Ternary Phase Diagrams

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Phas DiagamsUdstadig th BasicsF.C. Campbll, dito

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Chapter

10Ternary Phase Diagrams

TernAry SySTeMS a thos havig th compots. It is ot pos-sibl to dscib th compositio of a ta allo with a sigl umb

o factio, as was do with bia allos, but th statmt of two id-

pendent values is sufcient. For example, the composition of an Fe-Cr-Ni

allo ma b dscibd full b statig that it cotais 18% C ad 8% ni.

Th is o d to sa that th io cott is 74%. But th quimt

that two paamts must b statd to dscib ta compositio mas

that two dimsios must b usd to pst compositio o a complt

phase diagram. The external variables that must be considered in ternary

costitutio a tmpatu, pssu, compositioX

, ad compositioY.To costuct a complt diagam pstig all ths vaiabls would

qui th us of a fou-dimsioal spac. This big out of th qustio,

it is customa to assum pssu costat (atmosphic pssu) ad to

costuct a th-dimsioal (3-D) diagam pstig, as vaiabls, th

tmpatu ad two coctatio paamts. Thfo, i a applica-

tio of th phas ul, it should b calld that o dg of fdom has

been exercised in the initial construction of the 3-D diagram by electing

to daw it at o atmosph of pssu.

10.1 Space Model of Ternary SystemsTo pst compltl th phas quilibia at costat pssu i a

ta sstm, a 3-D modl, commol tmd a spac modl, is quid;

th pstatio of compositio quis two dimsios, ad that of

tmpatu, a thid dimsio. Th modl usd is a tiagula pism (Fig.

10.1), in which the temperature is plotted on the vertical axis, and the com-

positio is pstd o th bas of th pism, which ma b covitl

tak as a quilatal tiagl. Thus, i Fig. 10.1, th vtical sids of th

pism pst th th bia sstms,AB,BC, adAC, that mak up

th ta sstm,ABC.


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192 / Phase DiagramsUnderstanding the Basics

A hpothtical ta phas spac diagam mad up of mtalsA,B, ad

Cis show i Fig. 10.2. This diagam cotais two bia utctics o th

two visibl facs of th diagam, ad a thid bia utctic btw l-

mtsB ad Chidden on the back of the plot. Because it is difcult to use

Fig. 10.1 Sc modl fo ny s digms

Fig. 10.2 hyoicl ny s digm. Biny s digms sn long fcs. add fom rf 10.1


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Isopleth Plots. Ctai goups of allos ca b plottd as vticalsections, also called isopleths. These sections often represent a xed

compositio of o of th lmts, whil th amouts of th oth two l-

mts a allowd to va. Ths plots show how th phass ad stuctus

chag wh th tmpatu vais ad wh two of th lmts pst

chag thi spctiv amouts. Ti lis usuall do ot li i th pla of

a vtical sctio ad caot b usd to obtai amouts ad compositios.

A isoplth though th hpothtical diagam (Fig. 10.2) at a costat

40% Cis show i Fig. 10.5. A allo cotaiig 30%A ad 30%B will

bgi to fz a 350 C (660 F), with pima forming rst. Near275 C (530 F), will also begin to form. Finally, at approximately 160C (320 F), forms and the last liquid freezes. The nal microstructurecotais , , ad . Isoplths a quit valuabl i showig th phassthat a pst duig quilibium coolig ad hatig. Th also show

th tmpatus at which th vaious phas chags occu.

Single-Phase Boundary and Zero-Phase Fraction Lines. Two-dim-sioal (2-D) sctios of a multicompot phas diagam, whth it is

a isothm o a isoplth, ca b ad b focusig o two lis that f

to o paticula phas. Ths lis a show i th Fig. 10.6 isoplth foF-17%C-%C allos.

Fig. 10.4 Isoml lo oom mu fo yoicl ny sdigm. add fom rf 10.1


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Chapter 10: Ternary Phase Diagrams / 195

Fig. 10.5 Isol oug yoicl ny s digm consn40% C. add fom rf 10.1

SPB Line. Th sigl-phas bouda li is foud o a sctio that

cotais a sigl-phas gio. Th li is what its am implis. It is th

boundary line around that single-phase region. It can be used, for example,

to dtmi compositios ad tmpatus wh a allo ca b tho-

oughl solutioizd.

ZPF Line. Th zo phas factio li is a li that suouds all

gios o th diagam wh th phas occus. O o sid of th lith a gios with th phas, ad o th oth sid of th li th a

gios without th phas. Bcaus th li suouds a gio of compo-

sitios ad tmpatus wh th phas foms, it ca b usd to avoid a

phase, for example an embrittling phase, or promote a phase, for example

a pcipitatio-hadig phas.

B dawig ths lis, th ad is abl to focus o o phas at a tim

ad igo th lis that coc oth phass. Although it is tu that th

lv ul caot b usd h, it ca b assumd that movig clos to a

SPB li will likl icas th amout of th phas, whil movig clos

to th ZPF li will dcas th amout of th phas. Th liquidus adsolidus lis a SPB ad ZPF lis fo th liquid, spctivl. Also, it is


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woth otig that a isoplth is a collctio of ZPF lis fo th vaious

phass pst. Comput pogams that pdict phas diagams ca giv

a phas diagam i th fom of ZPF lis alo. I this cas, th lis a

labld istad of th gios.

10.2 The Gibbs Triangle

Bcaus of its uiqu gomtic chaactistics, a quilatal tiagl

povids th simplst mas fo plottig ta compositio. O th Gibbs

tiagl, which is a quilatal tiagl, th th pu compot mtals

a pstd at th cos,A,B, ad C, as show i Fig. 10.7. Bia

compositio is pstd alog th dgs, that is, th bia sstms

AB,AC, adBC. Ad ta allos a pstd withi th aa of th

tiagl, such as at poit P i Fig. 10.7.

If lis a daw though Allo P paalll to ach of th sids of thtiagl, it will b foud that ths hav poducd th small quilatal

Fig. 10.6 C-C-F isol sowing singl-s boundy (SpB) lins nd zo-s boundy (ZpB) lins.Souc: rf 10.2


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tiagls: aaa, bbb, ad ccc. Th sum of th lgths of th i sids of

ths th tiagls is qual to th sum of th lgths of th th sidsof th majo tiagl, ABC, withi which th a iscibd; o th sum

of th lgths of o sid fom ach of th mio tiagls is qual to th

lgth of o sid of th majo tiagl: a + b + c =AB =AC=BC. Also,

th sum of th altituds of th mio tiagls is qual to th altitud of

th majo tiagl: a + b + c =AX.

If o sid of th Gibbs tiagl is dividd ito 100 qual pats, p-

stig 100% o th bia compositio scal, it is foud that th sam

uits ca b usd to masu th compositio at poit P. Lt th lgth a

pst th pctag ofA i P, th lgth b th pctag ofB, ad

th lgth c th pctag ofC. Bcaus ths lgths total th sam aso sid of th Gibbs tiagl, ad togth th must qual 100%, it is

vidt that 1% has th sam lgth, whth masud alog a dg of

th diagam o alog a iscibd li paalll to a dg. A simila sult

could b obtaid b usig altituds, but this is lss covit. It should

b otd that i ith cas, th pctag ofA is masud o th sid of

P awa fom thA co ad similal withB ad C.

Fo covic i adig compositio, a quilatal tiagl ma b

uld with lis paalll to th sids (Fig. 10.8). Compositio ma th b

read directly, for example, P = 20%A + 70%B + 10% C. At poit P, th

pctag ofA is pstd b th li Pa (o quivaltl Pa), which is20 uits log; th pctag ofB b th li Pb (o Pb), 70 uits log; ad

Fig. 10.7 t Gibbs ingl. add fom rf 10.3


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th pctag ofCb th li Pc (o Pc), 10 units long. Other examples

show i Fig. 10.8 a: AlloR = 30%A + 40%B + 30% C, Allo S= 80%

A + 10%B + 10% C, ad Allo Q = 60%A + 0%B + 40% C.

10.3 Tie Lines

If any two ternary alloys are mixed together, tie lines can be shown. The

composition of the mixture will lie on a straight line joining the original

two compositios. This is tu gadlss of th popotios of th two

alloys in the mixture. Conversely, if an alloy decomposes into two frac-

tios of diffig compositio, th compositios of th two potios will li

o opposit ds of a staight li passig though th oigial compositio

poit. Cosid Fig. 10.9. Poits SadL pst two ta allos of

spctiv compositio: 20%A + 70%B + 10% Cad 40%A + 30%B +

30 % C. Suppos that o pat ofSis mixed with three parts ofL ad th

mixture is analyzed. The analytical result will be:

0.25 20%A + 0.75 40%A = 35%A

0.25 70%B + 0.75 30%B = 40%B0.25 10% C+ 0.75 30% C= 25% C

Fig. 10.8 t Gibbs ingl wi comosiion lins. add fom rf10.3


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As ca b s b ispctio of Fig. 10.9, this compositio lis at P, which

is a poit o th staight li coctig SadL. rgadlss of th com-

positions chosen or in what proportions they had been mixed, the total

compositio would hav occud o th li joiig th two oigial

compositios.

It is vidt that th li SL has th chaactistics of a ti li: It is both

isobaic ad isothmal, bcaus it lis i th compositio pla, which is

drawn perpendicular to the temperature axis and corresponds to the case

of costat atmosphic pssu (i.., it would b daw ppdicula to

the pressure axis if a fourth dimension were available). The lever principleis applicabl to this li. Thfo, th li SL might pst th codi-

tio of a allo of compositio P that is patiall foz, at th tmpatu

ud cosidatio, ad cosists of 25% solid of compositio Sad 75%

liquid of compositioL:

% SPL

SL= 100

%L

SP

SL= 100

Fig. 10.9 t Gibbs ingl wi i lin. add fom rf 10.3


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10.4 Ternary Isomorphous Systems

A tmpatu-compositio (T-X-Y) diagam of a isomophous sstm

is shown in Fig. 10.10. The composition plane forms the base of the gure,

ad tmpatu is masud vticall. H, th liquidus ad solidusbcom sufacs boudig thL + spac. Abov th liquidus, all allosa full molt; blow th solidus, all a compltl solid. As i bia

sstms, th two-phas gio, L + , is composd of ti lis joiigcojugat liquid ad solid phass. I th ta sstm, howv, th ti

lines are not conned to a 2-D area but occur as a bundle of lines of vary-

ing direction, but all horizontal (isothermal), lling the 3-D two-phase

spac.

Isothermal Sections. Th locatio of th ti lis ca b visualizd

mo asil b fc to isothmal (hoizotal) sctios cut thoughth tmpatu-compositio diagam at a sis of tmpatu lvls.

Th th isothms pstd i Fig. 10.11 a tak at th tmpatus

dsigatd T1, T2, ad T3. It is seen that the rst tie line on each edge of the

L + region is the bounding line of the gure; that is, it is the binary tieli at th tmpatu dsigatd. Th dictios of ti lis lig withi

Fig. 10.10 tmu-comosiion sc digm of ny isomo-ous sysm. add fom rf 10.3

Ternary Phase Diagrams

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