Chatterjee, S C

Gupta, M P

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j m l m n  J .  P h y s  49, 742-745 (1975)On the stacking-fault densities of ternary copper alloysS C CjiatterjeeD e j ja r lm e n f  o f  PJufsic-h, ColJrjja, J a m s h e d p u r ,  B i h a rANDM V  GuptaD e p a r fm e a t  o f  P h j j i iw s , ,  R a n c h i  I I n i v e i s i i y , H auchi^  B i h a r  (R e c e iv e d  2 A n i / u s l  J074, re v is ed  J2 M a y  J<)75)A ll iiddmve.-n^laiiousliip ]ias l)(;m ob,s(‘Jved to Jiold Joi‘ .stackuis*-faiilt- paraincU'i' (SFF, oc) o f the a l p h a - t i a n a r y  (u)ppor alloyw 3 opr(‘- Heiitod by,log a  -  K ^ p  |A Z l)- |- lo g a owhia'ci tli(‘ islopo of the line 7C 0 II and th(  ^ of ihi‘ solvent ((!oiipo]“), a„ — :b3 y  10 “1 IntroductionA lthm igli l]i(i bmaj'y syjSLenis l»,av(5 been (ixlensivi^jy studied since tlu‘ Llieoretieal discussion on SF P  o f fee m etals and alloys by j^abason (J05i^), ilu ‘ tern a iy  alloys se.em to  liave claimiul miioli less fifitentmii Cu-Ge-Si ci)>[)ears to  be Gus fust' ti'iinu'y alloy investigated  in u ‘e(‘nf> tumps' (Foll(‘>, et a!  1003).0In file  present work it is shown tlia t starting from i-ln* d ala  on corri'spoiiding b in a iy  alloys, it  is possible to (mmpiit(‘, the valtii’ ot the SF P  (a) in siu li tu iiary  system s wbei'c tlie, soliiUts do not iu l ract w ilh (‘ai li otb,er Tb,(^  existeniti ol any inter action be,tween the solute.s in a tiirnary alloy can bi‘ ascertained by di‘tcj- mm ing ns latluie-paranuaer (Siirling R aynor 1955)b\)llowing Gidehonzee ^  D eruyttcre (10(>7), lh e  SFR ol a binary system  is given by,a  —  a„ exp K p  | AZ |so that assum ing an additive law  to b,old for the SF P  of a ternaJ’y system, one m ay wi'ite,a -  a„(!xp(/s:/j,)|A^5,1 |-a„ (ixp (/ip ^ )| A Z „ |,wliei'e K  IS a constant for an alloy series a,, denoti'.s 1-h.e. SF P  ol tin' puj'c solvent., P] and P 2 ari^  thi' solatia concejiti ations in at. %, | A^j | and [ AZ,  ^| art) l]u' valcnc;\ -742^Stacking-fault dcnsiU ca o f ie n ia ry  copper a llo y s  745difforojicoy bt^tweoii soluto iiiul tJu* ,s(ilv("ii1 iii ilu* two r(^loVfiut biniiry isvstoiiisrospeci/iV(ilyThen,H(‘uco finally,lop, a  ( p  I AZI )-|- lop a„2. E xptjuimrntal PRorMPUiinTluj ooiupOiSitJons of t]i(‘ tevnary alloys (prepared fioni spiH'troscopically ])uv<- iTK t^als) wei'(‘ sel(H'V(‘rl; so as lo  (‘onfino tlu'iii ro th<^  ])J unary solid-solution- I'aiipc  ^ judging Iioin the avai|af)ic j)liii,se-duigranis ol i.io])pt‘r-ahiminii]in-t-in (Loach & H ayuor 195^) and coppor-alunnniuin-indium (Stirling Raynor 1055)TUo D(d)y(‘"Scliorror CD-iS) patterns \^ T*ro obtained for all t}i(‘, alloys, from  annealed fine-filmgs, using CuK„-radiation The recording-film Avas m ilu' Slrau- m:\nis-mounting inside a Philips ijondei cam oni TJu^  lattici'-parametiu’ (bP) A\ as finally dcn.erminod Irorn lh.e N elson tK: U iley  (1945) extrapolation. Tlu  ^ D -8  patterns also eonfinned tlit' fee stnietuK^ o f all tlu  ^ alloys Tin', additivi^ relation- sliip in r('Spo(;t i)f the LJ’ ol the ternary alloviS Avas Awifi(;d using tin* aiithojs, data  (Chatt(‘ij(\e iS: Gupta 1975) tor LI’ ol tlu  ^ eorri'spondmg b inaiy  system s (Cu-Al, (^i Til and Cu-8n).Km t]i,(j (‘Stim atioii ol tb.e iSKtMilings from alloys were p]'epar(‘.d at rooin- t,empfii*atur(\ sicm'.d through a 300-inesh and pr('.ss(;d into stainless stts’.l jiolders of tlii5 dilTra(!tometei TJu‘ line-jirohJos o f both (111) and (200) diffraction-peaks lor t)i(\ filings, AAere n'ooidod by  poiiii-coiinting at inu^rvals of 0 05'" in 2 0  lor the  geiKwal baokgiound dtici easing to 0 01° in 2 0  near the m axim a ol the jieaks, when' 0  IS the TTragg-angle Th(' background m ionsity  was cari'fully fixedT\) find th(' peak-position for the /v^tx^-itomponeiit, the m ethod o f Papoulis (1955) was em ployed Tlu‘ peak position  (in 20)  fo  ^ (^acli sainple (filings) was determ ined for botli a.s-Jih0 a v d  a n i i m M  states TJie cliange A(2^^oa“  20^jy) produced by eold-AA^ o^ ’k (filing) in tlie  separation (^^^oo~^^in) fh(' peaks o f  an amu'-aled sam ple could  iiow \u) caleulated E m ploying WaiTtm’s relation  (Warren 1959), a \\^as thus estim ated for eacli alloy3 OnsTimVATiONSFigure 1 .s1i,oavs tJie sem ilog plots o f a  against the factor 2 (p . AZ  plot approxim ates to  a straiglit line a\m1Ji a sm all scatter in the pointsTheThe values of thii S F P  o f copper, tlie pure solvent, (ap) is found )iy extrapola­tion to  be 3 3 X 10“  ^ w hich agrees AVtfil w ith the accepted value,744 S. C. Chatterjeo and M. P. GuptaTlir vahio ol tlic slope of ilir  Inie, determ ined from the from t)i(‘ plot, is K  — 0 1059 for IJm eopppj'-liasod alloys wlieh is in agreement Avitli the value (/T — 0.10) reported earlier by Delelumzee't^" D eruyttere (1967)Kig 1. Soniilo;^  i)lot <»f tli(‘ SFO (a) vs ij(j) ) Iru O h' Ifriiury L‘op])(.*r u-Unys.4 .  D i s c u s s i o nT ntlie present w oik, foi‘ the estim ation ol SF P , only tluj (111) and (200) pair of refloedions have been used N ow , it had been observed earlier by  (Chatter jee 1072), tlia t l)V assum ing an additive law, th(‘, value o f the L P of earli alloy could be com puted lau ly accurately >starting from the LP o f the correspond­ing binary system s 'Phis m dieaies th a t in the select.ed alloys the solute atoms wlv-cli produce' tJie lattioi' ('xpansion in the parent m atrix do not exert between them selves any app^eeialih^ solute/solute interaction I t  was therefore felt that it  m ay be possible to  find a similar additivo-law applicable to  the SF P  of the, alp]ia-phas(‘ ternary alloys o f copper Tlie straight line obtained in figure 1 justifies This assum ption to  a fair ex ten t The scatter evident ui data  points of the Chi-Al-Sii senes o f alloys, m ay how ever, b(? due to  several factors such as the atoinic-sizc-tactor (Chatterjee el a l  1973), solute-segregation at the faults (Suzuki 1952), solute/dislocation interaction  (Gallagher 1970) etc., which tend to  render the value of a  apparentTJxe ajiplieation of the suggested empirical relation to the results of F oley  et aJ (1963) for the Cu-Ge-8i system  (figure 1) shows a completeiigi'oonKmt. Evcai ho, tJin j|itro(lu(!tit)ji of lonm arising oui of the Holnte/sohito interaction into the relation would much widen its range of application. This. Jiowcvor, requires a further probe.AcknowledgmentOne of us (SCO) wi*shits to tl;ank Pj'of(‘KSor A DeruytUW(‘> (University of Letiveji, Belgium) for ]j,is valuable suggestion TliankiS arc^  also due to Dr. A K Lahiri and Dr J K. Miikherjoe (formerly of the- National Metallurgical Laboratory, JainsJiedpur) for their continued lielp when tins work was m progress thenvStacking-favU densities of ternary copper alloys 14^ :Refebenobs(liattdi-jpn iS (' & Gupla M I’. 1975 7^. Apjtl  Cry i^t (Oornmumratod)nuiUtirjoo S- 0., Mukherjoo J K & Lahin A K. J97H tSenp, Met 7, 35.()hattci‘]oo S. C. 1972 Ph I). Thesis, Panchi (Jtmwrsity, HanrhiIJolohouzMO L & Doi'uytiurP A 19(i7 Act. Met 15, 727Ft)loy 3. H , (’aim K W. & Kayiif.r G V. 1963 Act Met 11, 355Gallat^ hor V V J 1970 Met, Trans 1(9) 2429Lnarli J S L <fe Eaymn C3 V 1954 Pro, Roy  ;Voc, A234, 251NeiHon J, B. & R \ h y  D. V. 1945 Proc, Phy  Noc, 57, 160I’apouliB A. 1955 Rev Set. fnstr 26, 423OaltPi-Kmi M S 1952 J. A ppl  Phy. 23, S05StirliTipr V T4 k  lUvnov G V. 1955 J Just. Met B4, 57Suzuki H. 1952 S a  Rep Res htsi  Thoht University, A4(5), 455.WuiTpn 13 L. 1959 Proji Mel P h y  8, Perga?non Press, Loud on

On the Stacking-fault Densities of Ternary Copper Alloys

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On the Stacking-fault Densities of Ternary Copper Alloys

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