Thermodynamic assessment of the Al–Au system

Journal of Alloys and Compounds 385 (2004) 199–206

Thermodynamic assessment of the Al–Au system Mei Li a , Changrong Li a,∗ , Fuming Wang b , Degui Luo a , Weijing Zhang a b

a School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, PR China School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, PR China

Received 19 April 2004; accepted 6 May 2004

Abstract The Al–Au binary system has been thermodynamically assessed by means of the computer program Thermo-Calc. The Redlich–Kister polynomial was used to describe the solution phases, liquid (L) and fcc. The sublattice-compound energy model was employed to describe the compounds with homogeneity ranges, (Al2 Au), ␸(AlAu2 ) (␸ = ␣, ␤ and ␥) and ␤(AlAu4 ). The compounds, AlAu, Al3 Au8 and AlAu4 , were treated as stoichiometric phases. The parameters of the Gibbs energy expressions were optimized according to all the available experimental information of both the equilibrium data and the thermodynamic results. A set of self-consistent thermodynamic parameters of the Al–Au system has been obtained. The calculations agree well with the respective experimental data. © 2004 Elsevier B.V. All rights reserved. Keywords: Al–Au system; Phase diagram; CALPHAD technique; Thermodynamic equilibria

1. Introduction The Al–Au binary is one of the most extensively studied systems because of its practical application as the metallization schemes [1,2]. The thermodynamic description of the relevant alloy system is of importance for understanding the physical properties, the chemical behavior and the technological applications of its alloys and compounds. The phase diagram of the Al–Au system has been studied many times since the pioneering work of Roberts-Austen [3]. The first evaluation was performed by Eliott and Shunk [4], followed by Murry et al. [5] who also assessed the system thermodynamically. However, the stoichiometry of the compound existing at ∼72 at.% Au was reported to be either Al2 Au5 or Al3 Au8 [6–9] in this system. In 1989, Range and Büchler [10] confirmed that Al3 Au8 is the correct stoichiometry. Moreover, (Al2 Au) and (AlAu2 ), optimized as strict stoichiometric compounds by Murry et al. [5], exhibit the homogeneity ranges between 32.9–33.9 at.% Au and 65–66.8 at.% Au respectively. And there are three allotropic phases of (AlAu2 ), i.e. ␸(AlAu2 ) (␸ = ␣, ␤ and ␥). In the present paper, the phases with homogeneity ranges or the non-stoichiometric compounds are indicated with the round brackets as (phase name). The purpose of this work is to ∗

Corresponding author. E-mail address: [email protected] (C.R. Li).

0925-8388/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2004.05.007

re-assess the Al–Au system thermodynamically, while considering the stoichiometry of Al3 Au8 and the homogeneity ranges of (Al2 Au), ␸(AlAu2 ) and ␤(AlAu4 ) phases. 2. Experimental information 2.1. Experimental phase diagram data The Al–Au system was first studied by Roberts-Austen [3], who described (Al2 Au) as the purple compound and noted its high melting point and its large heat of formation. In 1900, Heycock and Neville [6] determined the liquidus completely and the eight invariant equilibria, as listed in Table 1. This was one of the first investigations using the microscopic technique along with thermal analysis. The liquidus was also determined by Charquet et al. [11] and Predel and Schallner [12]. The liquidus of the entire compositional range [6] indicated the existence of five intermediate phases, AlAu4 , Al2 Au5 or perhaps Al3 Au8 , (AlAu2 ), probable AlAu, and (Al2 Au). Heycock and Neville [6] suggested from their liquidus that there was a phase with the composition of Al2 Au5 (28.6 at.% Al), while the microscopic results of this phase pointed to be Al3 Au8 (27.3 at.% Al) [6]. Coffinbery and Hultgren [7] confirmed this phase with the composition closer to Al3 Au8 from X-ray data. Based on the crystal structure study, Range and Büchler [10] demonstrated that Al3 Au8 is the correct stoichiometry.

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M. Li et al. / Journal of Alloys and Compounds 385 (2004) 199–206

Table 1 The invariant reactions of the Al–Au system Reaction

Heycock and Neville [6,9]

Present work

X(Au) L → (Al) + (Al2 Au) L + (Al2 Au) → AlAu L → AlAu + ␥(AlAu2 ) L → ␤ (AlAu4 ) + Al3 Au8 a L → ␥(AlAu2 ) + Al3 Au8 L + (Au) > ␤(AlAu4 ) ␥(AlAu2 ) → AlAu + ␤(AlAu2 ) ␥(AlAu2 ) + ␣(AlAu2 ) → ␤(AlAu2 )d ␥(AlAu2 ) → ␣(AlAu2 ) + Al3 Au8 Al3 Au8 + ␤(AlAu4 ) → AlAu4 ␤(AlAu4 ) → AlAu4 + (Au) L → ␥(AlAu2 ) L → (Al2 Au) a b c d

0.011 0.565 0.600 0.785 0.720 0.800 0.65 0.662 0.668 0.727 0.811 0.66 0.333

0.0006 0.3392 0.500 0.727 0.667 0.84 0.5 0.663 0.667 0.802 0.800 0.66 0.333

0.3292 0.5000 0.650 0.80 0.727 0.812 0.651 0.661 0.727 0.800 0.862 – –

T(K)

X(Au)

923 898 844 800 848 818 818b 833b 833b 783c 773c 897 1333

0.0171 0.5817 0.6065 0.779 0.722 0.79 0.656 0.663 0.668 0.727 0.806 0.666 0.3332

T(K) 0.0010 0.3381 0.500 0.727 0.669 0.848 0.5 0.6655 0.667 0.8025 0.80 0.666 0.3332

0.3291 0.500 0.6555 0.804 0.727 0.807 0.659 0.665 0.727 0.80 0.858 – –

923 897 852 812 848 818 820 833 832 784 773 896 1333

Au2 Au5 was modified to be Al3 Au8 by Okomoto [24]. The data is taken from Puselj and Schubert [17]. The data is taken from Murry et al. [5]. The eutectoid type was suggested by Okomoto [24] while it is assessed to be of the peritectoid type.

The intermediate phase (Al2 Au) was firmly established by many investigators [3,6–8,13–16] using X-ray analysis. From the lattice parametric data, Straumanis and Chopra [13] proposed the homogeneity range of (Al2 Au) as from 32.92 to 33.93 at.% Au for alloys furnace cooled from the temperatures between 573 and 673 K. The X-ray patterns indicated that the stability of AlAu is limited to a very narrow composition range [7]. From the shifting of the X-ray diffraction lines, Coffinbery and Hultgren [7] estimated the homogeneity of (AlAu2 ) to be between 64.0 and 66.4 at.% Au at 773 K and between 65.4 and 66.4 at.% Au at 673 K. Based on the X-ray diffraction work, Puselj and Schubert [17] reported a high-temperature phase, ␥(AlAu2 ), with a homogeneity between 65 and 66.8 at.% Au and two low-temperature allotropic phases, ␣(AlAu2 ) and ␤(AlAu2 ), with the estimated homogeneities of 65.1–66.1 at.% Au and 66.3–66.7 at.% Au respectively. On the basis of microscopic evidence, Heycock and Neville [9] reported the high-temperature ␤(AlAu4 ) phase. Kuznetsov and Ravezova [18] and Francombe et al. [19] found that the disordered ␤(AlAu4 ) phase transformed to a new phase AlAu4 on cooling below 673 K and that the transformation on heating occurred at about 773 K. Coffinbery and Hultgren [7] and Ullner [8] confirmed the existence of AlAu4 but did not mention the associated equilibrium. The eutectic point of the reaction, L → fcc(Al) + (Al2 Au), has been determined twice: as 0.7 at.% Au at 915 K by Ageew and Ageewa [20] and as 1.1 at.% Au at 921 K by Heycock and Neville [6]. In a directional solidification study, Piatti and Pellegrini [21] found eutectic microstructures in the range between 1.1 and 1.7 at.% Au. Many authors [7,8,11,22,23] determined the solidus boundary of the fcc(Au) phase by X-ray analysis. From the in situ nuclear magnetic resonance (NMR) study of the two phase equilibria between the fcc(Au) and liquid in the Al–Au alloys, Gunther et al. [23] determined the solidus boundary

of the fcc(Au) phase. The latest results from Gunther et al. [23] agree with those from Charquet et al. [11]. Table 1 shows the invariant reactions of the system. 2.2. Thermodynamic data The Al–Au alloys have been studied thermodynamically by several investigators [11,12,25–30]. Ferro et al. [25] measured the enthalpies of formation of (Al2 Au), AlAu and (AlAu2 ) at 400 K by direct synthesis in an isoperibolic calorimeter. Using the differential thermal analysis (DTA) technique, the enthalpies and the entropies of formation of the intermediate compounds, (Al2 Au), AlAu, (AlAu2 ), Al2 Au5 or Al3 Au8 , and ␤(AlAu4 ), as well as the enthalpies of formation and the partial excess entropies of the fcc(Au) were determined by Predel and Ruge [26]. The aluminum activities were measured using the electromotive force (emf) method by Charquet et al. [11] between 933 and 1373 K, by Predel and Schallner [12] between 1150 and 1430 K, and by Yazawa and Lee [27] between 973 and 1273 K. Erdelyi et al. [28] determined the thermodynamic activities by Knudsen cell mass spectrometry in two laboratories within the temperature ranges between 1420 and 1740 K and between 1320 and 1660 K respectively. The mixing enthalpies of the liquid phase were directly measured by Hayer et al. [29] using a high temperature Eyraud–Petit type calorimeter between 1356 and 1587 K and by Itgaki and Yazawa [30] using an adiabatic calorimetry at 1373 K.

3. Thermodynamic models 3.1. Pure elements The stable forms of the pure elements at 298.15 K were chosen as the reference states of the system. For the

M. Li et al. / Journal of Alloys and Compounds 385 (2004) 199–206

thermodynamic functions of the pure elements in their stable and metastable states, the phase stability equations compiled by Dinsdale [31] were used in the present optimization. The equations are of the Scientific Group Thermodata Europe (SGTE) format: 0

φ

φ

Gi (T) = Gi (T) − HiSER (298.15 K) = a + bT + cT ln T + dT2 + eT3 + fT−1 + gT7 + hT−9

(1)

where HiSER (298.15 K) is the molar enthalpy of the element i at 298.15 K in its standard element reference (SER) state, fcc for both Al and Au. The Gibbs energy of the element φ i (i = Al and Au), Gi (T) in its SER state is denoted by GHSERi , i.e. fcc SER GHSERAl = 0 Gfcc Al (T) = GAl (T) − HAl (298.15 K)

(2)

fcc SER GHSERAu = 0 Gfcc Au (T) = GAu (T) − HAu (298.15 K)

(3)

3.2. Solution phases In the Al–Au system, there are two solution phases, liquid and fcc. Both of them were described by the substitutional solution model. The Gibbs energy function of the solution phase φ for 1 mol of atoms is described by the following expression: φ

Alm Aun is expressed as follows: 0

m Aun = GAlm Aun − mHSER − nHSER GAl m m Au Al

Alm Aun 0 fcc = m0 Gfcc Al + n GAu + Gf

m Aun GAl = a + bT f

3.4. Intermediate phases with homogeneity ranges 3.4.1. (Al2 Au) and γ(AlAu2 ) phases The intermediate phases (Al2 Au) and ␥(AlAu2 ), each of them having a homogeneity range, were treated as (Al%,Au)m (Al,Au%)n by a two-sublattice model [32,33]. The symbol % denotes the major component in the corresponding sublattice. The Gibbs energy per mole of the formula unit (Al%,Au)m (Al,Au%)n is given by the following expression: (Al%,Au)m (Al,Au%)n SER Gm − H(Al%,Au) m (Al,Au%)n 1 2 0 Alm Aln 1 2 0 Alm Aun 1 2 0 Aum Aln = yAl yAl Gm + yAl yAu Gm + yAu yAl Gm 1 2 0 Aum Aun 1 1 1 1 + yAu yAu Gm + mRT(yAl ln yAl + yAu ln yAu )

(4)

2 2 2 2 m (Al,Au%)n +nRT(yAl ln yAl + yAu ln yAu ) + E G(Al%,Au) m

φ where 0 Gi

i

The parameter i Lφ (i = 0, 1, 2, . . . ) is the ith interaction parameter between the elements Al and Au and to be evaluated in the present work. Its general form is as the following: i φ

L = ai + bi T + ci T ln T + di T 2 + ei T 3 + fi T −1 + gi T 7 + hi T −9

(6)

where ai , bi , ci , di , ei , fi , gi and hi are the coefficients to be optimized. In most cases only the first one or two terms of the above equation are used.

(9) SER where H(Al%,Au) is the abbreviation of (my1Al + m (Al,Au%)n SER + (my1 + ny2 )H SER . y1 and y2 are the ny2Al )HAl i i Au Au Au site fraction of the component i (i = Al and Au) in the m Aln first and the second sublattices respectively. 0 GAl , m 0 GAlm Aun ,0 GAum Aln and 0 GAum Aun represent the Gibbs m m m energies of the hypothetic and stoichiometric compounds Alm Aln , Alm Aun , Aum Aln and Aum Aun , formed when each of the sublattices is occupied by only one component Al or Au (yAl =1 or yAu =1), and they were modeled by (Al%,Au)m (Al,Au%)n Eqs. (7) and (8). E Gm is the excess Gibbs energy expressed by the following expression: E

(Al%,Au) (Al,Au%)n

m m (Al,Au%)n = y 1 y 1 (y 2 L G(Al%,Au) m Al Au Al Al,Au:Al

(Al%,Au) (Al,Au%)n

2 + yAu LAl,Au:Au m

)

2 2 1 (Al%,Au)m (Al,Au%)n + yAl yAu (yAl LAl:Al,Au (Al%,Au) (Al,Au%)n 1 + yAu LAu:Al,Au m ) (10)

3.3. Stoichiometric compounds According to the Coffinbery and Hultgren [7], AlAu and Al3 Au8 have very narrow or even unnoticeable solubility ranges. In the present optimization, AlAu, Al3 Au8 and AlAu4 phases are treated as the stoichiometric compounds. Owing to lack of experimental measurements, it is assumed that Cp = 0. The Gibbs energy per mole of formula unit

(8)

where a and b are the parameters to be evaluated in the present work.

φ

is the molar Gibbs energy of the element i (i = Al φ and Au) with the structure of φ. E Gm is the excess Gibbs energy which is expressed in Redlich–Kister polynomial:
E φ i φ Gm = xAl xAu (5) L (xAl − xAu )i

(7)

m Aun where GAl is the Gibbs energy of formation for per f mole of formula unit Alm Aun . It can be given by the following expression:

Gφm = xAl 0 GAl + xAu 0 GAu + RT(xAl ln xAl + xAu ln xAu ) + E Gφm

201

(Al%,Au)m (Al,Au%)n

LAl,Au:k

=




1 1 n (an + bn T)(yAl − yAu )

(11)

2 2 n (an + bn T)(yAl − yAu )

(12)

n=0

(Al%,Au)m (Al,Au%)n

Lk:Al,Au

=


n=0

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M. Li et al. / Journal of Alloys and Compounds 385 (2004) 199–206

where LAl,Au:k and Lk:Al,Au represent the interaction parameters between the elements Al and Au in the related sublattice while the other sublattice is occupied only by the element k (k =Al and Au). 3.4.2. ϕ(AlAu2 ) phases Since the homogeneity range of ␸(AlAu2 ) phase (␸ = ␣ and ␤) is to the left of the mole fraction value of the strict stoichiometric AlAu2 , the two-sublattice model, Al(Al,Au%)2 , is used to describe this intermediate phase. The first sublattice contains only Al and the second the random mixture of Al and Au. The Gibbs energy function of ␸(AlAu2 ) phase is as the following: ␸Al(Al,Au%)2 Gm − H␸SER Al(Al,Au%)2 ␸AlAl2

= yAl 0 Gm

␸AlAu2

+ yAu 0 Gm

2 2 + 2RT(yAl ln yAl

␸Al(Al,Au%)2

2 2 2 2 +yAu ln yAu ) + yAl yAu LAl:Al,Au

(13)

SER 2 where H␸SER Al(Al,Au%)2 is the abbreviation of (1+2yAl )HAl + ␸AlAl

␸AlAu

2 2 2 H SER . 0 G and 0 Gm are the Gibbs energies of 2yAu m Au the hypothetic compounds ␸AlAl2 and ␸AlAu2 respectively ␸Al(Al,Au%) as were modelled by Eqs. (7) and (8). LAl:Al,Au is the interaction parameter between the elements Al and Au in the second sublattice as was modelled by Eq. (12).

3.4.3. β(AlAu4 )phase In contrast to ␸(AlAu2 ) phase, the homogeneity range of the ␤(AlAu4 ) phase is to the right of the mole fraction value of the stoichiometric AlAu4 . The two-sublattice model, (Al%, Au)Au4 is used in this case. The Gibbs energy function of the ␤(AlAu4 ) phase is as the following: ␤(Al%,Au)Au4

Gm

− H␤SER (Al%,Au)Au4

␤AlAu4

1 0 = yAl Gm

␤AuAu4

1 0 + yAu Gm

1 1 + RT(yAl ln yAl

␤(Al%,Au)Au4

1 1 1 1 + yAu ln yAu ) + yAl yAu LAl,Au:Au

(14)

SER 1 where H␤SER (Al%,Au)Au is the abbreviation of yAl HAl + (4 + 4

␤AlAu

␤AuAu

1 )H SER . 0 G 4 4 yAu and 0 Gm are the Gibbs energies m Au of the hypothetic and stoichiometric compounds ␤AlAu4 and ␤AuAu4 respectively as were modelled by Eqs. (7) and ␤(Al%,Au)Au (8). LAl,Au:Au 4 is the interaction parameter between the elements Al and Au in the first sublattice as was modelled by Eq. (11).

for the Gibbs energy of the individual phases as previously described, the analysis of all the related experimental data available, and the computer-aided nonlinear regression for minimizing the square sum of the errors between the experimental data and the computed values. The experimental data from [6–9,11,12,22–29] were used in the optimization. The data from Heycock and Neville [6,9] were offered relatively large weight factors since they constructed a reasonable phase diagram over almost the entire composition range. The large weight factors were also offered to the results from [11,23] because of their good agreement with each other. In this study, the thermodynamic parameters for the liquid and the fcc phases were optimized at the first stage based on the enthalpies of mixing of liquid alloys [11,12,27–30] and the phase boundary information [6–9,11,12,23]. The parameters of the intermediate phases (Al2 Au), AlAu, ␸(AlAu2 ), Al3 Au8 , AlAu4 and ␤(AlAu4 ) were optimized subsequently. Finally all the parameters were simultaneously optimized with the integrative consideration of all the experimental data of the equilibria results and the thermodynamic information of the phases. The optimization of (Al2 Au), ␸(AlAu2 ) and ␤(AlAu4 ) was carried out in two steps. In the first, (Al2 Au), ␸(AlAu2 ) and ␤(AlAu4 ) were assumed to be stoichiometric compounds, and in the second, they were treated two-sublattice model. The parameters obtained from the first treatment were used as starting values for the second. Alm Aln m Aun The 0 Gm and 0 GAu with (Alm Aun ) strucm ␸ AlAl ture in Eq. (9), the 0 Gm 2 with ␸(AlAu2 ) structure in ␤AuAu4 Eq. (13) and the 0 Gm with ␤(AlAu4 ) structure in Eq. (14) are the hypothetical forms of the corresponding pure elements, and the parameter a of their Gibbs energy expression as shown in Eq. (8) was ensured to be a sufficiently positive value relative to their SER state. In order to reduce the number of optimizing variables, it is as(Al%,Au) (Al,Au%)n (Al%,Au) (Al,Au%)n sumed that LAl,Au:Al m = LAl,Au:Au m and (Al%,Au) (Al,Au%)

(Al%,Au) (Al,Au%)

n n LAl:Al,Au m = LAu:Al,Au m . At the beginning of the assessment, each item of the selected information was offered a certain weight factor by judgment. During the period of the optimization, the weight factors were adjusted by trail and error. The final data set was obtained until the squared sum of the errors between the experimental data and the calculated results was reduced to a certain level.

5. Results and discussion 4. Assessment procedure The thermodynamic optimization of the model parameters of the Gibbs energy expressions is an application of the calculation of phase diagram (CALPHAD) technique with the help of the PARROT module of the Thermo-Calc software developed by Jansson [34] and Sundman et al. [35]. Its procedure consists of the choice of thermodynamic models

The thermodynamic description and the optimized parameters of the Al–Au system are listed in Table 2. The phase diagram calculated by the present parameters is shown in Fig. 1(a). Fig. 1(b) and (c) are enlarged sections of Fig. 1(a). In Fig. 2, the experimental data from [6–8,11,12,22,23] are indicated with different symbols for comparison with the calculated results. The liquidus and the solidus of fcc(Au)

M. Li et al. / Journal of Alloys and Compounds 385 (2004) 199–206

203

Table 2 The thermodynamic parameters of Al–Au systema Phase

Structure model

Liquid

(Al,Au)

Fcc

(Al,Au)

(Al2 Au)

(Al%,Au)2 (Al,Au%)

Parameters 0 Lliquid

= −131996.19 + 36.42T

1 Lliquid

= 40781.83 − 1.896T

0 Lfcc

= −102335.39 + 34.18T

1 Lfcc

= 48202.11 − 12.63T

2 Lfcc

= −339.93 (Al Au)

0 GAl2 Au m

2 = 0 GAl:Au

0 fcc = 20 Gfcc Al + GAu − 109468.39 + 24.15T

(Al Au) 0 fcc = 0 Gfcc Al + 2 GAu − 34736.68 + 29.36T (Al Au) fcc 2 = 0 GAl:Al = 30 GAl + 23478.70 0 GAu2 Au = 0 G(Al2 Au) = 30 Gfcc + 30266.05 m Au Au:Au (Al2 Au) = −127363.65 + 101.80T LAl,Au:Au (Al2 Au) = −127363.65 + 101.80T LAl,Au:Al (Al2 Au) = −24092.22 + 37.21T LAl:Al,Au (Al2 Au) LAu:Al,Au = −24092.22 + 37.21T 0 GAu2 Al m

2 = 0 GAu:Al

0 GAl2 Al m

0 GAlAu m

AlAu ␥(AlAu2 )

␥(Al%,Au)(Al,Au%)2

␣(AlAu2 )

␣Al(Al,Au%)2

␤(AlAu2 )

␤Al(Al,Au%)2

0 fcc = 0 Gfcc Al + GAu − 70626.80 + 15.04T

0 G␥AlAu2 = 0 G␥(AlAu2 ) = 0 Gfcc + 20 Gfcc − 88701 + 9.25T m Au Al Al:Au 0 G␥AuAl2 = 0 G␥(AlAu2 ) = 20 Gfcc + 0 Gfcc − 15023.6 + 3.99T m Au Al Au:Al 0 G␥AlAl2 = 0 G␥(AlAu2 ) = 30 Gfcc + 46077.6 m Al Al:Al 0 G␥AuAu2 = 0 G␥(AlAu2 ) = 30 Gfcc + 12106.8 m Au Au:Au ␥(AlAu ) LAl:Al,Au2 = −197980.3 + 121.00T ␥(AlAu2 ) LAu:Al,Au = −197980.3 + 121.00T ␥(AlAu2 ) LAl,Au:Al = −11378.2 ␥(AlAu2 ) LAl,Au:Au = −11378.2 0 G␣AlAu2 = 0 G␣(AlAu2 ) = 0 Gfcc + 20 Gfcc − 93373.11 + 14.82T m Au Al Al:Au 0 G␣AlAl2 = 0 G␣(AlAu2 ) = 30 Gfcc + 64753.58 − 4.31T m Al Al:Al ␣(AlAu ) LAl:Al,Au2 = −212222.01 + 135.52T 0 G␤AlAu2 m 0 G␤AlAl2 m

␤(AlAu2 )

= 0 GAl:Au =

0 G␤(AlAu2 ) Al:Al

0 fcc = 0 Gfcc Al + 2 GAu − 93373.11 + 14.83T

= 30 Gfcc Al + 36694.67 − 1.2T

␤(AlAu )

LAl:Al,Au2 = −184104.01 + 126.06T AlAu4

0 GAlAu4 m

Al3 Au8

0 GAl3 Au8 m

␤(AlAu4 )

␤(Al%,Au)Au4

0 fcc = 0 Gfcc Al + 4 GAu − 135127.51 + 47.57T 0 fcc = 30 Gfcc Al + 8 GAu − 322472.66 + 67.55T

0 G␤AlAu4 m

␤(AlAu4 )

= 0 GAl:Au

0 fcc = 0 Gfcc Al + 4 GAu − 124300.01 + 33.86T

0 G␤AuAu4 = 0 G␤(AlAu4 ) = 50 Gfcc + 25018.07 m Au Au:Au ␤(AlAu4 )

LAl,Au:Au = −34.50T

a

In J/(mole of formula units); Temperature (T) in Kelvin. The phases with homogeneity ranges are indicated with the round brackets as (phase name).

fit well with the experiments from [6,11,23]. The calculated solubility limits of Al in fcc(Au) below 818 K are consistent with the data from [22], but lower solubility limits were reported by other investigators [8,11]. The calculated invariant reactions are listed in Table 1 and compared with the experimental results from [5,6,9,17]. The type of invariant reactions are consistent with the microstructure reported by Heycock and Neville [6] except the reaction L + ␥AlAu2 → Al2 Au5 . Because the compound

Al2 Au5 was modified to be Al3 Au8 by Okomoto [24], the reaction was changed to L → ␥AlAu2 + Al3 Au8 . The compositions and temperature of invariant reactions also fit well with the experiments [5,6,9,17] except for the eutectic reaction, L → Al3 Au8 + ␤(AlAu4 ), for which the calculated reaction temperature is 12 K higher than experimental data. The calculated enthalpies of mixing of the liquid phase at 1356 K and the experimental measurements from [11,12,27–30] are shown in Fig. 3. There exists great

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M. Li et al. / Journal of Alloys and Compounds 385 (2004) 199–206

Fig. 1. (a) The calculated Al–Au phase diagram using the present thermodynamic description; (b) and (c) enlarged sections of (a).

Fig. 2. The calculated Al–Au phase diagram, compared with the experimental data [6–9,11,12,22,23].

Fig. 3. Calculated enthalpies of mixing of liquid at 1356 K with the experimental data from [11,12,27–30].

M. Li et al. / Journal of Alloys and Compounds 385 (2004) 199–206

Fig. 4. Calculated activities of Al and Au in liquid at 1338 K with the experimental data from [11,12,27,28].

diversity among the values reported by several investigators. The experimental data measured by Hayer et al. [29] and Charquet et al. [11] are in good agreement with the present calculation. We also confirmed the conclusion suggested by Hayer et al. [29] that the enthalpies are not dependent on temperature between 1356 and 1587 K. Fig. 4 shows the activities of Al and Au in the liquid phase at 1338 K, calculated by the present work and measured by several investigators [11,12,27,28]. In Fig. 4, the calculated activities of Au agree well with the experimental data, while those of Al deviate positively from experiments. Fig. 5 shows the enthalpies of formation of compounds with the experimental data from [25,26] and the present predicted values using the Miedema mode [36]. Fig. 6 shows the calculated excess entropies of the liquid phase at 1600 K and the experimental data from [28]. The calculated entropies from literature differ widely

205

Fig. 6. Calculated excess entropy at 1600 K in the Al–Au system with experimental data from [28].

from each other. Predel and Schallner [12] gave highly positive SE , while the SE from Charquet et al. [20] were near zero over the entire concentration range. Positive and even zero excess entropies, however, are very improbable in a system with highly exothermic behavior revealing strong interaction. Therefore the entropies from Erdelyi et al. [28] are selected for comparison. Within the experimental uncertainties, all the mostly concerned experimental data are well reproduced by the present calculation.

6. Conclusions All of the experimental phase equilibria and thermodynamic data of the Al–Au system from the available literature have been critically evaluated. Within the regime of CALPHAD technique, the thermodynamic models for all the solution phases and the intermediate compounds are selected and the Gibbs energy functions are optimized. Especially, the phase Al3 Au8 in stead of Al2 Au5 is considered and the homogeneity ranges of (Al2 Au), ␸(AlAu2 ) (␸ = ␣, ␤ and ␥) and ␤(AlAu4 ) phases are reproduced. A set of consistent thermodynamic parameters for the Al–Au binary system is obtained. The calculated phase equilibria and thermodynamic properties, including the phase diagrams, the enthalpies of mixing and the activities of Au in liquid alloys, agree well with the experimental data.

Acknowledgements

Fig. 5. Calculated enthalpy of formation in the Al–Au system with the experiments from [25,26] and the present predicted values using the Miedema mode [36].

The authors would like to express their appreciation to the Royal Institute of Technology Sweden for supplying the Thermo-Calc software. This work was supported by the National Natural Science Foundation of China (No. 50371008) and the National Doctorate Fund of the State Education Ministry of China (No. 20030008016).

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