9

Calphad, Vol. 27, No.1, pp. 27-37,2003 by Elsevier Science Ltd 0 2003 Published 0364-5916/03/$ - see front matter

Pergamon

PII:SO364-5916(03)00028-2 DOI: 10.1016/S0364-5916(03)00028-2

Thermodynamic

Reassessment

of the Au-In Binary System

H.S. Liu’, Y. Cui’, K. Ishida2, and Z.P. Jin’* 1. School of Materials Science & Engineering, Central-South University, Chang-Sha, Hunan, 410083, P.R.China. 2. Department of Materials Science, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan *. Corresponding authour’s e-mail: [email protected] (Received October 30,2002)

Abstract. Through CALPHAD method, the Au-In binary system has been thermodynamically reassessed. The excess Gibbs energies of the solution phases, liquid, fee, c 1, and hcp were formulated with Redlich-Kister expression, while the y and ‘Ir phases with narrow homogeneity ranges were described with sublattice models, and other intermetallic phases were treated as stoichiometric compounds, A set of self-consistent parameters has been obtained, which can reproduce most experimental data of thermodynamic properties and phase diagram of this binary system. Additionally, the standard formation enthalpies of all intermediate phases have also been calculated. 0 2003 Published

by Elsevier Science Ltd.

Introduction Au-In alloys are of importance as candidate materials in electronic packaging. Phase diagram and the related thermodynamic property of this system may play an important role in developing new Au-base alloys. The Au-In binary system was previously assessed by Ansara and Nabot [l]. The assessed results [ 1] were reasonably consistent with most experimental data of phase boundaries and thermodynamic properties of this binary system. However, the calculated solubility of In in fcc(Au) [l] trends to increase when temperature is lowered to about 180°C as shown in Fig. 1. Such tendency is not reasonable. Moreover, v and I, which have homogeneity ranges, were treated as stoichiometric compounds [ 11. Such simplifications may bring about some problems when extrapolation is undertaken to high-order diagrams involving the Au-In binary system, e.g. Au-In-Sn ternary system. In view of this, thermodynamic reassessment of the Au-In binary system is performed. Evaluation of Experimental Data Figure 2 is the phase diagram of the Au-In binary system reviewed by Okamoto and Massalski [2] on the basis of the boundary data reported by Hiscocks and Hume-Rothery [3], Owen and Roberts [4], Kubaschewski and Weibke [5], Nikitina et a1.[6] and Schubert et a1.[7]. The boundaries in the field where liquid and fcc(Au) coexist, and the In-rich region measured by Nikitina et al.[6] show obvious difference from those reported by Hiscocks and Hume-Rothery [3], Owen and Roberts [4] and Kubaschewski and Weibke [5]. Especially, the boundary data for liquid+fcc two-phase region reported by Nikitina et al.[6] show much disparity, and were

27

H. S. LIU et al.

28

given up by Okamoto and Massalski [2]. The experimental data in other parts of the Au-In system in all references agree well. Temperatures for the invariant reactions involving liquid reviewed by Okamoto and Massalski [2] were in agreement with those lately measured by Mikler et al.[8] using DSC. In the present work. all the liquidus and the solidus of fee in Ref.[3-5,7] are given higher weight durmg optimization while the boundaries concerning the o 1, -1 and Y phases and the invariant reactions adopted in this optimization arc taken from Ref.[2] and Ref.[8]. Although the i ‘# E order-disorder transformation at about 340-C was reported 121, it will not be taken into account in the present work due to lack of other experimental information considering its composition range Compositions and on this transformation. t ’and E are treated as A& crystal structures of all phases in the Au-In system are listed in Table 1. Table 1. Phases in the Au-In Binary System and Their Models Adopted in This Work Composition Structural Prototype Model Phase at.% In Designation Al 0 to 12.7 cu Fcc(Au) (AuJn) 12 to 14.3 DO24 NijTi (AuJn) ul 13 to23 A3 Mg Hcp (AuJn) 21.5 to 22.2 p 1317tn775

R ' r ____ E"

-_.

E >a hi

Y’ Y AuIn AuIn2 TetrlTn) ‘:

._

--..

I

-

..,“__,

24.5 to 25

I

\----I" ,!~.",..lh22222

(Au)0 -is(

24.5 to 25 28.8 to 31.‘I 29.8 to 30.t i

DOa D83

35.3 to 39.5 50 to 50.1 66.7 100

D513

p CuxTi Cu9A14 Au&i,

1NizAI?

25 (Au)o.7s(In)o 25 (Au)0 6923i(Au,In)o 23077(In)O 07692 (Au)0 7(In)o 3 1Muh c(Au,In)o ~~~~~(In)6 16667

1

] / t i

(.W~s(Wos

Cl Ah

CaF2 In

(AU)0.33333(In)0.66667

IIn~

F and E ’are regarded as one phase in this paper.

Only thermodynamic properties of liquid in this system were reported. Kameda et a1.[9] measured activity of In in liquid Au-In alloys. Itagaki and Yazawa [lo] measured the mixing heats of liquid at 1100°C. which differ much from those lately reported by Castanet[ 1l] who measured the enthalpies of mixing of liquid Au-In alloys at different temperatures. According to the discussion by Wasai and Mukai (121, the enthalpies obtained in Ref.[ 1l] were more reliable, thus were given larger weight in the present optimization. Additionally, mixing enthalpy of liquid alloys measured by Castanet [l l] show its dependence on temperature. Thermodynamic Models Solution Phase: Liquid, fcc(Au), ~1I and hcp Gibbs energies of the solution phases in the,Au-In system are expressed as following: Gm = ~x,‘G,‘+RT i=,&.,n

Cx~In(r,)+x,,x,~~“‘L:,,,~(x,” ,=Au,,fl ,=6

-x,~)’ .._....

where 4 denotes all the solution phase, and O’L”

,~“,,”= A, + B,T + C,Tln(T) . ... .... .... ...._....................................................................

and XA”and XI, are the mole fraction of component Au and In, respectively.

(2)

“G,’ is the molar Gibbs energy of

THERMODYNAMIC

REASSESSMENT

OF Au-In

BINARY SYSTEM

is the interaction parameter of the solution, where A,, Bj, and C, are

pure element i in status of 4. “‘&,~

constants to be optimized. And m is a non-negative integer, always taking a value smaller than 3. Because mixing enthalpies of liquid Au-In alloys were reported to depend on temperature [ 111, C, is introduced for liquid, but not for fcc(Au), cr 1and hcp. The y and B phase The 7 phase has Al&us-type structure. Considering the radius of the elements and the location of atoms is denoted by a 3-sublattice model: in this kind of lattice, the thermodynamic model of y (Auk, 69231(Au,In)a23077(In)O.O76s2, and the Gibbs free energy of y is formulated as: GY = Y::GL AuLn+ Y/l:G:, In:,,,+ 0.23077RT{Yi ln(Yl:) + Yi ln(Yl)}

+ Y”AuY”LY ,n A” Ru,,“:,n

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(3)

where G;, A“.,” = 0.92308’G,/t’ +O.O7692’Gr

+ E, + F,T ... ..... .... .... ......... ....... ..... ....... ... .... ... ....(4)

+ 0.30769’GF

+ E, + FJ . ...... ........ .... .... ... ..... ... .... ... ..... ....... .....(5)

G:u:,n ,n = 0.6923l’Gz and

LYAuAu.,n.,n =Cx+&T. . ..__....................__...........__................_............,. where E, ,F,, CJ, D3 are parameters

to be optimized,

and ‘Gc

and ‘Gr

..__._(6) are the molar Gibbs energies of

standard pure elements, respectively. TheI phase has isotypical structure of NizA13, which has recently been modeled as (Al)s(Al,Ni)@i,Va) by Ansara et al [ 131. Considering the fact that the misfit of atoms between Ni and Al does not differ so much from that between Au and In, a similar model (Au)s(Au,In)a(In,Va) may be adopted to describe rP However, the atomic radius of In is very large compared with that of Ni, so substitution of vacancy for In may be much difficult. Accordingly the above model is simplified to (Au)o.s(Au,In)o.~333s(In)o.i6667 in the present work, of which the Gibbs energy is: G’ = YltG,Yu-Au:‘ n + YlG,W,,,,,.,”+ 0.33333RT{YL ln(Yl:) + YL ln(Y,f )}

+ Y;;Y,;L;u:,” ,“,n.,...,..__..................................................................................................,

(7)

where G,W,:,,.,”= 0.83333’GE

G,‘.,n ,n = OS’GZ has and LLAu.ln I,,

+O.l6667’GF

+0.5’Gr

+E, + F,T ...... ... ...... ... ...... ... ..... ... .... ... .... ........ .(8)

+ E, + F,T .. .... ..... ... ..... .... .... .... ...... .... .... .... ... ..... .... .... ... ....(9)

the same form as that for the Y phase.

Stoichiometric Compounds: fi , fi ‘, y ‘, Au&, AnIn, Au& Because the homogeneity ranges of these phases are no more than 2at.% In, they were simplified to be

30

H. S. LIU et al.

stoichiometric as:

compounds.

By using Neumann-Kopp

rule, Gibbs energies of all these compounds are expressed

G”,,R”=a’G,/:’ +b’G,‘,“’+ E, + F,T .__._..........._.............. where

A(, B,, represents

..(lO)

all the compounds, a and b are the ratios in the formula, and Es and Fs are parameters to

be optimized. Results and discussion By CALPHAD method and by using the lattice stabilities given by Dinsdale [14], the thermodynamic parameters of the Au-In binary system have been reassessed as listed in Table 2. Compared with the assessment by Ansara and Nabot [l] listed in Appendix, the parameters of liquid in the present work have been changed much and one more parameter has been introduced to describe fee, while the parameters for most stoichiometric compounds varied slightly. Meanwhile, improvement on assessment in the present work is evident as indicated later. Phase Diagram Evaluation Figure 3 shows the calculated phase diagram, and comparison of the calculated diagram with experimental boundaries is shown in Fig. 4. In combination to Table 3, which gives all invariant reactions, it is clear that reasonable agreement has been realized between the calculated and experimental data of phase diagram. The present work are in agreement with those by Ansara and Nabot [I] in the part from 50 to 100 at.96 In of the phase diagram, while improvement on the other part of the phase diagram in the present work is also noticeable as analyzed below. (1) In the Au-rich comer, the phase diagram assessed in the present work is more reasonable as it is much closer to that proposed by Okamoto and Massalski [2]. Due to different crystal structure, large misfit between atomic radius, and due to different electronegativities of Au and In, it may be more acceptable that the solubility of In in fcc(Au) should decrease steadily with temperature. The presently assessed diagram reproduces such tendency but that by Anssra and Nabot [ 1] does not. (2) Not only the composition ranges of y and y have been reasonably modeled, but also the differences of crystal structures between 13 and 0 ‘, and Y and y ’are taken into account. of invariant reactions, L-*fcc+ a 1 and L+ a i+hcp calculated by Ansara and Nabot values [2] and the lately measured data [8], whereas the corresponding values in the present work show deviations no more than 2K. (3) Temperatures

[I] differ more than 5K from the reviewed

In addition, a: 1is calculated to be stable down to room temperature according to the present work, this is in consistence with the reviewed relations in Ref.[2], while Ansara and Nabot [l] calculated the temperature for eutectoid reaction (y.i+fcc+hcp to be 177’C. Whether o I can be stable down to room temperature or not remains uncertain. Evaluation of the Optimized Thermodynamic Data Comparison between calculated and experimental mixing enthalpies of liquid at different temperatures is shown in Fig.5. It can be seen that the calculated values of mixing enthalpy agree well with experimental data in Ref.[ll] while deviate much to those reported in ReE[lO]. As mentioned earlier in Section 2, the enthalpies

THERMODYNAMIC

REASSESSMENT

OF Au-In

BINARY SYSTEM

31

obtained in Ref.[ 111 were more reliable than those in Ref.[lO]. Hence, the calculated enthalpy of mixing of liquid is acceptable. Table 2. Assessed Parameters of the Au-In System in This Work Liquid: (AuJn)

,(11 L”,,,,,,=-76196.19+64.2914T-6.6375TLn(T) “,

U)LLlll =-31134.02+81.3582T-8,5134TLn(T) A”.,”

FCC:(AuJn) WLhCC ,,,,,,,=-48493.65+46.6237T-6.8308TLn(T) a 1 : (Au,In) ‘“‘L”’

(I)LFCC AU,,” =498.45

* (lattice stabilities ofAu and In in a I status were cited from Ref.[l]) “‘L”’ Au,,n=-48.36-16.7932T

,,,,,,,=-48238.66+5.355lT

Hcp: (AuJn) ‘“‘L~;,,,=-55780.55+13.8198T

“‘Lz,“=6788.95-32.8937T

Y : (Au)o.69231(Au,In)o.z3o77(In)o.o76g2 G i,UlU,,,=0.92308°Gi;l’+0.076920G~

-2830.47-2.519lT

G:, ,,,,n =0.69231 ‘G,/:‘+0.30769’GF

-11992.16-3.65llT

rIr

: (AU)o.5(AU,In)o.33333(In)o.16667

GYu

4" 6,=0.83333°G~+0.166670G~

G:, Au.,n.,n =2 144.6

+2153.38-8.039T

GYt. ii irr =0.5°G~+0.5”G~-18225.14+3.0T

G;U,U,,n,n=-15683.16

fl : (Au)o.m(In)o.zls

GP=0.7850G/CC+0.2150GTe” ,n -8980.42-3.3042T A”

s ‘: (AU)o.77778(In)o.zzz22

G” =0.77178°G,/:‘+0.222220G~

Au3In: (Au)o.75(In)o.2s

GA”>‘=0.75OGe ” +0,25”Gp

Y

‘: GWdWo.3

-9382.52-3.1015T

-10582.67-2.9323T

GY’=0.70GA/:C+0.30G~-12813.11-2.0538T

AuIn : (Au)o.s(In)o.s

G A”‘“=0.5°G~+0.50G~

Auh

G Auf+=0.33333 ‘Gfcc ,” -26129.06+11.1133T Au+0.66667 ‘G=’

: (AU)O.33333@)0.66667

Tetragonal: (In)

-20188.37+2.3786T

Gik =OGT

Figure 6 illustrates activities of In in Au-In liquid. It is clear that the calculated activities of In in liquid are reasonably consistent with experimental values measured by Kameda et al.[S].

H. S. LIU et a/.

32

Table 3. Calculated and Experimental Data for Invariant Reactions Composition (at% In) Reaction Temperature( % ) 642 L-’ u ,+Fcc 0.240 0.142 0.125 649 0.225 0.145 0.138 649 L-r (Y,+Hcp 0.244 0.228

0.143 0.147

0.292 0.290

0.230 0.209

0.157 0.159

I. +Hcp+Au3In

L-+Au3In+ y

0.311 0.296

0.290 0.288

634 641 641 493

Reference I11 I2J This work

111 / 121,

~

This work

487 487

ill 121 This work

482 479

[21 This work

/ 4

L-+1, +Y

0.350

0.310

0.360

I,+ Y +AuJn

0.340 0.398

0.302 0.385

0.361

0.408

0.393

l.+AuIn+AuIn2

L-‘AuIn2+Tetr(In)

455 1459 450 454

121 181 This work

456

j j I‘his work

0.553

495

0.542

497 496

0.998

156

155

[iI

lisl 121

!

I This work

I !

PI IX1

0.999

156

’This work

0.383 0.379

458 461

121 This work

L+AuIn

509 509 506

I21 IX1 This work

L-+AuIn2

541 539 539

/ 1x1 1This work

375 380

This work

L +w

Au3In+ y ---t y ’ y+y,+m Au3In+Hcp

0.306 0.301 0.308 0.306

+ B

0.361 0.371

365 361 337 337

‘P

Au3In+ 13--t fi ’

295 fi -+ /3 ‘+Hcp Y -+ y ‘+AuIn

0.390 0.390

-J

I21

121 [21 This work [21 This work

I ~ i

PI This work

PI

275 275

This work

224 224

This work

PI

Gibbs energies of formation of intermediate phases have been further calculated as listed in Table 4. In combination to Table 2, it is interesting to note that Gibbs energies of intermediate phases at 25°C decreases

THERMODYNAMIC

REASSESSMENT

OF Au-in

BINARY SYSTEM

33

with increasing In while the formation entropies for linear compounds show opposite trend. Table 4. Gibbs Energy of Formation of Intermediated Phases Calculated in This Work. Reference States are Pure Solid Comnonents.

I

Phase

B P’

I

Composition (at.%In) 0.215 0.215 0.22222 0.22222

I

Temperature 25 277 25 200

(Cc)

I

nG(J/mol)

I

-9965 -10798 -10307 -10850

Conclusion Phase diagram of the Au-In binary system has been reassessed on the basis of phase diagram and thermodynamic data of liquid. With consideration of the homogeneity ranges of y and Y , and the structural differences between y and y ’, fl and /3 ’, a set of parameters has been obtained which can satisfy both the experimental data of thermodynamic and phase diagram. Acknowledgment This work was supported by the Grant-in-aids for Scientific Research from Ministry of Education, Science, Sports and Culture, Japan. One of the authors, H.S. Liu thanks for the financial supports from Marubun Research Promotion Foundation, Japan. References [l] I. Ansara, and J.-Ph. Nabot, CALPHAD, 16(1992), 13. [2] H. Okamoto, and T.B. Massalski, Phase Diagrams of Binary Gold Alloys, ASM International, Metals Park, OH, (1987),142. [3] S.E.R. Hiscocks, and W. Hume-Rothery, Proc.Roy.Soc.(London), A282(1964),318. [4] E. Owen,andE.A.O. Roberts, J. Inst. Met.71(1945),213. [5] 0. Kubaschewski, and F. Weibke, Z. Metallkd., 44(1938),870. [6] V.K. Nikitina, A.A. Babitsyna, and Yu.K. Lobanova, Izv.Akad.Bauk SSSR, Neorg. Mater., 7(1971),371. [7] K. Schubert, H. Breimer, and R. Gohle, Z. Metallkd., 50(1959), 146. [8] J. Mikler, A. Janitsch, and K.L. Komarek, Z. Metallkd., 75(1984), 719. [9] K. Kameda, T. Azakami, and M. Kameda, J. Jpn. Inst. Met., 38(1974), 434.

H. S. LIU eta/. ]lO] K. Itagaki, and A. Yazawa, J. Jpn. Inst. Met., 35(1971),383. 11I] R. Castanet, W. Ditz. K.L. Komarek, and E. Reiffenstein, Z. Metallkd.. 72( 1981 1. 176 [ 121 K. Wasai, and K. Mukai, Fluid Phase Equilibria, 125( 1996), 185. [ 131 I. Ansara, N. Dupin, H.L. Lukas, and B. Sundman, J. Alloys and Comp.. 247( 1997). 20 114lA.T. Dinsdale, CALPHAD, 15(1991),317.

Appendix

: Optimized Parameters of the Au-In System in Ref. 1I ]

Liquid: (Au,In) ““LL”’ ,,,,n=-80027.7+89.7173T-9,5705TLn(T)

“ILL” ,,,,“=-34977.3+117.2938T-13.0337TIn(T)

FCC:(Au&) ‘OILkC ,,,,,=-61378.5+174.9882T-23.185lTLn(T) a, : (Au&) i(li

*

L&,,, =-54650.0+16.09T u

“‘L’;l,,n ==4460.9-23.64T

Hcp: (Au&) “‘L::‘;<,=-60630.1+16.79641

“‘L;,‘;,n=7870.9-27.3128’1 G”=0.62°G~+O+0.38”G;:“’ -14804.5-2.0931

y : (AU)o.6z(In)o.38 b

Or

fl ‘:

G”=0.78°G”c+0.~20G’ “’ Au

(AU)o.m(In)o.zz

,n

0

-9762.0-2.38031

G,,fit +0.3 0 G,ir” -12813.1-2.0538T

Y or Y ‘: (Auh7(Inh

G’=0.7

Au&:

G %‘”~0.75 OG/Cc1-0.25 OG,,,r ,,, -11054.5-2.166-I Ru

(AU)o.7Oh~

OG/”

AuIn : (Au)o.d~h

GAuln

Auh

2 G~+0.6667”G;:‘” G 4uh’=0.3333’

: (.+0.3333([email protected]

Tetragonal: (In)

G

=0,5

Au

+0,5

OGi,!

,,, -19639+1.84781

id, _~” G;ne”

*: The lattice stabilities ofAu and In in Q 1status were expressed as:

G’;; = 125 + 0.79T+‘Gc

Gz

= 520 - 0.384T+%r

-26730.8tl2.0162T

THERMODYNAMIC

REASSESSMENT

OF Au-In

BINARY

SYSTEM

0.8

1.o

1200

1000 0P ;

800

5 sLs

600

2 g

400

200

0 0.6

0.4

0.2

0 Au

MOLE-FRACTION IN

In

Fig. 1 The calculated phase diagram of Au-In binary system by Ansara and Nabot

: i

AU

:.

:c

i.:

MOLE-FRACTION

,:

,:

IN

.,,

111

I In

Fig.2 Phase diagram of the Au-In binary system reviewed by Okamoto and Massalski [2].

35

H. S. LIU et al.

36

600

400 1 200

I

I

0-l0 AU

0.2

0.4

0.6

MOLE-FRACTION

0.8 IN

-!

1.0 In

Fig.3 The calculated phase diagram of Au-In binary system in the present assessment

AU

MOLE-FRACTION

IN

In

Fig.4 Comparison of the calculated phase phase with experimental boundaries.

THERMODYNAMIC

REASSESSMENT

OF Au-in

BINARY SYSTEM

0 I-

2

-2

2

-4

% -6 13 5 -8 !z -10 5 ~ -12 2 -14 g -16 G

-18 cIl,,[Il

-20

I

0 Au

0.2

I

0.4

I

I

0.6

MOLE-FRACTION

0.8 I?d

1.b In

Fig.5 Calculated enthalpies of mixing of liquid in comparison with experimental data.

g

0.7 -

?: 0.6 5 i:

0.5 -

2

0.4 0.3 0.2 -

0.1 0 Au

0.2

0.4

0.6

MOLE-FRACTION

0.8 IN

1.0 In

Fig.6 Calculated and experimental activity of In in liquid (Ref.state: liquid In).

37