Lange Powder Processing

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J . A m . Ceram. SOC.,72 [ I ] 3-15 (1989)journal Powder Processing Science andTechnology for Increased Reliability

Fred F. Lunge*Materials Department, College of Engineering,University of California, Santa Barbara, California 93106

Issues concerning powder consolidationmethods compatible with the colloidalapproach and issues associated withother powder processing steps,viz., den-sification and microstructuralcontrol, arepresented with regardto research direc-tions leading to more reliable ceramics.[Key words: powder, microscopy, colloi-dal chemistry, processing, hetrogeneity.]

1. IntroductionWith their multiplicity of elemental com-binations and crystal structures, ceramicsexhibit unique properties that are still be-ing uncovered. Ceramics are needed toimplement many technology scenariosranging from advanced heat engines totransmission of information.Ceramic-processing technology hasadvanced little beyond the needs of func-tional ceramics. Traditional ceramicprocessing inherently lacks a clear ap-

proach for controlling microstructure het-erogeneties and microstructure uniformity.Property variability and, thus, ambiguousengineering reliability stem from uncon-trolled microstructures. Engineering relia-bility is a matter of processing reliability.Most forming methods are generally un-acceptable for ceramics. Their brittle na-ture precludes deformation methodscommonly used for metals. Melt castingproduces friable ceramics because of, inpart, uncontrolled grain growth duringsolidification. Some advanced ceramics,

ManuscriptNo 199141 Received September 261988, approved October 20, 1988Presentedat the 89th Annual M eetingof the American Ceramic Society, Pittsburgh PA, April 29, 1987(Paper No 199-8-87 (Sosman Lecture))Supported in part by the U S Air Force Office ofScientific Research under Contract NoAFOSR-87-0291*Member American Ceramic Society

viz., Si3N4 and Sic, decompose prior tomelting. Glass-ceramic processing, a spe-cial melt-forming method that takes advan-tage of Newtonian rheology to formshapes and crystallization after solidifica-tion to control microstructure, producesnonequilibrium phase assemblages andis limited to glass-forming chemistries.Columnar grain growth and uneconomi-cal deposition rates are disadvantages forchemistries that can be shaped by vaporcondensation methods. Liquid precursormethods, e.g., sol-gel processing, sufferfrom large volume changes during fluidremoval, pyrolysis, and/or densification,which limits this methodto shaping smallbodies, .e., particles, thin films, and fibers.Most advanced ceramics are formed aspowder compacts made dense by heattreatment. Although powder processing sa many-bodied problem prone to heter-ogeneities and nonuniform phase distribu-tions, it is the most efficient method to formceramics. The objective of this article istoreview new approaches and thinking lead-ingto the increased reliability of ceramicsprocessed with powders.

II. Heterogeneities Common toPowder ProcessingPowder processing involves four basicsteps: (1) powder manufacture, (2) pow-der preparation for colsolidation, (3)con-solidationto an engineering shape, and(4) densification/microstructuraldevelop-ment that eliminates void space andproduces the microstructure that optimizesproperties. Each step has the potential forintroducing a detrimental heterogeneitywhich will either persist during furtherprocessing or develop into a new heter-ogeneity during densification and micro-structural development.Because the number of heterogeneitiesper unit volume can be small, they arebest observed with an experiment sensi-

Dr.Lange is professor in the Depts. ofMaterials and Chemical and NuclearEngineering at the University of California,Santa Barbara. He received a B.S. inceramic science from Rutgers Universityin 1961 and a Ph.D. in solid statetechnology from Pennsylvania StateUniversity in 1965. After graduate studies,he spent two years in a postdoctoralcapacity at the Atomic Energy ResearchEstablishment, Harwell, England. During1967-76 he was with WestinghouseResearch and Development Labs, andduring 1976-86 he was with Rockwell IntlScience Center.A Fellow of the ACerS, he is affiliatedwith the Basic Science Division. In 1982he was a recipient of the Societys RossCoffin Purdy Award and in 1987 hepresented the Basic Science DivisionsSosman Lecture.


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4 Journal of the American Ceramic Society-Lunge Vol. 72 , N o. 1

POTCNTIAL STRLNGTI i

Fig. 1. Schematic plotof frequencyversuspotential strengthof different flaw populationspotentially present in a ceramc material Fre-quency distribution and ordering dependsonprocessing method and material charac-teristics

tive to heterogeneities. Because strengthis sensitive to stress concentrators, micro-structural heterogeneities that are stressconcentrators can be best observed byfracture and examination of fracture ori-gins.* As schematically illustrated in Fig.1 , many different heterogeneities maycoexist. Each can be viewed as a strength-limiting flaw population, ntroduced duringsome stage of processing. The orderingof the common flaw populations shown inFig. 1 and their strength-size distributiondepends on the material and its process-ing. For example, some materials, such asSic and P-A1203,are proneto develop amicrostructure containing large, platelikegrains. These platelike grains can be thefirst flaw population uncovered duringstrength determinations, whereas someother flaw population, e.g., cracklike voidsproduced by the differential shrinkage ofagglomerates, can be the dominant het-erogeneity observed either in the samematerials processed n a differentmanneror in other materials not prone to abnor-mal grain growth. Once the dominant flawpopulation is identified and eliminated byprocessing changes, another flaw popu-lation with a higher mean strength will beuncovered. Its strength-size distributionwill now dominate strength statistics. Theprocessor interested in eliminating heter-ogeneities must first identify the dominantheterogeneity observed at fracture origins,ascertain how this heterogeneity is rn-troduced during processing, and thenmake the appropriate processing changesto eliminate the heterogeneity. This is aniterative scheme.Many microstructural heterogeneitiesstem from the powder itself. Agglomeratesare a major heterogeneity in powders. Theattractive interparticle forces responsiblefor free particle agglomeration includevan der Waals and capillary forces. Capil-lary forces are produced when water va-por condenses at particle contacts. Aftera liquid has been removed by evapora-tion, particles can be cemented togetherwith previously soluble salts (e.g., withhydroxides) eft at contact positions. Mostceramic powders are manufactured bydecomposing and/or reacting a precursorat moderate temperatures. Nanometer-size crystallites, formed during pyrolysis,

*The strength of several ceramicscan be relatively insensitive to flaw size and t h u s insensitive to flawsintroduced during processing These ceramics include optimally aged transformation toughenedZrOP1and certain fiber composites with very weakfiber-matrix interfacial bond strengths 2 These relatively few ceramics possess a toughening mechanismthat increases the resistance of the material tocrackgrowth, I e , thecriticalstress intensityfactoras the crack grows Unfortunately these specialtougheningmechanisms are currently limitedto certain material systems and temperatures but whenfully exploited they could result instructural ceramics that are relatively insensitive to flaw populationsintroduced during processing and thus produce amaterialwith a relativeivnarrow strenathdistributionI e , high Wiebul modblus -

sinter togetherto a continuous low-densitycrystallite network. When the pyrolyzedmaterial is milled to make particles, theresulting particles can be partially dense,sintered crystallites, i.e., very strong ag-glomerates.

Current consolidation technology ISbasedon dry pressing and requires flow-able powders to uniformly fill a die cavi-ty. Particles within dry powders are heldtogether by van der Waals forces. Flow-able powders require large particles be-cause the separating force produced bydifferential acceleration during flow isproportional to particle mass. Becausethe separating forces produced by themicrometer-sizedparticles desired for ce-ramic processing are insufficient o over-come attractive (e.g., van der Waals)forces, ceramic powder slurries contain-ing polymer additions are spray dried topurposely form large (>50 p ) ggiomer-ates and a flowable powder.

Agglomerates with different bulk densi-ties can persist during powder consolida-tion to form cracklike voids duringdensification because of their differentshrinkage rates relative to the surround-ing powder cornpact.3 Agglomerates pur-posely produced by spray drying maynotuniformly deform to fill interagglomeratevoid space4 during consolidation. They willleave irregular voids that persist after den-sification. Agglomerates also limit densifi-cation.5,6

Powders contain organic and inorgan-ic inclusions introduced by both themanufacturer and the processor duringpowder preparation for consolidation.Some of these heterogeneities are in-troduced when powders are milledto re-duce the size of hard agglomerates and/orare exposed to the environment. Organicinclusions disappear during densificationto leave irregularly shaped voids.7 Inor-ganic inclusions can react with the pow-der during densification and/or producemicrocracks during either cooling from thedensification temperature or subsequentstressing. Clean rooms are ineffective be-cause the manufacturer supplies the inclu-sions with the powder.Postdensification hot-gas isopressingcan eliminate some voids that remain af-ter pressureless densification.8 Recentresults strongly suggest that void closureoccurs by deformation,g and cracklikevoids, e.g., those produced by thedifferentialshrinkage of agglomerates, arethe firstto close.10 Unfortunately, postden-sification hot-gas sopressing cannot elim-inate pores that intersect the surface andother heterogeneities, e.g., inclusions.Moreover, postdensification hot-gasisopressing can exaggerate the size ofvoids just beneath the surface when theligament separating the void from the sur-face punctures by deformation.9Many advanced ceramics contain morethan one phase and are produced by mix-ing two or more powders prior to consoli-


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January 1989 Powder Processing Science and Technology for Increased Reliability 5dation and densification. As discussedlater in this paper, a second phase canbe used to eliminate abnormally largegrains which are common heterogeneitiesdeveloped during densification of noncu-bic crystalline structures. Phase homoge-neity is a major issue in these multiphaseceramics, and even when the desiredhomogeneity is obtained during mixing,heterogeneities can arise if mass segre-gation occurs by sedimentation aftermixing.If reliable ceramics are to be produced,methodologies must be developedto en-sure, with a high probability, that heter-ogeneities will be eliminated from powdersand that they will not be reintroduced insubsequent processing steps. As dis-cussed in the next section, the colloidal ap-proach has this potential.

111. Colloidal App roachHeterogeneities must be separated from

current powders. When technologies aredeveloped to produce powders free ofheterogeneities, we must have a method-ology availableto process these powderswithout introducing new heterogeneities.Powders must flow to fill either die cavi-ties or molds to consolidate shapes. Oncea powder is fractionated and made flow-able, it cannot be exposedto an uncon-trolled environment prior to consolidation.As will be come evident, the colloidal ap-proach IS consistent with these re-quirements.Many of the heterogeneities discussedearlier in this paper can be eliminated fromtheir sources, i.e., the powders, bymanipulating and controlling interparticleforces as practiced n colloid science. Cer-tain aspects of colloidal processing requirerepulsive interparticle forces, whereasothers require attractive forces. Powdersdisperse to form a system of separatedparticles when repulsive forces dominateand they floc to form a low-density networkof touching particles when attractive forcesdominate. Repulsive interparticle forcesare usedto break apart weak agglomer-ates. fractionate nclusions greater than agiven size, and mix different fractionatedpowders. Once fractionated and mixed,the interparticle forces can be made attrac-tiveto forma low-density,deformable net-work that prevents mass segregation.Slurry rheology depends on interparti-cle forces and particle volume fraction.li.12Dilute, dispersed slurries exhibit Newtoni-an rheology (viscosities independent ofshear rate). At high volume fractions, theslurries become dilatant (viscosity in-creases with shear rate) because the sys-tem must increase its volume to allowclosely spaced, repulsive particlesto slippast one another. Flocced slurries exhibitpseudoplastic, thixotropic rheology (vis-cosity decreases with increasing shearrate and history-dependent viscosity) be-cause the applied forces separating attrac-tive particles depend on differential

acceleration (shear rate). Once separated,flocculation and network formation aretime dependent. Pourable, dispersed slur-ries can contain up to 60 vol% solids,whereas the volume fraction of pourable,flocced slurries is much lower (between5and 20 vol%) and depends on the parti-cle mass (size), which governs the forcesseparating particles during flow.

A number of fundamental interactionscan be usedto alter interparticle orces.13These forces include attractive van derWaals forces, repulsive electrostatic forces,attractive or repulsive steric forces, andattractive capillary forces. With the excep-tion of van der Waals forces, the manipu-lation of interparticle forces usually requiresthe addition of a surface-active agent toa liquid-particle system. Electrostatic re-pulsive forces develop when solute ions

are attractedto or dissociated from particle surfacesto produce a system of simi-larly charged particles Steric forces aredeveloped by macromolecules that attachthemselves to the surface of the particleCharged macromolecules, e polyelec-trolytes, can produce both repulsive elec-trostatic and steric forces Although thescience of interparticle forces has a strongtheoretical base verified through direct sur-face force measurements,13 the choice ofthe best surface-active agent usedto control interparticle forces is still a matter oftrial and error for most ceramic systemsFigure 2 illustrates one colloidal ap-proach to treat and store ceramic powders


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Vol. 72 , N o. 1Journal of the American Ceramic Society-Lange

Powder A

Fig. 2. One colloidal methodfor breakingapart weak agglomerates and fractionatingdesired particles from unwanted hard ag-glomerates and inclusions Each powder inamultiphasesystem is treated the same beforemxing.7

0 0.8-s -._- Flocced (pH 7)+05 0.6-*-*-By2 .4-N

-8-t-J- 0 --4Suspended (pH 2.5)O i I0 0.2 0.4 0.6 0. 8 1 0

,030 N.0.25 R

0-0.20 Z2E.a10 I

-02

-0.15

8Normalized distance t

TOPtBottom

Fig. 3. ZrlAl count raho (obtained from anEDX spectra) versus the normalized distancedetailing the ZrOP and Al2O3distibution formxed powder slurries centrifuged in the dis-persed and flocced states

prior to colsolidation.7 As-received, drypowders are dispersed in an appropriatefluid with a surfactant that produces nter-particle repulsive forces. These repulsiveforces keep particles separated onceshearing forces break apart weak ag-glomerates. Partially sintered and otherstrong agglomerates which cannot bebroken apart and inorganic inclusionsPowder B

greater than a given size are eliminatedby sedimentation. This step can beaccelerated by centrifuging. After the un-desired larger particles, strong agglomer-ates, and inclusions are removed, theretained dispersed slurry containing thedesired particles is flocced by changingthe interparticle forces from repulsion toattraction. Floccing concentrates the par-ticles to form a weak, continuous, touch-ing network which consolidates under itsown weight, partially separating the parti-cles from the liquid phase. Flocced slur-ries can be washed to remove excesssalts andlor surfactants. Centrifuging canfurther concentrate this particle network.As discussed later in this paper, floccingalso prevents mass segregation duringstorage even when acted upon by cen-trifugal forces.Figure 2 also shows that two or morepowder phases, separately treated assummarized in the preceding paragraph,can be mixedto form multiphase slurries.If the different slurries are colloidally com-patible, i.e., do not floc one another, theycan be redispersed (by again adding theproper surface agent) and mixed. Morecommonly, the phases are notcolloidallycompatible. These systems can still bemixed because flocced mixtures can bemechanically redispersed by a device thatproduces a high shear-rate ield (an ultra-sonic horn, high-speedrotor, etc.). As themechanically dispersed mixture leaves thehigh shear-rate field, it flocs to form a new

+BothA1203 and Zr02 can be dispersed at pH 2and are colloidally compatible when mixed, I e , theyremain dispersed Both can be flocced at pH 8

mixed-particle network which preventsphase separation during storage and fur-ther processing.The effect of interparticle orces on masssegregation due to sedimentation wasinvestigated14 by centrifuging both dis-persed and flocced slurries containing amixture of AI2O3and ZrOp(30volO/o) pow-ders colloidally treated and mixed as de-scribed earlier in this paper.? Thecentrifuged masses were dried, densifiedand sectionedto examine phase distribu-tion by scanning electron microscopy(SEM,using energy dispersion X-ray ana-lys (EDX). Figure 3 illustrates the ZrlAlcount ratio versus the normalized distancefrom the bottomto the top of the sintered,centrifuged mass. As shown, this ratio wasnearly constant (k 00)across the speci-men prepared from the flocced mixtureand equalto that of the initial compositedmixture. As expected, the dispersed slur-ry produced different results. First, al-though the ZrlAl count ratio was nearlyconstant (f 13O)across=90% of the nor-malized specimen thickness, it significantlyincreased near the top of the specimen.Second, the average ZrlAl count ratiocorresponded to only 4 4 voO/o Zr02;many of the smaller, less-massive Zr02particles were left behind in the cen-trifuged supernatant. In addition, as shownin Fig. 4, larger particles of both phaseswere observed at the bottom of the speci-men and smaller particles at the top. Simi-lar observations showed that both thephase distribution and the size of eachphase was uniform throughout the speci-men prepared from the flocced slurry.These results clearly show that the touch-ing particle network within a flocced slur-ry can prevent mass segregation due tosedimentation.The question concerning mixed-phaseuniformity and what tools can be usedtodefine its uniformity has recently been ad-dressed.15 The method is simple and canbe relatedto the slurry rheotogy,16 and ithas the potentid to access mixing unifor-mity during processing as a nondestruc-tive evaluation tool.When a multiphase body is observedby SEM, the X-rays collected produce anEDX spectrum that quantitatively definesthe atomic fraction of each element. Ifdifferent elements are associated withdifferent phases, the content of eachphase within the area scanned can be de-termined.At low magnifications, he EDXspectrum defines the fraction of eachphase within the large body. With reasona-ble counting periods, the standard devia-tion for different areas examined at lowmagnifications is low (usually


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January 1989 Powder Processing Science and Technology for Increased Reliability Iintermediate magnification, the standarddeviation will begin to depart from thatproduced by counting statistics. At thismagnification, he area scannedisstatisti-cally identical (within an acceptable stan-dard deviation somewhat larger than thatdue to counting statistics) with the largebody. The size of this area thus definesthe smallest area that contains the samephase distribution as the whole body. Thisarea (A,) can be defined quantitativelyand used to represent phase uniformity.The better the mixing, the smallerA,. A,is an extrinsic property of the multiphasematerial that depends on processing.15Values ofA, can be related to differentmixing methods and mixing periods, e.g.,different resident periods for mixed slur-ries within a high shear rate field, and tothe properties of the mixed slurry itself,Lange and Miller16 have shown that A,can be relatedto the viscosity of flocced,two-phase slurries, and they have sug-gested that an in-line viscosity measure-ment could be used to determine phaseuniformity (defined by a number, i.e.,A,)during processing

IV . Consolidation f rom theSlurry StateOnce colloidally treated, powdersshould not be dried. Slurries contain soh-ble salts, produced, e.g., by a reactionwith the powder itself, which can bondtouching particles when the last bit of li-quid evaporates from their pendular ring.That is, agglomerates, previously eliminat-ed by colloidal treatment, will reform dur-ing drying. Drying also reexposes theparticles to uncontrolled environmentswhich can reintroduce inclusions.Colloi-dally treated slurries could be piped direct-ly to a consolidation machine.A major issue for exploiting the colloi-dal approach is to directly form powdercompacts from the slurry state. Two con-ventional slurry consolidation methods, slipcasting and tape casting, can be directlyused with colloidally prepared powders,and, with some innovative changes, injec-tion molding could be adaptedto do thesame. Each of these conventional formingmethods is limited, e.g., slip casting bestproduces thin-walled bodies, and a largeamount of polymer must be removed af-ter injection molding. For these reasons,investigators are exploring alternativeslurry-shaping methods where either thesolidlliquid ratio remains constant duringshaping, i.e., slurry molding, or the parti-cles are partially partitioned from the liquidduring shaping, e.g., pressure filtration.Toavoid excessive shrinkage during flu-id removal andlor densification, moldingmethods require slurries containing thehighest possible fraction of particles. Mold-ing also requires flow. As detailed by Ak-say and co-workers,17 pourable ceramicslurries containing in excess of 60 vol%of particulates require highly repulsive in-terparticle forces. Inaddition, they have

also shown that the volume fraction of par-ticulates can be further increased with theproper particulate-size distribution.18 Asshown in Fig. 5, the addition of a givenfractionof finer particulatesdecreases theslurry viscosity.Once molded, the rheological proper-ties of the slurry must be dramatically al-tered to allow shape retention duringunmolding. This change can be inducedby a variety of different phenomena thatinclude freezing (used in injection mold-ing), gelation,lg and in situ flocculation.Each can change a flowable slurry into afirm body without fluid-phase removal.Rheological changes are not without prob-lems; they can produce strain gradients.For example, volume changes can ac-company freezing, and freezing initiatesat the surface. Inaddition, if capillary pres-sure arises during fluid removal, bodiesmolded with dispersed slurries will shrinkunless an attractive, touching-particle net-work is formed first (e.g., by in situ floccu-lation). Shrinkage and expansion gradientscan leadto significant stresses and/or dis-ruptive phenomena. The potential prob-lem of mass and phase segregationproduced by sedimentation within a highlyfilled, moldable dispersed slurry needs fur-ther study.Moldable slurries can also be achievedwhen flocced bodies are rapidly sheared.Forces produced by differential acceler-ations break apart the attractive particlenetworkto produce Newtonian rheology;the network reforms shortly after the shearfield is removed. Firm, fully saturated bod-ies containing between50 and 60 vol%particulates can be produced by eithercentrifuging14 or pressure filtering20 low-er viscosity, flocced slurries. When thesefirm bodies are coupled to high-intensityultrasound, they fluidize to fill a cavity.Once the ultrasound is removed, the rheol-ogy of the slurry quickly reverts to a firm,molded body. The author's experiencewith this innovative molding method sug-gests that attenuation of the ultrasound isone problem that must be addressed.Pressure filtration produces a fully satu-rated powder compact as particles withina slurry are partitioned as liquid flowsthrough a filter leaving particles behindtoform a consolidated layer. Hard ferrite par-ticles within a slurry can be aligned witha magnetic field prior to consolidation.Pressure filtration is usedto form ceramicmagnets with a variety of applications be-cause the desiredlpermanant magneticfield is produced during consolidation.21With the development of moldable cast-ing dies made of a porous plastic materi-al, an innovative pressure filtrationmachine has recently been introduced22that enables the rapid production of large,relatively complex shaped bodies. Al-though these new filter presses are cur-rently marketed to produce functionalarticles (from platesto sinks) with traditionalclay-based slurries, they represent the first

Fig. 4. Micrographs of dense, AI2O3-ZrO2composite ceramic formed by centrifuging adispersed slurry, illustrating particle-size andphase distributions at the (A) bottomand (B)top of the specimen

Fines f ract ionFig. 5. Viscosity (extrapolatedto zero shearrate)versus fine fraction for A1203 (0.55 volumefraction) slurries, dispersedwith apolyelectro-lyte, containing coarse (0.8pm) and fine (0.2pm) powders.18


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8 Journal of the American Ceramic Society-Lange Vol. 12 , No. 1

75

70--b'?). 5-c

a,$ 55-o-a

50-

45f

Dsspersed sluiry [atfraclivelnferparilclea * - IorCBSlap

Floeced s lu r ry/-IepuISIventerpanlcieIOICeS)

y9 I

generation of machinesto form advancedcomponents with advanced ceramics. Ithas also been demonstrated that pressurefiltration can also be conducted underconditions of isopressure,20 whichdecreases the probability of disruptivephenomena occurring by die constraintduring pressure release. In addition, withinnovative design, pressure filtration offersthe advantage that after consolidation,much of the liquid can be removed witha high-pressuregas, i.e., hrough invasionpercolation, before the body is removedfrom the molding die.The kinetics of pressure filtration obeysDarcy's differential equation23 for fluid flowthrough porous media, which, when in-tegrated with the appropriate boundaryconditions, shows that the thickness of theconsolidated layer (h)formed under con-stant pressure( f )s parabolically relatedto time ( f ) by

where u is the liquid viscosity and vo andv/ are the volume fractions of particulateswithin the slurry and consolidated layer,respectively The permeability (k) is in-versely related to the resistance of fluidflow through the consolidated layer As-suming that the particles are identicalspheres with diameterd , one can estimatethe permeability of a consolidated layerwith the Kozeny-Carman relation, whichmodels the layer as a bundle of tortuouscapillary tubes with hydraulic diametersresembling slits 2

d*(1 - v)3k = 36c$where the Kozeny constant(c)defines theshape and tortuosity of the flow chanels(c = 5 for many systems).

Applied pressure = Pa n

Liquid pressure =faNetwork pressure =PoLiquid pressure = PoNetwork pressure = Pa

Ambient pressure = PoSchematic of pressure distribution The mechanics of particle packing dur-during pressure filtration showing that a pres ing filtration and the mechanics of

ined for aqueous slurries containingA1203olidated particlespowder with a mean diameter of approx-imately 06 pm20 The electrostatic meth-od (pH control) was used to produceeither dispersed or flocced slurries Figure6 shows the relative densitv of consolidat

sure gradientexists wlthlnthe network Of Con pressure-filteredbodies have been exam.

ed bodies after filtration is complete, asplotted against the logarithm of the appliedpressure. Consistent with observations byFennelly and Reed,25 the highest packingdensity is achieved with dispersed slurries.Also, the packing density achieved withdispersed slurries is pressure independentfor pressures >0.5 MPa. Figure6 showsthat the packing of consolidated layersfrom flocced slurries is very pressure sen-sitive and appears to obey a consolida-tion law (relative density linearly relatedtothe logarithm of pressure) similar to drypowders.

The mechanics of particle packing dur-ing pressure filtration can be explainedwith the aid of Fig. 7, which schematical-ly describes the pressure distribution with-in the filtration system. Assuming that theparticles have not formed a continuousnetwork (the case of a dispersed slurry),the slurry pressure is identical with the fluidpressure and equal to the pressure (Pa)exerted by the plunger. Ambient, at-mospheric pressurePo exists on the ex-ternal side of the filter. The differentialpressure across the filter and consolidat-ed layer(fa Po ) s the driving force forfluid flow. A gradient in fluid pressure ex-ists across the consolidated layer; i.e., atthe slurry-layer interface, f = f a , nd,neglecting the pressure gradient acrossthe filter, f r = Po at the filter-layer inter-face. Because the total pressure within theconsolidated layer must be equal to theapplied pressure, the particle networkmust support a pressure gradient equal,but opposite, to the fluid pressure. That is,at the filter-layer interface, the networkpressure, P, = f a , nd, at the slurry-layer interface,f, = 0. Because networkpressure will produce particle rearrange-ment, during filtration, the packing densi-ty will be greatest at the filter-layerinterface and decrease to the layer-slurryinterface. Once the plunger meets theconsolidation layer, filtration will continueuntil the differential fluid pressure dissi-pates; .e., the fluid pressure decreasestoambient pressure. During this period, thegradient in the network pressure dissipatesto the applied pressure to produce a uni-form particle-packingdensity across theconsolidation layer.With the information presented in thepreceding paragraph and Fig. 6, notethat, during pressure filtration, flocced slur-ries produce large gradients in packingdensity relative to dispersed slurries. Forthis case, there is no clear demarcationbetween the slurry and the consolidatedlayer as there is for dispersed slurries.The mechanics of particle packing haveonly been addressed with static models,26which does not address particle re-arrangement. Why dispersed slurries pro-duce high packing densities at very lowpressures has not yet been detailed, butit must be relatedto the effect of repulsiveinterparticle forces on rearrangement.It is rarely recognized in ceramic tech-


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January 1989 Powder Processing Science and Technology o r Increased Reliability 9nology that powders exhibit nonlinear elas-tic stress-strain behavior similar to thatdescribed by Hertzz7 when spheres arepressed together. Walton28 has reportedthat the compressive stress-strain re-sponse of a powder can be expressed asa = 5~3'2,where B depends on the rela-tive density of the powder compact (aver-age number of contacts per particle) andthe elastic properties of the particles andis independent of particle size. Figure8(A)describes this response for A1203powdercompacts as determined with strain recov-ery measurements after pressure filtrationof both flocced and dispersed sIurries.20As illustrated, relatively small stresses pro-duce large strains and the compact be-comes stiffer as the stress is increased. tis not the porosity that produces this be-havior, but the large displacements be-tween particle centers when a "point"contact is elastically compressed into anarea contact. Thus, after a powder hasbeen consolidated and the pressure hasbeen released, large elastic strains arerecovered and the compact grows.The greater the consolidation pressure,the greater the recoverable strain. Inclu-sions within the powder which are eitherstiffer (e.g., dense agglomerates, whiskers,or fibers) or more compliant (organic in-clusions) will store less or more strain rela-tiveto the powder compact, respectively,during consolidation. Figure 8(A) also il-lustrates that the elastic response of adenseA1203inclusion(f=400 GPa) anda very compliant polymer inclusion( = 1GPa). The differntial strain relieved by theinclusion relative to the powder will pro-duce detrimental stresses during strainrecovery. Likewise, the powder compactcan be damaged by metal die cavitieswhich constrain the strain recovery of pow-ders pressed within them.

For consolidated dry powders, strainrecovery is nearly instantaneous withpressure release.As shown in Fig. 8(B),the strain recovery for compacts pro-duced by pressure filtration is time depen-dent20 e.g., a compact produced froma flocced slurry will continue to releasestrain and grow many hours after pres-sure release. This time-dependent strain-release phenomenon arises because fluid(liquid or air) must flow into the compactto allow the compressed particle networkto grow and relieve its stored strain.Release of the applied pressure will causethe fluid within the compact to share thestored network strain and thus place thefluid in tension. Fluid flow after pressurerelease is driven by the negative fluidpressure within the compact relative tothe ambient pressure outside the com-pact. Because the fluid must flow from thesurfacetothe interior, the strain within thecompact is not uniformly released; i.e.,strain is first released from the surface ofthe body.In practice, strain is likelyto be relievedfirst at one region on the surface. The

growth of this region during strain releasewill be constrained by the rest of thebody, and it will produce tensile stresssimilar to an inclusion. These tensilestresses can produce radial cracks.Cracks are more frequently observed athigher filtration pressures where morestored strain is released.As detailed else-where,20 cracking after pressure filtrationcan be avoided by increasing theresistance of the compact to crackgrowth, e.g., by adding small amounts(


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10 Journal of the American Ceramic Society-Lange Vol. 72, N o. 1

Fig. 9. Micrographsof sphericalZrOn(+ 8mol%Y203)particles producedbyelectrostaticatomzationof zirconia acetate (A) after sinter-ing by heatingto 1300C for 10 h, (6)samearea after further heat treatement at1300C for1 8 h, and (C) 1400C for 4 h, where simlarnet-work has undergone coarsening and furtherdensification3

1I 20"Clmm200i$00

Temperature ( "C)Fig. 10. Shrinkage strain rateversus temper-ature for identicalA1203compacts heatedto1500C at different heating rates Maximumstrain rate occurredata relative densityof0 77for a\ \three specimens

wheredA, is the change in surface area,dAb is the change in grain-boundaryarea, and y b and ys are the energy perarea associated with grain boundariesand particle surfaces, respectively.When a linear array of touching parti-cles sinter, they form an equilibrium con-figuration which satisfies Eq. (3). f massis removed from between particlecenters, the shrinkage of the linear arraycan be predicted with knowledge ofyb/ys. Although the linear array can beusedto estimate shrinkage during sinter-ing, it does not enclose and define a voidspace and thus cannot be used to fullyunderstand and predict the disappear-ance of pores within powder compacts.The void space within a powder com-pact can be structuraily defined as pores,which are defined by irregular polyhedraof touching particles connected to oneanother to form the particle network.30Each polyhedron contains one pore. Thenumber of touching particles surround-ing and defining each pore is called thecoordination number of the pore (n )(equivalentto the number of vertices thatdefine each polyhedron). The question swhether or not sintering can eliminateeach and every pore defined by the con-nective network of different polyhedra.To answer this question Kellet andLange'g used Eq. (3) to analytically de-termine the sintered, equilibrium config-uration of different regular polyhedraformed with identical, touching sphericalparticles. It was shown that pores withinall polyhedra shrink (decrease theirvolume) during sintering, but only poreswith a coordination number less than acritical value (n d n,) disappear. Poreswith n >n shrinkto an equilibrium size.The critical coordination number is relat-ed to the ratio,yblys;29 the greater y b l y s ,the greater n,. Itwas therefore conclud-ed that all pores within a powder compactwill shrink during sintering, but not allwould disappear; .e.,sintering alone maynot result in full densification.The sintered network of touching Zr02spherical particles developed by heatingat 1300C for 10 h is shown in Fig.9(A).Note in Figs. 9(B) and (C) that when thesame area is viewed after a subsequentheat treatment at 1300C for 18 h and1400C for 4 h, respectively, the particlenetwork appears similar. The micro-graphs show differences. First, smallerparticles (or grains) have become eithersmaller or disappear, whereas larger par-ticles become larger, .e., coarsening hasoccurred. Second, groups of grains rear-ranged relativeto others. Third, measure-ments show that some shrinkage, i.e.,densification, occurred. Fourth, very fewnew contacts are made. The more com-prehensive study31 from which thesemicrographs are taken show that oncethe initially touching particles sinter toform a metastable network, further den-sification is related to grain coarsening,

which continuously alters the networkconfiguration.Although mass transportto the contactregion may stop when Eq. (3) is satisfied,adjacent sintered grains will have differ-ent radii of curvature that will drive inter-particle mass transport. Interparticlemasstransport will cause coarsening; i.e.,smaller grains disappear as larger grainsgrow. Itcan be shown that the decreasein free energy for interparticle mass trans-port is much smaller than the decreaseassociated with transport to the contactregion. That is, the differential curvaturebetween two particles is much smallerthan the differential between particles andtheir contact region. In addition, duringcoarsening, the grains become larger.Larger grains result in larger radii and alower driving force for interparticle masstransport. Thus, one might expect the ki-netics for interparticle mass transportleading to coarsening (grain growth) tobe slower than the transport to the con-tact regions (sintering).

If we argue that rapid transport to thecontact region leadsto shrinkage by sin-tering and the development of a metasta-ble network similar to that shown in Fig.9(A) and that further shrinkage is con-trolled by slower interparticle transport,then the kinetics of densification shouldbe separated by two regimes: an initialregime controlled by sintering kineticsand a subsequent regime controlled bycoarsening kinetics. Because the sinter-ing regime results in shrinkage to ametastable network with a given relativedensity, further densification must be con-trolled by coarsening kinetics. Thus, thetwo regimes will be separated by the rela-tive density of the metastable networkproduced by sintering.Figure 10 shows the shrinkage strainrate determined when different speci-mens cut from a single powder compactofA1203were heatedto 1550C at differ-ent heating rates.32 In each case, theshrinkage strain rate increasesto a max-imum and then decreases.The maximumshrinkage strain rate corresponds to theinflection in relative density versus tem-perature curves commonly obtained indensification experiments. For eachcurve, the maximum shrinkage strain rateoccurs at the same relative density of0.77. These data strongly suggest thatsintering kinetics dominate up to a rela-tive density of 0.77, where coarseningkinetics dominate during further densifi-cation.The question of how coarseningphenomena are related to the ther-modynamics of pore stability can beviewed in two different, but complemen-tary, ways. First, it can be seen that coar-sening will decrease the coordinationnumber of stable pores, i.e., convert astable pore with n


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January 1989 Powder Processing Science and Technologyfor Increased Reliability 11in a powder compact when polymerspheres pyrolyze during heating will onlydisappear when grain growth decreasestheir coordination number below a criti-cal value.Second, the relation among coarsen-ing, configurational changes in the net-work during coarsening, and shrinkagecan be obtained by examining what hap-pens when grains disappear within a sin-tered network. Figure 1 1 A) illustratesthree truncated, spherical particles takenfrom a network which has shrunk to ametastable configuration by sintering.The dihedral angel qe defines theequilibrium between the surface andgrain-boundary energies which will beachieved when Eq. (3) is satisfied, viz.,2 cos ( qe /2 )= y b / y s . As coarsening pro-ceeds, the smaller grain becomes smallerand the neighboring grains become larg-er while qe is maintained wherever thegrain boundary intersects the surface. Atsome point during coarsening, the neigh-boring grains touch one another as illus-trated in Fig. 1 (C ). t can be shown34 thatwhen the neighboring grains touch, theangle formed by the surface tangents andthe new grain boundary is less than qe.Because V,


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12 Journal of the American Ceramic Society-Lunge Vol. 12 , N o. 1

I bGrain volume

Fig. 13 . (A) Two-dimensional schematic ofgrain boundaries of a tetrahedral grain inter-acting with spherical inclusions. Different po-sitions illustrate theshapeof the boundaryasitencounters and breaksaway from the inclu-sions.(B)Energyof the tetrahedral grainver-sus its volume as it encounters and breaksaway from inclusions.Three differentcurvesare for three different retarding stressesproduced by inclusions

number will not only require extensivegrain growth to satisfy its thermodynam-ics for instability, but its disappearancewill also be kinetically imited once it is un-stable.

VI. Cont ro l of Grain GrowthThe preceding section concluded thatsome grain growth via coarsening is re-

quiredto fully densify a powder compact.Although much of this coarsening takesplaceby the disappearance and growthof adjacent grains through intergranularmass transport, grain boundaries canalso move as they would in a fully densebody before full density is achieved. Be-cause matter needs only to diffuse overatomic distances, grain-boundary motionwill leadto more rapid grain growth thanthe coarsening phenomenon. Grain-boundary motion will also trap unstablepores within grains before they have theopportunity to disappear via grain-boundary diffusion. In addition, if a near-ly dense body remains at the densifica-tion temperature for a short time, grainsin many ceramics can grow more thanan order of magnitude larger than theaverage particle size used to form thepowder compact. Some grains in ceram-ics with noncubic crystalline structurescan grow to an enormous size relative totheir surrounding grains. Although thereasons for abnormal grain growth arestill unclear, abnormally large grains canbe a dominant, strength-degrading flawpopulation in many important ceramics.For these and other reasons, graingrowth via boundary motion must be con-trolled to optimize both density andproperties.Second-phase nclusions have becomeincreasingly mportant in controlling grainsize in ceramics. Inclusions generally giverise to residual stresses because ofdifferential thermal contraction and, there-fore, are usually thought of as strength-degrading flaw populations themselves.But, it has been shown, both throughexperimentation37 and theory,38 that, ifthe inclusions are less than a critical size,their residual stress will not inducemicrocracking either during cooling fromthe densification temperature or duringsubsequent stressing. Inclusions with asize that will not induce microcrackingcan be usedto both control grain growthand engineer new composites for desiredproperties without the fear of degradingstrength. For example, large andlor ab-normal grain growth can be prevented bythe addition of an appropriate inclusionphase as demonstrated by the dramaticstrengthening achieved with additions ofSIC to AI2O3,39Zr02 to p"- AI 2O3, 40ndAI2O3to cubic ZrO2.4' In each of thesecases, the inclusion phase eliminates themost detrimental flaw population, viz.,large andlor abnormal grains.For ceramics, inclusons used to con-trol grain size can be introduced by mix-

ing two-phase powders, e.g., via thecolloidal approach. Namely, the inclu-sions must be effective in retarding graingrowth before the powder compactachieves a relative density >0.9, whererapid grain growth is commonly observedin single-phase materials.35

Grains are classified by their size(volume) and polyhedron type, the latterdefined by the number of Asgrains decrease their volume, theyprogressively and sequentially decreasetheir number of faces. During graingrowth, the number of grains per unitvolume decreases; i.e., some grainsdecrease their volume and disappear.Only tetrahedral-shaped grains disap-pear. Thus, in modeling the effectof per-turbations on grain growth, one need onlyto model the shrinkage and disappear-ance of simply shaped, tetrahedralgrains. The tetrahedral grain decreasesits free energy as it decreases ts volume.(Grains with many faces (>14) willdecrease their free energy by growing.)The derivative of the free energy withrespect to the volume of the grain (theLaplace equation) is proportional to thegrain-boundary energy per unit area (yand inversely proportional to the radiusof curvature ( r ) of its grain boundaries,viz., dE1dV = 2yglr. dEldV has thedimension of stress and is referredto asthe driving stress (od ) to decrease thevolume of a grain. For the tetrahedralgrain, the radius of curvature is positive(grain boundaries are concave whenlooking from within), and r =0 .6Dt ,where Dt is the diameter (grain size) ofthe equivalent spherical volume of thetetrahedron. Thus, for the tetrahedron,

Zener43 was the first to explain how in-clusions retard grain growth. Zener's con-cept is visualized by Fig. 13(A), whichshows, in two dimensions, how a shrink-ing tetrahedral grain interacts with spher-ical inclusions of radius R.44 As theshrinking grain encounters the inclusion,an increasing proportion of the boundaryarea is removed from the grain. WhenNinclusions are simultaneously intersected,the maximum amount of grain-boundaryarea removed is N n W , which cor-responds to a decrease in free energyofNnRnyb. If the grain shrinks further, thegrain-boundary area adjacent to the in-clusions must bow out as it attempts tobreak away. This bowing and the fact thatthe grain boundary regains its areaoccupied by the inclusion during bowingcauses the free energy of the systemto increase. Using line tension argu-ments, Zener showed that, as the grainboundary breaks away, the inclusionsexert a maximum restraining "stress,"or = 0.75fyb/R, where f is the volumefraction of inclusions. Thus, the net driv-ing stress for the grain boundaries of atetrahedral grain to break away from theinclusions is

~d = 3.3yglDt.


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13anuary 1989 Powder Processing Science and Technology for Increased Reliability

If it assumed that the kinetics of grain dis-appearance (growth) are portional to on,then Eg. (4) shows that inclusions willreduce the kinetics for grain growth.The free energy versus volume func-tion for inclusion encounter and breakaway is schematically shown in Fig. 13(B)for the cases whereon >0,on = 0,andon


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14 Journal of the American Ceramic Society-Lange Vol. 12, N o. 1by the diffusion kinetics of the impuritycloud.sz Thus, the impurities will havevery little effect when the grains are small,but a major effect as the grains grow larg-er. Itis obvious that the greatest effect ongrain growth is obtained by choosing im-purities that maximizeAG.The same reasoning has been appliedto the case where phase partitioning isconcurrent with grain growth. It wasobserved53 that grains of the same struc-ture develop different compositions dur-ing partitioning. Grain growth in thetwo-phase compositional region s severlylimited relative to single-phase regions butsecond-phase grains which might hindergrain growth, as discussed earlier in thispaper for inclusions, are not observed53as initially postulated.54 If compositionaldifferences between grains did not alterduring grain growth (i.e., f boundary mo-tion is faster than the period required toequilibrate compositional gradients), itwas reasoned that the boundary wouldleave behind a "ghost" boundary withinthe growing grain where the latticeparameters change abruptly because ofthe compositional gradients. If the com-positional gradient between the twograins is a step function, then the ghostboundary would appear as a coherent in-terface. The different lattice parameterson either side of the ghost boundarywould produce a strain energy density,Use= KEZIE,where E is the strain duetothe change in lattice parameters,E is theelastic modulus of the material and K isa dimensionless constant.53 In the samemanner used to develop Eq. (5 ) ,the netdriving stress for shrinkage of the tetra-hedral grain is given by

3.3 2on = ad - 0, = -y b - K -Dt E(6 )As descirbed for impurity clouds,the grain boundary could easily moveto form a ghost boundary when D,is small (on>0), whereas as graingrowth proceeds, a condition will arise(D t>3 . 3 y b H K ~ 2 )where grain growth willbe limited (un


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January 1989 Powder Processinx Science an d Technology .fo r Increased R eliability 15"Processing-Related Fracture Origins. IV, Elimina-tion of Voids Produced by Organic Inclusions," JAm. C eram. Soc , 69 (11 66-69 (1986).8V Engle and H. Hubner, "Strength Improvementof Cemented Carbides by Hot Isostatic Pressing."J . Mater. So.. 13 [9] 2003-13 (1978).9B. J . Kellett and F. F Lange, "Experiments onPore Closure During Hot Isostatic Pressing and Forg-ing," J . Am. Ceram. SOC,71 [l ] 7-12 (1988).'OF F . Lange, "Processing-Related Fracture Ori-gins: I, Observations in Sintered and IsostaticallyHot-Pressed AI2O3/ZrO2Composites," J. Am. Cer-am. SOC 66 [6] 396-98 (1983)."J . W. Goodwin. "The Rheology of Dispersions";pp . 246-93 in Colloid Science, Vol. 2 D. H . Everett(Senior Reporter). The Chemical Society, London,UK, 1975.12M. D Sacks, "Rheological Science in CeramicProcessing"; pp. 522-38 in Science of CeramicChemical P rocessing E dited by L. L.Hench and DR. Ulrich. Wiley, New York. 198613J. N Israelachvili. Intermolecular and S urfaceForces. Academic Press, London, UK, 1985.14F. F . Lange, "Forming a Ceramic by Floccula-tion and C entrifugal Casting." U.S. Pat. No.4 624 808, Nov. 25, 1986.15F. F Lange and M M. Hirlinger. "Phase Distri-bution Studies Using Energy Dispersive X-ray Spec-tral Analysis," J. Mater.So. Len.,4, 1437-41 (1985).

16F. F Lange and K. T. Miller, "A Colloidal Methodto Ensure Phase Homogeneity in fi"-AI2O3/ZrO7Composite Systems," J. Am. Ceram SOC.,70 [12]896-900 (1987).17J . Cesarano 111, I.A. Aksay. and A. B leier. "Sta-bility of Aqueous u-A1203 Suspensions withPoly(methacry1ic acid) Polyelectrolyte."J. Am. Cer-am. SOC 71 [4] 250-55 (1988).18K. P. Darcovich and I. Aksay. "Particle-Sized Dis-tribution of Dense Ceramic Suspensions"; unpub-lished work19R. D. Rivers, "Method of Injection Molding Pow-derMetal P arts,"U S. Pat. No. 4 113 480, Sept. 12,1978ZOF F. Lange and K T. Miller. "Pressure F iltration:Kinetics and Mechanics," Am Ceram SOC.Bull , 66"(a) S. Strijbos, "Pressure Filtration of P ermanent

Magnetic Powders"; in P roceedings of the Confer-ence on Hard Magnetic Materials. Edited by H . Zi~l-stra Bond voor Materialenkennis, The Hague,Netherlands,1974.(b)C A. M. Van den Broek andA. L Stui]ts, "Ferroxdure," Phrlps Tech.Rev.,37 [7]157-75 (1977).ZZGebruder Netzsch, Maschinenfabric GmbH andCo , Technical Information Bulletin,GK 012, 0-8672.Selb, Bavaria, FRD, 1985.*3F M. Tiller and C -D. Tsai. "Theorv of F iltation

[lo] 1498-504 (1987).

of Ceramics69 [12] 882-87 (1986)I, slip Casting." J ~m deram soc ,24J Dodds and M Leitselement, The Relation Be-tween the Structure of Packing Paticles and TheirProperties", pp. 56-75 in Physics of Finely DividedMater. Procedures inPhysics. Vol. 5.Edited by NBoccara and M Daoud. Springer, Berlin, FRG, 1985

25T J . Fennelly and J . S. Reed, "Mechanics ofPressure Casting," J. Am. Ceram. SOC..55 (51264-68 (1972)

26R A Davis and H. Deresiewiez, "A DiscreteProbabilistic Model for Mechanical Response of aGranular Medium," Acta Mech SKI.. 27, 69-89(1977).z7S. Timoshenko and J N. Goodier. Theory ofElasticity,2ded; pp 372-80. McGraw-Hill,New York,195128K.Walton. "The Effective Elastic Modulus of aRandom Packing of Spheres,"J. Mech Phys.Sollds.35 [2] 213-26 (1987).

298. J Kellett and F F Lange, "Thermodynam-ics of Densification. I,Sintering of Simple ParticleArrays, Equilibrium C onfigurations. Pore Stability,and Shrinkage"; to be published in J. Am. C eram.SO C3oH. J . Frost, "Overview 1I.Cavities in Dense R an-dom Packing," ActaMeiail.,30 (51899-904 (1982)37E B Slamovich and F. F Lange, "ElectrostaticRoute to Micoro-S izedZirconia Spheres rom LiquidP recursors"; P roceedingsto be published in BetterCeramicsThrough C hemistry Ill,MRS Meeting, April

32F. F. Lange; unpublished work3 3 8 J . Kellett and F. F. Lange, "Thermodynam-ics of Densification. 111, Experimental Relation be-tween Grain Growth and P ore Closure"; unpublishedwork.34F. F. Lange and B. J . K ellett, "Thermodynam-ics of Densification: 11 , Grain Growth in PorousCompact and Relation to Densification," to be pub-lished in J . Am Ceram. SOC.35T. K Gupta, "Possible Correlation Between Den-sity and Grain Size During Sintering." J Am. Cer-

am SOC.,55 [5] 276-77 (1972).36E. A Barringer and H. K. Bowen. "Synthesis andProcessing of S ubmicrometer Ceramic Powders";pp 482-96 in Science of Ceramic Chemical Process-ing. Edited by L L. Hench and D. R. Ulrich. Wiley,New Y ork. 198637D B. Binns, "Some Physical P roperties of Two-Phase Crsytal-GlassSolids"; pp. 31 5-35 in Scienceof Ceramics Edited by G H. Steward AcademicPress, New York, 19623 8 0 J Green, "Microcracking Mechanisms in Cer-amics"; p 457 in Fracture Mechanics of Ceramics,Vol. 5. Edited by R. C. B radt, A. G Evans, D. P. H.Hasselman. and F F. Lange. Plenum Press, NewYork, 1983.39F. F Lange and M Claussen, "Some Process-ing Requirements for Transformation-ToughenedCeramics"; p 493 in U ltrastructure Processing of

Ceramics, Glasses, and Composites. Edited by L LHench and D. R Ulrich. Wiley. New Y ork, 1984.40D. J . Green, "Transformation Toughening andGrain-SizeControl in P -AI2O 3-ZrO2 omposites." J.Mafer So. , 20 (71 2639 (1985).41F. J Esper, K H. Friese, and H Geier, "Mechan-ical. Thermal, and E lectrical Properties n the Systemof Stabilized ZrO2(Y2O3)lu-AI7O3";p. 528-36 in Ad-vances in Ceramics, Vol. 12. Science and Technol-ogy of Zirconia 11. Edited by N Claussen, M Ruhle.and A. H. Heuer. American Ceramic Society, Colum-bus, OH, 1985475 K Kurtz and F M. A. Carpay, "Microstruc-ture and Normal Grain Growth in Metals and Cer-amics: Part I, Theory." J Appl. Phys , 51 [ l l ]572543C Zener, kindly quoted by C S. Smith, Trans.Mefall. SOCAIME. 175, 15 (1949)."F. F Lange, "Controlling Grain Growth"; pp497-508 in Ceramic Microstructures '86: Role of In-terfaces. Edited by J . P ask and A. G. Evans, PlenumPress, New York. 1988.45F. F. Lange and M. M Hirlinger, "Grain Growthin Two-Phase Ceramics. A1203 nclusions in Zr02."

J. Am. Ceram. SOC.,70 [ l l ] 827-30 (1987).460. L Olgaad and B. Evans, "Effect of Second-Phase Particles on Grain Growth in Calcite," J AmCeram. SOC., 9 [ l l ] C~Z72-C-277 1986).47M. F. Ashby and R . M A. Centamore, "TheDragging of Small Oxide P articles by M igrating GrainBoundaries in Copper." Acta Metall., 16 [9] 1081(1968).48C H. Hsueh. A G. E vans, and R. C. Coble,"Microstructural Development During Fi-nalllntermediate Stage Sintering. I, Pore/GrainBoundary Separation," Acta Metall., 30 [7] 126949F F. Lange and M. M . Hirlinger, "Hindrance ofGrain G rowth in A1203 by Zr02 Inclusions," J . Am.Ceram. SOC 67 [3] 164-68 (1984).50s. J Bennison and M P Harmer, "Grain-GrowthKinetics for Alumina in Absence of a L iquid Phase,"

J. Am. Ceram SOC.,68 [ I ] C-22-C-24 (1985).5'P J . Clemm and J . C Fisher, "The Influence ofGrain Boundaries on the Nucleation of S econdaryPhases." Acta Metall, 3, 70-73 (1955)52J W. Cahn. "Impurity Dray Effect on Grain-Boundary Motion," Acta Metall., 10 [9] 789-98(1962)53F F. Lange, D. B. Marshall, and J . R Porter,"Controlling Microstructure hrough Phase Partition-ing from M etastable Precursors: The ZO - Y z 03 Sys-tem", pp 51 9-32 in Ultrastructure P rocessing ofAdvanced Ceramics. Edited by J . D. Mackenzie and

D. R Ulrich Wiley, New York, 1988.54F. F Lange. "Transformation-Toughened Zr02.Correlations between Grain Size C ontrol and C om-position in the System Zr02-Y 203,"J Am. Ceram0

(1980).

(1982).

SOC..69 [3] 240-42 (1 986).

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