was oxidized for 30 minutes at 250°C while the! nickel specimen was oxidiz d 20 minutes a t 500°C, The oxide film on iron showa irregular; oxide crystals 500 to 1800 1 in s i ze partly oriented to he metal. For the nickel specimen, the oxide film cons is t s of irregular particles 300 to 1500 in s ize, The oxide crystals were randomly oriented to the metal.

i

I t was concluded id 1946 that most metals formed non-uniform granu ar oxide films for thicknesses which could be studied by electron optical methods (about 500 A .) The filme cons is t s of thicker and thinner sect'ions which may indicate a multilayer structure. Nucleation of oxide occurred not only on the metal surface having only the initial oxide present but a l so on top of the first layer of qxide crystale. Calculations showed the oxide cryetals to be 10-3 to 10-5 of the linear dimension of the metal grain and to l(r1° of the area. Although eome evidence was found for orientation in the filme conaisting of the larger oxide crystals, in general, very lit t le orientlation wa. found. The crystal .ire of the oxids crystals was a function of both time and temperature.

B. Work of the French kchool

In tho early 1950's ~ a r d o l l c and Bcnard atudisd the initial s tage of oxide formation on carefully annealed and electropolished Armco** Iron between 650' and 850°C in vacuum atmospheres of log1 to 10-3 mm of Hg. At pre.sures between l(rl and 1(r2 mm of Hg a t 850°C many oriented nuclei were f4rmrmsd on an individual metal grain. Under no condition was a single crystal of oxide formqd on the surface of a metal crystal. At pressares of lom2 to log3 mm of Hg a few well oriented nuclei of oxide were formed. The ehapes of the nuclei on different grains were dependent on the orientation. Originally it was thought that the space on the metal surface betweeh oxide crystals was not cove,red by oxide; however, Bdnard6 has s tated recently that the space is occupied by a thin film of randomly oriented oxide crystals. T h i s leads one to conclude that the large oriented nuclei are nucleated or grow from certain oxide cryatals in the thin oxide film.

C. Work at ~ e s t i n ~ h o u r b

Gulbransen, M c ~ i l l a n and ~ n d r e w ~ extendbd the s tudies of Bardolle and n nard^. Electron optical methods were ueed and the oxide crystals formed daring oxidation were covered with a thin plastic film and removed electrochemically from the metal. A high purity iron w a s u ~ e d and the oxidation conditions were carefully defined, A vacuum microbalance was used to determine the extent of reaction.

I

Vhia ie a propriatary trade nama for a grade of iron produced by Weetinghouea Electric Corporation.

**This i s a proprietary trada name for a made of iron ptoduced by Armeo Steel Corporation.

Figure 4 shows electron micrograph8 of etripped bride films forme; on hydrogen annealed elacttopolished "Puron" grade of iron. Part a shows n electron micrograph of an A iron specimen oxidized a t #O°C to an avera e thickness of 752 . The reaction time was 25 minutee and the initial presmnre was 2 x iO-Bmm of Hg of oxygen. On exposing the asmple to oxygen the pressure dropped to 10-4 mm of Hg indicating the reaction was nearly instan- taneoue and that carbon monoxide wae not formed. Part b shows a micrograph of an oxide film emoved from an iron aample oxidized a t 750°C for 30 minutes to an average thickness of 322 f . The s r y ~ t a l s i ze of the oxide cryetals in the film formed a t 850°C wae 1 micron or less while the crystallite s i ze in the film formed at 750°C was 0.5 microns or less.

We concluded from Figure 4 that the initial s tage of oxidation i s a nucleation and growth mechani~m with the crystal arrangement depending upon the orientation of the metal grain. The oxide crystals form along certain directions and form broken lineo on a particular grain. The apacing of the l ines of growth depends upon the crystal orientation and varies from 0.5 to 1.0 microns.

Circular growth patterne occur on aome of the metal grains. Thie i s illustrated in Figure 5. Here the oxidation conditions were the same a e for Figure 4a. Ve relate the circular growth patterne to etrees patterne around inclusions in the metal gr in. The oxidized specimens It were light blue in color and had an average oxide thickness of 752 .

The existence of l ines of growth for the oxide nuclei was studied by comparing the oxidation of vacuum annealed iron with hydrogen annealed iron and with iron annealed in very pure hydrogen. Figure 6 shows an electron micrograph from a atudy by Gulbranaen and Andrew.* Here the iron Specimen w a s annealed in high vacuum after carefully preparing the eurface. The apecimen was oxidized a t 850tC w i n g an initial oxygen pressure of 5 r lom3 m m of Hg to an average oxide thickness of 453 A. The micrograph showe a nearly random arrangement of oxide nuclai although each nuclei i s oriented to the lattice of the metal. A thin randomly oriented oxide is formed between the larger oxide nuclei.

O. Orientation

The orientetion of FeO on a-Fe was studied by Mehl and ~ c C a n d l e e s ' ~ and by Bardolle and Binard5 using x-ray diffraction. Culbransen and ~ u k a " studied the same problem using reflection electron diffraction and in addition rtadied the orientation of FegOg and -Fe. All of the results enggeet that the cube plane of FeO or F e Oq grows on the cube plane of u-Fe, while the [loo] direction of the oxide l ies parallel to t 1 e [110j direction in the metal.

E. , Picture of Init ial Oxide Formation

Our conception of the initial s t ages of the oxygen reaction ie shown in Figure 7. It may be poetulated that the first s tep involves a chemi-sorbed layer of oxygen atoms. This would be a very transitory s tage a t 850zC with the quantity of oxygen available. As the reaction continues to a thicknesa of 100 A; the formation of a film consisting of small oxide cryetallites of the order of the thickness of the oxide film was poetulated. The next s tage of oxidation appears to be nucleation and growth of larger crystals along certain l ines of the metal grain. Along these growth s i t e s a lower free-energy barrier appears to exist for the formation and growth of new oxide crystals.

The properties of these linear growth s i t e s suggest that they represent a substructure in the metal which i s influenced by the annealing environment. Hydrogen and impurities in the

hydrogen gae appear to order the s i t e s for oxide nucleation on pure iron, The mechanism of this process is not clear. ~

These larger oxide crystals are well oriented to the structure of the m e t a l grain. As oxidation continues, the crystals grow and new ones ate formed completing the mosaic etructure. This i s shown in s tep d of Figure 7. Finally, a granular oriented oxide film is formed. Although the oxide crystals 'were oriented, in no case *.a. a single crystal of oxide observed on a metal grain.

The effect of the annealing environments on the arrangement of the oxide nuclei may aid the understanding of the effect of annealing treatments on the mecbanical properties "Puron" and other pure iroqs. ~ t a n l e y ~ ham made a thorough study of the embrittling of L 1 Puron" when heated in high vacuum and in dry and moist hydrogen atmospheres a t temperatures of 700-llOO°C. "Purbn" i s embrittled in dry hydrogen atmospheres at a dew point of -6S°C in 1 0 hr. for the temperature range of 700°C - 1150°C. In moist hydrogen, "Puron" waa embrittled in about an hour.' Vacuum annealing did not lead to embrittlement. Light micro- graphic s tudies showed onlf minor changes in metal structure.

Stanley's observations on the embrittlement of iron a t 700°C and our studiers on the effect of hydrogen and i t s ippurities on the oxide nucleation pattern a t 700°C appear to be related. Atmospheres which embrittle iron give random nucleation patterns for oxide growth.

V. STUDIES ON LOCALI?ED CRYSTAL GROWTHS

A. Early Work I

We distinguish phenomenologically between oxide nuclei observed on iron during the early s tages of oxidation a t 650°C to 850°C and the formation of long filaments of oxide observed by P f e f f e r k ~ r n l & ~ ~ i$ Germany and by Takagil4 in Japan in the early 1950's. In con- t rast to the nucleation s tudies of Phelps, Gulbransen and H i ~ k m a n , ~ Bardolle and Bknards and Gulbransen, McMillan and Andrew,' Pfefferkorn and Takagi atudied the edge of wires and fine holes in metal shee ts {fter oxidation using electron transmimion microscopy. Unfortu- nately, the metals used in the experiments were impure and the reaction conditions poorly defined. !

Oh first consideration, one might suggest that oxide nuclei and oxide whiakers could grow from the Bame nucleating s i t e s on the metal a s the initial oxide nuclei observed in low pressure oxidation. Howevtr, i t i s impossible to judge from the shapee and growth character- i s t i c s whether the same s i t e s are involved s ince the conditions of growth of nuclei on a nearly bare surface are very differknt from the conditions of growth found in thick oxide films.

In this paper we have attempted to extend the work of Pfefferkorn and Takagi by using pure metals and controlled Axidation environments.

B. General ~ireurr io ; of Method

In discuesing our dork on the growth of localized crystals during oxidation of metals i t i s essent ia l to make cle* the basic philosophy. We assume that dislocations, precipitates, impurities and s t r e s s give time to active s i t e s where localized oxide growths can occur. We a l so assume that the type and extent of the active mites and the activity of the s i t e s varies with the metal, the metal st'kucture, the oxide film, the environment, the s t r e s s level and the

volatility of the metal. If the active s i t e i e a property of the metal or oxide film then gas metal reactions offere a good way to obeerve the effects of the s i t e s ince the reaction producta must accumulate at the s i te .

Four factors are important in diecuesing the $row& of oxide nuclei and the growth of'. oxide whiskers and plateleta. Theee are a s followe: (a) crystal etrueture or atomic geometry of the unit cell, (b) cryetal s i ze and shape, (c) particle a iae and ahape, (d) orientation of the oxide particles with respect to the underlying metal and ( 8 ) t h e nature of the s i te in the metal or oxide reaponeible for the growth of the oxide cryetal.

The crystal structure i s studied by electron diffraction while crystal s i ze and shape are etudied in the electron microscope.

C. Experimental

Direct transmiesion electron microecopy and electron diffraction methode were used. Disc, wire and tensile tes t epecimens were used. The edge of a 5 mil hole in the 5 mil thick disc or teneile test specimens and the edge of a 9 mil wire were studied in the electron microscope. The wire and tensile t e s t epecimene could be s tressed or reacted under e t ress if de- aired.

Five mil thick Annco iron, Puron iron and a zone refined vacuum melted pure iron were ueed for making the apecimens. 9 mil wire was prepared from the high purity iron.

Some of the iron apecimena were reacted in the laboratory vacuum microbalance ayetemU a t 0.1 atm of pure oxygen. A liquid nitrogen trap waa ueed to lower the water vapor concentration to a dew point of -196OC. A second reaction system waa used to react the wire or tensile tes t specimens under etress or without etreee, in steam + argon, steam + oxygen mixture8 and in steam + oxygen plus HCl vapore. Steam atmospheres were prepared by bubbling welding grade of argon through deoxygenated water a t various temperatures.

Both an EMB4 and an EMU-3D RCA electron microecope were used. The lat ter instrument wae used a t 100 kv and had vacilit ies for taking micrographs at 280,000,direct magnification. The crystal structures were determined in the diffraction adapters of the electron microscopee using TlCl a s a standard.

D. Types of Oxide Growths Observed on Pure Iron

Three types of localized oxide cryetal growths are found when iron i s oxidized in oxygen or water vapor. Theee are: (a) thin whiekera, (b) blade-shaped platelets, and ( c ) fan-shaped

I. Oxide Whiskws

Thin oxide whiekers are the most common localized crystal $rowths to form on iron. Whiskers are found alone or in combination with platelets of oxide. We have observed that whiskers are formed when annealed pure iron is reacted with dry oxygen. A few small fan-shaped oxide also form in the early etagee of oxidation.

Figure 8 shows an electron micrograph of an oxidized disc eample of Puron iron. The specimen wae reacted for 48 hr. a t 500°C in an atmosphere of dry oxygen a t 0.1 atm. having a dewpoint of -196OC. ,

0

Figure 8 ahowe the whiskere to be 300-600 A ip diameter and 15,000 in average length. Some of the w h i ~ k a r s grew ~o lengths up to 75,000 A. A aurface &neity of 5 x lo7 to lo8 whiskers per cm2 was estimated. Studies on spceimsna oxidized fa5220 hr. a t 500°C in wet oxygen atmospheres showed whiskers having lengths y to 500,000 A.

Studies on oxide whiskers a t high magnification show that great care mult be used in using the electron microscope if contamination i s to be avoided. Figure 9 shows an electron micrograph of a small iron oxide whieker a t high magnification. The microgmph howa a heavy eheath of contamination around the oxide core. The central core wae 100 to 150 in diameter. This value ia in agreement with the minimum whisker thieknearr obrmerved by

I TakagiL4.

The identificiation of the outer sheath a s contaminant was proved by two experiments. Firs t , continued electron bombardment of the whisker caneed the outer sheath to grow in diameter a t a rate of 1 to 7 1 per sac. Secondly, photograph. of whisken taken quickly a t low beam-intend i e s show very lit t le contamination. The oxide whielcere formed a t 400°C i were 100 to 150 in diameter.

Electron diffrastion analyses ehowed the whiekerta to be h e x a ~ o n a l a-FeZ03 with the dhkl values agreeing to 0.1% of the x-ray diffraction values, No evidence was noted for exotic crystal habits observed by other w ~ r k e r s . l ~ * ~ ~ * ~ Some of these exotic cryatal habite may be introduced by electron bombardment and by contamination,

Intense electron bombardment of the whiskers melte the oxide a t the tip or a t othsr points along the whisker. These whiskers when re-oxidized do not grow a t the tip although some growth may occur in their thickness. Growth may etop due to destruction of the growth rstep a t the tip. Heating the oxide whiskers in pure hydrogen a t 500°C reduced the oxide whiskers to metal. 1

The exietence of oxide whiskers having ltngtha to diameter ratios of 5000 sugger t s a calculation of t h e maximhm stress a t the mot of the whisker. Using the tlexure f ~ r m u l a S = MC/I, we have calculated the maximum stress S for a whieker 500,000 A long and 100 A in diameter. Here M i s the maximum bending moment and I/C i e the section modulu~. A s t rcas of 510 g/cm2 was calculated. This i s a very low s t rees considering the length to diameter ratio.

2. Thin ~ l a d t - ~ h i p d Platelets

If annealed or cold-worked iron wire i e reacted with water vapor, thin blade-ehaped platelet6 of oxide are f o r d d in addition to oxide whiskers. The genesis of the blade-shaped oxide platelet is shown in Figure 1 0 for a reaction temperature of 400°C and a 10% water vapor + 90% argon atmosphere. The reeults are a l so shown in Table 2, During the first 2 hr. of refction, both whiskers knd platelet5 were formed on the wire. The whiskers ware 100 to 150 A in diameter and aversge 10,000 A in length. The platelets were very thin, lQOd to 1500 A wide and grew to 12ngths up to 10,000 A long. We c ~ t i m a t s d the thisknese of the oxide platelets to be 100 A or less. After 6 br. of reaction, most of the whiskers have disap- peared and platelets were observed. A s the time of reaction increases, the s i s e of the platelets i pxeaees . After 23 hra. of reaction the platelets were 2500 to 6000 A wide and up

8 2 to 70,000 A long. The surface density was of the order of 1 0 per c m . The platelets grew in a parallel arrangement along the axis of the wire. About 0.6% of the eurface area was involved i n the reaction to form platelets.

Table 2 showe the results of an electron diffraction analysis of the thin blade-ehaped platelete. The dhkl values could be correlated exactly with the x-ray diffraction valuee for a-Fe203. The ehape of the platelets suggest that the reaction of water vapor with annealed pare iron starts a t a point. A s reaction proceede, certain nucleating centers broaden to form an array of blade-shaped platelete. Figure 10c shows a whisker growing a t the tip of a platelet. It appeare that platelet growth has taken over after the whieker was formed. Such being the caBe, one might then postulate that the traneition from whisker to platelet occurs very rapidly once the transition conditions prevail, One explanation for the transition of whiekers to plateleta i s that hydrogen diesolves in the lattice of the oxide or metal and en- largee the reaction area along certain crystallographic direetione.

TABLE II

Cryetal Structure and Habit of Localized Growths Formed On Lon Wire at 400' At 0.1 atm H20 + 0.9 atm Argon

Time 1 Crystal Structure

I

3. Rounded Platelets

up to 30,000 A long; d e d t y z 3.0 x 107/cm2

0

few whiskare, J00-150 A dim.,: 30,600 A long

none

meny. w 1 5 0 d i h . , 10,000 A loq, on average

Effect of Time Cryeta1 Habit

WhiaLere .-a

none

Plmtelete 0

maay,olOO A thick, 1000 too 1500 A wide; up to 10,000'A

7 2 long; density 2 2.0 x 10 /cm

0

many,olOO A thick; 2000 too 3000 A wide; up to 30,000 A long; density 2 ::08/mu2

0 manyglOO A thick; 2000 too 4000 A wide; up to 60,000 A long, dendty 2 1o8/cm 2

0

many,olOO1 A thick, 2500 too

6000 A wide; up to 70,000 A long; density 2 1o8/cm 2

Thin rounded platelete of oxide are farmed when cold-worked iron i s reacted with dry oxygen. Figure 11 ehbwe an electron micrograph of the crystal habit of the oxide film formed daring the oxidation of cold drawn iron wire a t 400°C for 48 hr. in 1.0 atm. preseure of ,dry oxygen.

Thin oxide platelete grow penendicularly along the axis of the wire to a height of 40,000 1 and to Len the op to 70,000 A. The thickncm of tho platelets was e~ t imated to be of the order of 100 f or the aame ae that found for the blade-shaped platelets. Internal and external etress wae probably important in the of oxide platelet^, The thickneee of the platelets appeare to be uniform over the platelet and appears to be the same for a large number of plateleta examined irrespective of oxidation time, Electron diffraction analyses show the oxide plateleta to be hexagonal a - Fe 0 . Streme calculatione a t the root of the platelets show valuee similar to those calculate 5 / or the oxide whiskers.

E. Discussion of Localized Growths

Two interpretation8 may be given for the origin of localized oxide growths. They may ar ise from nucleation s i t e s within the oxide layer or t hey may ariae from.hucleation e i tee in the metal. Le t u s consider, the two interpretations.

U-Fe203 and Fe304 are formed on iron when oxidized below S ~ O ~ C . ' ~ Electron diffraction etudies have shown that Feg04 is formed adjacent to the metal and a - F e Z 0 3 in the outer layer i ncon tac t with oxygen. Since the localized growths ere a -Fe2O3, i t is probable that the a - F e 2 0 3 crystals are nucleated on the FegOg interface a t c e r t a ~ n defects in the oxide structure. These ei tee could be areas of local s t reea in the oxide film, crystal boundaries, etc.

On the other hand, Bardolle and BQnard,5 and Gulbransen, McMillan and and re^,^ have shown that oxidation irs a discontinuous process. Oxide nuclei are observed a t a very early s tage of the oxidation process. These experiments euggert that oxide whisker growth may be a continuation of chemical reactivity a t the same nucleation eitea brought out by low- pressure oxidation. Gulbransen and Andrew8 have shown that the pattern of the nucleation s i t e s can be changed by annealing in hydrogen. Annealing in hydrogen leader to a linear type of nucleation pattern.

These observations together with the experimental work of this paper lead us to suggest a reaction mechanism in which the metal structure iteelf determines the localized crystal growths. The mechanism i~ supported by experimental observations that chemical composition of the metal, chemical environment and s t r e s s have major influence on the chemical reactivity of metals.

Figure 12 shows our interpretation of the formation of localiaed oxide growths in oxygen and in water vapor. Figure 12a shows a nearly random pattern of nucleation s i tes . We poetulate that a metal having this pattern of nucleation ei tee reacts with oxygen to form fine long whiskers of oxide in addition to the normal oxide film.

Figure 12b ehows our interpretation of the nucleation pattern of a cold-worked specimen of iron. An ordered arrangement of nucleation s i tee is formed in the metal by the metallurgical treatment. P la te le t s of oxide are formed whbn a metal having this metallurgical etructtue is reacted with oxygen. Line growth of oxide i s formed. The minimum$iatance between s i tee h a s not been determined but probably in of the order of a few 100 A to a micron.

Figure 12c shows the nucleation pattern after water vapor has reacted with ir,on. After reaction, pointed and blade-shaped oxide platelets are formed. Th i s fact sugges ts that water vapor during reaction ac t s to enlarge the reaction ei te pooeibly along certain cryetallographic directions. We poetulate that hydrogen ions from the water vapor reaction diffutie into the metal at 400°C and modify the impurity distribution or the nucleation s i tee. The water vapor generates new reaction s i t e s as reactio occurs. However, the growth of the reaction 8 eite appears limited to a width of about 8000 .

Earlier work has suggested that reaction occurs by surface diffusion of metal ions to the growth s tep a t the tip o f the whisker or platelet where reaction with oxygen occure. Th i s mechanism ie supported by the fact that localized melting of the whieker tip s topa growth of the whisker. We have confirmed this observation of TakapLU We have a l so noted that vacuum annealing doe8 not affect the length of the oxide whiskers. In the absence of oxygen no growth occurs. i ,

I

VI. EFFECT O F MOISTURE ON THE CORROSION O F IRON

The effect of humidity on the corrosion of iron i s well known. ~ u d s o n " and more recently CopsonlB have compared the rate of corrosion of ingot iron spec i rnen~ in dry and moist cli- mates and in industrial and marine atmospheres. Ingot iron in the dry atmosphere of Khartoum corroded at a rate of 28 millionths of an inch per year while a specimen in the wet country atmosphere of Llanwrtyd Wells corroded a t a rate of 1888 millionths of an inch per year. ' Ob- servations of this kind led vernonlg to make critical laboratory etudies on the effect of humidity on iron. From these studies he developed a generalization known a s the "Principal of Critical Humidity." For iron a t 2!j°C, the rate of corrosion increaeed rapidly for humidities above 65 percent. Dry oxidation changed to a rapid electrochemical reaction. Local electrochemical action was assumed to take place between local anode and cathode areas through an invisible adsorbed film of water.

Thia model of localized electrochemical action i s the bas is of present-day interpretation of wet corrosion. For pure single phase metale the s i t e s for local cathodes and anodes have not been identified. Par t of the difficulty i s that liquid phase corrosion reactions on iron are complex since hydrated oxides are often formed and the corroding metal ie often removed from the reaction aite.

To ehow the effect of water vapor on the corroeion of iron we will compare the reaction of pure zone refined iron wiree with oxygen, water vapor and several mixtures of water vapor and oxygen. For these gas phase conditions, electrochemical action and ~ o l u t i o n of the corrosion product in the liquid phase are eliminated. The complex hydrated oxides also are not stable.

Figure 13 shows four transmission electron micrographe of the crystal habit of the localized corrosion products. The specimens were reacted a t 4S0°C for 48 hrs. in the following atmospheres :

1. dry oxygen having a dewpoint of -78.S°C,

2. 1 0 percent water vapor + 90 percent argon,

3. 1 0 percent water vapor + 90 percent oxygen, and

4. 3.13 percent water vapor + 96.87 percent oxygen.

The latter gas mixtures have 02/H20 mole ratios corresponding to 70 percent and 21 percent humidity in air a t 25OC.

Figure 13a shows oxide whiskers formed when iron was reacted with dry oxyggn. These whiekera were 100-150 K in diameter and grew to an average height of about 5000 A. Electron diffraction analyees showed the whiskers to be only a - F e 2 0 These whiskere were formed in f addition to the normal oxide film. Figure 13a sugges ts that t e nucleation s i t e s on the metal or on the oxide were 100-150 A in diameter. Since the diameter was constant along the length of the whisker, we conclude that the area of the nucleation s i tea were not elongated a s the whisker grew. The area of the nucleation s i te appeared to be independent of time or the extent of oxidation.

Figure 13b shows the crystal habits formed when iron reacts with a 1 0 percent water vapor + 90 percent argon mixture. Many tbin pointed blade-shaped g la te le t s were formed. These were 100-150 X thick, about 7,000 A long, and about 70,000 A high. Electron diffraction analyses showed these to be only mFe203. The surface density of the plateleta was estimated to be about 108/crn2.

-125-

The shape of the oxide platelets suggests that the site for reaction enlarges ae the reaction proceeds, whereas in the iron-oxygen reaction the area of the site remains constant. The uniform thickness of the platelets suggests that the width of the nucleating area remains constant. One ax- planation for the effect of water vapor i s that hydrogen atoms or ione from the water vapor act to enlarge the area for reaction.

Figures 13c and d show the crystal habits of the eorro'eion product when iron was reacted with mixtures of oxygen and water wpor corresponding to mole ratios of 0 /HZO of 30/1 and 9/1. Oxide

wen the predominant crystal habit for both environments. $0 prevent the growth of oxide platelets the 02/H20 ratio must be increased to a high value. At 450°C the influence of water vapor on the localized corrosion process i s much greater than its influence on the corrosion of iron at room temperature. We conclude that Vernon's "Principle of Critical Humidity" can be extended to the gas phase corrosion reactions of iron. ;

. Let us consider in more detail the localized growths observed after reacting iron in oxygen and in water vapor plus argon atmospheres. Assuming the same surface density for the whiskers and platelets, the electron micrographs suggest that the reaction aites in the metal for the water vapor reaction are over 50 times the area of those observed for the dry oxygen reaction. The total mount of oxide in the oxide plateleta is about 250 times the amount of oxide in the oxide whiskera.

These experiments may help to explain the unique effect of water vapor on the corrosion of iron at ambient temperatures. Certain differences of course exist. The corrosion rate will be slower, hydrated oxides may form instead of U - F ~ ~ O , the corrosion prbduct may dissolve in the liquid phase, and electrochemical action may be present. B he factor which has not been foreseen in earlier studies i s the effect of water vapor itself on the reaction site without electrochemical action.

To control the corrosion of ingot iron in humid atmospheres, two factors must be considered in addition to any electrouhemical effects. Hydrogen hom the water vapor reaction with iron must be prevented from entering the metal, and growth of the localized reaction sites must be inhibited by the addition of suitable alloying elements.

VII. EFFECT OF STRESS ON THE CORROSION OF IRON AND STAINLESS STEEL

We have classified stresseffects into three typee: (1) internal stress due to cold work, (2) internal atreaa due to precipitation of a aecond phase, and (3) externally applied stress.

A. Effect of Cold Work ,

The effect of stress introduced by drilling a 5 mil hole in Annco Iron was studied. One specimen was drilled and then annealed in high vacuum of less t h h 1r6 mm of Hg at 850°C for 16 hours. A second specimen was vacuum annealed before drilling the hole. Both specimens were reacted at 500°C in oxygen at 0.1 atm for 66 hours without external load. Figure 14 shows electron micrographs of the two specimens after oxidation in dry oxygen. Small whiskers of a-Fe203 are found on the specimen drilled before annealing. For the specimen drilled after annealing, both whiskers and platelete of oxide are found. Stress introduced by cold working has a large influence on the extent of whisker growth. h addition, a large number of platelets of oxide form a~ a result of cold work.

6. Effect of External Stress

Two samples of 9 mil 304 stainless steel wire in the "as received" and cleaned condition are reacted at 500° C for 24 hrs. in 0.1 atm of dry oxygen. .A stress of 44,000 psi i s applied externally during reaction to one specimen, while a aecond specimen i s reacted without s t ress .

Figure 15 shows electron micrographs of the two 304 s ta in lese eteel eurfacee. The apecimen reacted under no s t r e s s conditions shows no unusual crystal habits in the oxidation products. However, the specimen reacted under a s t r e s s of 44,000 ps i shows a few well- de- fined platelet growths on certain a reas of the eurface.

The platelets grow along straight linee parallel to the axis of the wire. In addition, certain areae, 2~ on a n edge, show a concenuatign of oxide platelets. This i s shown in Figure 16. The platelets are of the order of 100 A thick, 30,000 1 high, and grow to lengths of 60,000 1. No whieker growths are observed. We conclude that s t r e s s i s a major influence on the crystal habits of the reaction producte formed when 304 s ta in lese s tee l i s reacted with dry oxygen.

VI I I . IN IT IAL STEP IN STRESS CORROSION CRACKING

Stress eor ro~ion cracking of s ta in less s t ee l s in high preeaure water-water vapor atmospheres a t 300°C i s the cracking of the metal under combined influence of etress and corrosion. The usual method for study i s to expose U bend apecimens in autoclaves. HOW- ever, only empirical information can be obtained from such teste.

Two etepe are ueually associated with s t rees corrosion cracking. These are the initiation of the crack and the propagation of the crack. The initiation etep i s probably one of localized corroeion under the influence of strese. It is usually assumed that crack initiation i i t i e d up with a special driving force which ac t s to give a highly localized corrosion re ac tioq.

Gulbransen, Copan and van FtooyenlB have proposed that a etudy of localized growths in gae phase reactions can lead to an underatanding of the initiation s tage of the s t ress corroeion cracking phenomenon.

We can simulate a s t reee corrosion system by ueing a reaction atmosphere of oxygen, water vapor and a trace of chloride ion in the form of a trace of hydrochloric acid. Streae can be introduced by an initial strain or by reacting under s t ress .

Table 3 ahows the resul ts of applying different loads to the s ta in lese s tee l wires, Increaeing the s t r e s s level in the material favors the growth of platelets. At the highest s t r ee s level large alone were formed. Figure 17 showe an electron micrograph of t h e m formed a t 600°C in wet oxygen t a trace of HCl in 138 hours under an initial e t ress level of 59,000 psi. Electron diffraction atudies showed the grvwthe to be the hexagonal oxide X203 where X was either iron or chromium.

Figure 18 ehowa a achematic diagram of how localized chemical reaction can lead to the formation of sub-microscopic trenches or cracks in the metal. Figure 18a ahows an oxide platelet formed a s a resul t of gae phase reaction of an ordered arrangement of nucleation sites. A deep trench may form at the root of the platelet. Although we have not demonstrated the existence of a narrow trench, the length to thickness ratio of 1000 to 1 for the platelet suggeste that the source metal for the oxide platelet must be very localized. The formation of trenches a few hundred angstroms in thickness can lead to a high stress concentration and to a condition for propagation of the crack nuclei.

TABLE Ill

Effect of Strain on Crystal Habit, Corrosion of 304 Stainless Steel,

Wet O2 + Trace of HC1 Vapor, 600°C, 138 Hrs. of Reaction

Strain

41,000 ps i

Crystal Habit

Platele s 100 1 thick, up to 30,000 9, high and long. Whiskera 300-500 A diameter up to 40,000 1

52,000 ps i

Figure 18b shows a schematic drawing of how localized chemical or electrochemical reaction can occur for liquid phase reactiona. We asaume the metal has a set of aligned nucleation s i t e s a s was demonstrated in Figure 1 5 and ehow ehcematically in Figure 18a. 8. The thickness of the active area for reaction was about 100 in Figure 15. In liquid phase reaction the corrosion product may dissolve and a s a resul t may not accumulate to form a coherent oxide structure. Again, we postulate the formation of a UEtROW trench which leads to a high s t r e s s concentration and conditione for propagation of the crack nuclei.

P la te le t s 100.X thick, up to 60,000 A high and long. Whiskers - a few

59,000 ps i

The chemical and electrochemical conditions of liquid phase reaction suggest that more rapid localized corrosion may occur than in gas phase reactione. Some of these conditione are: (1) diffusion of the metal ion through or on the surface of the oxide platelet ia not necessary, (2) local electrochemical ce l l s may accelerate the rate of localixed corrosion, (3) pH shif ts may occur a t the s i te of reaction which could accelerate the rate of reaction, and (4) a sharper radius of curvature and larger s t r e s s concentration may exis t a t the root of the trench if a coherent metal oxide structure is absent.

P la te le t s 100 1 thick, up to 100,000 1 high, 200,000 1 long. Whiskers - none

Although much experimental work remains to demon~tra te the role of this new structure element, we fee l that some evidence supports our point of view. Studiee on 20 chromium-80 nickel al loys and pure nickel showe no evidence for platelet types of oxide gowtha. These materials are reported to be l e s s sensitive to s t r e s s corrosion cracking.

IX . NEW MATERIALS

Three crystal habits hhve been demonstrated in this paper: (1) oxide whiskers, (2) oxide blade-shaped and (3) oxide rounded platelets. Selected area electron diffraction s tudies suggest that these crystals are probably s ingle crystalr.

Calculations show that these corystals have very high elast ic strain limit^. Thus, a 150 1 diameter whisker bent to a 1500 A radiurr gives an estimated elast ic strain limit of a t l e a s t 5 percent. Due to the difficultiee of handling 150 diameter whirrkerer direct measurements of the strength has not bee; carried out.

If these whiskers and platelete have high strengthe which are characteristic of metal whiskers w e may have new structural materiala which have high melting points, low vapor pressures, high elaat ic yield lirnite, non-corrosive and perhaps high strengths. The big problem is to find a practical way of growing and processing these crystals into usable shapes and sizes.

A. . Oxide Nucleation

Useful information can be obtained on the growth of oxide films a t high temperature from a study of the crystal habit and structure of the oxide film. These films are formed by reaction with limited quantitiee of oxygen a t low preeeures.

Electrochemical-stripping techniques were ueed to remove the oxide layer from the oxidized samples of highly annealed and electropolished iron. These samples were then studied in the electron-diffraction camera and electron microscope.

Several s t ages in the oxide-gowth process were studied over the temperature range of 650' to 8S0°C using different amounts of oxygen a t low pressures.

The resul ts suggest that the initial s tage of oxidation involves the formation of a thin uniform layer of small oxide crystallites. This was rapidly followed by the formation of much larger oxide crystals along certain parallel and regularly spaced lines on the metal grain. A s oxidation continues, the oxide crystals grow, and new crystals form filling the remaining area of the metal surface. Th i s results in the formation of a uniform mosaic of large oxide cryetals.

The origin of the l ines of $rowth of the oxide crystals on the metal may be related to the hydrogen annealing process.

It i s a lso concluded that the concept of a uniform growth of a n oxide film must be diecarded.

B. Localized C r y s t a l .Growths

Electron microscope and electron diffraction s tudies show several unusual crystal habits of the oxide film to occur when iron 4s oxidized in oxygen or water vapor atmospheres. These we (1) fine oxide whiskers 100-150 A in diameter, (2) r p d e d platelets of oxide about 100 di in thickness, and (3) blade-shaped platelete about 100 A in thickness.

In dry oxygen atmospheres whiskers grow on annealed pure iron specimens. Blade- shaped platelets grow in water vapor or in mixed water vapor and oxygen atmospheres. Rounded platelets grow on iron containing impurities when s t reas i s present in oxygen atmospheres.

Impurities, s t r e s s and environment appear a s critical factora in determining the type of growths of localized oxide crystale op iron.

Water vapor has a unique action in the corrosion of iron. Water vapor acts during reaction to increase the area of the s i te for localized reaction from a point s i te to a line site. This leads to a large increase in the extent of localized action.

The surface density of the whiskera and blade-shaped platelets i s of the order of 10*/cm2. The fraction of the surface area involved in oxide whisker formation i a l e a s than 0.1 percent.

If the origin of the nucleation sites and the mechanism of growth can be determined, we will then have a better understanding of corrosion and the substructure of metal@.

ACKNOWLEDGMENT

The author is greatly indebted to h i s present associates , Mr. K. ,F. Andrew and Mr. T. P. Copan and to h i s earlier aeaociates, Dr. ,R. T, Phalpa, Dr. J. W. Hickmen and Mr. W. MeMillan for carrying out most of the experimental work upon which thie paper ia based,

Recommended Research Activities

I . , Techniques

A. Develop furnaces, reaction s y ~ t e m s and methods for determining the kinetics of reactions a t temperatures above 1200°C. Progress in the field of high temperature s tudies are seriously limited by the present s ta te of technology in ceramic ware, furnace systems, temperature measurement and methods for measuring resction kinetics.

B. Develop methods for the determination of crystal structure and composition of thin and thick filme on metale "in situ" above 1200°C. Both x-ray diffraction and electron diffraction methods must be considered. Again, progress in the field of high temperature s tudies is limited by lack of structural facilities.

I / . Problems

A. Study of the role of metal structure including dislocations, impurities, inclusions and s t r e s s on the mechanism of oxidation of metals and the formation of localized growth a t the oxide-gas interface.

Th i s problem was diacuaeed i n my lecture to the 8th Sagamore Conference. I person- ally feel that a great deal of useful knowledge can be gained in these studies.

B. Oxidation of Alloys Having High Temperature Possibi l i t ies

1. Phase diagram studies of the oxides, 2. Crystal structure studiee, 3. Adhesion studies, 4. Kinetics of oxidation, 5. Composition studies, 6. Study of role of various alloying elements.

The object of these atudies would be to understand the basi.c processes occurring in the oxidation of alloys. Few people have tried to etudy the complete problem.

C. Mechanism of Oxidation of Refractory Metals and Alloys

1. Role of aolution of oxide in metal, 2. Mechanism of breakdown of oxide film, 3. Nucleation and growth of higher oxides, 4. Effects of impurities and alloying elements on the oxidation processes, 5. Cryetal structure etudies.

The mechanisms of oxidation of the refractory metals molybdenum, tantalum, niobium and tungeten are not understood. To attack these problems requires a large effort coordinat- ing many techniques. A number of groups have made a s ta r t on this problem but a new imaginative approach i s needed.

0. Reactions of Pure Metals and Alloys In HZO, H 2 0 + H2, CO + C02, CIZ, SO2 and Other Gaa Atmoephere~.

A few studies of gas &actions in t h e w atmospheres have been made but mach more work could be done. 1

E. Studiea on Oxide ~ h i i k e r s and Pla te le t s

1. Crystal structure and orientation on the metal, 2. Methods for study of mechanical properties and electrical proper tie^, .3. Methods for harvesting, aligning and consolidating crystals into fibers or aheets, 4. Application of new materials.

These s tudies are aimed a t finding whether these unique.cryatals cen be ueed to make new materials, These crystals appear to be elast ic , non-conoaive and strong. This project must be carried out by sc ien t i s t s of proven imagination.

REFERENCES

1. Wagner, C., "Diffusion and High Temperature Oxidation of Metals," in Atom Movements, A.S.M., Cleveland, 1951, p. 153.

2. Benard, J., Bull. Soc. Chim., France, 1949, pp. 73-87.

3. Chipman, J- and Murphy, J. W,, ~ndustrial and Engineering Chemistry, 25, 319, (1933).

4. Phelpe, R. T., Gulbransen, E. A., and Hickman, J. W., Industrial and Engineering Chem. 18, 391, 1946.

5. Rardolle, J. and Bhnard J,, Rev. Met., 49, 613, (1952).

6. Bdnard, J., Private Communication.

7. Gulbraneen, E. A., McMillan, W., and Andrew, K. F., Trans. Am. Inst. Mining Met. Engrs., 200, 1027 (1954).

8* Gulbraneen, E. A., and Andrew, K. F., Jnl. of the Electrochem. Soc., 106, 551, (1959).

9. Stanley, J. K., Trans. Am. Soc. Metals, 44, 1097 (1952).

10. Mehl, R. F., and MeCandlese, E. La, Trans. AIME 125¶ 531, (1937).

11. Gulbraneen, E. A. and Ruka, R. J.¶ ~ndmirial and Engineering Chemistry, 43, 697 (1951).

12. Pfefferkorn, G,, Naturwiss. 40, 551 (1953).

13. Pfefferkorn, G., Z. Metallkunde, 46, 204 (1955).

14. Takagi, R.,. J. Phys. Soc., Japan, 12, 1212 (1957).

15. Gulbransen, E. A., Advances in Catalysis, Vol. V., Academic Press, N e w York, pp. 119-175 (1953).

16, Hickman, J. W., and Gulbraneen, E. A., Trana. AIME, 171, 306 (1947).

17. Hudeon, J. C., ''Corrosion of Iron and Steel," Chapman and Hall, 1940, p. 93.

18. Copson, H. R., Corrosion, p. 533 (1959).

19. Vernon, W.H.J., Trans. Faraday Sot., 23, 162, 1927 - Trans. Faraday Soc. 27;264, 1931.

20. Gulbransen, E. A., Copan, T. P., and van Rooyen, D., Westinghouee Reeearch Laboratories, Scientific Paper 6-94602-1-R5, September 18, 1957.

@ ELECTRON HOLE Me 3+ I

0, ~ e * + VACANCY

OXlDAf ION SCHEME

FIGURE 1

OXIDE FlLM O F IRON

F e 30-250

o. E.M. STRIPPED FILM c E.D.R. FILM ON METAL b. E.D.T. STRIPPED FILM d E.M. STRIPPED FILM

6 L.M. FlLM ON METAL

19-066- l722/OR D-6 1

F I G U R E 2

OXIDE FlLM OF NICKEL

Ni 5-500 a E.M. STRIPPED FlLM b. E.D.T. STRIPPED FlLM

c E.D.R. FlLM ON METAL d. L.M. FlLM ON METAL

FIGURE 3

FIGURE 4

OXIDE FILM STRIPPED FROM PURON ANNEALED INHYDROGENPASSEDOVERHOTCOPPER.

H2- 850'C- 20 HRS. -COOL IN H2

A. 752; THICK OXIDE - 850%

6. 322; THICK OXIDE - 750%

FIGURE 5

CIRCULAR GROWTH PATTERN IN OXIDE FILM (7521) FORMED

ON PURON ANNEALED IN HYDROGEN PASSED OVER HOT COPPER.

H2- 850°C - 20 HRS. -COOL IN H2

19-066-1729/0RD-61

OXIDE FILM (453A) STRIPPED FROM VACUUM PRETREATEDPURON

VACUUM- 875% - 20 HRS.

FIGURE 6

FIGURE 7

F I G U R E 8

FINE OXIDE WHISKERS FORMED ON "PURON" AT W)O°C I N DRY OXYGEN FOR 48 HOURS. NO APPLIED STRESS. MAG. 8000X l9-066-l726/ORD-6 1

FIGURE 9

CONTAMINATION ON OXIDE WHISKERS FORMED ON "ARMCO" IRON. MAG. 90,000X

BLADE-SHAPED OXIDE PLATELETS FORMED ON ANNEALED PURE IRON IN 10% H20 AND 90% ARGON AT 400°C.

(A) 2 HOURS, (6) 6 HOURS, (C) 12 HOURS, (F) 23 HOURS.

19-066 l73O/ORD-61

FIGURE 10

ROUNDEDOXIDE PLATELETSFORMEDONCOLD WORKED PURE IRON IN 1 ATMOSPHERE OF DRY OXYGEN AT 400PC FOR 48 HOURS

FIGURE 11

FIGURE 12

EFFECT OF MOISTURE ON CRYSTAL HABITS OF THE CORROSION PRODUCTS FORMED ON IRON AFTER REACTING AT 450°c FOR 48 HOURS I N (A) DRY 02;

(8 ) 10% H20 + 90% Argon, (C) 1096 H 2 0 + 90% 02; and (D) 313% H 2 0 + 96.87% 02-

LA,

FIGURE 13

E F F E C T O F COLDWORK ANDANNEALINGTREATMENTOFOXIDES FORMED ON "ARMCO" IRON. (a) HOLE DRILLED BEFORE AHHEAL, (b) HOLE DRILLED AFTER ANNEAL.

FIGURE 14

EFFECT OF TENSILE STRESS ON CRYSTAL HABIT OF OXIDE FILM FORMED ON 304 STAINLESS STEEL. OXIDIZED 24 HOURS 0.1 ATMOSPHERE OF OXYGEN AT 600°C (a) NO APPLIED STRESS, (b) 44,000 p.s.i.

FIGURE 15

OXIDE PLATELET GROWTH 304 STAINLESS STEEL. OXIDIZED 24 HOURS 600°C, 0.1 ATM. OXYGEN. STRESS OF 44,000 P A I .

FIGURE 16

CRYSTAL HABIT OF OXIDE FORMED IN THE OXIDATION OF 18-8 STAINLESS STEEL AT 600°C IN WET OXYGEN PLUS TRACE OF HC1 VAPOR FOR 138 HOURS. PRE-STRESSED TO 59,000 p. s. i.

MAGNIFICATION: 9000 X

FIGURE 17

Cathodic b$ O2 t H,O + 2e 2 20H- or

A - Gas Phase Reaction B - Liquid Phase Reaction

TRENCHING BY LOCALIZED CORROSION

1 9 4 6 & 1 6 9 4 / 0 ~ ~ d l Rkl 15105

FIGURE 18

GRAIN BOUNDARY BEHAVIOR I N HIGH TEMPERATURE DEFORMATION AND FRACTURE

Dr. Arthur W. Mullendove

and

Dr. Nichols I . Grant

SECT ION I. I N T R O D U C T I O N

P r o g r e s ~ in the p a s t ten years in our understanding of the nature of grain boundaries and boundary p rocesses h a s been marked, but a great dea l h a s yet to be uncovered, a s i s evidenced by the volume of research which regularly appears in the literature. Historically, in teres t in grain boundaries in metals began in the l a te nineteenth century, when i t w a s noted that the boundaries between c rys ta l s exhibited a variety of character is t ics which were different from those of the c rys ta l s themselves. T h u s , Rosenbain' was led to regard the metall ic structure a s consis t ing of c rys ta l s cemented together by a layer of the same material in the amorphous s ta te . T h i s theory w a s used to explain the apparent difference in the temperature dependencies of the properties of grains and grain boundaries, a s evidenced by grain boundary deformation and intercrystall ine failure a t high temperatures, in contrast t o crysta l l ine deformation a t low temperatures. Most of the other observed properties of grain boundaries and grain s i z e e f fec t s in meta l s were interpreted in terms of the amorphous grain boundary concept. In 1924, Jeff r ies and Archer2 suggested the transit ion la t t ice concept of the grain boundary, and th i s s e t the s t a g e for much of the recent thinking concerning the nature of the grain boundary.

Several excel lent reviews of research on the nature of the grain boundary and grain boundary phenomena in metals have appeared in recent years. T h e s e include the works of McLean3, Weinberg4, and Arnelinckx and Dekeyser5, who have exhaust ively reviewed the important research in th i s area. Cifkins6, in addition, haa reviewed research in grain boundary s l id ing and fracture.

I t s h a l l not be the purpose of t h i s paper to review with the same thoroughness and deta i l a l l of the experimental r e su l t s in recent years on grain boundary phenomena, but rather to re ly on the ex i s t ing reviews a s background and then to s e l e c t particular i tems of research (when possible , from the authors ' laboratory) to indicate the trends of r ecen t work in th is field. We sha l l further limit the d i scuss ion to properties of grain boundaries which re la te to the e levated temperature behavior of grain boundaries.

S E C T I O N 11. S T R U C T U R E OF T H E G R A I N BOUNDARY

D i s l o c a t i o n Structure of Boundar ies

T h e modern theory of the structure of the grain boundary i s dominated by the concept of the transition la t t ice which supposes that near the boundary the atoms occupy their correct la t t ice posi t ions except for a layer one or two atoms thick right a t the boundary. T h i s concept was evolved into the dislocation structure of the grain boundary by BurgersB in 1939, in which he descr ibed the pure "tilt" and pure "twist" grain boundaries. With t h i ~ boundary structure,

a cont inuous transit ion between the two l a t t i c e s i s achieved by a n array of equal ly spaced dis locat ions . The ex i s t ence of this type of boundary h a s been wel l e s t ab l i shed in subsequeni years by di rect observatiorq7, and the dis locat ion model of the grain boundary h a s been ex-

tended to more general c a s e s involving both t i l t and twis t , that i s , re la t ive rotation of the l a t t i ces about a n a x i s lying both in and perpendicular to the grain boundary plane with various combinations of d is locat ions . T h e dis locat ion structure of the grain boundary h a s been d i s - c u s s e d very fully by Amelinckx and Dekeyse r5 , and only a brief summary wi l l be given here to re la te the s t ructure of the boundary to experimental observat ions .

T h e pure t i l t boundary, as defined by Burgers8 i s shown in Figure 1, which i l lus t r a t e s the symmetrical d isposi t ion of the gra ins about the grain boundary plane, whose normal is perpendicular to the pure edge dis locat ion l ines and which conta ins d i s loca t ions of just one type. A more general t i l t boundary, descr ibed by Read and Shockley9, i s shown in Figure 2. Again the grain boundary plane conta ins only edge d i s loca t ions and the or ienta t ions of the two grains are re la ted by a s imple rotation about an a x i s perpendicular to the Burgers t e c t o r and para l le l to the dis locat ion l ines . In t h i s c a s e , however, the boundary plane is no longer a symmetry plane for the bicrystal . T h e construction of a pure t i l t boundary with s u c h charac- t e r i s t i c s demands tha t d is locat ions of more than one kind be used. T w o t y p e s of edge dis loca- t ions with mutually perpendicular Burgers vectors are n e c e s s a r y for the description.

T h e second type of boundary, the twis t boundary, i s formed by a rotation of the la t t ice abou t a n a x i s perpendicular t o the boundary plane. A dis locat ion s t ructure of th i s type of boundary c o n s i s t s of two s e t s of para l le l screw dis locat ions which form a square array in the grain boundary plane, a s depic ted in Figure 3.

Using t h e s e two b a s i c boundar ies , i t i s poss ib le t o construct any grain boundary by appropriate combinations of the two; and one can do th i s without difficulty for low angle boundaries. A difficulty is encountered, however, with high angle boundaries in tha t the spac ing of the dis locat ions n e c e s s a r y t o produce the large angular difference between the adjacent gra ins is such that the d i s loca t ions become unresolvable. Since d i s loca t ions have around them a disturbed redion cal led the core, they l o s e their individuali ty when separa ted by l e s s than a certain cr i t ic le d i s t ance . I t t hus becomes n e c e s s a r y to develop a separa te model for high angle boundaries to expla in thei r properties.

Boundary Energy

The dis locat ion model of grain boundaries h a s been we l l e s t ab l i shed for boundaries of low angular misorientation both by di rect observat ions of the dis locat ion dens i ty in boundaries of a g iven misorientation ( s e e Figure 4) and by measurements of grain boundary in terfacia l energy, comparing the experimental r e s u l t s wi th the Read-Shockley equation for the energy of a grain boundary. Direct observat ions of e t c h pi t d e n s i t i e s on low angle boundaries are limited to very smal l angwlar misorientations because the resolut ion of the e tch pi t method i s low. How- ever, t h e d i s loca t ion model of the grain boundary a t a n g l e s l e s s than l degree h a s been c lose ly checked by th is method. S tud ies of the energy of grain boundaries in a number of mater ia ls have been made e i ther by measurement of d ihedral ang les formed by in tersect iong boundaries of t r icrys ta ls , or of the angle of the trough formed a t the in te r sec t ion of a grain boundary with a surface af ter thermal etching. chalmers16 and Weinberg4 have summarized invest igat ions in t h i s area.

Read and Shockley have shown that the energy, E, of the boundary is given by the equation

where Eo and A are cons tan t s for a given material and B is the angular misorientation of the boundary. The equation applies to pure twis t or pure t i l t symmetrical. boundaries. If the boundary i s not symmetrical, Eo and A become var iables where E o i s l inearly proportional to the to ta l densi ty of d is locat ions , and A var ies in a complicated way with the orientation of the grain boundaryg. T h e Read and Shockley equation can be put into a universal form3, applying to any material, by differentiating the grain boundary energy with respec t to 8, which g ives

and s i n c e the curves of E veraus 8 l eve l out a t a maximum s e t s aE/a€' equal to zero and obtains % 0, = A-1 when E into (1) and dividing the resu l t into (I), we obtain:

value, E m , a t some value dm, one = Em. Substituting- t h e s e . v a l u e s

Da ta from a number of invest igat ions on the ,energy of t i l t boundaries in various materials a re presented in Figure 5. T h e sol id l ine ind ica tes the theoretical curve of equation (3) f i t ted t o the data . It i s s e e n that there is good experimental agreement with the ReadShock ley equation up t o and beyond 0 a 8, which occure a t various misorientations for different materials, from 12 t o 30°. More recent d a t a for s i lve r l3 show that the value of 8, occurs a t even higher values (3S0) than for lead and tin, and the ReadShock ley equation holds up t o 0 of about 35'. Wagner and ~ h a l m e r s ' ~ have determined relative boundary e n e r ~ i e s for <loo> - t i l t boundaries in germanium for 0 up to 46' and found no sharp discontinuity of energy values for orientation dif ferences above that for which the Read-Shockley equation appl ies , and c u s p s in the relative energy boundary curve which might be aasocia ted with twin type interfaces are rare (See Figure 6). In s i lve r chloridelb, when t i l t boundaries with various crystallographic a x e s of t i l t a re examined, i t is found that different curves are obtained for the grain boundary energy as a function of orientation difference (Figure 7).

It should be emphasized tha t dihedral angle measurements yield only a boundary energy re la t ive to that of a large angle randomly oriented boundary of the same material. Thus , i t is qui te possible that the matching of the da ta with the form of the Read-Shockley equation a t fa i r ly large va lues of 8 may be fortuitoua. Absolute values of boundary energy are necessa ry for a true t e s t of the equation. C j o s t e i s and ~ h i n e s " have determined s u c h va lues for copper and find that the equation holds for mieorientations up to 5 or 6 degrees (dislocation spac ings of 1 0 atom diameters). Above this (up t o 16') other treatments of grain boundary energy, such a s van der Merwe'sfs, which account for the non-Hookian e l a s t i c s t ress-s t ra ined behavior near the core of dimlocations, agree better with the data.

Grain Boundary Melting

T h e grain boundary melting experiment in another which haa been uaed t o obtain some idea of whether or not the transit ion from the re la t ively low angle boundaries, which obey the Read- Shockley equation, to high angle boundaries with more or l e s s constant grain boundary energy i s del ineated in any c lear way. Weinberg4 haa summarized the melting behavior of grain boundaries a s follows:

(1) Large angle grain boundaries melt preferentially, a t e s sen t i a l ly the same melting temperature as crystall ine material.

(2) Small angle boundaries and coherent twin boundaries do not melt preferentially.

(3) A transit ion between melting and non-melting t akes place relatively sharpely at 8 = 12' for t in, and B = 14' for aluminum, independent of the type of boundary.

(4) In zinc, boundaries melt preferentially in the range of 6 from 27O t o 108O. T h e melting t ransi t ion angle depends on the orientation of the boundary plane.

( 5 ) The melting transit ion is assumed to del ineate smal l angle boundary s t ructures con- forming with the Burgers' model, and large angle s t ructures which are irregular.

I I

Grain Boundary Segregbtion

I t h a s long been supposed that solute atoms should segregate t o grain boundaries under - - - equilibrium conditions, and various experimental confirmations of th i s supposi t ion have been made. Grain boundary segregation h a s been detected by etching effects , by radioactive tracer techniques , by indirect evidence such a s i s found in bubble model experiments, and in measurement of certain grain s i z e effects . T h e reason for expect ing segregation a t grain boundaries is that large solute atoms should be ab le t o lower their energy by moving into regions of tension which e x i s t in the grain boundary, while smal l solute atoms can lower their energy by moving into regions of c o m p ~ e s s i o n . McLeana h a s considered the sub jec t of grain boundary segregat ion observations in detail . Thomas and C h a l m e r ~ ~ ~ measured the segregat ion of polonium t o the boundaries in bicrysta ls of lead as a function of relative orientation of the grains and obtained the resu l t s shown i n Figure 8. T h e resu l t s a re similar t o those mentioned for grain boundary melting in that a sharp t ransi t ion in the relative concentration of the solute element in the grain boundary occurs a t misorientations greater than lsO, but is a relatively minor effect a t angles below 15'. Thus , so lu te segregation would be expected to have a marked effect on grain boundary migration and hence should have in turn an e f fec t on grain boundary s l id ing and fracturd in creep.

Large Angle Grain Boundarids

Several models ex i s t for large angle grain boundaries which attempt to show a relationship to the observed properties of these boundaries. T h e s e include the models of K G ~ O , ~ o t t " , and Freidel , Culli ty and crussard12. In considering these models of large angle grain boundariea, i t may be significant t o remember that two of them, Keys and Mott's models, were conceived t o predict the behavior of grain boundaries under dynamic conditions, that i s , during s t ra in , while the model of Freidel e t a1 h a s been compared aga ins t grain boundary properties under s t a t i c conditions. There may be certain changes in the structure of the grain boundary under s t r e s s , and particularly during deformation, and i t would not be expected necessa r i ly that a model which is successfuf in ~ r e d i c t i n g properties during deformation is similarly s u c c e s s f u l in predicting s t a t i c properties of the grain boundary.

T h e Mott "island" model for large angle grain boundaries w a s advanced to explain grain boundary s l id ing and migration, and the temperature dependence of the velocity of these phenomena. Mott considers that a grain boundary cons i s t e of regions or "islands" where a good matching of the atomic l a t t i ces of the two grains e x i s t s , separated by regions of poor matching. T h e regions of $ood match are considered to be more or l e s s uniformly s ized a r e a s

s p a c e d regularly on a plane grain boundary. The transit ion from good t o bad regions i s rather wel l defined ins tead of showing a continuous gradation, It was considered that the i s l ands of good-fit offered l i t t le r es i s t ance to sl iding, whereas the bad-fit regions res i s t ed shear ; thus, the action of s l id ing necess i t a ted a thermal agitation in the bad-fit region around the i s l a n d s in order for the res i s t ance to s h e a r t o dec rease locally. T h i s would explain the v i scous nature of grain boundary s l id ing, and i s re la ted to KG'S observation that the ra te of sl iding, when extrapolated t o the melting point of the metal , corresponded to that which might be expected for c rys ta l s separated by a layer of liquid a few atoms thick.

Mott obtained an expression for the free energy of disordering of the a toms surrounding a n is land of good f i t by considering that a t the melting temperature, T,, the free energy of melting i s zero, and a t absolute zero i t i s nL, where L i s the la tent hea t of melting and n i s the number of atoms surrounding an is land of good fit. T h e free energy of melting a t intermediate temperatures i s assumed to vary in a l inear fashion with temperature between these two points. On application of a shear s t r e s s , V, to a boundary, disordering resu l t s from s l i p over a dis tance b corresponding t o the atomic diameter of the group of n atoms, and the work done by the s t r e s s i s unb3. T-he following express ion i s obtained for the velocity, V , of $rain boundary s l id ing a s a function of temperature:

where u

Kg11

is the frequency of atomic vibration and K i s Boltzmann's constant.

was one of the f i rs t t o observe that the activation energies for grain boundary s l id ing of metals , for which the appropriate da ta were avai lable , were nearly equal to the act ivat ion energies for self-diffusion. He reasoned that the grain boundary consis ted of an assembly of the same types of la t t ice faul ts which were responsible for grain diffusion, namely, la t t ice vacanc ies , or disordered groups. He showed that the ra te of s l id ing w a s governed by an equation of the form

where A io constant and Q i s the activation energy for sl iding.

T h i s resul t w a s cr i t ic ized by Mott on the b a s i s of experimentally determined va lues for t h ~ act ivat ion energy for sl iding, and he w a s able to show that the constant in theabove equation according to Ke's reasoning would be 6 x whereas the measured value w a s of the srder of unity. A dis t inct ion between Kg's formula for grain boundary s l id ing and Mott's i s that Mott's formula contains a figure for the s i z e of the i s l ands of misfit which offers a possible comparison between grain boundaries of differing orientation.

The Freidel , Culli ty and Cruasard12 model of the grain boundary makes poss ib le a calculation of grain boundary energy for particular orientation differences between grains. The technique involves ass igning bond energies from a n assumed law relating the energy of the bond to the dis tance of separat ion of the atoms. Neares t and next neighbors were considered. T h e energy tota l w a s worked out for s p e c i a l orientations and i t was assumed tha t the atoms would O C C U P Y their normal la t t ice s i t e s un less i t was found that when an atom w a s removed from the aggregate, that the one extended bond resulting h a s l e s s energy than the two shor t

o n e s which ex i s t ed before. A s in the Kg equation, they assumed that the free energy of bonding van i shes a t the melting point and t h a t a l inear extrapolation of the grain boundary free energy could be used.

S E C T I O N 111. C R E E P AND G R A I N BOUNDARY SL ID ING

Grain boundary s l id ing exper iments have been reviewed numerous t imes in the p a s t years , the most recent a r t i c l e s being those of Gifkins6, Weinberg4, McLean3, and Grant and Chaudhuri24. B e c a u s e the inves t iga t ions of grain boundary s l id ing h a v e been reviewed often and we l l e lsewhere , in t h i s sec t ion we s h a l l t rea t the r ecen t observat ions of grain boundary s l id ing, primarily from the authors ' laboratory, and simply show how t h e s e re la t ionships re la te to the measurements of others.

Sliding' in Polycrysta l l ine Metals and Al loys

The general fea tures of grain boundary s l id ing a re wel l known. Displacement t a k e s lace on grain boundaries tes ted a t e l eva ted temperatures in amounts which vary widely with temper- a ture and s t r e s s . In general , high temperatures and low s t r e s s e s favor large o f f se t s on the grain boundary; but a s will b e shown la ter , t h i s is not a lways true. T h e s l id ing often produces a region of heavy deformation in the grain opposi te the s l id ing boundary which we term a fold, and is a l s o often accompanied by ex tens ive migration of the grain boundaries. In tercrys ta l l ine cracking is often a s s o c i a t e d with the grain boundary sl iding, but again there are notable excep t ions to th is ; in particular, in high purity aluminum, grain boundary f ractures are not observed.

Quantitat ive measurements of grain boundary s l id ing from the displacement of reference s c r a t c h e s a c r o s s g a i n boundaries, or from sur face offse ts during creep, have been made by numerous invest igators , and equa t ions for the t ransla t ion of t h e s e d a t a in to v a l u e s of the contribution of the grain bo~undary to the to ta l extension of the specimen have been made by ~ c ~ e a n ' ~ , Fazan , Sherby ahd Dorn20, and Brunner and rant^'. T h e technique of ca lcula t ing the contribution of in te rna lg ra in boundar ies t o elongation f rommeasurements of grain shape following creep deformation have been developed by R a ~ h i n ~ e r ~ ~ . A brief descr ip t ion of one of t h e methods of Brunner a n d Grant is as follows: assume a long, narrow at r ip on the surface of t h e spec imen a long the a x i s between two gauge l ines. On t h i s narrow s t r ip , grain boundaries can b e approximated by s t r a igh t l ines in tersect ing the atrip a t arbitrary angles. Grain boundary s l id ing c a u s e s the displacement of the transverse.marker l ines a t the grain boundary. T h e a x i a l component of the gra in boundary displacement is ca l l ed A us. T h e amount of d i s - p lacement va r i e s widely from grain t o grain boundary. Aus h a s t o be averaged s t a t i s t i c a l l y to g ive a good quanti tat ive value. From SO t o 100 determinations of *us are ordinarily con- s ide red n e c e s s a r y to give good resul ts . If the grain s i z e is suff ic ient ly smal l , i t i s only n e c e s s a r y to sum these contributions over the gauge length, a s indicated by the following equat ion:

1 EGB = - *us % length

If, however, the gra in s i z e i s large, t h i s opelation muat be repated numerous t imes and the average of the v a l u e s of EGB taken, In th is equation, EGB is the grain boundary contribution to to ta l elongation and 4 is the d i s t ance between gauge markers before the t e s t s t a r t s . T h e to ta l elongation, ET, and the re la t ionship between to ta l elongation, grain boundary elongation and grain elongation are given by

8-4 ET =- 4 (7)

where EG is the contribution of the g ra ins t o total elongation and 4 i s the gauge length a t any given time.

Before considering the to ta l contribution of a l l the grain boundaries in a polycrystall ine specimen t o elongation, l e t u* examine the nature of s l id ing on s ingle grain boundaries, a s shown by Chang and Grant23 ior pure aluminum. It is s e e n in Figure 9 tha t a coarse grained polycrystall ine specimen (which yielded the usual smooth total creep curve) displays gross ly non-homogeneous deformation of individual consecut ive grain boundaries in the gauge length. T h e grain boundary displacement curves a re characterized by a l ternate periods of relatively rapid and very s low creep. Chang and Grant re la ted this behavior to a l ternate periods of grain boundary s l id ing (result ing in s t ra in hardening) and periods of recovery (associa ted with grain boundary migration).

T h e variation of EGB versus total elongation for a l l grain boundaries of A1-1.9% Mg spec imens is indicated by the curves of Figure 10. In t h i s case , because the t e s t s were performed a t a constant s t ra in rate, the a b s c i s s a a l s o corresponds t o a l inear time sca le . T h e variation of EGB with time for the to ta l specimen g ives a smooth curve which is quite s imilar to the overall creep curve in i t s character.

Brunner and Grant's26 resu l t s for EGU/ET cs a function of temperature for aluminum, aluminum-2% magnesium, and aluminum-5% magnesium (solid solution a l loys at t e s t temper- a ture) are shown in Figure 11. T h e s e a re da ta from specimens s t ra ined in creep a t a minimum creep ra te of 2.7 percent/hour. All the a l loys show increaaing grain boundary s l id ing with increasing temperature in the lower temperature range, which p a s s e s through a maximum, and thereafter d e c r e a s e s s l ight ly with i n c r e a s i n ~ temperature. T h e posi t ion of t h i s maximum is not well defined and apparently var ies with alloy content in an a s yet undetermined fashion. T h e maximum va lues of EGB/ET are rather similar for the three a l loys , fall ing between 13 and 15 percent.

Figure 12 s h o w s the dependence of EGB/ET on s t r e s s for the a l loya t e s t e d by Brunner and Grant, and for McLean's d a t a on pure aluminum. I t h a s been indicated by Harper, Shepard and Dorna7 that the ra t io of grain boundary s l id ing to to ta l s t ra in ahould be independent of temperature, but dependent on s t rees . Since the s t r e s s for a value of E p / E T of 10 percent is not single valued for pure aluminum, the d a t a c a s t doubt on t h i s conc union. M c ~ e a n ' s l ~ da ta on t h i s plot f a l l a t somewhat higher s t r e s s e s than the d a t a of Brunner and Grant for pure aluminum; however, if McLean'aa8 va lues are corrected for an error which Brunner and Grant de tec ted in their measuring technique, the valuee f a l l very well in l ine with those of Brunner and Grant.

Regarding $rain s i ze , the f i rs t and most interesting observation w a s t o the effect that coarse s l i p bande ere observed, with a minimum of grain boundary sliding, a s long a s the grain diameter is a t l e a s t twice the minimum a l ip band e p a ~ i n ~ ~ ~ a t any given s t r e s s . F i n e alip, a s obmerved by a number of invest igators , of bourse t a k e s place s t all-deformation stressem.-

T h e second observation is that the effect of grain s i z e on grain boundary s l id ing i s such that the larger the grain s i z e the greater the grain boundary displacement on the average grain boundary, This i e shown in Figure 13 for the resu l t s of Brunner and Granta6, and Mullendore and Grant25 for aluminum-magneeium. A semi-logarithmic plot i e used in t h i s c a a e because of the wide range of grain s i z e s ; however, s ince the s lope of the experimental l ine i s 1, a linear

relationship would be observed on a rect i l inear plot. McLean and Gifkins indicate the same sor t of trend for data of various invest igators in pure aluminum30, s e e Figure 14. T h e s e da ta do not, however, represent a n increase in the ra t io of EGB/ET a s a function of grain s i ze . T h e dotted l ine in t h i s figure ind ica tes the va lues of average grain -boundary s l id ing displacement necessa ry to give a value of EGB equal to ET, in other words, EGB/ET of 100 percent. T h e l ine representing constant EGB/ET va lues of 50 percent would be a s t ra ight l ine extending from the origin with the lower s lope, and zero percent contribution t o elongation would be, of course, a s t ra ight l ine of zero slope. Since the experimental points would intersect these radii of constant EGB/ET a t decreasing va lues of EGB/ET with increasing grain s i z e , the da ta indicate a decreasing contribution of the grain boundary to elongation with increasing grain s i ze . Pe rhaps the differing purity of the aluminum used for the va lues in th i s figure h a s an important effect on the data , for Brunner and Grant26 did not observe the same variation of EGB/ET with grain s ize . Their da ta for aluminum-2% magnesium i s indicated in Figure 15 by a plot of EGB/ET versus ET. At a value of ET of 10 percent, i t can be s e e n that the d a t a for grain s i z e s from 25 microns to 460 microns for aluminum - 1.9% magnesium a l l f a l l in the range between 8 and 11 percent for EGB/ET, indicating an approrimate constancy of t h i s value with grain s ize .

T h e effect of orientation of the grain boundary with respec t to the t ens i l e a x i s on poly- c rys ta l s of aluminum-magnesium h a s been invest igated by Mullendore and rant^^, who find, in agreement with othera20, that the orientation of the grain boundary with respec t to the t ens i l e a x i s h a s no systemat ic effect on the observed grain boundary s l id ing magnitude. T h i s is shown in Figure 16, where magnitude of s l id ing of individual grain boundaries in a s ing le polycrystal a t e plotted ve rsus the resolved shear s t r e s s on the grain boundary. Often grain boundaries with very l o q resolved shear s t r e s s give large amounts of sl iding, and i t w a s even observed tha t two grain boundaries gave negative va lues of sl iding, indicating s l id ing in a direction opposite t o that which would produce elongation of the specimen.

There was, however, an indication that the re la t ive orientation of the grains a c r o s s thei r mutual grain boundary did have an important effect on the observed magnitude of sl iding. T h i s i s indicated in Figure 17 where grain boundary displacements are plotted ve rsus an orientation factor c o s 6 s in U , where 6 i s the angle between maximum resolved shear s t r e s s slip direct ions in the two grains, and o is the angle measured on the grain boundary between the in tersect ion of the d i p planes of the two grains with the grain boundary2'.

I

One of the most controversial observations of p a i n boundary s l id ing h a s been tha t of - - R a c h i n g e P , who obtainled a figure for the contribution of interior grain boundaries t o elongation ~ f . ~ o l y c r y s t a l l i n e wpecimens by measurements before and after creep of the ratio of the length t o width of grains. In principle, t h i s g ives a n indication of the amount of the elongation contributed by grain deformation, and the grain boundary sliding contribution can be obtained by difference from the measured tota l elongation. IIe obtained va lues of EGB/ET as high as 95 percent; h i s r e s u l t s have not ye t been sa t i s fac to r i ly explained by invest igators working s t r ic t ly on surface meaeurernents. There i s , of course, the possibi l i ty that preferred direction of grain boundary migration with respec t to the t e n s i l e a x i s could maintain equiaxed grains , even in the presence of considerable grain elongation, but th is has not yet been es tab l i shed experimentally.

Recen t s t u d i e s of gcain boundary s l id ing in aluminum-3% copper, two-phase a l loys by 1shidaS3 have shown the remarkable differences in grain boundary s l id ing produced by var ia t ions in the s i z e and distribution of second phase in the material. Four different h e a t treatment8 of the alloy were used to produce the s t ructures shown in Figure 18. Following solution treatment a t 900°F, the aging treatments were a s follows;

1. Heat treatment Q5 - water cpenched, aged a t 500°F for 72 hours

2. Heat treatment F 5 - furnace cooled to 500°F, aged 72 hours

3. Heat treatment Q7 - water quenched, aged a t 700°F for 38 hour^, stabilized a t 500°F for 72 hours

4. Heat treatment F7 - furnace cooled to 700°F, aged 38 hours, stabilized 72 hours a t SOO°F.

All tes t s were performed a t 500°F over a range of s t r e s se s from 2000 to 6000 psi. Figure 19 ehowa representative creep curves for these materials; Figure 20 shows grain boundary contribution to total elongation versus total elongation for the same materials,

Table I shows the variation in performance of the alloys for the various heat treatments.

Heat Treatment

TABLE I

Data on Creep Performance for Four Heat Treatments I I I

Decreasing Particle Size Increasing Creep EGB/ET Increasing and Interparticle Spacing I Resis tance I I Ductility

It i e interesting and expected that creep reeietance increases with decreasing particle - . .

eize of precipitate and decreasing interparticle spacing, while total ductility increaaee in the reverse direction. It was unexpected, however, to find that the ratio EGB/ET increased with increasing creep resistance. While the grain boundary creep rate could not be compared directly for al l four heat treatment8 because of the large differences in strength, nevertheless it wae possible to observe that the grain boundary creep rate at a givenstreae increased in the order QS to F7, parellsling the trend of increasing total ductility.

8 icrystal S l i d i n g Experiments

Bicrystal eliding experiment8 fall into two groups, categorized according to the type of epecirnen used. One group involves the use of tensile apecimene with an inclined grain boundary s o that one obtains considerable grain deformation along with grain boundary eliding. The second type of teat i e that in which one attempt^ to subject the grain boundary to pure shear and to avoid, to whatever extent poesible, deformation i n the grains,

Gifkins6 ham eummarized the forms of grain boundary sliding vereue time curves which have been obeerved in various investigatione, These are shown in Figure 21. The general curve observed i s eimilar to the normal creep curvea5 and i~ indicated by curve X (aee a l so Figures 10 and 20). Teneion-type specimens have been shown by Rhines, Bond and Kiseelsq to produce curves of the type Y1 or Y2 with an incubation period for sliding, and a cyclical

variation in s l id ing rate. T h i s h a s a l s o been occasional ly observed in pure shear type spec i - mens. T y p e s Z1 and Z2 have a l s o been observed in shear specimens35. In addition t o the varying observat ions on the shape of the s l id ing curve, conflicting resu l t s have a l s o been reported on other a s p e c t s of the bicrysta l s l id ing experiments. In particular, the presence or or absence of grain boundary migration, the ex i s tence of subgrain formation ad jacen t to s l iding boundaries, the nature of the zone of sl iding, and whether or not s l id ing actual ly t akes place on the grain boundary. Many of these conflicting resu l t s may be due in part to di f ferences in purity of the mater ia ls investigated.

An area of b a s i c agreement between invest igators is tha t grain boundary s l id ing i s pro- foundly influenced by re la t ive orientation of the c r y s t a l s makinghup the boundary. Rhines , - - Bond and Kissels4 find tha t the magnitude of ,grain boundary s l id ing is a function of misori- enta t ions for randomly oriented bicrystals. Tung and addi in^^, who systemat ical ly var ied the relative orientation of the i r b icrysta ls found that the act ivat ion energy for s l id ing varied from 8.5 to 39.5 ki localor ies per mole a s angular misorientation changed from 20 to 88'. T h e s e da ta a r e shown in Figure 22. Similarl: Adai t and BrittainS6 have observed a marked dependence of grain boundary s l id ing on angular misorientation in z inc bicrysta ls . Their r e su l t s indicate that the variation in sl iding /hey note cannot be attr ibuted to var ia t ions in grain boundary migration, a s h a s been indicated by Couling and

Recen t s t u d i e s of grain boundary s l id ing in aluminum-2% magnesium b i ~ r ~ s t a l s ~ ~ , a l l tes ted a t 500°F, indicate th$t the magnitude of grain boundary s l id ing can be ra t ional ized on the b a s i s of continuity of s h e a r requirements. T h i s i s thought to conet i tu te one important factor in the variation of grain boundary s l id ing with re la t ive orientation of grains, although i t i s probably not the only oriehtation dependent factor, for i t d o e s not explain the orientation dependence of the act ivat ion energy for sliding35, I t is clear from the observat ions of ~ ~ i l v i e ~ ~ that in a polycrystall ine aggregate the relative orientation of a large fraction of the grains a c r o s s their mutual grain boundaries is such that s l i p can propagate readily from one grain into the adjacent grain, even in the absence of grain boundary sliding. At e levated temperatures, where grain boundary sliding( p resen t s another degree of freedom, it is even more l ikely that most grain boundar ies will bk penetrated by dis locat ions from the grains. When a dis locat ion i s forced into the vic ini ty of the grain boundary by the applied a t ress , i t must, in order to maintain the continuity of shpar , cause the activation of a t l e a s t two s l i p s y s t e m s in the opposite grain. A componenq of unresolved s h e a r remains from t h i s operation which can appear a s s l id ing on the grain boundary.

A two-dimensional representation of s l i p induced s l id ing is shown in Figure 23. In the schemat ic , s l ip in the top grain which c r o s s e s the grain boundary into the bottom grain, produces a s h e a r offset on the grain boundary a s indicated by the displacement of the dot ted reference l ine on the lef t hand s i d e of the specimen. I t should be noted that the reference l ine on the right hand s i d e of the specimen suffers no offset a t the ginin boundary. If one now imagines a whole s e r i e s of paral le l s l i p p lanes to operate a c r o s s :: s specimen, i t can be s e e n that the displacement of the reference l ine a t the grain boundary on the far r ight hand side of the specimen would s t i l l be qero, and that the displacement a s one moves a c r o s s the grain boundary to the l e f t would increase to a maximum on the far lef t hand side. In the three- dimensional c a s e , s l i p on one plane in one grain would have to be accompanied in general by grain boundary sliding, and, in the absence of grain rotation, by s l i p on two p lanes in :he second grain. T h e magnitude of grain boundary s l id ing would s t i l l go to a 'ro a t some point on the circumference of the specimen, and in general, t h i s would be a t one co91.er of t h e specirn2d. The grain boundary displacement would r i se to a maximum a t the opposite corner of the specimen. Th i s , of course , a s s u m e s that there i s no contribution t o grain boundary displacement

by independent grain baundary sliding. Th i s i~ substantially the behavior noted in the bicrystal t e s t s performed, a s shown in Figure 24. Assuming uniform distribution of s l ip across the diameter of the specimen, one would expect a linear increase in grain boundary displacement in going from the low corner to the high. The obaerved grain boundary displacements de- part to a small extent from this behavior, but this i s not unexpected. The ideal case assumes perfectly uniform sl ip across the diameter of both grains, and does not allow for changes which would result from closeness to an exterior surface, or from the operation of additional s l ip systems in different parts of the specimen. In addition, the experimentally determined grain boundery displacements do not p;o to zero a t a corner, but simply to a minimum value, indicating a contribution by independent grain boundary eliding. An approximate relationship between sliding and orientation factors based on t h i ~ model indicate6 that the change of grain boundary displacement with distance along the boundary ehould, a t a given s t ress , strain, and temperature vary a s cosw (1 - tan #tan a) where w i s the angle between intersect ions of the primary s l ip planes with the grain boundary, ,a i s the angle between the primary s l ip direction in one grain and the normal to the boundary, and f i i s the angle between the primary s l ip direction in the other grain in the normal to the grain boundary. The experimental data based on this relationship are shown in Figure 25 and are seen t o agree quite well with the model.

This model, when applied to polyctyatalline materiale, would predict that in the absence of secondary e f fec ts , EC; /E would be a conatant with changing ET in a given teat, as h a s been observed by McLeaJ9 . Tt further predicts that EGB,mT would be a constant for varying grain s ize , or that the average grain boundary displacement in a polycrystal would vary linearly with increase of grain size. This has been shown to be trueab; see Figure 13. It i s felt that the temperature variation of grain boundary sliding might then be explained on the bas is of the tendency of dislocations to penetrate the grain boundary, and t h i ~ would in part depend on the shear strength of the grain boundary.

Crussard and Freidela9 presented a model for the driving force for grain boundary migration which, if applied to sliding, i s rather similar to the above model and ehould produce the same results. They consider that when a dislocation i~ forced into a grain boundary along part of i t s length that, because the boundary i s unable to stand large tangential s t ressea, the dislocation line will spread by diffusion into a larger zone, which can be formally described a s a splitt ing into several dislocations with emall Burgers' vectors. The sum of these partial Burgera' vectors i s equal to the Burgere' vector of the original didocat ion, and have a tendency to be almost parallel to the boundary. If indeed theee partial grain boundary dislocations have Burgers9 vectors essentially parallel to the boundary, then Crussard and Freidal must assume that the component of shear perpendicular to the boundary has been tranamitted into the opposite grain. The spreading of the grain boundary dislocation i s then to be associated with grain boundary sliding.

Rhineeqo has interpreted his biciystal sliding resul ts in an entirely different way. He concluded that observed grain boundary displacements do not represent eliding on the grain boundary plane at all , but rather represent crystal elip in a zone close to the grain boundary. The alternate pe,riods of rapid and @low grain boundary sliding which he observsd are attributed to alternate periods of work hardening and recovery in thia grain boundary zone. The recovery process which he ca l l s upon i e polygonization, and i t i s this process which i s thought to be rate controlling.

McLean41 offere another explanation for the relationship between p i h ehear and grain boundary shear. He euppoaed that grain boundary sliding occure to the extent necessary to

accommodate the l a t t i ce -bending, which occurs prior t o polygonization adjacent to the grain boundary. T h i s polygonization of course i s dependent on the amount of d is locat ion pi le up a t the grain boundary. The implication is that t h i s in turn i s related to the misorientation of the shear ing e lement in the two grains.

Gifkins6 h a s proposed a model for grain boundary s l id ing which is designed to allow for the e f fec t on grain boundary s l id ing of dis locat ione reaching the grain boundary, and t o allow interpretation of the temperature and s t r e s s effects. He s u g g e s t s tha t the number of dis loca- t ions which reach the vicinity of the boundary is dependent on the eubgrain s i z e ad jacen t to the grain boundary. Assuming the subgrain wa l l s t o be effect ive barr iers to s l ip , the number of piled up d i s loca t ions on the grain boundary for a given s t ra in would be proportional t o the subgrain s ize . T h e s e d i s loca t ions then affect the grain boundary s l id ing through their effect on the vacancy concentration a t the boundary (via climb), and by their e f fec t on the migration of the grain boundary.

I t i s bel ieved t h a t experimental r e su l t s of different inveatigatore on grain boundary s l id ing a re suff ic ient ly contradictory that i t is not poss ible at t h i s time to conclude with any cer ta inty which model of grain boundary s l id ing is more exact. Carefully controlled experiments a re necessary, which a re epecif ical ly designed to test out the varioua models.

SECTIONS IV AND' V . GRAIN BOUNDARY RECOVERY PROCESSES

In the s tudy of grain boundary deformation and f racture p rocesses , one can never completely separa te the charac te r i s t i c s of grain boundary s l id ing from the e f fec t s of grain boundary migration and subgrain formation. In deformation s t u d i e s of polycrystall ine materiale, one rarely, if ever , obse rves grain boundary s l id ing occurring without some grain boundary migration taking place a t the same time. I t is quite probable that grain boundary s l id ing cannot continue u n l e s s there is a cer ta in amount of migration. When grain boundary migration is re- s t r ic ted, e i ther by so l id sollution alloying, impurity effects , or a second phase ex i s t ing on grain boundaries, grain boundary fracture8 often occur a t rather smal l amounts of deformation.

I

Several c a u s e s of boundary migration have been l i s t ed by Grant and C h a u d h ~ r i ~ ~ . T h e s e are summarized as followe: ~

I

1. Grain boundary s l id ing c a u s e s depar turrs from equilibrium a t grain boundary juneturcs. The non-equilibrium configdration of the grain boundary juncture which reeu l t s from a n offset on the s l id ing grain boundary g i v e s a n e x c e e s eurface free energy which cons t i tu tes a driving force for migration.

2. Interaction of s l i p with grain boundaries dhring creep resu l t s in the formation of subgrains a long the grain boundary. T h e difference in in tensi ty of the dis locat ion s t ructure on the two s i d e s of the boundary createe a n unbalanced ~ u l l and c a u s e s the grain boundary t o migrate in a more or less uniform manner t o one s i d e or the other of i t s original position.

3. Grain boundary migration in creep is a l s o affected by the same factors which control grain boundary growth, namely, the tendency to decreaee e x c e s s surface free energy. In addition to these , i t i s known that small angle boundary migration c a n be s t r e m induced. T h i e h a s been demonstrated by Washburn and P a r k e F , In t h i s came, the boundary migrationresultm in shear and t h u s occurs in a direction which a l lows the appl ied s t r e e s to do work on the specimen. Brunner and Grant have demonstrated t h a t t h i s kind of migration of subgrain boundariee occurs during grain boundary eliding.

It i s to be expected t h a t alloying will markedly influence the rate of grain boundary migration. I t will have i t s effect both by changing the energy of the grain boundary, which: a l t e r s the driving force for minimization of su r face free energy, and by affecting diffusion ra tes . Figure 26 shows the effect of alloying lead with tin on the mobility of both random grain boundaries and spec ia l ly oriented grain boundaries. Th ia w o r l P w a s done on bicryata le of lead and lead-tin a l loys which contained a lineage structure which gave the driving force for migration. An addition of 0.006 weight percent tin was found t o reduce the ra te of grain boundary migration more than a thousand-fold for random grain boundaries. Specia l ly oriented low energy grain boundaries were l e s s strongly affected by the alloying additions.

Subgrain formation h a s a l s o been shown to be intimately aseoc ia ted with the proceea of grain boundary sliding. During s l id ing, a zone of in tense polygonization a lmost invariably occurs along the s l id ing grain boundary31, as ehown in Figure 27. T h e role of th i s layer of subgrains a long the grain boundary in relation to s l id ing h a s been var iously descr ibed in the models for grain boundary eliding d i s c u s s e d in the previous sect ion; cer ta inly it must have an important effect of influencing the nature and degree of grain boundary migration.

In grain boundary s l id ing e tudiea of aluminum and aluminum-magneeium al loys , i t is found that the grain boundary becomes roughened during the course of creep and t h a t th is roughening of the grain boundary i s related to the aubgrain s t ructure along the boundary. F igure 28 shows a micrograph of the aerrated s t ructure of the grain boundary in aluminum - 1.9% magnesium. Becauee of the relationship of th i s s t ructure with the formation of intercrystall ine voide during creep, it h a s been s tud ies in some d e t a i l by Mullendore and Granta2. Measurements of the wave length of the grain boundary serra t ions in aluminum-magnesium a l loys revea l s the dependence on a l loy content, s t r e s s , and temperature as indicated in Figure 29. T h e factor which appeare to have the g rea tes t effect on the wave length of the serra t ions i s the s t r e s a , T h e higher the s t r e s s the amaller the serration. I t h a s been found that the eerrations represent in tereect ions of eubgrain boundaries with the grain boundary.

T o reveal the nature of the serra ted s t ructure of the grain boundary, in three dimensions, sequen t ia l p ic tures were taken of a grain boundary a s auccese ive layera of the surface of the specimen were removed by e l e c t r ~ p o l i s h i a ~ . Figure 30 ehows the topographical map of the grain boundary which w a s built up in th i s way, and revea l s that the se r ra t ions in two dimensions ac tua l ly represent elongated ledges on the grain boundary when viewed in three dimensions. T h i s s t ructure of the grain boundary of course h a s a marked influence on the behavior of the boundary during eubeequent s l id ing; and, as will be shown in the eucceed ing eect ion, i t a l s o strongly inf luences the nature of fracture in these materials.

SECTION VI. VOID FORMATION AND INTERCRYSTALLINE FAILURE IN CREEP

The volume of observat ions on the nature of intercrystall ine fracture and void formation during creep has , in recent yeare, reached massive proportions; and a number of fundamental treatments of the mechanisme of crack init iation and growth have appeared in the l i terature. In brief, two s c h o o l s of thought ex i s t ; those who regard the formation and growth of cracka s t r i c t ly as the resu l t of s t r e s s concentrations exceeding the cohesive strength of the material, and those who prefer vacancy condensation on ex i s t ing nuclei aa the growth mechanism. In addition t o examination of these two viewpoints, one must a l s o consider the quest ion of whether or not any or a l l intercrystall ine cracka reeul t from void formation. Becauee the

character is t ics of intercrystall ine failure have been reviewed adequately e l a e w h e r P , - a summary of observat ions i s suff ic ient for our purpoeee.

Almost a l l metals and alloys, a t temperatures low relative to their melting point, display ductile transcrystalline failures; a t some higher temperature they usually undergo a trans it ion to intercrystalline failure provided that the strain ra tes are suitable. The onset of intercrystalline cracking i s in general associated with decreased strength of the metals, as measured by rupture life or minimum creep rate, the onset of grain boundary sliding, and usually a decrease in elongation a t rupture of the specimen. The transition from transgranular to intergranular failure i s a function not only of temperature, but of s t r e s s or etrain rate, grain s ize , and metallurgical structure, including purity. Figure 31 i s a plot of rupture life versua s t r e s s for rr vacuum melted 80Ni - 20 Cr alloy showing the transition to intercrystalline failure (high s t r e s s discontinuities) a s a function of s t r e s s and temperature. The numbers on the diagram indicate the reductin9 of area values a t failure. In the vicinity of the transition the ductility s ta r t s to decrea-G asd accelerates with decreasing strain rate. Figure 32 compares the reduction of area values a t three temperatures as a function of rupture time for the same 80Ni - 2 0 Cr alloy, one a i r melted (3A) and one vacuum melted (2V). The very much lower ductility of the air melted alloy illustratee the profound effect which purity and cleanl iness have on fracture characteristicsG.

Some metals do not undergo intercrystalline cracking (high purity aluminum) or intercrystalline failure (although intercryatalline cracks may be present in significant amount). In other ca se s , for example 2s aluminum and high purity solid solution alloys, such a s aluminum- magnesium, intercrystalline cracking disappears a t high temperatures and long rupture times (very slow strain rates).

A typical example of a material which failed by intercrystalline cracking a t high temper- atnres4' is shown in Figure 33. The failure resu l t s from the joining of numerous grain boundary cracks ac ros s the width of the specimen. Although the total fracture i~ approximately normal to the s t r e s s axis, i t can be seen that the individual facets of the fracture surface are a t various angles to the s t ress axis. I t i s a l so obvious that in spi te of the brittle appearance of the fracture, considerable elongation (85%) prior to failure has taken lace in the specimen. Chang and Grant* have catekorized intercrystalline cracks a s shown in Figure 34. It i s interesting to note that types (a) and (b) show intercrystalline cracks resulting from sliding on an adjacent boundary, but occurring on boundariee which themselves do not s l ide, while type (c) shows the formation of intercrystalline cracks on sliding boundaries. More complex intercrystalline crack configuratitme were noted by Chang and Grant, and two examples are shown in Figure 35. These , however, are merely combinations of variations of the three types indicated in the previous figu.-;.

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The formation of voids along grain boundaries during elevated temperature deformation occurs in many metals and alloys and the relationship of these voide to intercrystalline failure has been the subject of many investigations. Among the firet observations of intercrystalline cavitation were those of Jenkins, Bucknall and enk kin so^^^, working with copper bare alloys. The f i rs t systematic study of the phenomenon was that of G r e e n w ~ o d ~ ~ , and Greenwood, Miller and Suiterq9, who oLjierved the formation of numerous small voids a t grain boundaries in brass, copper and magnesiurri. They related the incidence of cavitation as temperature or strain rate was varied to the s ta r t of grain boundary sliding and to a drop of ductility. A vacancy pre- Apitation mechanism was proposed a s a origin for the voids. Ultimate intercrystalline failure was though to result from growth of the voids t o the point where they coalesced into a continuous crack. Subsequent to ;he work of Greenwood e t a l t many investigators had etudied void formation. The work has been carefully reviewed by Gifkins6. Davis and ~ e n n i s o n ~ have also given an excellentreview of current theoriea of intergranular fracture processes.

Relation of Void Formation to Intercrystal l ine Fai lure

In d iecuss ing the re la t ionship of vo ids a n d intercryatall ine c racks , Gifkins6 h a s found i t useful t o d is t inguish between the type of wedge-shaped crack often a s s o c i a t e d wi th tr iple point cracking, and the smal l i sola ted rounded c a v i t i e s in the grain boundary by terming the f i rs t a "w" cavity, and the la t ter an "rt' cavity. Greenwood, Miller and S ~ i t e r ~ ~ working in copper and a lpha b r a s s , observed "r" type cav i t i e s distr ibuted a long grain boundaries usua l ly t ransverse to the applied s t r e s s , with a s p a c i n g of a s l i t t le a s 1 micron a t lower temperatures. T h e i r observat ions indicated that the voids l inked up to form continuous in tercrys ta l l ined cracks . T h e "r" type cav i t i e s were s p a c e d farther apar t on the boundariea a t h igher temper- a tu res of testing.

Other pertinent observat ions are tha t the incidence of cavity formation coincided with the beginning of gra in boundary sl iding, and tha t cav i ty formation w a s a s s o c i a t e d wi th a d e c r e a s e in duct i l i ty , indicat ing tha t th i s p r o c e s s w a s c lose ly a s s o c i a t e d wi th a l l in tercrys ta l l ine crackinp, i n creep. ~ c ~ e a n ' l , in examining the f racture cha rac te r i s t i c s of s e v e r a l commercial - - high temperature a l loys , found tha t the type of cav i ty or crack observed w a s dependent upon s t r e s s and temperature. H e found t h a t a t r e l a t ive ly high s t r e s s e s and low temperatures "w" type c r a c k s were predominant; a t intermediate temperatures and s t r e s s e s , mixtures of "w" and "r" typee were observed; and a t s t i l l lower s t r e s s e s and higher temperatures only "r" t y p e s c racks formed. In aluminum-mapeeium a l loys , Mullendore and Grant observed a var ie ty of grain boundary cavi t ies31 and the observat ions correspond c lose ly to those of McLean's in commercial a l loys . Examples of the cav i t i e s a r e ehown in Figures 36 and 37. Wedge-type c racks were &nerved in aluminum-5% magnesium t e s t e d a t 500°F, and a t a s t r e s s which would give a rupture l i f e of 0.53 hour. F igure 36 (a) s h o w s a n example of th is type of crack which h a s been impregnated with luci te and mechanical ly ~ o l i s h e d (not e tched) to preserve the de- t a i l s of the crack edge. Upon light e lect ropol ishing of th i s same structure, view (b), numerous smal l vo ids a long the grain boundariee which had been smeared over are revealed. T h u s i t appeare that t h e wedge-type crack may be formed by joining of t h e s e smal l vo ids a long the grain boundary. I t is not, however, c l ea r whether t h i s is a c a s e of growth of the vo ids unt i l they touch one another, or whether the s e c t i o n s of grain boundary separa t ing the voids s h e a r off to c rea te the crack. With the same alloy, t e s t ed a t the same temperature but a t lower s t r e e s e s , there w a s observed a d e c r e a s e in the numbers of voids a n d fewer "w" type cracks. The large cav i t i e s which do form a re rounded and give the appearance of having been formed by the joining of smal l vo ids (Figure 37a). Again i t i s not known whether the joining of the vo ids took p l a c e by s h e a r or by vacancy growth of voids from the appearance of the photomicrograph. Aluminum - 1.9% magnesium showed l e s s tendency toward "w" type cracks . Figure 37b s h o w s an example of the specimen t e e t e d a t 700°F with a 0.25 hour rupture life. Well sepa ra ted voids a re observed on the grain boundaries, and, al though the voids a r e fairly large, there w a s no tendency for voids to join to form intercrys ta l l ine "w" type cracks. At s t i l l higher t e s t e r temperatures , the amount of voids formation dec reased further. At t e s t ing temperatures of 700' and above, a l l f rac tures in t h i s a l loy were t ranscrysta l l ine in nature. A t high temperatures and low m e s s e s , i t w a s often observed that the gra in boundar ies would migrare completely away from the vo ids (which were few in number) and hence one would observe in the ruptured spec imens vo ids ex i s t ing within the grains. In high purity aluminum, voids were not observed e i the r a t grain boundaries or in gra ins , but grain boundary migration w a s very extensive .

One can conclude from the previous observat ions tha t under high temperature - low s t r e s s conditions, voids can form without leading to in tercrys ta l l ine failure. At ~ o m e w h a t lower temperatures and higher s t r e s s e s , voids are suff ic ient ly numerous on the grain boundar ies to join e i the r by s h e a r or growth p r o c e s s e s into "w" type cracks , which have near ly s t r a igh t

sides. In commercial alloys, wedge-type cracka are observedwithout any indication of void formation a t relatively low temperatures and s t i l l higher s t resses . It thus appears that the same conditions which favor the formation of brittle wbdge-type cracks a l so favor the formation of voids, but, s ince theae same conditions undoubtedly a l so favor the rapid propagation of "w" type cracks, i t i s ~ o s s i b l e for a long brittle crack to grow from the firet formed crack nucleus, thus promoting failure before many voids are formed,

Orig in of Voids

Voids have been observed to occur a t triple points, along apparently straight grain b o u n d a r i e ~ ~ ~ , a t the intersection of cub-boundaries and grain boundariess2, and a t precipitates along grain b o u n d a r i e ~ ~ ~ . Although Greenwood e t a1@ observed a preponderence of void formation along transverse boundaries, Gifkins6 in examining the work of various investigators in the field has found that they are observed on grain boundaries at a l l angles to the s t r e s s ax is (see a l so Figures 36b and 37a), except those which are parallel to it. In compression testa , voids are a l so observed on the longitudinal boundaries. There ia an indication that the relative orientation of grains constituting a boundary i s important to the formation of voids s ince in some instances voids were absent on a particular grain boundary only along that part of the bouudary where one of the grains w a s twinned.

GifkinsBS and Chen and M a ~ h l i n ~ ~ have developed models for void initiation at grain boundaries based on the experimental observation that the spacing of voids along grain boundaries i s about the same a s that of optically visible alip, in some cases . Gifkin's model for the opening of a void on a grain boundary i s shown in Figure 38. Slip crossing the sliding grain boundary creates a jog in the grain boundary which, due to d id ing and the action of the s t r e s s field of the piled up dislocations, causes a l o s s of cohesion a t the jog. Chen and Machlin add that the tensile s t r e s se s across the jog, which result from boundary sliding, should aid the formation of the jog, and McLeana has indicated that thie s t r e s s by itself may be sufficient t o open the cavity. Gifkins pointed out that the operation of the mechanism may be precluded by grain boundary migration, and relates the orientation dependence for void formation on sliding boundaries to differences in the s t r e s s at the jog from ~ i l e d up dislocations in one grain. Another orientation factor involved i s the direction of the shear with respect to the jog. If, in Figure 38, the shear direction were revereed, compressive s t r e s se s would develop along the jog and there would not be the eame tendency for opening.

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In aluminum-magnesium alloys where voids s t i l l form under conditions of temperature and s t r e s s where discrete s l ip bands are no longer visible and where even a t low temperatures the migration rate of the boundary i s probably sufficient to prevent the formation of voids by Gifkins' mechanism, i t appears that voide nucleate in a aomewhat different manner. Voids are associated with the grain boundary serration ~ e a k s noted in Figure 28. Figure 39 shows a grain boundary which is eerrated and contains voids on one side of the grain boundary associated with the serration These peakr, a e mentioned before, represent the intersection of a subgrain boundary with the grain boundary. The location of the voids to one s ide of the grain boundary waa establ ished by sectioning the grain boundary a t a low angle and e l e ~ t r o ~ o l i s h i n g downto it, a t the same time noting the location of the voids. The voids were found to occur to one eide of the boundary, and always on the eame side. These voids probably do touch the grain boundary, but this was difficult to establ ish with certainty. It i s felt that the configuration of the serrated grain boundary and subgrain boundary junction i s a modification of the grain boundary triple point configuration and hence one may apply the Zener mechanism for intercrystalline cracking a t a triple point to thie situation.

Weaversa, studying Nimonic alloys,.found that voids were often associated with carbide precipitates in the grain boundary. It would appear that this nucleation s i te for voids a s well a s that of the serratedgrain boundary, the jogged grain boundary, and the grain boundary triple point aite, a l l represent point of discontinuities in grain boundary sliding and clip in the grains, either in direction or in magnitude of the shear. Thus, in each case s t r e s s concentrations develop which may exceed the cohesive strength of the material. In the ca se of the eerrated grain boundary, the rupture occura on a subgrain boundary at the intersection with the grain boundary; and in al l other casea the rupture occurs on the grain boundary.

We must conclude that if the foregoing viewpoint i s correct, the ei tee of voids a l so repre- sen t points of low r desive strength of the material s ince similar discontinuities in hear a lso occur within the grains. The lower coheeive strength of the grain boundaries or the aub- grain boundaries may be affected by the segregation of impurities or alloying elements at these points. Bleakney'eSS experimente with copper indicate that the segregation of impurities ouch as oxygen may cause l o s s of coheeion a t grain boundaries a t certain temperatures. Similarly, Resnick and SiegleM found that the tendency towards cavitation in alpha brasa was dependent on oxygen content. The impurity effect may be twefold in that i t affects grain boundary migration ratee as well a s the cohesive etrength of the boundary. Ivanova and 0dingS7 believe that void formation occure on pre-existing micropores that are present in materials both in the e a s t form and the completely recrystallized state.

The eitc of formation of void nuclei ia extremely important to the theory baaed on the growth of voids by vacancy condensation. It i s important from the standpoint of the conditions for supply of vacanciee t o the nucleus for growth, a s well as from the standpoint that without a critical eize nucleua, precipitation of vacancies will not occur. Several investigatore have shown on a theoretical bas i s that a very large anpersaturation of vacanciee is neceeeary to form a etable cluster, hence i t i s unlikely that void formation originates by the precipitalion of vacanciee. Hull and Rimmerm have ehown that the critical s i ze of a nucleue which it neceeeary for growth by vacancy precipitation i s given by:

where 6 ia the critical radius of the void nucleua, y i s the eurface energy of the material, u the applied tensile atress , and P the superimposed hydrostatic pressure. If void nuclei are smaller than this critical s ize, they tend to sinter and disappear. For a s t ress of 1500 si (lo8 centimeters*2) and a surface energy of 1,000 erga/cm2, the critical void s i r e i s 2 x 10m5 cm, which i s a t the limit of the resolving power of a light microscope.

McLean3 hae applied S t r o h ' ~ ~ ~ equation for the e t ress a t the end of a d i p band, coneiating of a pile-up of edge dislocations which will initiate a crack perpendicular to the Burger's vector, to situations involving grain boundary sliding, such a s the jogged grain boundary, or the triple point crack. Stroh suggeate that a crack will form when the s trees at the end of a s l ip band eat isf ies the Griffith condition that the energy of the new surfaces created i s l e s s than the elast ic train energy released. This gives:

where T,, ia the applied ahear s t ress , and h i s the enerEy per centimeter2 of the crack surfaces, and n is the number of dialoeationa in the pile up. Since a depends on the length of the shear interface a t the applied etrees, according to the Eshelby, Frank and N a b a r r ~ ~ ~ relationship:

where L i s the slip distance and subetitution into equation (10) giver

McLean applied this equation to the eituation a t a triple point-with the assumption that the grain boundary eliding i s equivalent to the passage of dielocation~l, Thus, the aurface energy term now becomea the difference in surface energy of the grain boundary and the surface free energy, and L i s asaociatad with the length of the sliding grain boundary. For a grain s i z e of .l mm, he finds the critical applied tenmile s t r e s s for crack formation to be about 8 x 10 8

cm2 (10,000 psi) for copper. Th i s figure seems high for intercryetalline fracture in copper when compared to experimental data, however, the equation might give quite reasonable m e s a if. applied to stronger materials, such as .h igh temperature nickel base alloys. In addition. so:ute segregation a t grain boundaries could decreaee the difference of - ~ u r f a c e and interfacial energy and hence give a lower value for the critical applied tensi le etrses.

Growth of Voids

A sugg-tion by Greenwood e t a1d9 that the growth of voide occura by condeneation of vacancies would lead one to the conelusion that the bast way to verify the mechanism i s by a study of the rate of growth of voids, Such a study, however, requires that one have a reasonable model for the process, One neede to know the eouree of the voido, how they nucleate, and the rate of the transport process., ~ a c h l i n l ~ evaluated the rate of growth of voids, aasum- in s that the source of vacancies was the grain, the necessary vacenciee being $enerated during creep by the migration of euitable dieloeation jogs.

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Baluffi and SeigledO su iges ted that i t i s more reasonable to aasnme that the vacancies for void growth arise from the grain boundaries due to the tensi le etreeaes on the boundary, a s in the Nabarro and Herring expression for creep by diffursion of vacancies. Thie c a m e of vacan- c ies agrees better with the bbeervation that greater numbere of voide occur on transverse grain boundaries in teneion teats , whereas they occnr on longitudinal grain boundaries in compreeaion tests. McLean used th i s model in developing an expression for the volume of cavities which resulta from vacancy precipitation. He found that the rate of of cavities in nickel-base -

high temperature alloys was in reasonable agreement with hie calculations, Hull and Rimmar examined the relative contributions to void gtowth by lat t ice diffueion and grain boundary diffuaion, using the equation:

Dl.- Pa

where D ~ a n d Dg are rsspectively the lat t ice and g a i n boundary diffusion coefficients, p~ i s the void radius, and 6, i s the grain boundary width. Thie ratio gives the number of atoms transferred from a void to the boundary by lattice diffueion to that by grain bousdary diffusion. Substituting appropriate values for copper a t the temperatures of testing (400 to 500°C), they found that the contribution from lat t ice diffusion wae only 6 percent of the t a d , and therefore aet up a relationship for void p w t h based on p i n boundary diffusion, Thira was then related to the time to rupture for creep specimene by assuming that rupture takes place a s aoon as the

voids in the assumed equare array go to the point where they touch one another. The express ion for rupture time i s a s follows:

where K i s the Boltzmann constant , T the temperature, a the spac ing of the square array of void nuclei , T the apelied t e n s i l e s t r e s s , P the superimposed hydrostatic pressure , and fl the atom volume. If the spacing of void nucle i and the in i t ia ls ize of the void nuclei were as con- s t a n t as the equation presumes, then the rupture time would vary only as (u- P). Although the experimental determinations of the curve of rupture time versus tension s t r e s s at var ious v a l u e s of hydrostatic preasure did agree in form with the equation developed, it w a s found tha t i t w a s necessa ry to u s e different value8 of void spacing in order to superimpose the curves for different va lues of (u- P). In the t ens i l e s t r e s s range investigated, 4,730 to 6,000 p s i , i t w a s necessa ry to u s e va lues of a = 2.1 - 1.1 microns. In other r espec t s , the equation agreed quite well with the experimental data. T h e observed activation energy for void formation w a s 25,000 * 3000 cal/rnol, which i s a reasonable figure fo r ' the activation energy for - grain boundary diffusion in copper. A t e s t in which the value of ( r - P) w a s zero gave no evidence of any void formation in the creep specimen.

~ o s t t n e r ' a n d Robertson6' recent ly s tudied the growth of vo ids in copper during creep by measuring the change of dens i ty of such specimens. Their r esu l t s , shown in Figure 40, in- d i c a t e tha t the volume of voids produced during creep is a function of the to ta l s t ra in and i s different for different va lues of the applied s t ress . They a l s o obtain a n act ivat ion energy for the growth of vo ids equal to 29,000 cal/mole, which is in good agreement with the r e s u l t s of Hull and Rimmer. They conclude that g o w t h of voids does occur by a vacancy condensation mechanism.

Kramer a n d Machlin, on the other hand, have measured the fraction of to ta l grain boundary a r e a occupied by c racks and voids by l inea l ana lys i s , and have found t h a t t h i s measurement i s a l inea r function of percent elongation in creep62. They sugges t th is l inear response, us ing McLean's19 observation that the amount of grain boundary s l id ing is proportional to the amount of creep elongation, t o be dependent on the magnitude of grain boundary sliding. They contend that thei r r e su l t s confirm the generation of c r a c k s by ehear, and argue aga ins t the vacancy condensation mechanisms.

Seigle63 had subsequently cr i t ic ized the conclusions drawn from t h e s e data from the standpoint tha t neither of the crack growth mechanisms h a s yet been developed to a suff ic ient extent to s a y whether the l inear re la t ionship between crack grain boundary a rea and tota l elongation would e x i ~ t .

Mullendore and Grant have examined the change in volume of aluminum - 5% magnesium epecimene in creep a t 500°F, and find that the rate of growth of void volume in the second and third s t a g e a of creep ie approximately l inear, a s shown in Figure 41b. The s i z e distribution of vo ids under these tes t ing conditions i s indicated i n F i g u r e 41b. Application of the Hull and Rimmer formula to t h e s e da ta ind ica tes that the observed ra te of growth of voids cannot be explained so le ly by vacancy condensation and a certain large amount of the void growth must be due to a shear mechanism.

SUMMARY

It is p e r h a p obvious to the reader, even without comment from the authors, that the pas t fifteen years have witnessed a major advance in our understanding of high temperature deformation, even though the resul ts of the large amount of work cannot be neatly packaged into a s e t of conclusions. High temperature fracture, on the other hand, while definable from a mechanistic point of view, is very much more poorly understood.

There obviously remains much to be done. Additional work is necessary to se t t le a number of disagreements, however, the a reas of disagreement can be sharply defined and the necessary experiments and calculations A number of new approaches and afbae of intererst must be initiated to take advantage of the progresa already made.

In particular, these items or a reas can be selected for continuing, or for future research:

1. A check on Rachinger's high value of internal grain boundary sliding.

2. Does sliding take place on the grain boundary, or near the grain boundary?

3. The interplay of strain hardening and recovery on the creep process.

4, The role of solute segregation on boundary sliding and migration, and the change of grain boundary energy with aolid solution alloying.

5. A more positive check of intercrystalline crack initiation and the mechanism of crack growth and propagation, Thia work should be done in pure metals or simple solid solution al loys for the time being, s ince i t will serve aa a bas i s for studiee in complex alloys ( see below).

6. Does fracture occur in the grain boundary, in one grain, or does i t encompase both Grain boundary serrations would indicate a preference for the third cam.

7. The study of deformation and fracture should be extended immediately to two-phase alloys, including solid aolution mixtures and precipitation or dispersion hardened alloys. The very large variation in the ratio EGB/ET for aluminum - 3% copper alloys, as a function of heat treatment (structure) poEnt to very interesting and useful studiee. Fracture in these systems has been looked a t only in a very preliminary manner.

8. An extension of the s tudies to body-centered-cubic and hexagonal metala i s long overdue.

Finally, i t is expected that such atudies will, over the near term, permit tailoring al loys for optimum creep resistance with a maximum safety factor of high fracture ductility. The data should permit, for example, alloy development in which the $rain boundary is pinned by large precipitates and the graina strengthened by a fine precipitate, once the desired formula is known.

Recommended Research Activities

1. The interplay of strain hardening and recovery during high temperature deformation. Because strain rate as well as temperature are important variables, along with considerations of the structure of the material, the interplay of strain hardening and recovery must be better understood. The balance of these two forces determines the interplay of local processes, expecially the balance between grain and grain boundary behavior. The inbalance between these two phenomena has an extremely important bearing on the initiation and propagation of fracture.

2. The role of solute segregation on the grain boundary as well as along sub-boundariee, and the effect of such segregation on boundary sliding and migration. Consideration should be given to changes in grain boundary energy, surface energy, recrystallization phenomena, and fracture characteristics.

3. A detailed inveetigation of the initiation of intercrystalline cracking. Because of the extensive disagreement regarding the initiation of intercrystalline cracks, and the role that vacancy condensation plays in modern theory, this subject deeerves much greater attention. Once crack initiation i s better understood, i t should be possible to devote more time to crack propagation. For the time being, this work should be concerned with the behavior of pure metals and in simple solid solution alloys, avoiding for the moment two phase alloys.

4. Does sliding take place on the grain boundary, or near the grain boundary? Paral lel with thie problem i s the question of intercrystalline fracture., Does the fracture follow the grain boundary, does i t include the grain boundary and one grain, or does i t encompass the grain boundary and both grains? The recent observation of grain boundary ,serrations would indicate a preference for the third case.

5. A check should be made of Rachinger'a very high values of the contribution of grain boundary sliding a s measured internally, in contrast to the more extensive work based on surface measurementer.

6. An initial effort should be undertaken to s ta r t looking a t commercial alloys, or a t tailored two-phase or multi-phase alloys to s e e how both grain boundary sliding and grain boundary fracture differs in these more complex al loys in contrast to pure metals and simple solid solutions. A few recent observations have indicateda very large span of values of grain boundary contribution to total deformation a e a function of heat treatment (therefore structure). There is enough background of t e s t work, theory, and experimental techniques to permit a good star t in this direction.

1. W. Rosenhain and J. ,C. W. Humphrey, J. Iron S tee l Ins t i tu te , 1913, 87, 219.

2. 2. J e f f r i e s and R. S. -Archer, "Science of Metals", McGraw-Hill, 1924, p. -73.

D. McLean, "Grain Boundar ies i n Metals", Clarendon P r e s s , Oxford, 1957.

S. Weinberg, "Progress in Metal Physics" , 8, 1959, Pergamon P r e e s .

S. Amelinckx and I. Dekeyser , "Solid S ta te Physics9 ' , 8, 1959.

R. C. Gifkins , "Fracture", Ed i t ed by B. L. ,Averbach, D. .S. Felbeck, G. -T. ,Hahn, and D. A. Thomas. r h e Technology P r e s s and John Wiley and Sons, Inc., 1959.

F. -L. Vogel, W. G. -Pfann, H. -E. Corey and E. -E. Thomas, Phys . Rev,, 90, 1953, 489.

J. .M. ,Burgers, Proc . Koninkl. -Mad. .Akad. Wetenschop, 42, 1939, 293, 378.

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B. Chalmers, " ~ r o k r e s s in Metal Physics" , 3, 1952, 293.

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J. H. v a n de r Merwe, Proc. Phys . Soc., ,463, 1950, 616.

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22. W. A. Rachinger, J. Inst. Metals, 81, 1952, 33.

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24. N. J. Grant and A. .R. Chaudhuri, "Creep and Recovery", ASM, 1957, 284.

25. A. W. Mullendore and N. J. Grant: to be submitted to AIME.

26. 11. Drunner and N. ,J. Grant, Trans. AIME, 218, 1960, 122.

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33. Yoichi lshida: private communication.

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FIGURE 1

BURGERSm MODEL OF A SYMMETRICAL PURE T l L T BOUNDARY (5)

FIGURE 2

ASYMMETRICAL PURE T l L T BOUNDARY CONTAINING TWO SETS OF EDGE DISLOCATIONS, ACCORDING TO THE MODEL OF READ AND SHOCKLEY (9)

FIGURES 1 & 2

SQUARE GRID OF SCREW DISLOCATIONS FORMlHG A PURE TWIST BOUNDARY- SOLID CIRCLES REPRESENT ATOYI UNDER THE PLANE OF THE DRAWING; OPEN CIRCLES ATOMS ABOVE I T (5)

FIGURE 3

FIGURE 4

DISLOCATIONS IN A SMALL ANGLE BOUNDARY IN GERMANIUM REVEALED BY ETCH1 NG (7)

FIGURE 5

COMPARISON OF THEORETICAL ENERGY OF DISLOCATION BOUNDARIES (CURVE) WITH MEASURED ENERGIES OF GRAIN BOUNDARIES (POINTS) (AFTER READ AND SHOCKLEY) (9)

o Dunn Silicon iron (110) series, 8, 26.6 Dunn silicon iron (loo) sarlos, om = 29.8

0 Aust m d Cholrner's tin, ern = 122 Auat and Chalrner'a lead, 6, = 25.7

FIGURES 4 6 5

FIGURE 6

RELATIVE BOUNDARY ENERGY OF < 100' TILT BOUNDARIES IN GERMANIUM, AS A FUNCTION OF BOUNDARY ANGLE (14)

ORIEWTATIW OIFFERLNCC 16191wat - FIGURE 7

RELATIVE BOUNDARY ENERGY AS A FUNCTION OF ORIENTATION DIFFERENCE FOR SILVER CHLORIDE TRICRYSTALS OF c loo>, < llo>, AND < 11e ISOAXIAL ORIENTATION (15)

-178- FIGURES 6 & 7

mENfAflON mF ARE= ( DEOREES)

FIGURE 8

RELATIVE GRAIN BOUNDARY CONCENTRATION O f POLONIUM, AS A FUNCTION O F BOUNDARY ANGLE I N A LEAD - 5% BISMUTH ALLOY (29)

' 1 1 1 ' 1 1 1 ' 1 I . Across Boundory Between Groins R ond P 11 K D h R III A Across Boundory 0etween Groins C -

0 6 I0 20 30 40 50 60 7 0 80 eo Time In Hour6

FIGURE 9

COMPONENT CREEP CURVES ACROSS GRAIN BOUNDARIES OF AN ALUMINUM POLYCRYSTAL TESTED AT 7W0F (23)

FIGURES 8 & 9

.r

Or

0.01

402

0.0

3

00

4

0.0

s

0.0

6

0.07

0.

08

am

0(

&T

EGB V

ER

SU

S E

T F

OR

CO

NS

TAN

T S

TR

AIN

RA

TE

TE

STS

OF

A;-1

.9

PE

RC

EN

T M

G (

25)

and

GR

AN

T

FIGURE 11

CONTRIBUTION OF GRAIN BOUNDARY SLIDING TO TOTAL ELONGATION, IN PERCENT, FOR PURE ALUMINUM AND TWO ALLOYS, AFTER ABOUT 10 PERCENT STRAIN (21)

FIGURE 12

COMPARISON OF THE PRESENT TEST RESULTS WITH THE PUBLISHED DATA OF MCLEAN (2 1)

-181- FIGURES 11 & 12

FIGURE 13

FIGURE 14

GRAIN BOUNDARY SLIDING PLOTTED AGAINST GRAIN SIZE (30)

Materlal and Treatment 99.95% Al; 10.12 grdna/mrn; E = 0.1% ht. 99.98% Al; 2-73 gralndmm; E = 0.1% hour 99.994% Al; 1-0 praln/mm; stress probably 250 lb/ln2 99.99% Al; 0-4 graln/mm; skess 250 lb/in2; E r m g d from 0.2%/hr ot 3 3 7 O ~ to 73Whr at 4 7 4 O ~

FIGURE IS I C O W RlBUTlON PF GRAIN BOUNDARY SLIDING TO TOTAL DEFORMAtlgN VERSUS STRAIN FOR PURE A1 AT 940 F (STRAIN RATE Z4WHR); Al-1.9% MG ALLOY AT 500 F STRAIN RATE 0.9%/HR); AND A14196 MG (STRAIN RATE Z6%/HR). LISTED FIGURES ARE GRAlN DIAMETERS (26)

-1 83- FIGURES 14 & 15

cos 9 cos hoes

MAGNITUDE OF GRAIN BOUNDARY SLIDING VERlUS RESOLVED SHEAR STRESS ON THE GRAIN BOUNDARY FOR AN A1-1.9% MG POLYCRYSTALLINE SPECIMENS (91)

FIGURE 16

SIN 6 COS u,

GRAIN BOUNDARY DISPLACEMENTS AFTER 5-1/2% ELONGATION VERSUS SIN 6 a w , A GRAIN ORIENTATION FACTOR, FOR Af-1.9% MG POLYCRYSTALLINE SPECIMENS AT 500°P, € - 2IHOUR (25)

FIGURE 17

STRUCTURES PROWCED BY DIFFERENT HEAT TREATMENTS OF A1-3% CU (33) 500X

FIGURE 18

20 30

Time (hr 1

TYPICAL CREEP CURVES FOR Al-3% CU (33)

FIGURE 19

Tima ( h r )

FIGURE 20

GRAIN BOUNDARY SLIDING CONTRIBUTION TO ELONGATION VERSUS TIME FOR A1-3% CU AS A FUNCTION OF HEAT TREATMENT (33)

Tim - FIGURE 21

FIGURES 20 & 21

FIGURE 22

PLOT OF ACTIVATION ENERGY FOR GRAIN BOUNDARY SHEAR VERSUS BOUNDARY MISORIENTATION ANGLE 8 (35)

BEFORE SLIP b. SLlP AND SLIDING

0. BEFORE SLIP b. SLIP AND SLIDING FIGURE 23

SCHEMATIC OF SLlP INDUCED SLIDING (25)

FIGURES 22 & 23

BICRYSTAL 4

BICRYSTAL 2

GRAIN BOUNDARY DISPLACEMENTS AROUND THE CIRCUMFERENCE OF Al-1.9% MG

BICRYSTALS AFTER CREEP AT S0o0F. E * HO HOUR, Et 2 SJZ (25)

FIGURE 24

FIGURE 25 tan P

lcos w, (1 - -) I tan a

GRADIENT OF GRAIN BOUNDARY SLIDING VERSUS A RELATIVE ORIENTATION FACTOR FOR A1-1.9% MG BICRY,STALS (25)

OW31 0 i 0 0 2 M 4 ,006

WElGnT PERCENT OF TIN

F I G U R E 26 THE R A T E O F GRAIN BOUNDARY MIGRATION O F ZONE-REFINED L E A D AS A FUNCTION OF THE WEIGHT PERCENT OF ADDED T IN FOR "RANDOM" AND "SPECIAL" GRAIN BOUNDARIES ANNEALING TEMPERATURE 30O0C (43)

-191- FIGURES 2 5 & 26

FIGURE 27

SUBSTRUCTURE NEAR SERRATED BOUNDARY. POLARIZED LIGHT. lOOX Al-1.9%MG (31)

FIGURE 28

EXAMPLE OF SERRATED GRAIN BOUNDARY WITH VOIDS. 100X. Al- 1.9% MG (3 t )

FIGURES 27 & 28

1000 10000 STRESS - PSI

SERRATION WAVE LENGTH VERSUS STRESS FOR RUPTURE CREEP SPECIMENS OF A1 - 1.9% MG (32)

-1 93- FIGURE 29

FIGURE 30

FIGURE 31

I Rupture life, hours

REDUCTION OF AREA AS A FUNCTION OF RIJPTI,IRE LIFE FOR 80 NI-20 CR ALLOYS (2V IS VACUUM MELTED) AND (3A IS AIR MELTEQ). TESTED AT 1200°, IHNL~, AND 1600'~ (45)

FIGURE 32

80 NI-20 C R VACUUM MELTED, TESTED AT 1800O~, 2750 PSI. RUPTURE LIFE - 347 HOURS, TOTAL ELONGATION - 85% 10X (45)

FIGURE 33

SCHEMATIC VIEWS SHOW THREE OF THE SIMPLE BASIC MEANS OF INITIATING INTERCRYSTALLINE CRACKS DUE DIRECTLY TO GRAIN BOUNDARY SLIDING. THE ARROWS ALONG A GRAIN BOUNDARY INDICATE THAT THIS BOUNDARY UNDERWENT SLIDING (46)

FIGURE 34

SCHEMATIC wews SHOW THE MORE COMPLEX INITIATION OF INTERCRYSTALLINE CRACKS WHICH ARE BASED ON THE SIMPLE CASES SHOWN IN FIGURE 34 (46)

FIGURE 35

CRAtKS AND WID) IN Al-LlO% YO TgSTEB AT WF, 0.53 HOUR RUPTURE LIFE, 100X. (3D (3 LUClTC IWRtGNAtED rSnD MECHAWICALLY POLISHED (b) SAME AREA ELECTROLYTICALLY POLISHED

FIGURE 36

GRAIN BOUNDARY SERRATIONS AND VOIDS. 10OX (31) (3 I l O W Ye, W F , 5P00 PSI (b) l.9%MG, 700@F, 4000 PSI

FIGURE 37

bECHANISM FOR VOID INITIATION ON A JOGGED GRAIN BOUNDARY (53)

FIGURE 38

TOP

OG

RA

PH

Y O

F G

RA

IN B

OU

ND

AR

Y 1

1.

A 1-

1.9%

MG

PO

LY

CR

YS

TA

L,

500°

F,

15-1

/25

ELO

WG

ATI

OH

, E

= l%

/HR

. 40

0X

(31

)

STRAIN. IN /IN

VOID VOLUME AS A FUNCTION OF CREEP STRAIN AT SOO'C IN ARGON FOR SPECIMENS FROM FIVE BARS OF OFHC COPPER. AT 200 PSI SPECIMENS WERE TESTED IH ARGON AND,IN AIR (61)

FIGURE 40

VOlD DIAMETER - MY

.003 - A l -5.1 O A MG W ° F 11000 PSI 1/4 HR RUPTURE LIFE

-002 - L

qs .001 --

I 1 I I I I 12 I4 16 18 20 22 24 26

ELONGAY ION - PERCENT

b

INCREASE I N THE NUMBER OF VOIDS AND VOlD VOLUME WITH ELONGATION IN CREEP OF A1-5, 1% MG A t MOOP (31)

-205- FIGURE 41

LIST OF ATTENDEES

Abrahamaon 11, E. .P.

Ale~ande r , J. .A.

Avery, D. -H.

Backofen, W. A.

Barrett, J. C.

Bachtold, J. .H.

Bhat, G, -K.

Birchenall, C. "E.

Brittain, John

Burke, J. J..

Chang, W. H.

Cornthwaite, C. -R.

Cuff, Jr.; F. B.

Cupp, C. R.

Darcy, G. A,; Jr.

Davis, R. S.

Decker, R.

dulier, E. J.

Elbaum, C.

Farnsworth, H, E.

Galbraith, R. A.

Grant, N. J.

Grcwal, K. S.

Galbransen, E. A.

Hagel, W. C.

Hodi, F. S.

Watettown Areenal, Watertown, Masa.

Watertown Arsenal, Watertown, Maae.

MI T, Cambridge, hiasa.

M IT, 35-238 M IT , Cambridge 39, Maes.

Office of Director Defenae Reaearch & Eng., Pentagon, Waahington, D.C.

Weetinghouse Electric, Reaearch Labs. ,Bedan Rd., Pittsburgh 35, Pa.

Mellop Institute, 4400 Fifth Avenue, Pitteburgh 13, Pa.

University of Delaware, Dept. of Chem. Eng. Newark, Del.

Northwestern Universitys Evaneton, Illinoie

OMRO, Watertown Areenal, Watettown, Masr~,

General Electric, Flight Propulsion Lab. .Dept. Cincinnati 15, Ohio

DA, OCO, Waahington 25, D.C.

Advenced Metala Reeearch, 625 McGrath Highway, Somerville, Maee.

International Nickel Co.; 8 Cattier Circl'e (P.O. Box 236) Deep River, Ontario

OMRO, Watertown Areenal, Watertown, Maes.

A. :D. Little, Ine., 15 Acorn Park, Cambridge 40, Mass.

International Nickel Co., Bayonne, hew Jeraey

Crucible Steel Co. of America, 234 Atwood St., Pittsburgh, Pa.

Brown Univereity, Providence 12, R. I.

Brown University, Providence 12, R. I.

Syracuae Univereity, Bldg. 6, Campus, Syracuee 10, N. -Y.

MIT, 8-305 MIT, Cambridge, Maee.

Syracuee University, Bldg. D d , Collendale, Syracuae 10, N. Y.

Wednghouee Research Laba., Churchill Borough, P i t t ~ b u r ~ h , Pa.

General Electric, Reeearch ~ a b . , Sehenectady, N. Y.

OMRO, Watertown Arsenal, Watettown, Maarr.

Huminik, Jr., J. Value Eng. Co., 2320 Jeff Davis Highway, Alexandria, Va.

Inverarity, B. I Adirondack Museum, Blue Mt . Lake

Jacobson, M. M.

Jaffe, R. I.

Jones, A. F.

Kaufman, L.

Keller, D, V.

Kleppinger, D. H.

Kula, E.

Latorre, J. .V.

Lesl ie , W. C.

Levitt , A. P.

Lowrie, R.

Maltz, J.

Markus, H,

Moran, Jr., J. J.

Newkirk, J. B.

Paekman, P.

Pope, H.

Pechera, K. -G.

Queisaer, H. J.

Radavich, J. F.

Reed, N. L.

Robertson, W. D.

Schaeffer, G. T.

Schuetz, A. .E.

Sessler, J. G.

Shepheard, R. .G.

Sullivan, J. F.

Takimoto, A.

Watertown Arsenal, Watertown, Mass.

Battelle Memorial Institute, Columbus 1, Ohio

OMRO, Watertown Arsenal, Watertown, Mass.

Manufacturing Lab., 21 Erie St., Cambridge, Mass.

Syracuse University, 344 Hinda Hall, Campua, Syracuse 10, N. Y.

Frankford Arsenal, Philadelphia, Pa.

Watertown Araenal, Watertown, Mass.

Syracuse University, Bldg. .D-6, Collendala, Syracuse 10, N. Y.

U.S. S t ee l Corp., E.C. Bain Lab. for Fundamental Research, Research Center, Monroeville, Pa.

Watertown Araenal, Watertown, Mass.

Union Carbide Reaearch Institute, P. 0. Box 278, Tarryton, N. Y.

Bureau of Naval Weapons, Navy Dept.; Washington 25, D. -C.

Frankford Arsenal, Tacony & Bridge St., Philadelphia, Pa.

International Nickel Co., N.Y. 5, N.Y.

Cornell ~ n i v k r s i t ~ , Olin Hall, Ithaca, N. Y.

Syracuse University, Bldg. D-6, Collendale, Syracuse 10, N. Y.

Mellon Institute, 4400 5th Ave., Pittsburgh 13, Pa.

Marschall Space Flight Center, NASA, Redstone Araenal, Ala.

Shockley Transistor, Stanford ladustr. Park, Palo Alto, Cal.

Purdue University, W. Lafayette, Inc.

OMRO, Watertown Areenal, Watertown, Mass.

Yale University, New Haven, Conn.

Syracuee University, Bldg. D-6, Collendale, Syracuse 10, N. Y.

Sikorsky Aircraft, Div, of United Aircraft Gorp. Stratford, Conn.

Syracuee University, Bldg. D-6, Collendale, Syracuee 10, N.Y.

Elec. Boat Co., Div. of General Dynamics, Groton, Conn.

Watertown Araenal Lab., Watertown Arsenal, Mass.


Tarpinian, A.

Warmuth, F. J.

Warnas, Albert

Weddeling, F. K.

Weigle, R. E.

Wainberg, F.

Weiee, V.

Werner, I?. E.

Wilsdorf, H. G. F.

Wimmer, A.

Wong, A.

Wyman, L. ,L.

Widmer, R.

Zwileky, K

Jaffe, H.

Watertown Arsenal Lab., Watertown Arsenal, Mass.

Special Metale, Inc.; New Hartford, N.Y.

OMRO, Watertown Arsenal, Wstertown, Mass.

U.S. Army Reeearch Office (Durham), Box CM, Duke Station, Durham, N. C.

Waterdiet Arsenal, l a t e r d i e t , NI Y.

Govt. -of Canada, Dept. of Minee and Technical Surveye, 568 Booth St., Ottawa, Canada

Syracuse University, Bldg. .Dd, Collendale, Syracusa 10, N. Y.

Weatinghouee Electric, R e ~ e a r e h Laba,; Bealen Rd,, P i t t ~ b u r ~ h , Pa.

Franklin Institute, Philadelphia 3, Pa.


Watertown Arsenal, Watertown, Maas,

National Bureau of Standards, Dept. of Commerce, Washington, D. C.

New England Materials Lab., Medford, M a ~ e .

New England Materiale Lab., Medford, Mase.

ARDE - Portland, Paramus, N. J.

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