Lehigh UniversityLehigh Preserve

Theses and Dissertations

1973

Effect of lattice strain on the sintering behavior ofalumina powdersJay P. PageLehigh University

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Recommended CitationPage, Jay P., "Effect of lattice strain on the sintering behavior of alumina powders" (1973). Theses and Dissertations. 4214.https://preserve.lehigh.edu/etd/4214

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EFFECT. ·OF t.ATTicE···STRAI·N .ON cTHE··· • •. - . . ' . . . >. . . - l • • ' . • • '

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SnJ·TERING BEHAVIOR OF ALUMINA :POWDERS

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·:e~e,se-nted. to the Graduate Committee : . . . . . . . . . . . . .

of Leh_igh University.

in Candidacy for the ~gi--~e- o·f

Master- bf Science

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Lehigh Univers·ity ..

1973

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CERTI1FICATE OF APPROVAL

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ACKNOWLEDGEMENTS .. \

The author expre.sses his s~ncere gratitude to P:r.ofe·ssor D:.1>·.II. - ' ' i .. .. \' Hasselman for his enc.ouragem~nt and guidance throughout this· war~., · 1

A specj.al thanks is extended to Dr. :D. J •. Sll,anefield of ,, ·i

~e~t:ern Ele~·tric· Research Cent.er f:or· ·aid. i~ experimental sectir,iis.· ·. t

\· 'C)f· t.hi.s work, as well ·as· for :pr.ovlciing. advice and assistance ·at a.1·1.

·<

' ~~, time~. The. support ... :~f· Dr. R. E. Mistler:, Re.sea;rch Leader of the ·~ .. ,.

-1 group in whi.ch this ·work was performed, _is· also) appr~ciated. · ··The

author is simi.lariy indebted to Dr. E. A. Metzbower. of. the· Na.val . .,, ,. Re~~~ch ,'Lab:ora.t·ory at Washington D. C. , fC>r his ~idanc:e. and. ·.· ...

i:nt:er1)r..etation of the x-ray diffraction ~n.~ly.sis •.

.A.cknowledgeme~~s also go to ·the foiiow.tng We.sterµ <E1e¢tr~c:

·~,~eople:

B. ii. Mant.z ·of Allentown for h.e.ip ·in x-ray analysis, ·,. J .,

:S. J·. F·e.:l:~han1 of .Allentown for S.E.M. and T.E.M. analysis, " ' and. tcY t· .. E ~. .Trego :and M·.. J.·. Andriej co for thei:r guidance and

~si:;:i.sta1.ce inl.ab. work 13,t the Engineering :aeseaJ:"ch Center • ....

ta~rt, ·but :z:rot: :I~ast, the aut.hor thanks his wife, Jill, for her

. enthu:s f·es~m.,.:.~·d ~en:oo~ggermeirt o~~·rtblte P.p,att ttv10yy1,:ai,s • •. ·, 'I

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.TABLE· OF CONTENTS ~.·

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Acknowlegements [ ,, '1

• • • • • • • r • • • ••• • • '. •.c_ •: •. • • ,.

· List of Tables • • • • • ,e; ·• :,e . :·• .• .. . .. • • • • •• • ••

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Introduction .• · ... :• • • • ., • • .• • .: .• . ·•: . E_xperimental ·.Procedure { . '

• •• . ·• • • •• •• •• • • . ; .. •:

A.

B.

Materials. •. • • • •• •

Sur.fac·e ~e.a. ..

:P.articie · Si:ze. • . . . . ' . : ' - . . •

3.

4. . Chemi:cal Purity

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• • • • • • it ·• • • . :. . . ' . •

. . . . ·• .•. . :•. . .•. . •. . . . . . I

Strain and Domain Size , •• • •• •• . .. •· • • •• 7. <~ . ., .

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6. Parti.cle Distortion ·• • •. • .• .• .• • • .: • • :. ·~ .·17·

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7. Green Density. • •. •. .• ,. • ·~ • • •.. • :.· • • •. •. •

c. • • • • • • •••• •• •• •• • •. .• .. • •

D. Sintering Experiment.s .• ··· • •· . . . •: . :., . . •.: . .• • .,

Re·sults . • • • •: ... .• •. .•. •· • ·e: •· :. : .• • . .. ... ., •. .;.. .•. .

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Powder Charac·terisi ttcs:. . • ,. . • • .· • •. =• .... • • :.· • •

. Eleqtron Micr.oscopy.

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Sinterip.g Data • • •. • •= •. • • • .• . •. . . . . " . .•· ' .• • • • ... ; ,) Discussion· • . .• ' ' . . . . ' . . . •.' ' . . ' . . . ,. .• •. ' . ' . ' . .. ', . ·,. '

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1 Mechanisms and Ma.thmatical Models, f'or Sinter·ing of '·1

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Spheres . • • . . ·. • • • . • • • . • • • • . . • • • • . . ~ · 7 '

Powder Characteristics and Fired :Density ~ - .f .

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·chemical Pur-.:i.ty of Powders • • • • • • ii .• • :• ·• -:.,, .• • ·25

Characteristics Determined by X-Ray Analysis- .. , . ... .. ..... . .. 26 . . . '

Strain and Free ·Surface Energies and Slope o..t· log:-· Log Shrinkage Ver:sus 'Time • • • • . •. • . • •. • .• • •. 27

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Ef·f ect of Green D~nsi ty, Mean Strain and Dislocation Distribution on the Fired Density (Y) of As-Received

.;;::.:,L .. Powders Determined by the Multiple Regression ~-.Analysis Based on th~ Linear Equation:

Y = Ao + A1 X1 + A2X2 + A3X3 ,:: • • •. it. • •. • ,. • '28

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::7 Eff e·ct of Green Density, Mean Strain and Disloc.at::i.on -l

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Distribution on the Densificatie:t1 Parameter. (Y): of ·' As-Received Powders Determined by the Multiple Regression Analysis Based 0 0n the Linear Equation:-:

, _t Y = Ao.+ A1X1 + A2X2 + A3x3 • • • •• ·• • • ••. -.29 1 •• ,:,

Effect of Mean Strain, Total Energy and Surface .Are.a oh the Fired Density (Y)_ of Impacted Powders Determined by the Multiple Regression Analysis Based on the Linear Equ~tion:

, y ·.== Ao + A1 X1 + A.2X2 + A3X3 . . •. .•. . •. • i.. _:.i. :•. r. .. ,.

Effect of Mean Str~in, Surface Area, and Dislocation. Distribution on the Densification Parameter (Y) of Impacted .Powders Determined by the Multiple . Regression ·Analysis Ba·sed on .t:t\lt. Linear Equation:

y = Ao + Al Xl. + A2X2 + ~X3 , • • • • • • • •· '

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'LIST-OF FIGUBES • ~· '; ' l

Geome-try and Atom Flux. Paths for Init:i.·Eill.. :st;age .. Mod.el. ,·'i . ! of Sinteri!lg • • • • • • • • .. • •. . /. • •. • • • . -~

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Particle Size· ·Distribution !'or ·sample A .• · ••

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Shrink_age Rate for Samp,&e D • • • • • • • • •• ... .• ,. I .

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/ a:o Shrink_age Rate for ·sample E • • • • • •: • • • • . • •: -•. .21.

6 Transmission. Electron Micrograph Showing a High . ) . .

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Uniform ·Distribution o.f Dislocations. • • • • • . .• .• •. -32·

Transmission Electro:n Micr~graph Showi~g Low Localized Strain Areas .• • • • • • • • • • • • • •

Transmission Electron Micr_ographs Show~g Internal structure of Sample D Before and After Impacting. • i

• •

Transmissi_on Electron >Micr~graphs Showi~g Internal Structure of Sample E: 'Before and After Impact~g ••

Transmission Electron ~cr_ographs. Showi~g I.Dops in Bowder. :Sa.mple s. • • • • • • • • • • • • • • • • •

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1.1 Scanning Electron Micr_ographs of Sample D Showi~g

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Particle Size and Shape After Impacti~g • • • • • • • . :37

Scanni!lg Electron Micr~graphs of Sample E Showi~g Particle Size and Shape .Aft·er Impacti~g • • • • • •

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ABSTRACT ...... ·1:

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Differences in .sinteri~g behavior of as-received and impacted

al11mi na powders were·, interpreted in terms of' powder surface area, ,-• I

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particle sfze, particle size distribution~,. ~een d~nsity, ·particle

strain·, coherently .diff'racti~g doma.:in size, .·dislocation density,

and· disloc-ation distribution. Multiple r_egression analysis of I

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·the experimental res·uits. of the ·impacted powders showed that lattice ,.

, ~t·rain has a marked e ffe.·ct .on sinterabilfty. Similar -,. · analysis

:of the as ... recei ved powders showed t:P,at, green density, ( the prima.r.y .

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variable effecting ·sinterabilit·y)' was ·attributed to enhanced . '

p'arti cle-to-parti cle contact and cha~1gi~g_ ·_part.icle morphol_ogy.

· The increase fnssin~etability of the im:pt:i.cted powders was attribu"teci'.

to an increase in· the contribution ·c,t.· vol11me diffusion to· ·the tot.al

mass. transport .as tll.e re·su1t. :o:f .i·n:qre~:ed .:availability qf ·1ow re-

sistance diffusion p:at·hs:. Jft was: conclude·d that lattice strain .; - . . ... ' . .. .

. should be cons.idered :a. :prip..cj.ple va.rl>ab·l·e in the characterization I

o.f cerami· c. :powders:, in addition to the comm?nly· .measured v:ariabl.es·:

such as. part:i:c1e- ·size, surface area, particle1

si.z.e. distrib·ution.,.

t~uri ties an~ green density.

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·IN'I'R0DUCTION . • .. ,, . .

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In the areas of· e;t.ectroni,;cs·, chem:bcals, aeronaut-i.cs, and

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· .ato.inic energy.~ the.· growing need for technical ma.terials with I greater

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. temperature 1;-.-esist·.ance, superior ·high. -y_emp.erature mech.a.riical proper"!9 .. /

ties or, greater· chemic.al res-i:stan.9e is resulting· iµ th·e -increase4.

app.lication for ·te·c:hr1icai· c.era.tni.:cs .• : · T_o·.f-~conomically meet:. thi·s .... . . . . . ;, ~'.,1'll.t,...

. . ' ' [ .. . ·incre·a~ed deman~,. it: ll:~s been ·ne·cessary to aut··om~te ~-a me:chanize,

:Consequen.t:ly, ,prog.uct unifo~ty fs ·

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.,. t-hed .. r Jn~lting: ·poi·p.t. :Starting wit·h the ce:ramic ·in. powder· form, th:e : ..

g~n~ral processing_ technique involves: :a ·:forinln/g_. st.ep (such as ·dry

pressing, slip_ c-astin.g, extrusion:, etc,.). which resul·ts :iri a powder

:c_ompact which .is s·ubs:equent:;J_y sintered.. Obviously then-, any hope in

applying .st·atistic·al qµ.aiity contr.o.l .for uniformity rei;te,s· up.on the

knowledge o·f: the complexi,ti:es, .o.:f' ·the -re_lationships between the cepfJJrt~ c ... powder and, t·he· ;fabrication:. ·pr·ocess .•

··by :s.urface area·, green density, part.ic·1e si-ze ~o. ~i:ze .. dist·rzibuti·on.,.

and i_mpu.rity content. However, .due -to the compl-exities of relation-­

ships between powder properties and sinterability, two seeib.inW

identical powders may exhibit distinctly different sintering behavior I

·which presents a major problem· liznit:t·ng.,product uniformity.~.- This

differenc.e in sintering behavior t:s'. -~ttribut~d. to· powder "activity". • ' ' 1 '''. • ' '

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.An active powde~ gerie.r2:a.:Lly ij:int~rs: ·ttr. ·a· 11:igher· density. and fin.er

grain size .• 2 · · .. ' !

Since most peysical- properties· of ceramics depend t.o a sub­

stantial degree on :inic·:rostructure (~p.cll as density, grain size, etc.)

the characteri:zatfon :of pqw4~r a.et!vit.y .is· :necessary ·rrom a stan~

point of product u.nifo~:f;y ,and. quaJ.'ity... J:towever, the miderstanding

·of powder activity .i-~. a.J.;so .r1ec.ess.ary for t4e· theo.r.eti·ca1. understanding

quality con.t.r:ol c·a.n be 'achievec:l. t.o improve: ,:ceramic pr@d~ct pir-. ·. ~ .

·forman.ce.

-'3ll .. active ,cera.mic· powd~r·., ·t.h:e· ftiJ;ld·amental. fact.·or$ ·contro1·1i~~ s·inter--

rn sintering_,. t·he- ·princ;i·pl:e· d:r;ivir1g :f'orc·e: iJ3 the ex.c:~s,s fre·e ..

ene:rgy q.f t.he pa.rticle .s~·f'acer. 3 :Th:eoret·i.cal. stuqief?,. of: sint·eri~g

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e·hown ·schema.t·iq:aJ.l_y in :Ei-gu.re .J:. The .ourva.t:u_re· of :t·he- ··ne·ck are~ (.p:·). . - . . ·- . . . . . . ' .· . . . . '. . . . ..

(1 = "Y/p . (

(,,; )· _.u.:.: ·.· .

.. di:tr:erenc_~-- in vapor pre;ssure and. vacancy ·cencentration. e_p.sts be-

' tween the neck area and the· particle surface equal to;

. -~' r ..

-~C = aP_= _ "YVo. C0 P0 RTp

..

3 ',:

,. '

'

'·I

'r ,.

. .._

·'

:\ J

.,:.'::

. ..

,·

. ,.,, .

•

~--------------------

r

' --'

A --------......... D .

,._ ___ . ______ -"'I

8

2 'Y.. ' ,.,

..

FIGURE 1. GEu1EIRY Ar{) J\TCT1l FWX PATHS FOR n:rnf\L STP1GE ft)DEL, A, BAND CARE VOUJ1E DIFRJSION ..

D IS GRAIi~ BCUiDMY DIFFUSION, E IS SL!f.fi\CE DIFRJSI01t F IS VAPOR -ffiANSffiRT, r IS THE PAR­

TICl£ R/\DIUS, X IS TI IE rlECK RPJJIUS, ~JlD P 'IS PJ\DIUS Cf CllRVAllJPE OF rlECK AREfl ..

•

•

•. I

':· .'

.f·

..

'•:.,

where AC is th.e· excess· conc·entration· of vacancies:·. iri the.· neck . ,I area, V0 is the· inoleci:J.lar volume· of solid, ~p is ~:he·· decrease in

pressure in the· n~c]r ar~-.a', .P0 -a.nd C0 are the· pre·ssu.re and equili-,

.:bri um conc,ent·rat.~on: o.f ·vacan.o .. ies ·, · R is the· gas canst ant and T is 'the· -~.

•. ~

.·, ~

absolute t.emperatur,e. :rn the·· later· stages; of: sintering, when Sj;>heri-,

c.al· pore·s ~re f.ormecl~ t·he· stress is equ'al.. .·to·:5

a= 2Y . I

I : . ; ~?;.,.!_

ilC = Co Yal 2rKT

(

r ; (''!" .... ·)·· . ~ . . . " .·

(4:)

where ~-3 is the: voiwne of' a lattice. v.acan.GY :an:~. K. iL?. t_he:· .:Soltimsn constant·· These cha.ng:es in va.Gan.cy cortcentration .and vapor .pr~s1:u~e provide t·he driving force :for .mat:.erial. transport by .an:y:, :one. 0£ the

~·

fiux .pa.ths in Figure 1..... Mas:s: t.rans.:port can occ,ur· by yolume di:trus:f.9n.:, ,··s-ur:f'ace :.diffusion, grain boundary diffusior1, evaporation~condensa.tton ·and. ;vi e·,991el.S 00r:ppl.ast ~c :t1':ib-GW?6 Mliweve:t; , ee·1.t~po~at i-0:a--ecorl.deBaa:ti:bon amid viscous flow are raxe in cryst·~lin.e soli~ .• 7 It ·should also be noted th.at-: i.t is generalJ.y ~cc.e.pt:ed that surface diffus.i.on :doe··f:> not: result in :a.ppro~cb.· 0.:f· part-:Lcl~ centers' ·(shrinkage) and :L~, gene.r·ai1y· '.ti'.ot er·:rective, i.n final stages qf siptering. 8 General .-·~quations ·re­la.t:trrg· neck diameter to particle size.· .as a :function :of t;ime for t·he dif:ferent ]nechanisms are listed .. :in ·Tabl~ _1.:9

:In terms . of the rate of shrink.age of a powder compact the ex~ pressions in Table l- ·cart pe ~r:itten in th~:· general form:10

-. -.,.-,. . t . . ~ ~-? '

·- ". ·--:"~; ... I • , ,,1,1 I ,

' ~·

·; .. -. i', I ' 'i

,f

'" '. !·,I'

..

' .

·,, I

•,\.

-~.

.... \· .~

... .. ~ ...... --- ~- --- ', '.. .

. . ,,

:~·

,· .(.5} .

where ~L is th·e' :linear shrink_age of a po~der compact, -R- is.· the· 0

.. particle stz:e,. 1\f i:s a :c·otrs-t~t which is a function ·.of part·_i·cle

geometry and diffusion :path,· n 0 m, arid- p a,reb coef':t~ioiehts: whose:

·values depend 011 t·he_ particular tra.rispo·rt mec.hantsm,. and t _i:s -t;·:Lme. : . .

,I D is the · appro.priate diffusion c:o·efficient· an.d c·an be de.scribe:d

by:11

:n. = D0 exp [-Q/R T] (6):

w:n~re. :p0 ·i:s .a c·onstant and Q is the apparent act:iv~tion energy with:

(7)

:where Qv is :t;he. energy needed to .-ore.ate: a. vacancy and ~,- is, ·the

activation energy for vacancy ·mob-ility:.

,, ·~

Ut-ilizing these re-1-at __ i:on-ships , .. Jtage112; et al have shown. :·th:a.t·

:cr~o.3 siriter.s. ~Y volume: di:ffusio:p.. The apparent activation_ e·ner.gy ..,,

(,-1.00kcaJ./mole) cal:cu1ate:d fro111 tn·e.ir· data is in excellent agreeID.ent

with values report~ed: for t·p;e: act:i.vat:.±on energy for o:xygen diff\lscion

~11 Cr203. Similar re.slllts have ·been .reported for n 2o3 13 and

uo2 1.4, while studies on Th02 15, BaTiOg 16. and Pb (Ti ,Zr )o3 l't have

_i:n-d:i_cat.eq; ::rn~-s t·ransport by grain boundary di.ffusion.

··:en te:rrois of' the factors which cont.rel s,~ntering:,:, as describe.cl

result of: a) decre·asing the radius of' curvature and particle size,

p) increasi:D,g the surface energy, c) changi~g the diffusion path or, . .i, .. ·. d) increasing the diffusion coefficient. . . ..-... '

.. t.·. ~-~~:. ·.' . . . ,, .. ·:,

6'

•

,. ~..,..;;,;" . . "t·

: .. ! •.

' ' . ~: ~I ,jr~ I • ' ' ';.:,i. '

',,• . ' .

•·

..iHIIJ.•., •

. I ,

,·- .

.. ~

·1 i, .. :.

'' · .. ' ' ' ~-

.,.,;· ,. :

I . ';,

. ··· , \ I

. '.

,·,. . .'

.~ ,.

,. '

;'·i

'·

I

. ' . ,

'.' ' .. l ' . .

1·, •

' -,~- _,.,,, •-• --•~··•·•·•·•-••·"''"''"''"·•·--·••· - .............. ,,, • .,. .. ,~ ...... ....,., .. ,,.., "' "'·""

. -~' • If I·-·-

. .

TABLE 1. M:CIW~Isrfi AND W\llW\TlrAL MJIELS FOR SI~flERlffi .Cf SPHERES ·

1. VISCOUS OR PLASTIC FLO#

2. EVAPORATIGJ­. CONDENSATIOO

3. VOWM: DIFFUSION

4, GRAIN B'Ol.NDARY DIFFUSION ~ . _-:,i-:J"-

5, SURrACE DIFFUSION

' ' MJIEL

. X - 3Yt • ... ~ ·- 2TJ ..• .. r x2 _ 3'Y4 Dv r· -2KT t

... . ..

x3 ::: 91rv0 YPc, t r 2MRT

..

·.-~.

, .. 6 N '\Vi .· X - ~ 0 t r 2 - RT.

·. 7 NYVi to !__= Q_ st r3 RT

. .

WHERE X ANDr ARE DEFINED IN FIGURE 1, M IS MOLECULAR VOLUME,

. -

TJ IS VISCOSI1Y COEFFI Cl ENT, R IS GAS CCl\JSTANT, U, IS VOLUME DIFFUSION COEFFICIENT, D9 IS GRAIN BOUNDARY ~IFFUSION COEF­FICIENT, D1 I~ SURFACE DIFFUSION COEFFICIENT, AND ALL OTHER TERJVE ARE DEFINED IN lHE TEXT,

.\. , . . . ·-·

1. (

I ' • '

I,,~,.."; '', I -:, '.•"

•• c- : •• ' - .'_. '· : • .. • '

' ' . I·' ,• :·-'. ',' \ ,,

• :-.,- -. 1' ·,

-a.-·

. ; .. .; l :·:· ...

.... '

·'

~ . ~ . '

l ' •• '"~;

• • "• ( I • • ' '., • •. '

. ·- -

" - . . ' . . . - .

' - " I ' '

. . .,. \.

;,

.,.

,.

, ... ' - ; ... I•

,.,

·1 ' ''" ., .....

- ~. .,,.... •:

' . - ..

...

, r .. -. -..

'·

"!~ . .

' . '

,.

I '

1·. I J,.-.,,

,·

:'1'

Decreasi:0-g the p'articJ._e · ·size·. t:P. .· order·. to: enh.a:b.ce · sinteri:llg has • I •

·a two-fold effect.~ First·;·.it will· decrease·the'.'·radius ·of curvature,

and second it will reduce the· pore size· .• · In .both· instances: the

driving force.· ·wi11 · be increased·. Decreasi~g the particle si:z.e: t,o·.

eil:t:i.~ce sintering ll~S 1)e(:?n shown to be effective for .A12q3 18 a.rid

',.Tungsten.19· However.; :at ve:ry fine particle size·,, lYlurray-2:0 shows , t:l1at ·the ·Sin.t:e·r!n:·g ·r.at·e. m.a.y b~ .reduced. Thi:s ,. P,O:Wever, is· ,C.~Ufle.d b.Y.

,·

·po.or .P.a¢k:fr:ig of extremely fine particles. resl.l.lti~g :in ·ifq.~ n'Ull1.ber ,of'

.p~ic.l~. t:o particle contact5: causing le'S:$ mas,s, t 0ra.nsport,:. ' . ···'

·.Increasing the sinter:ing rate by i.n·cre'tising 1:{h,e sur:face energy

of> :a particie: is ~· more co:inp.lex problem.· Surf:ace st.r.ucture: and .. ·. . . ..• . .

partii·cle ~1:t.ze irtcreases the· ·~pe.c.i·:f'ic surface ene.;rgy· by i·n.c.::re@·i11g

, .. , t:he· ·surface to volume ratio :O.f' the particles .. :21 The, .. s:µrfa·cef ae:creases:

in re.lat.ion to particle di.a.meter squared. ·w.-hil.e t:he v.olJttne deereE)$·es

proportior1al to· the particle diameter cubed. .• ·Th:ts .res:ults in a .net . . . . . . •' .- ~- .

i;rrc.re.ase o.f ·s.11~ci.f'ic: .s·tirface energy with deq~eas.i~g parti~l~ s.iz.~ ..

de:fects .. such as:: 1) c~ystalline line: def'ects, s-q.Gh as dislo.cations .

int~rsecting the surface, 2) cryst~llin'e point defects in the. form of s:urface ~tvacancies and of vacancy clusters, 3) grain bbtl!ldaries,

sub-boundaries , an_d :twin: boundaries intersectin·g the surface, 4) . . .. ,

e.dges and steps, and 5) surface im.purities: •. 2~: Such surface defects

represent high energy sites and can enhance material. transport as

well. However, experimental observations have.· ·eho~ that t·~e· defec~

I ,

I ,i .,

' I

•. i .y:

.l•'.

. ,' . ' .

.. : i· • ··,

• ~ ' • -.• ', '·. J

' .. ·, 1,. '

·,

I '.' :• ': •

.. ' 'II

. . : , ·,

..

).~ •.. :: ..

l ., '·

'I . ._,.

,f' I

structure: .·. the· or.:tentation and· the· distribut·ion of these surface_ .. ,. . . . . . .. ·. . . ' defects .a.re n:ot a1w~s detectable·.. Consequently·,· their effect on·

. .

sin-ter~b.ility is inconc:Lusive. 23·. · .,

iSin·c·e diffusion cont.·rolled· mass· t:ransport t-akes place by the

·r·everse flux of v.aca.nc:Les', diffusion paths· are determj_.ned by the·

'l;.ypicaJ. vacSl:).cy sinks: ~re grain boundaries, plane· or -convex s::t1.rf.~:c¢S.,

large pores·, and disioc~tions, while .s111a,ll pores, concave, .sur_fa:ce_s;

and dislocations r~pr~aent; source·s for vacancies .24 -Cor1s~quen.t·:1y,

,latt·ic·e diffusj;on. ta.ke·s pl.ace by' t,J;ie :re·ve·r·se flux 'Of. ·y~c·@.ctes. t·he '

s:-«~:lf~di:ffusion coeff.icient· c.an b~ ·writt.:e.n .:45

... I Di. = D_. n·N. V . (\.8:-.c)·:_ . ! : :: :. .... _.·--. . ..

where ·D1 is ·tJ1e ·1atti:ce sel:t~diffusion,_ .. c.oe:f·ficient, Dv .is t-h~

·vac~cf· di_ffusi·on coeffic·ient, p. ts the n.umber c>:f.· vacant si te.s .,· and

N ·is t·he ,numbe·r: ·or lattic.~ -E1ites~ An in·c.re .. as:e: in vacancies will

increase the ·ai.ffus,ion .coe"f'fi·c·ient • . .. -· .· . . .. •. . . . . ...... .

. .

In the case o-f. ionic: compounds, increase:d vacancy· conqent~;at.:ionf?:.

can be created by the addition of impurities •·26 - To conserve

ste,ichiometry' impurities .of a h_igher vaJ.ence than the host mat:~.rial

will create cation va.canc~es. 27. For instance, the add.ition of Ti 02 . . : ...... - . ' ·has l>e~n shown to inqrease the· densific.~t.ion rate of ~gp by incre.as-- ·

' I ••

n_ . -:1 .. "· ..

•• ·,,,. I

. . .:. ...

,, .

·-

··,··

..

. ,

·-·- . .1-;;·.;Z<

--.--

ip.g the Cation vacancy concentra,t.:ion •28· A si.mi.la.r effect has beett r .

observed' for 'ZnO · where additions, of Ti02 .. ~ncreased: the· cation ..

vacancy concentration. A decrease· in the· rate:·. of $:interi~g ZnO was ·~ . ,

•' ·• .

observed upoi::,, additions of Ga+ 3 _and Al+8 v{}:J.:i.ch would decrease the

q.q~~.-e,p/4r.$t:·ion. ·of cation vacancies. ~9-.

Sinterabili ty can also be enlla.nce.d oy ·contrdlli:ng t,he the:rinat:

and ·environmental .con·d~ti:op.f1 i·n s-t1cn. a man.n·er ·t·hat. mas.s transfer will

occur by the me.-¢h~.~sm: yi.e·l:o.ing the·Jna.ximun1 :tat·~ o:f' densification.

In ·high purit,y· 1n.at·.er·i.a.l-s. a .pre·domin·attc·e· .o·f- .$-urface diffusion ma¥ ..-, , l • . • . .. ..

dc,c!ur at lovr ·tempe.ratures. 30 · Since sµrfa.c.e di:f'.fus.ion ·does not c~use

d,.eqs·iflcat·i.op.·~Jl the temperature shoul.d be adjusted ·s,o tha.t yolume or

g:r.ai:n bdun.da:cy ,diffusion becomee t~e p·ri.mary· mo:a.e: of:· :m~ss·. transport. . . . .

:.An.other reas:on· to suppress surface di'f"fus:i.on l.·s: that it tends to ~ ' •i

,~liminate s·tirf'ace defects, :reducin.g ·the. s·urfac~ energy and driving

. ;. ·\. .:~·

:©ne ·obvious factot~· ·whi:clt .. will enhance :rnate:r-i:al tr·a.nsport by

:gr:a.in. boundary diffusi:on. is· a decrease in tne. :grafr1 size of ;poly--·

·c.cy.:st·a.lline parlicl.es. 33.. :This increases the ·a.mo1lil.t: ~J:r· grain b-cJurtci.­

aries or s;inlts. 'Gl·ear~., for later st.ages of sintering, the inc,reas­

~ed rate of m.a~s. t .. r~s·port c.an. b.e maint·ained py inhibiting grain ... 2'.: • ""<'!.;, ........ ;

growth. 34

High dj,:s.10:c~tion densities sh6u21..¢1 be· .~other met:hod. :of :.prov-id-­

ing diffusion pat~ij .. and/or vacancy sources ·and. ·sinks to :i.ncre·ase

:sinterabili ty. Pines and Sirenko, 35 in the~r suu_dy of ·cold wetiteia,·­

:copper powders, concluded that sinteri:rig was enhanced by increasi:11g

.... ' . '

. -~ ' ' • .. 10 , . _. ~· .. .. :.. .- .

• '

- ' .. ' ----· ..

. ' ,-,

·., •,!._,. • •

!i-. )---:---·1 ,, .~'

<,,.,.._.....,, .. : ....

i ; '. ' .. r.;

~ •. - . ' ,.

·'

,,

.. ·. •:·,·

l. --·, ••

,.

. . \.

•

' -·-·-------.... ~ .. --.-.. -~~ .... ·-·'••••••••• .... _ .. ~:L,.:,._,,;., ... ,,_, .... ,i..~,,.;..~-..... ~•-,••·<• • ••••• ,,<>

, I/"

• the dislocatiOn density. Federchenk0·,36 ascribed the superior

sinterabili ty of. carbonyl nick.el compared to electrolytic nickel

to dislocations and lattice strain. · Also, it bas been established

'. 1:11,

•••

tl.iat· aliJmina powder is more .active when it is_ ground for a lo~g time

(a.f'ter 9alcini~g. at a h_igli temperature). Again the. increase was f 1,,·,c·.,,.

ass1Jmed to be .due to lattice defects introduced as the results of

h · . . :a,. • 3 7 . · mec anJ.CfU WOTAJ.~g.

Since l~ge differences in sinterability can be: found for

powders with .identicaJ. particle size, .surface a.re:a., and impurity

levels ,38 it appears that the increased concentration of lattice

defe·ct.s, .·such as vacancies and d.i.sJocat.ions, mli.$t; :be re·J:];>.omsible

:.fc:>r enhan:ced sinteri.ng rate~·.·· This conclusion ~s .reinfor.c,ed by ,

noti~g that. ge:neraJ.ly th~ ·IIlanut'acturip.g of reactive powde.rs· includes

a mechanical t:reatm~nt (such as dry baJ.l mill·ing or imp~ct-dis-. . . .

int~gration tec_bn.iques) which leads to h_igh defect concentrations.,

.Altho_ugh th.e iIILpOrtazrae of lattice defect concentrations on sintera­

bility _is rec.ognized, li tt-le effort appears to have been directed· in

developing measurements of lattice defect · c;oncentrations 'into a t.ool. . .

for powder characterization.

It is the -.purpose of this :study to relate lattice strain and ......,__ 1-- u...

other characteristics of ceramj c powders to sinteri~n-g behavior in

order to enhance the understandi~g of powder act~vity.

- '. . ' "'·,I'·,'.

, .. ·• '

' ' ,; ·1 '·J '

'' ., .. ·-' ··•·hi~·· < . ... ·'

•. li . :

'' . ' .

' '. "I

·, '

. '"\

r 1· •

. '

. ..

,. ' -: -'

'' ' . ',: I ', ',' ! •

• i, I • -

.. ·'' ' . ' 1.:,' I ,. i , ,

' • l '. : ,. ,' :': "' ., • • • i ' ',· .':..I : \ .,. < '

,, '' . •,: ' . :\ ~',';' . '

,., (,

''·

I . ,

'' ·,:·· ": ~

-.

i,

lo 'I··"·"

- - • • .... ,~1 ' ' • ,.

-..

'-.,• • I I

) '

• ,1 •

A. MATERIALS

Five a.1:umina powders were chos·en on the bas-is .o'! their distinct-,-

ly different sinteri.ng behavior. Powders A, B, C, and D were manu-

factured by the ·Aluminum Company of .America. (A 16) while E was· ®

manufactured by Reynolds Al11mjnum Company. ··'..." .a•

";1, B • -POWDER CHARACTERIZATION TECHNIQUES

/I_

,1,'·

, I ' ,

For each· powder the followi~g character·istics were dete~ned:

1. .Surface Area

Th "" d t . d b th B- E T th -d39 • : e .Sur.Lace ·area was e ermine y __ e • • • me o . -us1.~g

n.itr.ogen absorption. Approximately a three. gram sample was .o'll:tgassed 40 at 300°c in a helium ~tmosphere. / Data points were t-aken usi~g

·five equal nitr~gen dos.es o:t' 250 cc and recordi;ng the appropriate

equilibrium pressure-a on an .Aminco Sor Bet Surface Area Analyzer.

The . surface area i_.s .:t:hen caJ.culated from area occupied by a si.ngle O• 2 absorbed molecule of n:i trogen (16 .2A < ) and the monolayer vol11me of l

nft·r9gen dete·tmi.ned from the equilibrium pressure measurement. The

free surface ene.rgy of the powder was then obtained usi~g the sur-

41 ( .-2) face area and the . surface ene;rgy 1000 e.rg cm - •

2. Particle Size

The particle size distribution was determined using a Micro-.... ,_ . .

meritics Particle Size .Analyzer Model 500. The apparatus, utilizi~g

x~ray absorption to measure the concentration _of' .powder remaini~g in·

. suspension, plot is tb.e. mass percent finer than versus the equivalent

', ,, '

·· ......

.... ,'1-11 ,·'

.. '

'.

. .

. l, '. r,•' '

·' ' ,: ' \ ,, :'i .. ~·~~- .... ·

·., ...

' , . '~''I • -,, -,.;,'., I

·' .. , ' .

,' 1 ,. ..

L_' ,•

l l . I I

. . ::! ' L "

'·I' '1', :

•/ ,•

- _-.........._,.. .. ,......_._..,...._,,_ .... _ ........ __ ,,.~--~-- , ...... __ ... ._--., ......... ~.-~.-·---"·--·····-·-·-·~" ·~·- .,u ••. ,. -··· . • , ' , I

.•

spherical. diameter between 35 -microns to 0.2: .. IDicrons. Approximately I

4.5. grams of ea.ch powder was dispersed --in. a 40 milliliter solution of

distilled _.H20 and O •. 1% TSPP (trisodi~ pyrophosphate)._ The dispersion -consist~d of four cycles of two minutes stirri~g · (ffl:8,gnetic stirrer) .

:t'olldweq by a five :m:i.nute agitation in an ultrasonic bath. 42 As . , ·illustrate·d in F.:igure 2, the median p·article size and ninety percent

band . .'width were determined as i-llustrated in F_igure 2. · '.

~-· ·t'

3. Particle Sh·~pe

The differences in particle shape was studied, by th~ u13·e;: ·O:f -a

l. Ca.mbri.dge .. scanni~g electron microscope.

4 ... _ChemicaJ. Purity ,.,

·­.• •t'

The chemical purity of e·ach powder was determined usi:ng optic~

'~ni:i.·s·_sion and ion-mass .s:pectroscopy.

5. st:rain ·and. Domain Size

The strain and coherently di·ffrt3.cti;ng: -domain s-ize we·re. deter­

:mined by the Warren..,.Averback method. 43 The diffraction profiles were

determined usi~g a General Electri~ XRD-6 goniometer and ·a Siemens

K-4. generator. Nickel filtered copper radiation wa.s us.~d and int·en-

sit.ies were· measured using a s-~fiiid.L~t~iCon counter n.th a single . •. . - ,. . ' .

channel analyzer .accept4lg ninety percent of the Ka peak.

Two samples were taken from each powder. One .was annealed at

·1475°C for f9ur hours and sieved thro:ugh a .a25 mesh sieve. Both the

un:aime-al.ed and annealed samples were then mixed with petroleum jel4"

and mounted ·on diffractometer powder slidefl .. • The .(012) peak and

its second order reflections .(024) and the {113) peak. and its seCC>Ild -. . . ! ,_,; •• ;,)·~:<>;,· ..

,' . '

I •

/ . ' '•,, .

··1··_· .. ·.3·· '-· ;.

' ' . '

' -··, .

I'•,·': .. ' .

l·r

. -' . _.,,,· ' •. ~, -

-. .

- .,.

-·. ·.

- :;.. . '

...

.~. •

·, - 1oor------------............................... et: 90. --- -------- ---------- -------~ w Z 80 -LL

t- 70 :z w (.) 60 0:: w

.J:

LL 50 ---- - ----- - ----- - ------ - _ __., en ~ 40 5

f-l W 30 I

. I

.i

-J -

MEDIAN PART, SIZE

: ... ,

• -r=- > •

I I I 1·

-~ 20 _J =.> ~ ::> u

!O I -----~-------------------,--------~-------. · 1.. BAND· WIDTH » 1

30 20 10 8 6 5 4 ~ 2 I 0.8 0.6 0.5 0.4 0.3 . 0.2 EQUIVALENT SPHERICAL DIAMETER, MICRONS

FIGURE 2. PARTICLE SIZE DISTRIBUTION FOR SAMPLE A~

.. ,·

.o

--.... ~­

:t; .:--- -

----- _ .. __ _

~--. ',i •.

;' '

- " -: . -

. ~ - --

.. - _;

. -.. .,, ... _

. - . -- . _··_ - ,-~ . - .

{ ..

~ . - -

. : . ( :. ,

. . x\ .. -.: . -__ .

________ ........ ___________________ _

;·

•::•~:"

orde.r reflection. . (226) were. step. scanned. at o·.05° . 26 usi~g a time

· constant of 20 seconds. A total o:r 81 readi_ngs were made for each

1. pe~. ~gure 3 shows the peak profiles . .-tif an impacted and as-

received powder.

The raw data was·then ted directly i.nt.o a computer which cor-',

re,cte·d the ·profiles for polarization and.: geometric factors, atomic

.sc·a.tt.eri.ng factors, and the :Ka doublet. Then, these corrected pra­

ttles were represented by Fourier series: ·which were corre·cted .for

;instrument broadening by the Stokes method,. 44 The· Warren-Averback

method43 was Ufled. to separate stl'ain and domain size. The mean

strain tabulated was. t-he average of the mean s-trains perpendicular .! .

t·o the ·(012). :and (1:13) 1>i~es :fit a dist}mce of ·5oi. The -various

operations we_·re ·perfo~il by .a c·omputer. ·pr9gram,.:ft1rtrt;~ni1~nd·}·s1iper-. . . ' .

. b .E . .M ·t· 'b 45· i, 46 .,_ t N R .h t: .... ·b . vised y _· •. A:. •-· e z .... owe:r · · · · a;.., he ava1· ese-arc · .· :;ua,- :s in

Wa.shi~gtt>n , D·. C •

J;i'rom the mean strain ( E ) and· domain s:ize (TJ)- ., dis-1:o.cat-ion

47 den.·s.:i.ties can be calculated. Usi:ng dome.in size,_ the. :dislocation.

'den-sity ( Pp,) is:

'R' .. :3n_: :'tj.:;: -~ .... D-

where n is the niunber of q.i~l,9cations .per domain face. For· a minimum

dislocation density, n is ass11med to be one.. The dislocation density

( p5 ) can aJ.so be d~termined from. the mean strain ( 'f ) usi_ng the

relation;

.. .;..--''.' '

. : ' . ' .

. ·. ~ ... ~ . '/ ·.

.·15·,

-· .... 'J

" '

• ,. .

-, ",'~'! . I

r· .... .>,.., ' •• I" ' 'I •'

, ') ' '~ ,' • - I I ••• ·-, ·, ,•,_ _ \' /

(•' I • ; ' ' '

. '

. 'I ' ,- ' 1 ..• . ·. ·_ ··, ..

N, ~·°"•,' / lj '

,\.,. ', '''""'1;

"

. ,'; \··

·,

I''

• i -

' '

' 1'1 , ,- ,I

1r '. '," :·, .,

I '

•

•

~-

. :•,

•

1.0.-----.-----r----r----r----r----,-----..----,----r-,---,----,.----..---~----T----..----..----.----...---..... -----

o.a

o.e

~-

. -~ o.e .....

. CJ)

. ffi . t= o.s :? 1..-1 ... _

0\ t-4

·. ~J. ?-; 0."

~ ~:. Oe3

"0.2

0.1

.. ;. _ . .,;' .. .. ·-

'\

I.

... • -\ ".f' - .. • ' ' ..

AS~RECEIVED

IMPACTED

..

. I

'

D.EGREES 2 O

FIGUJt 3·.· FfJlK PRJFI1£ OF IMPP.CTED JlND Nl'JEAL.El) POrJlIR

•

l:

-.. ,.... '\ .... __. . ' - ' . . .. . .,

,, ··1·

,_ -,

...

.... .... , .

. ,·

. t

"

•

' '

~--

. I

I ' 1· I-•

'.' I 'I

.·,

• , • .1 '

'.; ... \,.

(:io) .

• where K is a material. constant, F is the inte·raction factor, and b is

the Bll:rgers vector.

di t. . b t. . 48 . _ s n u 1 on •

---·~ -~ ::

F is assinned to be::1~one· for minimum dislocation /

A measure of the. :uniformity of. t.ll~ ··dislocation distribution with­o ·in the particle was determined by subtracti.ng p

61 from p0 .• Accordi.ng

to Willimnson and SmaJ.lman, 49 the dislocation density caJ.culated

from domain size ( pr?r) i·s the .nunimum disloc~tion. density. If the .·. .

di·sloc··ation density caj.cu.lat:ed from st.raj;n. :C:p.5.) is less than p1 ( ~0 - p5,>·0), then t~e ·g.;l.slo.cations ·axe· itt an a.rr~gement which re-

. duces their st.rai·n fields, (e.g. polygonized). If, however, p5 is

.. gre·ater th·.$n-- ;PD ( p0 - p5.-.< ·O), the strajn effects are ID:agnified by

dis.location pile up. Since strain energy is proportional. to ( b ).2.$ -in ~~,;L~ up b becomes nb where :n is· the ::rrumber of llislocat·ions .i:r} p:i..1:e·

Up·· .•. ·- :t~ n - P. ( n n ~ O)'·.· a un.1.··.·.·:·f'o. rm., distribution is indica.te. ·.·a .. ·:.•.··.· J. 's - o·!ifj) 1> - rs-=-.·· ' '

The strain energy (u8 ) was caJ.culated Ue!iµe; .Faulkner' s50 re-

·1:~ti,onr

(U.) · .. · ..

where E i.s the elastic modulus ~d .,~:.:ts Poi.sson:t s ·rat:it>. .- ··. -. '. - . . ... .

6. Particle Distortion

.... ,. The p·owders were analyzed usip.g a transmission electron micro-. scope to .qu.alitati vely determine the amount of' ~start.ions in the

•o: ....

" .. .... .

. ', I, -

' . \

I' •.., :, ... , .. . ···,· . . ' ... ·.~.··· .. ·. '. ··J... -'I:. '

. tj

',~: ,', •, I •· •

• ·1·1 ·r . . ' . . '

., ., ,c ,, . ' ... ·r1 ' { ' ~· .

• •--' ''1

....

I '--' '

, I • •

_::.

·t, ... , .. · ...

I

---.. ,.--.. ~,,....-....... ~ ....... ,.~----,......_.....,, .. ___ ,_.,..,__~_.......,.,,........,..,._ ... _~_

f I

i , . .~ . ,,, '

.,

I I ' .

powder. Br.ight and dark field micrographs were taken to. det·erinine · . . ,; , ~· \ , . 51 whether,the distortions were .due to dislocations. -. ·----1-1

7. ·Green Density

'! -. Green density· was calculated to find the ch~ge in density on · .. i·:;

.Pt.:. • ·i.1.r1~g. Powder samples were pressed. at ·30·00 psi in a 7·/a inch cylin-

dri-caJ. die to a thickness of ap~ximately 0.100 in-~p. The samples

we_igb.ed, dimensions measured, and the. green ·density c.aJ.culat·ed. ""-'·

C'. IMPACTED POWDERS

Powders D ·and E were .inip_acteci us:ing _a diamond crusher. The-. . . ..

samples were impacte·d. once., three., and. ·seven times and des_i.gnated •·-, .,> ~· • .L.

Dl, .D2, D3 and :n._.l -::m2. , __ E3. :The pow~e_rs were then characterized

.. ~.d. :fire_d t.d ·an-~yze .diffe·rence~: ·c;a.u·s_ed by shocki~g.

D. · :s:r:NTE:RING EXPERIMENTS ..

Qb:rnI?acts of powder pres$e·d- at 3000 ps4 tot' .. . green. de-nsity measure-

·ments were fired at -1475°c,,_.·:ror se_.vep. ho-urs. The ·fired tiensity was _"f -

determined usi~g ASTM .C20-70. ·The .method involves taki!-1:g dry, -

_saturatedta'!"suspended, an.d .suspended we_ights. The media used was

~toluene. The densities were determined twice and aver.aged. The

reetctivi.ti .of the powders w:ere .. de.te.rnQ.ned using Hirschhorn':s .52 ·.- r . ~, ...

,_. I

,.· ,," .. ... 7::. . .. ,

Densi:f'ication = Sinte!~d Density - Green Density , (l2:) Parameter Theoretical Density - Green Density

' ·,. '.~:

,! •'• . '·,·

I• • C •,

r "I ,

,;., .1

···.·1;·a· - :-- '· I •,' : '• ,'";" .•, I

, - I 1

,' ,• I ,

• I

• .. J ,.:/

. : ' ' . ; i .•"',''.

. . :- ' . ~. '_, •\;

. i

( I ' I'\

'

• J' I ' • ',

f ~ ·-..

···11

.... .

, ... , .... V;··,l'f

'"I

·• ... ''\ ..

..

. Act-uiil vaJ.ues will be: between zero and one, and rep:r;-esent the · fraction

· of the ma,ximum·amount _of densification. possibl~-.--;bich is a.function

of the powder's reactivity. The importance of .. the different powder

. ·•

.·

characteristics (section .·B) in determini~g th_e .fired density· and the .

densificat·ion p~;rameter were then analyzed ·usi~g a .multiple r~gression

analysis.

Specimens of the sho~ed. 'p_owders were·· ~so _i.sostatica.]ly pressec:I. ..

·at 7500 psi to a diameter of approxi~ately.1/2 inch. The specimens:

were ms.chined to a length of 1/2 inch + 0 .002 inch and fired at . . -. -

' -1475°c in a dilatometer to measure shrink_age as a. function of time:.,

:The slope of the ·plot. ·of l_og shrink_a.ge: vetr$·ij.S i_og time, which is . .

., ~qllal to- m- in equ~ti·on =5.,. was used to :d~t.ermine the effect _of

-shocki~g on th~ s.hririk;ag~ rat.e arid the diffusion path.

plots are sl:lowp. j_p. :F.igures· lt ~-a 5·,.

... ·-· .•

.,'

/• \ "

,,

'" ,: . '.'

\

.. ' ' . . ,·'. ' . ~ •, ,.

.J ,.

,._, ' . •: I •

• 'r • .' ••

. '

Two .such

. ,~- ..

I •

~- .. ;

.,

'I.• ~.·· ' .

'.·

• . I\) 0

,

~L Lo

0.20

0. I 0 0.08 0. 06

0. 04

0.02

SLOPE= 0.34 ·;;..-

0.01 ..____. _____ __.. ________ .._____. ____ ..._._ _________ ~ . I 10 100

Tl ME ( rv1 IN UT ES)

FIGURE 4. SHRINKAGE RATE FOR SAMPLE D.

-. •.

_,

•

..

I

•

. . , f\) -: f,-J

---a!

AL Lo·

0.20

0. I 0 0. 08 0. 06

0. 04

•

0.02 · ·

•

SLOPE= 0.43

0.01 ...__ ___________ .._... ____ _._ __ _,___.._...._. ___ ____.___, . I

•

10 100 TI M E ( ~A I N UT ES}

FIGURE 5. SHRINKAGE RATE .FOR SAiv1PLE E

,•

•

;

"

}' {:"' ~-- '. .,

!• .

·J

i' .

·• .

·.'. r- ,· _, . :, . . .

...

. . .·. ..

. :1Il . :BESU11IDS ,•/' '.' I •

• l ' ' •

. ,;.:f' .

. /11.. ·.r.OWDER . CH.ARACTERISTI CS ., '

J· ., I

' "', '

' :/ ','.:",', · ..

The ·values deteT.tnined for· the .surface ~a, ·me·d4-ar13?pa:rticle

:size, particle band width,. ·green density, mean strain, domain size, -

. dislocation density cal.Gul·~~ed from strain ( ~s- )_, dislocation .. I

I \~· • ..!:.'

.. den·sity. caJ.culated ·from domain1 size. ( ~b) , total free ene!gy, . ( p0 - p5 .. J, 40 · · -

and impurities :1i[.lpa,rt.s.'.per million are listed -in Tables 2, 3, 4 and

5. Usiµg a- multiple r~:gression anaJ..ysis th~se para:meters were

correlated wit·h the fired density and the densification parameter, ... ..: .. ..., ··- . ' '

;

- ' . th ' uJ.·t· ' ·h ' . . T 1-..1 /···6· P' ' •' ,' d'' rt : . .p' ' .. . t·lLil "'' ,i ... l"' ' ,;;/ ~" . . : .• ' '.,. ·~.:: ',,t,-,,:.:.:;i, •.• ' ..... ' .. ' ..:;( d wi res · s s · own 1 n au es(, .. ~,1,· an: -~--- ·1 o; -.a:. 0,'::2 : ).1e:r,}::asv~ne pe,~?V~~r:~;c]>.~Wue rs an .

__ .~0'1:l?lX.·:J:G!f'.i.Vat-i,a,tiid>h:.J.8.li'P._rib:ute.:dt~.te··~!ie~aebl~azrlil,abie.Je·'.a:Jtl'Cleifbl)EtJJneip·jjafned

'~~rs:.rea···~·dual.·:··:vari.•a.iii:oia·':.~.a·r·~!_';,;~;~ror ~·;·/•.t~'."'."!, ... ·. . ·~' ...... . .. ,.,. "'" .. ~ .... : . -~·' ' ' .. .. ,;:,<,:,_.,.,,' . .. •

B. ELECTRON MICROSCOPY

~igures 6 thro:ugh 10 are .¢1ectroii transmission- micrographs. '

' .· -~ .. ··. ·--- I .. ----F.igures 6 and 7 show intema1 .structure of powders A and B. I?-gu.res

8 and 9 show ·br_ight and -dark field micr_ographs of powders D and E,.

re spe cti vely, before ( a and ·b) · and after impacti~g . ( c and d).

~igµre 10 shows. loops or pores in various powders.

~igures 11 and .12 are scanni~g electron micr~graphs of powders

.D and E, respectively, shc;rwi~g powder mo:rphol_ogy before (a} .and.

·after impacti~g one (b) three, (c) and seven. (-d) times. Powder· s A.. B ,.. .. , and C were observed .t.o · be similar· iri.. morphology to powder D. , • , i •1 '• . ~

' . . I • .

- . C. SINTERING . DATA - . ' . . .

• ·~,' . -., I • '. •

The fired densities-• • impact~d · and as-received powders . .

•:' ... ,,.

22

...

.· ,'\ .... _·~-·' -

'. .... . '

j

,,. .... ···-,'

are 2.

The slopes determined from the l_og~l.og· piots were of shrink.age .. ... versus time for ~he ·impacted powders which are listed • in Table

-·r

. •''"'<\ l

·I 'l i

·.:·

·":··

1.-

,,._ .... ~~· •i,··.,·1: .. -······

.. . -. "'

. ' ·. - ~: - .. I ! - _.

'. ' . ' - .... '.' ~

--~.

. - . - _.,." -::, : ' -

-· . . . . \, _I

\•

. . ; _; TAB E. 2 I fU\'OER C!~CTffiIST]CS A1 ID FIRED D61lS IlY ... ,- -' .

-

. - . .. :

-

MEDIAN OOID SURFACE GREB-J - DEr~SIFICATION FIRED • •

PART, SIZE WIDTI{ AAEA DENSI1Y PARAMETER ·DENSITY ,. .

.• . ·-, MATERIALS .. ..

~ . ... . ~ . (µ) (Al)

r)

(GR/~) (GR!~) -

~/GR) . ._. ~

' '

. --.. - ,

A 0.45 1.00 ·14.20 2.265 0.96 3.931 -

C --

B 0.39 0.92 10.24 2.126 0.89 3.793 'r···

~ -~-,-~ -'

-·., • . -.N> . . - .....

- ' ,---:~- -

' . . l

' . . __ · ,' -- -

C 0.91 1.15 10.15 2.127 0.9'2 -3,343 .1

I . -- '

~-.

. ; -_, ·~ - .

-.-· '\ ~

I .D 0.38 1.06 11.28 2.090 0.84 3.G91 - . ---- --

D 1 0.43 1.10 .10.93 2.133 0.84 3.695 --

• --

-

.: '' D 2 0.35 1.01 10.83 2.138 0.87 3.749 -., -.. - ' . -

. s D 3 0.45 · l,07 .ll.23 2.lffi 0.83 3.689 ' E 0.61 1.35 9.59 2.llf8 o.oo 3.815 • L ._.

. - - .:· - .- .

-

' . ·1 ... El 0.57 1.24 9.68 2.165 0.92 3i851 ;\

-

--

.. ; ~ ••. - , ·-_ · 1 .

.

";c -

-~. . ' E2 0.60 1.27 9.75 2.281 0.92 3.853 .. ' . . ' .

' ..... <

~ . -· --

' E3 .0.62 1.31 ·g,81 2.273 0.92 · 3.856 ' - '",.-. , .. . . ·:... .-_ --·. . . ~- . . . • , ---;:

.c - -

---...... .......---.-~ ... ,-- - . -

. ~;

• •

~:-"' ·,

. ---· ,-

- - - -

·-- - '. .•·.

-. - .-

-.,

.,

l . t --

-! i l J j i

i -· ... -·--.

f ' { l .. l

1 I l i;

IMPURITY

IRON f\ll\Gf'JES 1u·i1

SILICOf·J ·r11:r1r J IUf vl

\ CALC IU·,-J ;

SODIUI't·l

G/\Ll.lUf.1 ffiTASSILf,1

LITI1Il1il IAA1u~1

BOROf·J

FLOURif·JE •

SJU:UR -·

·u.

~--

,,

SAMPLE A

(PPM)

gJ

525

~9 <50

2IJ 520

25 (50

68 70

7

67

93

~. . .

•

_-.

TABLE 3. CHH .. 1ICAL HJRilY OF PO~OERS

SAMPLE B

(PPM)

70

350

516 <50"

<100

23

<:D 40

<50

12

J.02

106

. SAMPLE C

(PPM)

61 365.

(9)0

<50

<100 450

18

<:D •

;

38 <:iJ

NA 0 -

NA

SJ\MPLE D SJ\MPLE E .

(PPM) (PPM)

82 144 450 <250 407 7 402 <50 <50 250 360

I

550 530

20 • 72

<50 <:D 45 39 90 <~

. 12 4 69 . l()CJ

64 41 I I

I !

b

.# :

- I

.- -.,,,;;

I· .

···;,r

- '

.•

'

-'

-" • ~

,,

:

--

• .,

-.

' ··:

.~ ' ..

·'

' I i ·, ;

' . ' ·;

l _, -

; ~

:.:i A

t) t

'"-' :-1

---- -·~--~_.,,,_ __ _......,.~--....... -------

- -. - - . . ' - . . -. -- -

.·, . - - ·,_- -.-~' .- . : -.

'-

-. -

. :: .

-. - . -- -. -

-- -, ~- . - . . -. - ::- - . . , . . .

. - - -~ ._ . . . . : . . .

; ·: :: - . ' ~- . -· .

- i . - ·. . :.._' ~. . - . ' MATERIAL .

A B

ro C . - 0\

D

·Dl-D2 . .-

,•

- ..

. .

D3 E ·•

El

E2

B . t J

...

•. l

T~ F 4, CH'\R/\CTERISTICS DEIIBHIHED BY X-MY Ai·U\LYSIS

MEAN ·001l\IN DISLOCATlOi~ D8'JSilY DISLOCATIOf~ DEt-~SilY STRAIN SIZE (FROM STPAIN) (FROM D0~1AIN SIZE) cxio-3) (AO) (xl()li1cr-f) cx1ollj~)

3.143 393 1.36 1.94 2.3G9 376 0.77 2.21

.,. ·• 1.39 . 1.64

' .- . 3.175 428.

1.917 393 0.51 1.94 2.053 411 0.58 1.78

..

2.072 414 0.59. 1.75 li765 383 0.43 2.05

, ,· 2.G?D 352 . 0.95 2.42 2.777 349 1.06 2·.46 .. ,

}

. 4J!'

2.795 349 1.08 2.46 2,865 366 l.]3 2.24

f

<

·_ =- - ,.,· _-,

. ' . -

J -~

--._"..:.-.i -C:- -,-,- a • - \. --'

. . . :) - . "· -

,, J ' - . . • ! . . -- 1- -

. .J

---~' .

..

DISLOCATior~ DE[,JSI1Y - - - - - .- - - -

. - - ..

DIFFERENCE .'

-

(xloll/ (M2) L

. -•.

_i . .

0.58 " l,lJ4

·l ..

0.25 1.43

1~20 1.16 . - .< - ~r . ;'. . . ,. -..

" --· -. .

1.62 ' ,_

. . 1.47 J. .

• l.LO

1.38 . ~-

: . .I l.ll I .

-- '. . 1 -. . ' . --.

·.···' .._!I • -.

- '

___________ ....... llllllllalllla!_______ . a

. , -

•

. - ' ·.--- . : ~ . ' . .

. .• . . .

r '

. · .· ' . · • ·. · TAll.£ 5. S1Mil'J NID FREE SUP.fACE EIJERGIES Al'ID SLOPE Cf LOG-Lffi SHRINIQ'.\GE VERSUS TIME · • - FREE SUFACE

. ' .. . ·: :, - · __ .:-, - _- Ml\TERIALS . · E~lERGY

u· • .' "• - ' -.~, • • • >. -: ' -:• - - .. - . ·- . -

- (JOULES/ GR I ) .

.. '. ;. ~

A 14.2 B 10.2

. ·N>'. ;, ·- ·., . ,. . C 10.1 . .....q . . .. . '

D .

ll.3 •

-- . -'~., . - .. -

Dl • -

10.9 - ·-

,- ·:,· . -

D2 10.8 -- it: . / •. - -

D3 ' n.2 •.

E 9 •. 6 ;

.. El 9.7 . ~ .

. E2 .... 9.8 B 9.8

. ·STORED STRAIN ENERGY

(JOULES/GR)

3.03 1.72 3.08

1.13 1.29 1.32 o,·95 \

2.]2

2.36

2.39 2.51

TOTAL ENERGY · SLOPE OF LOG•LOG PLOTS

'

(JOULES/ GR,) l (M. IN EGUATIO~J 5);

17.2

11.9 13.l 12·.·4

12.2

12.1 12.2 Jl.7

12.1 ..

J2.2 12i3

•

NA·

NA NA

0.34

0.35 ..

0.35 0.31.

..

·0.43

0.45

0.46 . .

0.48

. i

-· ,i,

.. '·

- - ...

. ;.

. . -• ' J

' ·.'! _.., '

. - . _._

..

~-- . .

, .

t .

I::

.,

,,,

.,i ..

, ..

t ~ _. -~ I - : -- '

·-·-- ;. . : '-. - , ··:.-.

. .

. ·f

. I

. I

I

'

I

',

.{ . . -.. ., . ,.

. ,', / '_

..

.: ·.:

:.. .

' .

. ' i'·' ..

. . .

TPBLE 6. EFftCT OF GREEN IINSI1Y, r'EPN STPJ\IN AND DISLOCATION DISTRIBUTIOf~ ON THE FIRED DB~SITY (Y) OF AS=-RECEIVED POWDERS IITERVIIi~BJ BY THE MULTIPLE REGRESSION ANALYSIS BASED ON THE .. . - .

LINEAR E(lll\THl'J: Y = \ + A1X1 + ft;_'k;_ + ~X3 I . ,

• - ' ' ., • • • Ii

....... ~ ~·· ······--· ..... ... .... .... . . SOURCE OF VARIATION -COEFFICIENT. PMf, OF VAR, %RED. -IN VM,

. COOST ANT · . . - . Xi (GREEN DEN~ITY)

Xz (MEAN STRAIN) X3 (PD - Ps)

.

-Ao = +2_.20894 A1 = i0.48931 ft;_ = i{)_. 10061 Ps. = i{).07932

. . .

o.~ O.Wll O.CUll

. RESIDUAL OR l.NEXPLAINED VARIATION o.cxm

. .

TOTAL VARIATIOO IN DATA 0.0312

PPBJICTED·vs ACTUL\L RESULTS

POWDER. ACTUAL PREDICTED . . ..

A 3.93100 . 3 •. 93100 ..

B 3.79300 3.79158 C 3.84300 3.84302 D 3.69100 3.69153 ..

E 3.85100 3.85187

·~·

-8).1 .13.2 6.7

> •

o.o ...

100.0 ·

DEVIATION

.

-o.cxxm ' .

i{).001LQ . .

-0.00002 -0.00053

. .

-0.(Il)87

Co' '

·. ' . •' " 1 • • •

'.-. - ·:. ';' ;,, '·.

'

\'.·.

·-' (.'

I .

' ' .

' ' 'I; r•

,I ,·-,'I'·

. ''"'f

..... :: .' ·, · .. ··, 1' I I

·.,

. . ' . ..

< ,, ") I ',•

. I . .

. ~--··----· .. ;

'.

'' ;,

1' •• '•

i . ' .... I' 't

. .

· · · TABLE 7. EFFECT OF GREEN DEf-~SITY, fffJ-'N STRAIN NJJ D ISLOCTff IOi~ · DISTRIBUTION ON 11-JI: LfNSIFICATION PARPME.lER CY) .OF AS-RECEIVED

~,,. • ·')-_ e• .' •' ··•· i •

ro~DERS DffiA'·iH~ED BY THE r,:LJLTIPLE REGRESSION ftj.JALYSIS BASED ON . TI-IE LINEAR EQUATION: Y = Ao + A1X1 + fviYv;_ + PsX3 . ·

.. ..

•. .

. ~4'.. ~ . . . • ;. . .

SOURCE OF VARIATION ,AMT, OF VAA. .. %RED, .. It-1.VAR,

CONSTAf~T . \ = f{J .12593 ~ : .. '

X1 (GREEN DENSI,-Y)i A1 =·+0.27700 0,0063 81.7 ....__

~ (MEAN STRAIN) -·~.

~ = +O.ffi367 o.ocm ll.8 X3 ( 'b - Ps ) ~ =+0.01J26 O.OCC4 5.2

..

RESIDUAL OR UNEXPLAINED VARIATION 0.0001 1.3 . • q

TOTAL VARIATION IN DATA 0~0071 100.0

PRED I CTE1J VS ACTUAL JESULTS . . .

. . FO'IDER • ·ACTUAL PREDICTED DEVIATl(J\j

A . 0.9&,'U) 0.96000 -o.oocm. B o.~ 0.88190 -t-0.00810 C 0.92000 0.92010 -0.00010

,"l • '

0.84000. o·.84304 -0.00304 D ' ... ,··· . . ' ' -~ .. . '

•' ' . : ~: ... _' ',,,. .. :. .•, . ' ' · 0.90000 0.90496 -O.CXJ496

'' . ·:'· e· .

----- , I ., ' ' • ,, ' ,."', .-·, .• f· •.· •:\'·, ',, ',• .,, ).·\"•:-;·~':':, :" .·.:,·' .,_'. >"< ·, ... ,·, .. '·:· .,_ ''. - ', .. .

I. . ' .. 6

,.j ... ,, .. -­'

' I '

TABlE 8. · EFFECT OF r£M STRAIN, TOTAL ENERGY A"ID SUffACE Alf.A 00 lHE FIRED DB~SITY (Y) OF Iflf>AOED POWDERS DETE™INBJ BY lliE

· MULTIPLE REGRESSIOi~ Ar\JALYSIS BASED or~ THE Lir~EAR EQUATIOii: I _ •••

y = fo + AJ.X1 + Prf2 + Af 3

. - .

SCXJRCE OF VARIATIOO CCEFFICIENT · JlMT, OF VAR.

CONSTANT . .. . . . .. . .

X1 <MEAN STRAIN) ~ ( TOT Al. ENERGY) X3 (SURFACE~

Ju = +3.93915 A1 = t0.49488 ~ = --0.29545 Pr:, : tO I 21796

0.0399 0.(ID4 o.oon

RESIDUAL OR ll'JEXPLAINED VARIATIOO 0.(Xl)l . . . - . . - . . . .

TOTAL VARIATIOO IN mTA 0.0415

PCWIER

D """'

ff D2 D3 E

El E2 E3

PllDICfED VS ACTIJAL 1£SULTS

ACTUAL

3.69100 3.69500 3.74900 3.6g:J(X) 3.81500 3.85100 3.85300 3.85&1)

PREDICTED

3.68ll09 3.70464 3.75]32 3.68657 3·81626 I ..

3.84956 3.8LJ419 3.?i:Jl51

. , ' I

96.2 · 1.0

2.6

0.2

100.0

DEVIATI~

. t0.00691 --0.00964 -0.00232 +0.00243 --0.00126 t0.00144 t0.00881 -{).00637

,·

. .. ~, .· . ', .

- ' ' ' · .. \ ' . "

,.; : .. . ' . ' ~ ' - \ ·, • I I \

,', ·, '

: ' '

' ' .. : . ~ . ' '

ft • L - ·~ 0 ,I,'·,:"~•,,. ,' '. •'' , : ' '\ .' '

- .. ' . ~ ·,· ''•\ .. ' :; ·,~ ·-. . ' ' '.

·:· ,· ' ' ",·· .;·· ' .'-,.. ' . .,., . .; . . .. ' '

• • ,' 'f

,' - .

I. ' '; I 'i . . ' . ' . '

•I L -·' ••'

• • "'. '1,'. • I::'·•;

'· . ··., ,,:. :·30·

• ,.,__ .. - .---... -..----·-·•cO ......... ,•••---,.,,•--.-~···"~

.. .

.•.. _,-r·....-1 :l

•

, .. '?:,//f·'•/'.·.1"'•?·'.' .. :··,. ,_,: .. ' '." .. ,..

,,,,:.,.J: .

. '

' '·.\ '.' .. ' . . l''1i 'I,' ,

..

TABII 9. EFFECT Cf r£AN STRAIN, SUlfACE Af£.A, ll'ID DISLOCATION DISTRIBlffION 00 11-IE DENSIFICATION PARAMElIR (Y) (f IMPACTED POWDERS IITERMINED BY THE fVllLTIPLE REGRESSION PNALYSIS BASED 0~ 11-IE LINEAR EQUl\TION: Y = J\o + AJ.X1 + /l,f2. + ~X3

.. ,' i ' ....... ' ' ' ::,

. . . . . . . . . . . .

SOURCE OF VARIATION CCEFFICIENT .4MT, OF VAR, %RED, IN VAR,

Co.JSTANT ' . . .. - .

· X1 <MEAN STRAIN)

Xi (SURFACE ARF.A)

~ Ci - 'sJ

. .

fto = +0.76312 'AJ. = +0.07665 '2 = -0.00581 ~ = d-0 ,00271

0.0106 ,

0.(ID) · O.O(ll)

96.·4 o.o o.o

RESIDUAL OR LNEXPLAINED VARIATICN

TOTAL VARIATIOO IN DATA

O.OOJ4 -·~ 3.6

o.ono - 100.0

PIEJIC1ED VS ACTUPL RESULTS

POtlIER ACTUAL PREDICTED ~VIATION ..

D 0.8400) 0.8LI069 -0.00069 ..

nl 0.840l) 0.85377 -0.01377 ..

n2 0.87(D) 0.85598 +0.01408 ..

n3 0.83(D) 0.8'2882 +0.00118 ..

E 0.9(IDO 0.90915 -0.00515 ..

El 0.92000 0.91598 +0.00402 ..

E2 o·.92011 0.91701 +0.00'299 ..

I E3 0.92000 0.92276 -0.00'276 I,\

I '~.., ,(;"c

. '

' .. '

,.' .. ' .. ' . . ,, .:: . . . . . ' . ' .. , ' ·.··:·,.,_. ·_ ... •·· ...... :.\' ... ·: . '. : ·.. . . .

. '' ,' ··., ' ·.. ' . \

' ,·,, ,, ,·, ' ' ,, ·• ' ' • l ";- ,

' • I r ( ' ' • I• ' ' • ' ,·' l ' '.,,

. ' , --_ ,' I.. , ' '.' ,' _' , ..

I, ' . . J • . ,;: ,:;'·

I • ,•• ,

_ •• I

. ' ' ·•

• ... ·'. ,' • ~ ' I ,

/,

I. '' - '' 11··1·

' .. , .. , - '

' -,

··i'"I

r - • ' t. '

. ' . '

'' • ' ' r • ' • ' .. r '·."'''

'' : ;-,<.;:, ·, ·,

' l I

-- • I \! /

·" I>-!

o! 10).( ' ! ', . '

FIGURE 6, TRANS'11SSIQ~ ELECTRot~ MICRffiRAPH SHOWING A HIGH UNIFOR'l DISTRIBlJTIOJS (f DISLOCATIONS

'l

32

· ~t·1

.. 'i •j

I

FIGJRE 7. TPANS\11SSI00 ELECTRON MICRCXiOJ\PH SIIMif6 LCM LcrAL.IZBJ SlAAINED ARfAS , r .

33

I ! I

0.2 SJ.A;-./ t

•

--

A, BRIGIT FIELD-AS RECEIVED ([)) B, DARK FIELD-AS RECEIVED ([))

C, BRIG-IT FIELD-SK>CKED (D3) D, DARK FIELD-SHOCKED ([)3)

. .

FICiJRE g~ TJW611&)100 B.fCOON MIOOiPAffiS SKMIK1 ·1trrEPJW.. SlRJClURE a= SLY1flE D BEFORE Atll ff- I ER Ift'PA&rI1~

.34

I '

A, BRIGHT FIEU>-AS RECEIVED (E) B, DARK FIELD-AS RECEIVED (E)

CI BRIGHT FI ELD-SK>CKED . (B) D, DARK F !ELD-SHOCKED (B) ..

. .

FIWRE ·I. TPArffll~ION Elf.COON MICl«iJ\mS SKJWlt{j INTmrt\L ' '

35

IL

A, St«KED S#1PLE B BI AS RECEIVED SAMPLE A

c. SI-DCKED SAMPLE D3 D, AS RECEIVED S6>1Pl.E ·D

FIOtffi·lO .• TPArffllSSION El.EClROO MlcmAPHS SlOWirti LOOPS IN . .

RM)ffi SltlflES

36

..

A, SAMPLED B, W1Pl.E Dl

c. WiPLE D2 o. SAff>LE D3

FlGU1£ ·11.-. ~Itil 8 FCll{)N MICRCXi~ a= Sol'1flE D SIOIIMi PARTICl£ SIZE PW ~ AF I fR ·I_r,ACT·INt

.37

'

A, SAMPLE E B, SAMPLE El

C, W1PLE ~ D, SAMPLE B

FIGUIE J2:~. SCJ\ft!Itli ELf.CTlm MICl«lRAPHS (f S'V1Pl.E E SOOtllffl PARTICLE SIZE AND ~PE fJf lER ltfACT-ltE

38

\,:,1.: if''

, ,,. , . 11

I

'!

''.

,I.·

. .-. ·- ! ,;:

• ..

IV. DISCUSS!t)N .,,,_·

.. t•,, . . ·:e;robably th~ most s.ignificant · f'indi.ng of the present study .

. J·s. ~he :substant.iai effect of lattice strain_ on fired density.

'·The mult~ple .. r_e.gression analysis of· t-he data for the impacted :1.,

. ' powders (Tflble 8) shows that la.ttice -strai_n · accounts-· for 96·. 2 ·I,

perceI1t· of the variation in the, ·:f'ired. <lens.ity·, Cons.equently, · ·· • I .•

i i-'1 1 latt-~_q.e strain is e;t,-1e·1y= respoi.fs.ibl:e- for tne·. incr·ea.sed fired . '

.

. de:nsity of= ·the impa.c-te.d: powders sinc:e. tilther powder character~

:istics- 'have .. litt.le ·-or no effect. This ;conclusion is -consiste:nt . . . . ,· . ' ··• '

witn ·the snialJ. -.r.~g~ ,_of values of surfa.ce: area., p~t.icle size

'._and particle pa,nd ·-wi-d.th :for· each sequence of .µµ.p~ct.ed powders.

In co:q.t_ra,st to ·the imp·aGted powders, s:Lnt_er'abilities of

the as-received powd~rs a.re effected primtarj.ly by· _green density.

Thi~ :i.:s: reflected: :(n the simil:ar-i1iy of the .st:atistical analysis .

. Qf fi.red ·den$·:ity ·(Tt:tb:le :6.) and the_ dens-ification parameter

(-Table 7}.~ T_hi:s. :sembla.n.-c-¢ is ·du_e· t·o· :the registry between the:

g;re.en depf>ity· and· the :f1r.ed ·d.en_s-ity, s-ince the den$ification.

p·a.rameter is determined by their· d:tt:f'.erence. In addit-ion. to

the effect of green density, on th~ -fir$d. density for the as.-

, received powders, lattice strain an.d: to .. e,. lesser degree dis­

location· distribution (Ie0--lp5,) are both Significant source$ of ~.-;, r··-~·

I';'":.

variation i;n the t~,ed density aeco~t,~ip.g :for 13 • 2 ELp;4 · 6 • 7 · ·· ·

., .,. • ' I'•, ' '

. . ,f "::\ ... : ,. : •.: ' '

J :·

: .•

. . '\

s)•

J 'J

1:!.

.. - '/

,,. ' ,.. ~ < ' .. )~

\\,.

. i ' ,, . . ,' ' • - . " ' ,. ~· . • . ., . '' . ..

. ,_''. '· :·.· /'· :1 , .< .',, : ... -i~,-" l .. :·,·, i\ .... :..,.: .:: ,., :. ,\. ',

.. -' /.

- . ' . '·, .. ·· _.t ·, ..

• . /:'1' :percent resp~ctiv~ly.

,',I' ' - .I •.

.-· ,:; , '

. : , .r

.. ,,,;_., ., . \. '·. '

~ _, '

', . ,.:,:-:--.. ·' :· ;. : ... - . . ,• .

. '• -,. '1 .

. '

' ' i . '

..,.. : . -·

r .

~·

'

.. ,1 •

r-·.1'

, ..

I I

• ~ I ••

• i • .. '.I ·ij.' ,. . • ' I 'I

~' . ' . . :The. role of strain in sl.@.tering behavior,, as indicated. by . · ·. " ' .

'l'&bles 6, 7; 8 -~nd 9·-~ is to increas.e both the fired :density r·

I '

and the s1inter:i~g:: . rate of the powders. Increasin·g lattice '

. s·train riesul ts in an increase in the rate- of d.e·nsif'icatio:n · . • . ' ' ·. ' ' . . ' •. ,. . • • ' ·1 ',

·: 11-

as indicated l?Y the values of m listed in Table 5 ,: ·1

An increase .·

in the value· or· ·m. is probably indicative of a .. greater contri-~ ... .· ·ou.tion to densifi·c~tion by volume diffusion.

I :

Quite. l~kely ., · ttiis is ·the resuit of· an .. increase in the diffusion coefficient

. J

(D, ) and/or a: decrease in ·the act.i va.tion e.nergy ( Q) for· vo-lume ·. 0

' .. . diffusion. Since all ·sinteri_ng experiments were conducted at

t·he same temperature, it cannot be positively co_nclu.ded t·ha.t

the decreas .. e ·i.s in .Q. However, in sintering studies of cold \

worked metals, Thununler and Thomma, 53 and Hirscbhorn, 54 found

that the Q for volume. diffusion in a distorted latti_c:e i.s far

below the st·andard value. As a re.s_ult-, the present- observ.ations­

can partiy· be· attributed to the lowering of t.he activation

energy by·, t:be _increaseg. concentration of lattice defects and

stress e:tlha.nc.ed qiffus.ion as the r.esul t of strain introduced

·-:i.n impacting •

The role of dislocat·ion distribution ('. fp:..·Ps:l. is sim.l~.

·to that of strain, in that increased sinterabili ty due to ...

( p0-p5) is most likely the result of enhanced diffusion. ·

'•.·, ' Increasing ( p0-p5 ) .indicates a tendency toward -a polygonized

array ()f µis locations. ·_ Th:µs,. as ( .P0

- p5 ) increases, the extent

1,

. ·"' , .... , 40 •' '•O ,~•,' e.l

. .

';. l ._

-----------------=--------~~·"-'--···-·"···

. . .

" .

1, 11 I ' •

"I_

•·

: •. . . 1

.. . ..,. ..

. '. ' "j l •.

. . ·' ~

r

... ' ~ ... " . ·"• · 1·

D

', / ·. .

;.

. r'>-

t CJ>f polygoni.zati~ i~creases;·,in the material. At some value of ( P0 - 's ) , the polygonized dislocations become low angle boundaries · which ~1,e eff'eGti ve as pipes or ·channels f'or mass transport by I •

· diffusion ,and/ or vacancy sinks in the inaterials. Consequently,· , • I • ·1ncreasi_rtg ( ~- P; ) · creates low resi·stance- diffusion· paths in . : ' .. ,

w ... the material.· :11·

• • I

,., I The results of the electron transmission microscopy are .. :not '1

. ··-11· \·-'

. 1i

-~Otfc·l us i ve • H:owever, _ it can be d~~ermined · from the contrast patterns ·of the particles, that a more active powder (Figure 6)_ exhibit:, more · st:ra.in, indic~ting the probability of a higher internal distortion-. . .

.

than· ·a less reactive pti'litCier (F:igure 7). :·This' is ·a1so true of powders D (F_igure 8) - and E (~igure 9) before and alftter impacti~g.- · -.­Dark field micrographs (~igures 8D and 9D) strongly indicate ~hat much of the contrast effect is caused by dislocations. How,ver, diae to the effect of' various particle thi:cknesses· anq. orienta-_ tions, the dislocation distribution an,d. dislocation.~ensities . . .- • . ' 7'. ...... :.. 1' •

C.lllcu.lated from the x-ray results could not- be vejf.ified py ..

ele_ctron microscopy. Qualitatively, h:igh. dislocation densities_ · were observed in singular particles as shown in Figure 9C at1q. what are tho_ught to be vacancy or dislocatio:a loops aa:e slio~ -

.. /J!,l) ~ -·- l't'' .

• J ,· •• ~ '.

in Figure 10,_ but the.se are both isolated instances where· p~tj.eJ_e

thickness and orient,ation were favorable • -::,,- ...

The role of' green density in determini:ng the fired density, --_ '. 'Q:f-the as-receivedpowders•_._c:an,.-.·"R_.~i··a-ttributed to two effects. i: ,- ..

.. -,

.. ,,:-:;.":."\ ...

v]{lr

~ . ·,

rl '·

. ,,,

- '

.\l·t'

, I' ,

·/

'·, ·,

11 .. ·.

' _, ,,

First; increaf=lii;tg gree:m1·density· incr.eases, part.icle to. particle • I • ·•

. "'

- contact, creati_ng ttJ.~re pat,hs for mass transport, resulti_ng in _

·at! increase in the t _sinte~i~g rate. Secondly,. i·nareasi:ng green ..,;.,.. ... •• ., ... -ol.. -····~·

j_,. ' - ' ' . .-' , . ' ! den~i ty i.s . a functioµ of :P$rticie ~orphol:~•:• - The dependenc·e

:l ,11··' ' ',··1·:

of' gre:n density (Y), on. suf.face area (~), particle size (:x:2},' · · .

and .particle band width (~) determiried, by a -separate Jllul:t;iple

r_~gression analysis resulted in·:. ·-

Y =1

1.65038 + o.o3Br2iS_ + o.81616x2 .. 0 •. 28681~ (13)

where the pe~}cent variation q.U;~ to -~urfa.ce area is 63 perc~·nt,

to part.icle size is 22 per.cent,. particle band. width: is :4. percent,

.. ann to ·unexplained. :r.e:sidual error _is :11 percen~ •: .

The surf ace ~ea :.i.f3 ;related i·nvef.$.~l..y to: the. part·icJ~e

size .• · Therefore, an increa.s.e ·in powder surface area shoul·a. be

a9comp~;ni~d "by· a co~responding decrease in particle size. ... •. .

·con.~equent.1y·, the si·mu:Lt·.Eµ1.equs .requirement of increasing surface

:area with iricrea$ing: pa.rt~icle- size ( in equation 13) to achieve

:nigh green density appears. to be. i~consistent. However, this '

,; .

:c·an be eJ.C,plained rationallY1~- i:f' -en increase in surface area with ·

an increase in particle size is accompanied simultaneousl~ by an

increase in particle ~gulari ty or flatness. This conclu·sion is

, verified bf Figure \l£i,. where it is shown that the larger particles ·-.r·

' i:r;ideed do tend to be plate-like, while the fin~p particles are • • I -

•

more equiaxed. Therefore.,. it e.ppears that !n order to achieve

. '.' < /. '•

;:., ' . i .' I

',{.

' ,,, '

'i I 'L1. I. 1,·

! I_ '.

..... ~ .. ,

1 I J

I

~-----------------------------··.1--··'1 -

' "-· ·',

a high green density, the total distribution of the particle f .-

·.~ ,, .. \: sh~pe should contain some fraction of plate-like particles.

• I •

., 11 '

The negative sigI1 . for the coeff.i·cient · of' x3 indicates , a. de- ... '' .-, .. · I , creasing b~d width ·associated with increas:t.ng green density. : ~ .1, ... ,·

.: !J ,. ' I' I :,.

'I ' -1

'

''J·:"

. • I. ' . ti • . • • • This is consistent with the low:,packi.ng densities generally ob-

. ' I

served with fine ceramic powders, since· a fairly narrow band ~

width would indic,~t.~. fewer fines whi:ch· may cause separation of r. i'

the larger particles resulti.ng .in: great·er porosity and lower

,gree;n ·densi t_y.. This -effect is commonly. :referred to a,s bridging.

Smboe_ green .dens:ity· is :not a .s·owce: -of variation: in the

impa_cted powders, the particle~ ·morpllology- mu.st not: be effected

by impacting. Figures ll and 12:' .show powders :n ~d E, ree_y

specti vely, after different c\egree:s. Of' impacti~g, and no ap-

p:are:nt change in part:ic-le Ino:rphol.ogy has occur.r.ed .•

:'.I'he e.Jtperimental ~e~ults f'or the magnj_ tud·e. :o:f· s·tra.i:Q in ·the

powders investigat·ed in the :.present study, .. compare favorably

with the corresponding res:u,I:ts of other investiga.tors55,56,57 ,..

.''r ,_ ,,, 'I

ffom ar:v Oati mi1!ea: a.nil e:icprcS~ivelJ Shocked AJ.20 and MgO powders,

The observed higher f'ired density Jjf the impacted powders is alsp

consistent with the findings of' Bergman and Ba.rrington58 , 'f1ho

. found explosively shocked powders when sintered resulted in

higher fired densities. In aa.cii tion, Lewis and Lindley59 · found

that increased strain intfoduce4 ,by dry ball milling improved

t~~- :0~1;1$hing stren·gth .o:f · s:1n"l}e:ted powder compacts, an indication • ' ,: ,•; •' ,' ' ' L ; ' • •, • .. • ' ' '

. ,, .

1 ' ·, .. ' . ." I ,"l'r•'; .'',I

. .,. :: ',' ,: __ ,., :.,. '

. ; ' ·',:;,' ' ~ '

, -, ,., . .· .. ·.4····:· .. ·.··· .. ' . ,, 3 ·.

'.. ,•' ' . . . ·.,· .

:: .. · .-·' ......

;.,: •c , • •

. ) ' . . .

'· ' r t I

i .

' 'I -'. \,,.'

' •_•',,:-' '',, LJ •' 0 ,-_" :• '.

I ,.

' ''

, I

-,

,., ....

·, ~-

:..,~.

of a h~gb.er fired densit)t.2! t~

.'.'I'\ \..

'!'

It is clear, ~erefore, that in addition to the usual -111.

., I , ••

parameters s~ch as particle size, ·parti'cle si'ze distribution, sur.

face area, ~~ qeen· .. deniifity, the results; ·o,f this study .show that ........... -.. ,...- , I .

powder character;i.zation sho'Uld also inc-lude neasurements of lat-·',ii''

·tice strain· and '·diE:J:location. di-st:rib.u~i.on.

!:':"

, . ..... ~ ,, '

.. ,I .. ' '

II I' ':j

' '·

:-w.-1•,

I•

,, I !

I I

' • I

. !. ~

/'

.·~,' 'I

.jl ....

" '

. _·•,, _- :c ~- ·., ",'.',1 ';. "', , "

' :?:'..': :: {~*t :: I

1,.

·1.,

•, ·-.1, _•I

I ,

•,+ . ,1 • ·,. ;·;''

' ·'

. \ ·;.

',..j

' .

,.

--.-~ , . . '. ,"' ',

• ~· ' ',. ..!,

·/:

I ,·,•.1 1.1.

-1 i !.

,,

o..,: ·1·_-' • '

•. ' . ', i . '

' '

,. 11 ' ·'

I

' , ;., ' . I

V. SUMMARY AND CONCLUSION. ~ .. ·

' • I '

..

,.

. ' . The ,different sintreri.ng behavior of' five a$L-received

1 •

-az.}9, ·six impacted alUIX1ina powders wer ... e interpreted in· terms {° I

of: .. 1) surface area calculated using the ·B. E. T. method

:from'· nitrogen· absorption data, 2) particle size and size

distribution measured by a sedimentation techniq-u,e, .3)· green . . ' • • '-I •

··:---! ,'

·gens:ity calculated from we:ight and physical dimensi.o:hs' and , , ·:·~.·-. ·.)

--~· part:ic·Ie .s~rain and .coherently .. diffra.cting doma"in size

determine4 PY x-ray. analys:is·.

: The D;Lost significant conc:tu1?;ion. ·a.ra:wzi: from tJ:ie multiple

r.egres~ion analysis of t·he· ·e.xpe:r.iment·a1 ·res.ults. -is the pro­

.l!l~nent role that lattice strain play:s in: the -sintering behavior

:.of the. impacted powders which· was :attr.ibuted to a decrease in

·t·he activ~tion?)ienergy for· volturie' di:f'fus .. ion.. This was corr«fb­

otat~:·q.·. 7bY... the increas:e in the _slope_ o·t. -t:he shrinkage versus .. t:iilie plots with increas.ing strain., ,!:ndi.cating an increase..· ·in

tne :contribut-ion .. o·f volume d-iffusion to: ·the tqt~l. m~ss- trans-- ;,ft:·'·.

port •.

A similar analys·is· of the as-receiv:ed powders showed that

the main sources of variation. in the sintering ·behayior .wer.e

green density, me.an str·ain, and dislocation distribution. 'Dhe ·"··',_ ;_·., ..

·effect of green density on sin_terability 6:e the as-received .· . . ' ' . ,·,

· .. powders was concluded to be due to : l)· ~'·increased particle

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to particle contact caused by a D::tgh green d.e~sity,$ld ~) .the Ii ' I

dependence o~ green _density on particle morphol_ogy. Mtilt~p·le

regression analysis .. revealed that. green density. was .incre:ased . . by increasin·g surf'a.ce area, increas.i_ng particle size and . a. ·

narrow band width. These effects were supported by ·the result . ·-ii . ' .

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of the scanning e1ectro_n microsc.opy .. JJ .

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Sinterabili ty du..e -to di·s:location cfistri bution was- shown ,

t·o inc·rease with incre11$i:n·g po~ygonization of the di·slocations ·

which ·could result .in low- ~rigle bountl.aries :act·i~g as: low:

resistance diffusion. channel~ :or, pipes and./.or vacancy s:inks •.

· TransJili,.s-si:on electron. lP,ioroscopy showed particles with.·

h:~,gh_ q.islocation densit.ies end the probable exi·stence of

ve.c:ancy or dislocation loops· :in the particles, but quantitative.·

v.e:rific:ation of 'the disloc-at·iort density or ·distrib1J.tion was . . . . . '1· .. not poss·ibl~ due to powder· thi.ckp.ess. vari·at·iorts and orien-

tation~ effects.

~he ·major findi_ng of the :prese·nt· st·udy .is th,at latt:l_ce.

,strain and to a lesser degree disloqa~ion .a,.i·str-ibutibn Illus;t ' '

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be considered principle variables in the characterizat:ion ·pf

.. ceramic powders, . in. :_addition to the commonly measw,ed v.apiables,

such as_ particle size, surface. area, particle siz~. ·distribution, . I

4ap'1X'ities, and green density.

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BIBLIOGRAPHY .

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1. t1Skorohod, V. V. , V. A~~ Smi.rnou, A. F. ,Hrienko,. P. P. Uskokon c, Physics o:f Sintering, 4(1), Jan. (1972) p.47 •. I (

'

I l 1

2. Gequzin, Ya.E. ~ ·Physics ·or Sirtterine;, l(l~B) July(l96~) N.-1. I I p

3. n~~ry, .v,l.D., Introduction ·to ·~ra.mi·cs, Wiley an~ So~s, ~e.· .. Nev York, N. Y. , (1967)p. 371. ..,.· .. · . '

' . ~

. . .· . ,.....,, .. ,(i . ,. . . .. . ;;. Kuczynski, G.C.; ·powder Metallurgy, Interscience 1._Publishers·, · New York, N~·Y.,(1961)p. 11.

4.

·5 .• Coble, R.L., Ji~E. Burke_~:Progress in·eera:mic.Science,Vol .. III, MacMillan Company, New :YoTk·, N ... Y.(1963) p~ 197. · · · .

6.. Kuczynski , G. C. , Tran AIME, 185 (194-9) pp. 1·69-177. r ..

. ·7. Barta, J. , Powder Met. Int. , 2 (2) (19·70) p. 52.

:e. Jom;ison, D.L. and L. Berrin~ ·siri~eririe;,:~~-·~el~~eg.,,·1pt;_e~_9~~~, Plenum Publ!:shi~g Corporation, New York, N.Y. -.(196·5) p. 365.

~. Kuczynski, G.C., Powder :Metallurgy, Interscience Publishers, New York, N.Y. (196·1) p.li.

10. K~gery, W .D., Ref. (3) p. 376.

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., .. 4 '

12. Hagel, W.C., P.J. Jo!gensen, and D.S. TomaJ.in~ ·J~. ·.Am.· Cer. Soc.·~ 49 (1966) p.·23.

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:L4. Amato, J. , R. L. Colombo, and A.M. Protti, J. Nue. Mat. , ll (1964) p. 278.

. ;,;. 15. Daniels, A.U. and M.E. Wadsworth, U.S. Atomic Ene!gy Conunission Publ., TID 20/.50 (1963).

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' '

17. Iwasaki, H. ~ Jap~7s~ ·~·£.A~p~. P;tiysics, 4 (1965) p. 19,Q~:-., ', .... ':. ·. ,'

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<.

- 1

• :1 'f,' .

. . . l

·. ;. ... ,

' .

. 1'

·.I

,' ·.

i,.I. I, I, 1 . I .

, t . ._ ..... , .. ao. Murray, P.:; .. ,Age;lomeration~ Interscience Publisher, New York,_ N.Y. (1962). p.93. ,.- ·1 ~

'J','.' " .,·:

,

4 > ·~ :• ••• , ~ i- .,

, I

·~f'"l • 1 '

'I

. :21. Hirschhorn,. J. s. ; · Powder ·Met • IIit • , 2 {:3) (19·10) p·. 85 • :

22. Hirschhorn, J.S., Ref. (2·1), p· •. a4. 23. · Hirschhorn, J •. s., Ref. (21.), p·.84.

'"l ·.

. i .

. 24. Fis~meist·e·r, H.J:c1and E. Exner; ·MetalJ, ·18 (196.4)- p .... '932_ .•.

25 • Bart ai, J. , Ref. ( 7) , p. :5 4.

:26.· Kr~ger, F.A. ~ ·Th~ ·Che~~~r.t.·o~ ·~ll$>ert~c~ ·~ty:s~·a,J;s; Jl)lm Wiley ·, and Sons, New York, N.Y •. (1964) p. 818.

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28. Polyboyarinov, D.N. , Refractories (Moscow)- 27 (1962·) ·p. 137 .• :

~9. ·WeyJ.,. W.-A., Cera¥1jc ·A~, 60::(195·2) p. 28 •

• 30.. 'l'b.11:rmnJ er, F. and W. Thomma, ·Me.t ·Revs. , ·12, "(1967:) p·. 7·3-. .

.

:3l·. Coble, R. L. and E.!.. Aiken~ ·Proceedin~ ·of ·the · Conference ·on Nuclear Ai>J?lica.tioiiS of Noii~Fissic>riable . Cerfi.mi. cs,' Wasl?.ll*on (1966) p. 364 ~ I p . p . . .

0

32 • Bart a, J. , Ref. (. 7 ) , p • 5 4 •

3.·3. Se.igle, L.; Kinetics of Hi · ·Te · ·era.ture ·Pr.ocesses, Jobn Wiley and Sons , New York, N. Y. · 195:9 p. -1 72 ..

:34. Burke, J.E., Cera.mj· c Microstructu.res, John Wiley and Sons, New York , N. Y. (196:8) p. 681 ~ '· ' · .

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· 36 •. Fedorchenko, I.M. and v.v. Sk.orok.hod; ·sov~ ·Powder·Met~ ·Metal . ·eeram.~GlO (58) (1967) p. ·ao5.

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'..38.. Gequzin, Ya.E. , Ref. (2), N, 2. .. ' . :'·J

. ' ',' \ '~. •,• I

. :. :4··.·o·.· .. ·.'' ,:,··· .. ,.- e'.··,. - ·.· ' ..

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·······,

,', I i,.

• I

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Ir ,,I· ' '.·: . .. ;.

I

)

39. Bruriauer, s~, P.H. Emmett, and E .. Telle.r; ·J.· ·Am~ ·Chem~ ·soc.,.

-4o.

41.

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. /· .. '. . Shenefield, P.J., frivate Gommunicatf-on .(with permission).

Ryshk.evitch, E.; ·Oxide ·ceramics, .Academic Press, New York, N.Y •. , (1960) p .. 169.

,, 42. Tr~go, L.E • .-, Private Comm,mication ( with permissi·on ) .• · ?

· -43. Warren, :a.E. and B.L. Averbach~ ·J~ ·flppl..· :~ts,.,. 21 (195:0) p_~_595 ....

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· 45. Metzi.bower, E.·A •. ; ·Met~ :Trans •. , 2 (1971)' p.· 31.'oo.

: :46. Metzbower, E.A. ~ 'NR~,-~~l??tt.·725~, (1971) p. 13·.

47·. Williamson, G.K~, ..,and R.E. Smallman, Phil. Mag. 1 (1956:) .p~: 34. /

48. Williamson, G: •. K. and R.E. Sllla.l.lman, Ref. (47) p. 36.

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51.: Whelan, Mi.J .• ; ·J~ ·To.st~ ·Meti, 87 (195·9) p. 392 •.

Hirschhorn, J.S. ~ ·Introduction ·to ·Powder ·MetaJ.l'lirfaY:, Colonial Press Inc., New York,· N·.Y- {196:9)&.p. 206. · ·

:52.

53. Th11mml er, F. and W. Thomma, Ref. (30) , p. 85. )

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55. Heckel, R.W. and ,J.:L. Xou,ngblood, J. ·Am.ccer.· Soc., 51 (196:8) p. 398.

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:5:7 •. Ilein, M.J., F.A. Ro~gh and c.c .. Simons; ·J~ ·.Am~ ·eer~ ·soc •• 46 (1963) p. 357.

·5.S. Be_~ginann, o.:a;.· ~:d J. Barri~gµon·~ ·c1~ ··Am.· ·eer.: ·soc., 49 _(19'66} · p. 502.

5.9,. lewis, D. and M. W. Lindl.cey ~ · J.· ·1,m..· · Cer ~ ·Soc. ,, 49 (1966 J p. 49 •. · · ' '"

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;· .,

Jay P •. -~age was barn in Genes~, Illinois in 1947, the··;.·i~on of \ I,.

Mr. and Mrs. Warren T. :i?age. He w~s gr~u13,t'eld from Gibson Ci,ty · .

High School in 1965 and in the f a,11 of tliat year began · ~tudies ilf ·. • I

engineering at the Iiniversity of Ili·inois·. In 1969 he married the ..

·forltler Marsha J'ill Burns. In January of 1970 Mr-~ Page received. a ' t

.S''.b.eet- :D~pa.rtment.

. :.:en· J1ily of 1971, he became a -c:andidate tor ·the·· degree- of.

-M:~:st..er·· of Science in Metallurgy· .and Material S.cience at Lehigh

·pn-~yer.sity through the Lehigh .Master's. Program of Western Electr·ic.

-at :the ·Corpo~a.,te: .Education Center· ·:in: -Fri.nceton, New Jersey •.

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