Formation the NiIAVNi joint structure isothermal ... · solidification path; rcduccd klNn + klN3 + klNl + kZNZ and full klNo 3 klNl 3 klN1 + k2N2 3 k3N2 + kJVdF "hjstoricaI", solid

1897-33' lume 8

A,,

puolenea quarterly as Ihe organ of the Foundry Cornmissbn of the Polish A m t m y olSdslnces

Formation of the NiIAVNi joint structure applying an isothermal solidification

W. Wo1cq6skia'*, J . .Szlnczak-Rusch ", %. PogodnC "nstitutc of Mclallurgy and Materials Science. Polish Academy of Scicnccs . Rcyrnonta 25 ,30 059 Krak6w, Ibland

1, Laboratory of Joining and Intcr~aace Tcchnology, EMPA, Diibcndorf, S witzcrlnnd Institute of Mazhcmatics, Jngicllonian Univcrsity. Rcymonta 4,30 059 Krakhw, I'oland

"Corresponding author. E-mail address: nmwolczy @imim-pan.krakow.pl

Received 26.02.2007; accepted in revised form 1 9.03.26308

Abstract Thc NilAllNi joints havc bccn oblaincd undcr thc imposcd constant ma[ tcrnpcralurc as rcquircd by ihe joining iechnology. A significsnl iindcrcooling nppcars and vanishcs cyclically during the formalion of intcrmctall ic multi-laycr, l'hc obtni~icd sub-lnycrs wcre forrncd i~ndcr mctastablc condilions. At first liquid A1 transrorms into i ~ s cquit ibrium solution as dcfincd by ~ h c intcrscclion of ~ h c rcnl ~cchnological tcrnpcmturc with thc Iiquidus linc. Dissolution tcnds to creatc a typical Al- solutc conccntniion cqusl to ihc No, just at thc surracc of subs&atc. So, thc equilibrium solu~ion tmnsForms into supcrsau~ratcd solulion of thc Ni and A!. A supcr-snl~zration occurs until ihc supctsnturnlcd zonc crcntcd at thc substrate surface bccomcs liquid. Thcn thc soIidificat ion hcgins m ~ d protnolcs 1 hc Formation of rhc A13Ni and AIJNi2 intcr~nctalIic sub-layers wilhin thc joint. Thc Gibbs phasc rulc is satisfied during solidific;ltiun accompanied by dissol iiiion and super-saturation. Thc Al-sol utc redistribution mcasurcd across rhc sub-laycrs confirins ~ h c ~hcorc~ical prcdiciion suggesting thc rorrnation of both mcntioncd intcr~nc!altic phzcs undcr ~ncrastablc condition crcalcd during ~ h c isoihcrmal solidification. Thc for~naiiat~ of the intcrmctalIic phascs is rclated to the undcrcooIcd peritcctic rcactions.

Kcywords: Thcory of Crystallitat ion, Solidification Process, Undcrcoolcd Pcritcct ic Rcaciion, Inlcrmctnllic Phascs

1. Introduction

Thc liquid intcrlaycr rc-solidilics isothcnnally at thc bonding rcal tcmpcwture during isothcrlnal solidification. Duvall et nl.. [I] . Thrcc phcnomcna arc obscrvcd: dissolution. solidification and solid I solid transformations. Tuah-Poku ct al., 121. A dissolulion or sabsiratc by the liquid [illcr mctal occurs conrinually within zonc rlx , Figgurc I.

Thc dissolution crcatcs a zonc c/x , for solidification, Kloch er 01.. [3]. Subscqucntly. thc undcrcootcd pcritcctic rcactions nccompnny a solidification, Figurc 2. According to thc conccpt of Chuang er ab. /4] he undcrcoolcd pcritcctic reactions takc placc at thc solid I liquid intcrfacc.

The ~ r i t cc t i c rcaclions occurring at thc solid 1 liquid intcrfacc of cells, formed within a givcn sub-Iaycr, arc schcrnatically marked with some arrows in Figirrc 2.

The intcrnal channcls within cclls arc clnploycd for thc flow of dissolved substrate towards ihc solid I liquid intcrfncc.

Thc dissolved strbstratc containat within zonc {tx , has thc soIutc conccntra~ion cqirat to No , as shown in Figurc 1

Undcr dcscribcd conditions, a bonding proccss can rcsi~lt in n joint rcprodiicing micro-stnrcturally a scqucncc of intcr- rnctallic compounds or phascs ;IS i t is visiblc in an ndctptatc phase diagram of stablc cquilihrium, Lopcz er ul., [S] nnd Wolczyiski ef al., [61.

H~rthcrrnorc. chcrnicnl scgrcga~ion i n both thc solid and liquid phascs can havc a hugc clfcct 011 surracc and intcrrrlciat cncrgics.

It is cvidcnt that knowlcdgc OF scgrcgation resuliing from solidilicatioii is cruciat in thc technology.

An analysis is focuscd an thc formation of thc NiJAIINi joints in relation to thc diffi~sion soldcring. Thc analysis should cnablc to proposc ncw modcl for thc sotidification prcccdcd by dissolution

A R C H I V E S ol FOUNDRY E N G I N E E R I N G Vo lume 8 , S p e c i a l I ssue 1 /2008 . 3 3 7 - 3 4 2 ?aJ

Thcrcforc, lllc snolpis i s conncctcd with the formation of Zrn Expcrimctnt and mode] assumptions intcr-metallic pliasc / compound in scqucncc during - solidificntion.

Thc theory for 3D dcndsitic micro-segrcgtionl Ircdistribution dclivercd by Schcil [7] ~ v a s first dcvcloped by nrody and Flemings [8] to 2D directional groiHh with applying the back- difision phcnomcnon. In thc case of 2D growth thc dclinition of back-diflitsion pnramctcr a: = cottsr., Tor ccllularldcndritic growth is:

Fig. 1, llissolttiion o f the Ni-substntc within a zonc (/.T duc to diff~asicm o f liquid solution ofthc filler metal. throt~gh channcls bctwccn sornc cclls formed in a given sub-laycr.

Ar 11ic snmc timc tlrr equilibrium liquid solution of the fillcr mctnl, N", trnnsforms into its supcwnt~lntcd solution, No. accortling lo thc t"o1lowing reaction:

Thc assumptions for 2D model arc cxplaincd in Fig. 2.

Fig. 3. Solid J liquid volume clcmcnt dcfincd for 2D ccllular / dcndritic growth with: X" - paramcicr rcprcwnting freezing; A - distance, f - time. Volumc clcmcnt invorves. A' -

distancc and r U - local timc; both conncctcd with frcczing and amount of Frozcn solid, X' wl~cn solidification is arrcstcd. Ar is total sizc of half a ccll, with A" - boundary bcrwccn primary phasc and prccipitatc; X' - amount OF primary phasc: model assumcs 1" = I ' for local timc of solidification.

Thc 2D modcE cxplaincd in Figurc 3 can bc applicd to study thc formation scqucocc of pcritcctic phascs / compounds within multi-laycs formcd on the substmtc. For this rcason the meaning o f soinc parameters is tmnslatcd horn thc schcme of 21) growth, to the schcme of 1 D growth, to dcscribc thc rolc of panrnctcrs rcprcscnting formation muhi-laycr, Figure 4.

Thc back-diffusion paramctcr ol: , rquation ( I ) operates in such a way that hypothcticaI lecslizntion of the s/l intcrfacc.

Fig, 2. Thc imdcrcoolcd pcritcctic rcactions at the front of cclls. N' (x*; 0, LO, N ~ , k) is translated to its new position,

N I dcnoics thc soll~tc conccntntion within thc ~~ndcrcoolcd defined by conccntr3tion: N.T ( X O ;a a, N o , kS. liquid for rhc first pcrifcctic rcaction.

Figure 5. N 2 dcnotcs tl~c soltltc conccntntion within the undcrcoolcd Howcvcr, solutc redistribution coefficient detcrmincd as n lrquid for thc sccnnd pcritcctic scaction. product Arrows show thc localization of thc pcritcctic rcac~ions at the solid I liquid intcrfacc. P ( x ; x ' , ~ , L ' ) = j ! 3 e x ( ~ ; ~ f l , ~ Q ) f l i r r (~ ' ,a ,L" )

338 A R C H t V E S o f F O U N D R Y ENGINEERING V o l u m e 8 . Spec ia l Issue 1 1 2 0 0 8 , 337-342

of cxtcnsion and intensity of solute redistribution is rcsponsiblc for a shin ofsolidlrs linc from its stablc posit ion. A thickncss of sub-layers depends on solidification path dcfincd on lirpridlts linc for a givcn phasc diagram along which a solidification proccss occurs, Figurc 6.

Fig. 4. The role of the X' - parameter in solidification of thc AIJNi2/ hlJNi rnu[tilaycs on a Ni-substratc at: d a givcn step of ~ h c multi-layer formation, bl complction of the multi-laycr formation.

Concentration, N / mole fr

Fig. 5. A physical mcaning o f the a =aD back-diffusion parameter, shown for an arbitrary phasc diagtmrn prcscnting an eutcctic reaction. This explanation docs not cnvisngc pcritcctic reactions characteristic for thc difision soldering or brazing. Thcrefole, the model, explained in Figurc 4, should be improved to describe the formation of inter-metallic phasc by considering peritectic reactions. However, it is suficicnt to dcscrihe thc formation of inter-metallic compound by both partationing with varying, k ( N ) , and redistribution, only.

Thc system sclccts onc and only onc nominal concentration of thc mlutc, N o , at a givcn tcrnpcnturc, TR . Thc sctcction of

No - parameter by thc system occurs in such a way to cnsurc

thc infinitesimally small laycr, dr , (zone dr ) crcatcd at the surface of substrate to be liquid, Figure 1. R is cvidcnt that thc liquid laycr, dr , i s strongly undcrcoolcd from its liquidus tcmpcraturc.

Thus, dissolution occurs at a given temperature, TR , as

long as necessary to transform solid substrate layer, d.r , into liquid substrate layer d.r . When the d.r - laycr bccomcs liquid and its concentration

achieves sclcctcd No (For thc NilAl/Ni system) then,

undercoolcd d.r - liquid laycr is rcady to be subjected to solidification involving n~cta-stablc pcritcctic reactions. The number of nppcaring pcrircctic phascs depends on a longr of solidification path for n givcn phasc diagmm, Figure 7.

0.5 0.6 0-7 0.8 0.9 Al Concentration, N I mole fr.

Fig. 6. Reduccd No + N I + N t and full N, + Nl + Nz + N~ solidification path; rcduccd klNn + klN3 + klNl + kZNZ and full klNo 3 klNl 3 klN1 + k2N2 3 k3N2 + kJVdF "hjstoricaI", solid / liquid interface path.

When TR = 700 OC, thcn No = 0.66 molc fr.. as rncasurcd. Thc solidification model assurncs somc simplilications. Thcrcfore, constant partition ratio, k , is applicd for the Formation of inter- metallic phasc. Othcnvise, the description is analytical one, so that constant partitioning is justified. Howcvcr. in thc casc of the description of the inter-mctallic compound formation varying partition ratio should be used. Thus, thc universal definition of k -parameter is to be introduced into thc rnodcl.

The proposed definition of partitioning is as follows:

A R C H I V E S of F O U N D R Y ENGlHEERlMG V o l u m e 8. S p e c i a l Issue 1 l 2 0 0 8 , 3 3 7 - 3 4 2 339

Whcn, in simplification, for thc for~nation of inter-

~netallic phascs, k: = 0 , thcn: k, = k: = corrsr.

Ilowcvcr, if k,! = 0 , thcn kj varics hyperbolically with

thc liquid conccn tn t ion , N , and can bc applicd to . .

dcscribc ihc for~narion of inter-mctallic compound, In gcncral, definition (3) is able to teproducc thc position of both Eiq~tidtts and solirli~s lincs Tor cach phasc diagram,

Since the currcnt modcl is rcfcrrcd to thc phasc diagram for s tablc cquilibrium, so, ~ h c calculaltions require to cnvisagc t hc for~naiion of primary phascs, x i ,

which take part in adcquatc pcritcctic rcaclions according to the following relationship:

Fig. 7. 111 sit11 obscrvntioo o f lhc binh o f thc couplcd ~ h a s c AllNi on a surhcc o f dominan! phasc AljNi2 formcd for 9 scconds.

Thc birth o f thc A13Ni couplcd phasc cnswrcs a rormation of rhc final rnelti-layer consisting of two phascs, F i p r c 7. Thc birth o i ihc coitplcd A1,Ni phasc is so dclaycd that it can bc obscwcd cxpcrimcntally, Figurc 7.

I:~nally two intcrmctallic phascs cot~ld bc obtaincd as a rcsult of solidification proccss as it is shown in Fig. 8.

Roth, pcrirecric rcaction and isothermal solidification itsclf occur in such n way that number of dcgrccs of frccdom is equal to zero. f = c-p+l = 0. According to qua t ion (4): c = 2 (Ni, 121) p = 3 (x,, liquid Nj, intcrmctallic (AIJNil)). For a solidification process: c = 2 (Ni, hl) , p = 3, (hl,NI,, AIJNi, undcrcoolcd Liquid (Nn)). Thc mcaarrcd hl - solutc concentration within thc liquid frllcr equilihrittm solurion, N~ ( F i p ~ r c 8) can bc applicd to show thc driving rorcc Tor solidification, AT. Figure 9.

- m u 0 0 I 10 15 20 25 30

dis tance . 2. S pm i . - - . . . - .- -. - --

Fig. 8. A morphology of thc NilAlCNi in8crconncction for thc arrested solidification proccss stoppcd ancr P5 s of solidification undcr a vacuum. Thc N' - liqttid solution rcvcalcd duc to thc EDS mcasurcmcnt of hl - solutc conccn!r;ltion.

,I I I

>.

2 I E 1 >. 1; I = I .L 1 5 I I

: AlNi i A ~ A I ~ N ~ ; liquid jA13Ni i h'n Nhr, N2 NF Np+ N2

Fig. 9. Undcrcooling AT rclatcd to solidification path: N, - N ~ .

The undcrcoaling vanishcs whilc solidification tends towards the PJF - point sitnatcd on 1iquidtr.t linc and rcsulting from thc intcrscction o f rcal technological tcmpcnturc imposed by technologist and liqlrid~a linc itsclF.

It is cvidcnt [hat undcrcooling vanishes and appcars cyclically to promotcs thc conzinuous ihickcning of thc intcrmctallic sub-laycrs contained within thc joint.

Thc AlNi intcrmctailic phasc s h o w in Figurc 9 is thc so- caltcd initial transient phasc rcsulting liom thc stablc formation of phasc, Figure 10.

A R C H 3 V E S o f F O U N D R Y E N G I N E E R I N G V o l u m e 8 , Special Issue 1 1 2 0 0 8 , 3 3 7 - 3 4 2

Fig. t On SchcrnaticalDy shown thc initial transient pcriod of solidification during which n AINi 3 AI3Ni2 transformation rakrs plncc. Thc AI-fillcr mctal is rnclting at the sarnc timc: AI(s) 3A1.

Thc Gibhs phnsc rulc can be npplicd for this pcriod of the process undcr investigation. Thus. tlic number of dcgrees of frccdorn is equal to 7cro. f = c-p+l = 0. According to equation 44): c = 2 (NI. Al) p = 3 (liquid Nn, intcrmctalfic (Al,Ni,) and primary phasc (AINi)).

Thc in~zial transicnt stnblc solidification disappcnrs so quickly that i t cannot bc arrcstcd and obscrvcd within tlic frozen morphology. Ncxt, rhc A1 - liquid tilIcr mctal transforms into its couilihrium solution. N ~ . F i~urc 1 1.

Fig. 1 1 Transformation o f the A1 - liquid filIcr metal into its liquid solution blF. Both snturatcd - s, and supersaturated - ss, zoncs arc also Ibrmed during this pcriod oftimc

Sclcclion of tlic don~inant phasc A13Ni2 by n systcni, Figure 10, is justificd duc lo tlic criicrion of ninxirnuii~ tcnlptnfurc of thc solid / liquid intcrfacc. As a rcsult rhc stablc phasc hlNi transiorms into thc don.rinnnt mctas!ablc plinsc AljNi2. T ~ c transformation occurs tliongh ~ h c undcrcooling cnvisagcd for solidification of primary plrnsc AINi (according to phasc diagram of stablc equilibrium) is gtcatcr than ~~ndcrcooling for solidification of doniinnllt pliasc, Al1Ni2, Figurc 9.

Whcn transformation is clonc rlicn n~ctaslnblc solidification lakcs ptacc ns cxplaincd sclic~nnt ically ill Figltrc 2.

An intcrprctation of tlic crilcrion o f rnaxin~um tcrnpcnlurc of thc solid I liquid inrcrracc is cxplainctl in 1:lgurc 12.

0.14 I

0.6 1 .Q Al - concentration, N / mole fr.

Fig. 12. Thc Ni-Al phosc dingran1 with two mctnstnhlc snlirirr.~ lines for A1Ni - phasc and plinsc hl,Ni?. f ~ c intcr~cctlon o r t l~c characteristic Al-solutc conccntmtion N,,, will1 both rnctnsrnhZc solidus lines dcfincs tlic zcrnpcraturc of thc soliti /liquirl interface during mctastablc solidificnlion.

According to schcmc shown in Figurc 12

Thcrcforc. thc mctastablc phase AI,Niz is formcd instead of stablc phase AlNi as i t is cxplaincd in Fig~rc 10 as lvcll as obscrvcd cxpcrin~cntally, Fi y r e 8. Somc mcasumments of thc A]-solurc contcnt across thc joint can bc fitted by a curve resulting from a currcnt modcl according to adcquate theory, [9], Figure 13.

A R C H I V E S o f F O U N D R Y ENGlNEERlNG Vo lume 8. Spec ia ! Essua 1 1 2 0 0 8 , 3 3 7 - 3 4 2

I . - : : E ' L - ibN1 *...*..- : ; s

I I : ; e k - 1 1 r r rn I . I

, , rn 0 Y E ia 01 I . - 2l - 0 m

a

0 0.2 0.4 0.6 0.8 1 Solid amount. x

Fig. 13. Reproduction of both constant pcritcctic concentration of the Al- solutc across a half multilaycr AI3Ni2lAlJNi and sub-

lnycrs thickness ratio: A: / g = ,vYax /XY + x3 ~irnulatcd

for fuI1 solidification path No - N~ of thc liquid11~ lint from thc Ni-A1 pliasc diagram.

Mcasurcmcnt points from EDS annlysis. Solidification arrcstcd

aflcr 12 1 s. s,!""' = 0 in the Figure 13 for local coordination systcm, xi"" calculntcd according to thc pcritcctic rcaction, equation (4). ,r,!"'" -.r,'""' denotcs thc amount of intermetallic phasc as resulting form thc undcrcoolcd pcritcctic rcaction, dimcnsionlcss, for i -rangc o f solidification rclatcd ro rhc solidificntion path dcfincd in thc Ni-Al phasc diagram for stablc

4. Conclusions

Since the rcal p m c s s of thc joint formation occurs undcr merastablc conditions it is ncccssary to work out a modificd mode[ for the isothermal solidification which could bc fully referred to thc phase diagram for metastable equilibrium.

l i c n , equation (4) will not bc applicable in sim~llation. This will be focused on the solute redistribution afler back-dimusion.

References

[ I ] D. Duvall, W. Owczarski, D. Paulonis, TLP* Bonding: a Ncw Mcthod for Joining Heat Rcsistancc Alloys, Wclding Journal, vol. 53, (1974), 203-2 14.

[2J 1. Tuah-Poku, M. Dollar, T. Massalski, A Study oFTransicnt Liquid Phasc Bonding Proccss Applicd to a AdCuJAg Sandwich Joint, Metallurgical Transactions, vol. 19A, (1 988), 675-686.

[3] J. Kloch, E. Guzik, J. Janczak-Rusch, D. Kopycinski, T. Rutti, J. Kim, IF. Lcc, W. Watczydski, Morphological Characteristic of the Multi-taycr / Substrate Systcms. Procccdings of the 9-th Errtopcan Congrcss on Stcrcology and Image AnaIysis, Zakopanc, (2005), 375-382.

[4] Y.K. Chuang, D. Reinisch, K. Schwcrdtfcgcr, Kinctics of the Diffusion Controlled Peritcctic Rcaction during Solidif cation of Iron-Carbon Alloys, Mctollurgical Transactions, YO]. 6A, ( 1 975), 235-238.

[ 5 ] G.A. Lopcz, S. Sommadossi, W. Gust, B. Mittcrncijcr, P. Ziqbn, Phasc Chmctcrization of Diffusion Soldcrcd NilAVNi Intcrconncctions, lntcrbcc Scicnce, vol. 10. (2002). 13-19.

[GI W. Wolczyhski, J. Kloch, 1. lancznk-Rusch, K. Kurzydtowski, T. Oknnc, Scgrcgation Profilc in Diffttsian Soldered NiJhllNi Interconnections, Materials Science Fomm, vol. 508, (2006), 385-392.

[7] E. Scheil, Uber die Eutektischc Kristallisation, Zcitschrif? fur Metallh~nde, vol. 34, ( I 942), 70-80.

I S ] H.D. Brody, M.C. Flemings, SoIutc Redistribution in Dendritic Solidification, Transactions of AIME. vol. 236. ( I 966), 61 5-624.

193 W. Wolczyfiski, E. Guzik, D. Kopycihski, T. 1 Iimcrniya. J. A model For the formntion Ni/Al/Ni Cntcrconnection is givcn. Janczak-Rusch, Mass Transport during Dif is ion Soldcring

Thc modcl is rclatcd to an isothermal solidification but or Brazing at the Constant Tcrnpcnturc, Procccdings of thc solidification path sih~ntcd on thc phase diagnm for stable 13Ih International Hcat Transfer Confeerence - Sydney, cd. equilibrium. begell house, inc, publishers, eds G. de Vahl Davis & B. Somc interpretations o f the proccss under investigation are Lconrrrdi, CD, (2006), MST - I I , I2 pagcs. only given by rncans of thc phasc diagram for n~ctastablc

Ksztaltowanie struktury zlqcza NilAl/Ni przy zastosowaniu krystalizacji izoterrnicznej

Streszczenie U7,yskano ztqcza NilAl/Ni w warunkach zadancj stnlcj tcnipcratury rzeczywistej tak jak tego wyrnaga technologia. Proccs

krysfalizacji znlrzyniytvano po sbtnych okresach cmsu i obsetlvawano zamrokonq morfologip zlqcza. Na tcj podstswic opracowano zalotcnia mudclu krysralizac,ji odniesioncgo do diagramu fazowcgo r6wnowagi stabilncj. Ponicrvnt proces prxhiega w warunkach rnctast~hilnych zalcm ~vprowadzonn pcwnc rozwaiania zwiqzanc z diagramem l'azowym rbwnowagi mctastabilncj przy okazji znstosorvania krytcrium rnaksynialncj ternpcntury frontu krystalizacji. Przeprowadzonn symulncja profilu stqkcnin w poszczcgblnych podrvarst\vnch a zwtaszc7~ proporcji szerekoici podwarstw d o symulowanej proporcji iloici Ihzy pcrytcktycznej sq zadowal;ljqcc. Jednak, wniosktrje sic rnodyfi kacje modelu celcm wyznaczania produktbw scakcji pcrytektyczac,i przy znstosuwaniu diagram~t fazowcgo rbwnowagi mctastabilncj.

342 A R C H I V E S of F O U N D R Y E N G I N E E R I N G Volume 8 . S p e c i a l I s s u e 112008, 3 3 7 - 3 4 2