Intermetallics 11 (2003) 987–994 www.elsevier.com/locate/intermet
Thermodynamic assessment of the Au–Zn binary system H.S. Liua, K. Ishidab, Z.P. Jina,*, Y. Duc School of Materials Science and Engineering, Central South University, Changsha, Hunan, 410083, Peoples0 s Republic of China b Department of Materials Science, Graduate School of Engineering, Tohoku University, Sendai, 980-8579, Japan c State Key Lab of Powder and Powder Metallurgy, Central South University, Changsha, Hunan, 410083, People0 s Republic of China a
Received 1 January 2003; accepted 20 May 2003
Abstract The phase diagram of the Au–Zn binary system may play an important role in developing new Au-base solders. In this paper, the Au–Zn binary system has been thermodynamically assessed with the CALPHAD method. Excess Gibbs energies of solution phases, liquid, fcc, hcp, and E were formulated with the Redlich–Kister expression, while the intermediate phases were modeled with (Au,Zn)0.5:(Au,Zn)0.5 for b0 , (Au)0.6:(Au,Zn)0.2:(Zn)0.2 for a1, (Au)0.64286:(Au,Zn)0.25:(Zn)0.10714 for a3, (Au,Zn)0.15385:(Au)0.15385: (Au,Zn)0.23077:(Zn)0.46153 for g, and (Au)0.12:(Au,Zn)0.16:(Zn)0.72 for g3, and the other phases including a2, E0 , Au5Zn3, g2 and d were treated as stoichiometric compounds according to their composition ranges. Based on the reported thermodynamic properties and phase boundary data, the thermodynamic parameters of these phases were optimized, which give a reasonable agreement between thermodynamic properties and phase diagram. # 2003 Elsevier Ltd. All rights reserved. Keywords: Au–Zn binary alloy system; Thermodynamic assessment; Phase diagram
1. Introduction
2. Evaluation of reported experimental information
Low melting-point Au-base alloys may be used as soft solders in photo-electronic element packaging. Thus thermodynamic information of the related systems may provide a helpful tool to facilitate design of ideal compositions of such solders and/or to simulate evolution of microstructure of the solder during the soldering process and consequent heat-treatment. In order to get comparatively complete thermodynamic information, a thermodynamic database of the related alloy systems needs to be constructed, which involves Au, Bi, In, Sb, Sn and Zn. So far, most Au-base binary systems have been assessed including Au–In [1], Au–Sn [2], Au–Sb [3] and Au–Bi [4]. As a promising candidate additive, Zn may be introduced into these alloys in order to satisfy different property requirements in the packaging industry. However, until now no thermodynamic optimization of the Au–Zn binary system has been published. In view of this, the Au–Zn binary system is to be assessed in this paper.
2.1. Phase diagram The phase diagram of the Au–Zn binary system was reviewed by Okamoto and Massalski [5] based on the reported phase boundaries from different sources [6–10]. There are 14 condensed phases in the system: liquid, 2 terminal solutions, fcc(Au) and hcp(Zn), and 11 intermetallic phases. Structures of these phases are listed in Table 1, and details of the boundaries of these phases are available in Okamoto and Massalski [5]. After Okamoto and Massalski [5], new data were reported by Prasad et al. [11] and Ipser and Krachler [12]. The newly reported solidus and liquidus of fcc [11,12] are consistent with those reviewed [5]. However the liquidus of g and the invariant reaction involving L, b0 and g reported [12] differ from those reviewed [5]. It is difficult to say which set of experiments is more reliable. Hence the present assessment will be based on both reviewed [5] and newly reported phase boundaries [11,12]. 2.2. Thermodynamic property
* Corresponding author. 0966-9795/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0966-9795(03)00115-8
Thermodynamic properties of some phases in the Au– Zn binary system have been extensively measured by
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H.S. Liu et al. / Intermetallics 11 (2003) 987–994
using various methods, and reported results from the literature are reviewed. 2.2.1. Liquid By measuring electro-motive force (EMF), activities of Zn were determined in the temperature range from 900–1300 K by Prasad et al. [11], at 1173 K by Gerling and Predel [13], at 1023 K and 1073 K by Kameda [14], and at 1173 K by Ipser et al. [15] using the vapor pressure method. Due to high vapor pressure of Zn, the activities of Zn measured by vapor pressure method may have high accuracy, like those by EMF. If reasonable deviation is taken into account, activities of Zn reported in different sources are compatible. So all these activities of Zn can be utilized in the optimization. The activity of Au in liquid Au–Zn alloys at 1023 K was also measured by EMF by Yazawa and Gubcova [16], and deduced from partial Gibbs energy of Zn in liquid by Prasad et al. [11] and by Ipser et al. [15]. However, as can be seen later, the activities of Au calculated by Prasad et al. [11] deviate significantly from those given by Ipser et al. [15] and by Yazawa and Gubcova [16]. Because large error may result in the calculated activity of Au [11], those measured by Yazawa and Gubcova [16] are more reliable. Even so, activities of Au are not used in the present optimization. They are only used for comparison with assessed values. The enthalpy of mixing of liquid Au–Zn alloys was measured extensively, at 1040 K using high temperature calorimetry by Hayer [17], and at 1173 K using EMF by Gerling and Predel [13]. Because data given by Hayer [17] are more reliable due to the fact that calormetry is more suitable than EMF in determining enthalpy of mixing and they are newer, these data are given higher weight during optimization. 2.2.2. Fcc The activities of Au in fcc at 900 and 1000 K were extrapolated by Prasad et al. [11] from the partial Gibbs energy of Zn in fcc. Because a large error may be arise in such extrapolation, activities of Au in fcc [11] were only employed as a reference and not used in optimization. Activities of Zn were measured at 850 K by Alderdice et al. [18] using the vapor pressure method, and at 800 K by Masson [19] using atomic absorption. By calorimetry, heat of formation of fcc alloy (containing 25at.% Zn) was measured at 798 K by Carpenter et al. [20], and at 717 and 850 K for various compositions by Alderdice et al. [18]. 2.2.3. 0 The activity of Zn in b0 at 923 K was measured by Ipser et al. [15] and at 850 K by Alderdice et al. [18] using the vapor pressure method, and at 700 K by Pemsler and Rapperport [7] and at 800 K by Masson [19] using atomic absorption spectroscopy. The heat of
formation of b0 at xZn ¼ 0:5 was measured at 322 and 800 K by Carpenter et al. [20], and at a different composition at 717 and 850 K by Alderdice et al. [18] using calorimeter. 2.2.4. The activity of Zn in the g phase at 923 K was measured by Ipser et al. [15], and at 850 K by Alderdice et al. [18] using the vapor pressure method. 2.2.5. The activity of Zn in the E phase at 643 K was only measured by Anantatmula [21] using atomic absorption. No heat of formation of E was reported. 2.2.6. 1 and 2 The formation enthalpy of alloy Au0.75Zn0.25 was measured at 594 K for a1 to be 16,730J/mol, and at 322 K for a2 to be 17,061J/mol20.
3. Modeling 3.1. Solution phases Liquid, fcc, hcp and E are described as substitution solutions. Gibbs energies of these phases are formulated as follows: X
G ¼
xi 0 Gi þ RT
i¼Au;Zn
þ xAu xZn
X
xi lnðxi Þ
i¼Au;Zn n X ðxAu xZn Þ j ðjÞ LAu;Zn
ð1Þ
j¼0
where 0 G i denotes the lattice stability of element i in state , and ðj Þ LAu;Zn
¼ Aj þ Bj T þ Cj TlnðTÞ
ð2Þ
is the jth order interaction between elements Au and Zn in phase , where constants, A j , Bj and Cj are to ðj Þ be optimized. When j=0, LAu;Zn is the nearest-neighbor interaction. Additionally, although E and hcp are structurally isotypical to Mg, the lattice stabilities of Au and Zn in E status are still assumed to be that of hypothesized bcc(Au) and fcc(Zn), respectively, differing from those in hcp status, in order to simplify optimization. 3.2. Intermediate phases with solubility ranges Solubility ranges of a1, a3, b0 , g and g3 exceed 5at.%. Considering their crystal structures as listed in Table 1, they are described by using different sublattice models as follows.
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3.2.1. 0 b0 has the CsCl structure. Taking into account its homogeneity from 38 to 57at.% Zn, a two-sublattice model, (Au,Zn)0.5: (Au,Zn)0.5, is adopted. The Gibbs energy of b0 is formulated as X 0 0 YiI YjII Gi:j G ¼ i;j¼Au;Zn
"
þ 0:5RT
X
I
YiI ln Yi þ
i¼Au;Zn
X
þ
X
# II
YiII ln Yi
i¼Au;Zn 0
I I YAu YZn YiII LAu;Zn:i
i¼Au;Zn
X
þ
0
II II YAu YZn YjI Lj:Au;Zn
j¼Au;Zn
ð3Þ 0
where Gi : j (i,j=Au,Zn) represents the Gibbs energies of bcc(Au), bcc(Zn) and of the hypothetical bcc compounds Au0.5Zn0.5 and Zn0.5Au0.5, respectively. YIi and YII i are the molar fractions of element i in the 1st and 2nd sublattice, respectively. For the bcc structure, due to 0 the0 symmetry of this model, it is assumed that GAu:Zn ¼ GZn:Au ; and if Neumann–Kopp rule is adopted, then 0
0
0
bcc bcc ¼ 0:5 0GAu þ 0:5 0GZn þ A þ B T GAu:Zn
their thermo-chemical properties are hence thought to differ little, the g phase in the Au–Zn binary system may also be described as (Au,Zn)0.15385:(Au)0.15385: (Au, Zn)0.23077:(Au,Zn)0.46153. However, since a few number of sites in the 4th sublattice can be taken up by Cu atoms, and the mismatch between the radius of Au and Zn atoms is larger than that between Cu and Zn atoms, when Au substitutes for Zn in the 4th sublattice, a larger elastic energy may result because Rau > Rcu > RZn (R denotes radius of different atoms). In order to simplify the model, it is assumed that only Zn atoms take the sites in the 4th sublattice. Therefore g is described as (Au,Zn)0.15385:(Au)0.15385:(Au,Zn)0.23077: (Zn)0.46153 in this work. Then the Gibbs energy of g is formulated X YiI YjIII Gi::Au:j:Zn G ¼ i;j¼Au;Zn
þ 0:15385RT
X i¼Au;Zn
þ 0:23077RT þ
X
YiI ln YiI YjIII ln YjIII
j¼Au;Zn
X
I I YAu YZn YiIII LAu;Zn:Au:i:Zn
i¼Au;Zn
ð4Þ
þ
X
III III I YAu YZn Yj Lj:Au:Au;Zn:Zn
ð5Þ
j¼Au;Zn 0
0
The interaction parameters LAu;Zn:i and Lj:Au;Zn may 0 0 take similar form to that of liquid. A and B are parameters to be determined. 3.2.2. The g phase has the brass structure of Cu5Zn8. The Cu5Zn8 phase has been recently modeled by Ansara et al. [22] as (Cu,Zn)0.15385:(Cu)0.15385:(Cu,Zn)0.23077: (Cu,Zn)0.46153, which becomes a common model used to describe such structure. Due to the fact that Au and Cu are located in the same column in the periodic table and
where LAu;Zn:Au:i:Zn and Lj:Au:Au;Zn:Zn also take a similar
form to that of liquid. YiI and YiII are molar fractions of element i in the 1st and 3rd sublattice, respectively, Gibbs energies of the terminal members of g are expressed as follows when the Neumann–Kopp rule is assumed: hcp fcc GAu:Au:Au:Zn ¼ 0:53847 0GAu þ 0:46153 0GZn þ C1
þ D1 T
ð6Þ
Table 1 Crystal structures and thermodynamic models of condensed phases in the Au–Zn binary systema Phase
Composition (at.% Zn)
Prototype
Symmetry
Thermodynamic model
(Au) a3 a1 a2 b’ d Au5Zn3 g g2 g3 E E’ (Zn)
033 1019.5 20.528.5 24.525.5 3857 56 37.5 62.576 7576 7883.5 8489 8486 92.5100
Cu Cu3Pd Ag3Mg
Fcc orthorhombic tetragonal orthorhombic Cubic
(Au,Zn) (Au)0.64286:(Au,Zn)0.25:(Zn)0.10714 (Au)0.6:(Au,Zn)0.2:(Zn)0.2 (Au)0.75:(Zn)0.25 (Au,Zn)0.5:(Au,Zn)0.5 (Au)0.44:(Zn)0.56 (Au)0.625: (Zn)0.375 (Au,Zn)0.15385:(Au)0.15385: (Au,Zn)0.23077:(Zn)0.46153 (Au)0.25:(Zn)0.75 (Au)0.12:(Au,Zn)0.16:(Zn)0.72 (Au,Zn)a (Au)0.15:(Zn)0.85 (Au,Zn)
a
CsCl
Cu5Zn8 H3U Mg Mg
orthorhombic Cubic cubic hexagonal hcp orthorhombic hcp
In order to simplify optimization, lattice stabilities of Au and Zn in E status are assumed to be those of bcc Au and fcc Zn respectively although the E phase has same structure as hcp(Zn).
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H.S. Liu et al. / Intermetallics 11 (2003) 987–994 Table 2 Thermodynamic parameters of the Au–Zn binary system assessed in this worka
hcp fcc GZn:Au:Au:Zn ¼ 0:38462 0GAu þ 0:61538 0GZn þ C2
þ D2 T GAu:Au:Zn:Zn
¼ 0:3077
ð7Þ fcc GAu
0
þ 0:6923
hcp GZn
0
þ
C3
Liquid (Au,Zn) Liq LAu;Zn ¼ 96492:26 þ 42:71334T 3:041479TlnðTÞ
ð0Þ
Liq LAu;Zn ¼ 5576:71 þ 0:0152769T
ð1Þ
þ D3 T GZn:Au:Zn:Zn
¼ 0:15385
ð8Þ fcc GAu
0
þ 0:84615
hcp GZn
0
þ
C4
fcc(Au) (Au,Zn) fcc LAu;Zn ¼ 95112:59 þ 101:68716T 11:896693TlnðTÞ
ð0Þ
fcc LAu;Zn ¼ 452:29 þ 7:53974T
ð1Þ
þ
D4 T
ð9Þ
hcp(Zn) (Au,Zn) hcp LAu;Zn ¼ 49193:15 þ 11:77016T 3:351968TlnðTÞ
ð0Þ
hcp LAu;Zn ¼ 21680:40
ð1Þ
fcc here Ci and Di are constants to be optimized, and 0 GAu 0 hep and GZn are the lattice stabilities of Au in fcc status and Zn in hcp status, respectively.
3.2.3. 1, 3, and 3 a1 is an Ag3Mg-type tetragonal phase. However the location of atoms in the lattice is not clear. Only taking into account the homogeneity of this phase, we adopt the model, (Au)0.6:(Au,Zn)0.2:(Zn)0.2, to describe it. a3 has the Cu3Pd-type structure with orthorhombic symmetry. When the atomic locations in the lattice of a3 are considered, a3 is described as (Au)0.64286:(Au,Zn)0.25:(Zn)0.10714. The phase g3is of hexagonal symmetry with the atomic locations in the lattice unknown, so a model of g3 is assumed here as (Au)0.12:(Au,Zn)0.16:(Zn)0.72 to simulate the homogeneity range from 78 to 83.6at.% Zn. Gibbs energies of these phases are given as
hep fcc a3 GAu:Au:Zn ¼ 0:89286 0 GAu þ 0:10714 0 GZn 9311:19 þ 2:57814T hep fcc a3 GAu:Zn:Zn ¼ 0:642286 0 GAu þ 0:35714 0 GZn 22289:48 þ 5:43904T a3 LAu:Au;Zn:Zn ¼ 7219:33 0 þ 0:58907T 0
a1 (Au)0.6:(Au,Zn)0.2:(Zn)0.2 hep fcc a1 GAu:Au:Zn ¼ 0:8 0 GAu þ 0:2 0 GZn 15608:02 þ 2:24721T hep fcc a1 GAu:Zn:Zn ¼ 0:6 0 GAu þ 0:2 0 GZn 24122:73 þ 6:25277T a1 LAu:Au;Zn:Zn ¼ 6343:17 þ 3:24779T 0
a2 (Au)0.75:(Zn)0.25 hep fcc a2 GAu:Zn ¼ 0:75 0 GAu þ 0:25 0 GZn 19009:0 þ 3:07438T
b’ (Au,Zn)0.5:(Au,Zn)0.5 0
hep fcc GZn:Au ¼ GAu:Zn ¼ 0:5 0 GAu þ 0:5 0 GZn 262274:87 þ 1:98614T 0
0 LAu;Zn:Au 0 LAu:Au;Zn
0
¼ LAu;Zn:Zn ¼ 12308:84 0 þ 0:001471T
¼
0 LZn:Au;Zn
¼ 15420:59 þ 3:62717T
d (Au)0.44:(Zn)0.56 0 hep GAu:Zn ¼ 0:44 0 G fcc Au þ 0:56 GZu 24752:6 þ 1:03656T
g (Au,Zn)0.15385:(Au)0.15385:(Au,Zn)0.23077:(Zn)0.46153
IIp0 ! IIp0 ! G ! ¼ YAu GAu:Au:Zn þ YZn GAu:Zn:Zn X þ bRT YiII ln YiII
0 hep GAu:Au:Au:Zn ¼ 0:53847 0 G fcc Au þ 0:46153 GZn 19637:07 þ 1:031134T 0 hep GZn:Au:Au:Zn ¼ 0:38462 0 G fcc Au þ 0:61538 GZn 11525:07 þ 0:17828T 0 hep GAu:Au:Zn:Zn ¼ 0:3077 0 G fcc Au þ 0:6923 GZn 21018:35 þ 0:50509T
i¼Au;Zn
þ
a3 (Au)0.64286:(Au,Zn)0.25:(Zn)0.10714
0 hep GZn:Au:Zn:Zn ¼ 0:15385 0 G fcc Au þ 0:84615 GZn 11851:15 þ 1:60228T
II II ! YAu YZn LAu:Au;Zn:Zn
ð10Þ
LAu;Zn:Au:Au:Zn ¼ LAu;Zn:Au:Zn:Zn ¼ 4474:2 LAu:Au:Au;Zn:Zn ¼ LZn:Au:Au;Zn:Zn ¼ 8260:71
g2 (Au)0.25:(Zn)0.75 0
! GAu:Au:Zn
0
! GAu:Zn:Zn
and are Gibbs energies of the here terminal members of o (denoted as a1, a3, and g3, respectively), which are expressed as
2 0 hep GAu:Zn ¼ 0:25 0 G fcc Au þ 0:75 GZu 19681:56 þ 1:32858T
g3 (Au)0.12:(Au,Zn)0.16:(Zn)0.72 3 0 hep GAu:Au:Zn ¼ 0:28 0 G fcc Au þ 0:72 GZn 19681:56 þ 1:32858T 3 0 hep GAu:Zn:Zn ¼ 0:12 0 G fcc Au þ 0:88 GZn 19681:56 þ 1:32858T
0
! GAu:Au:Zn
fcc GAu
0
hcp GZn
0
D1! T
ð11Þ
hcp fcc ! GAu:Zn:Zn ¼ a 0GAu þ ðb þ cÞ 0GZn þ C2! þ D2! T
ð12Þ
¼ ð a þ bÞ
þc
þ
C1!
þ
3 LAu:Zn:Zn ¼ 0:3445:87
E (Au,Zn) 0
where a, b and c are sublattice ratios in the models of a1, a3, and g3, and Cj! and Dj! are also to be optimized. All interaction parameters in these models take similar form to that of liquid. 3.2.4. Line compounds According to the phase diagram [5], a2, g2, E0 , d and Au5Zn3 have narrow solubility ranges, so they are treated as line compounds. According to the composi-
ð0Þ
" LAu;Zn ¼ 82852:97 þ 26:40577T " LAu;Zn ¼ 58047:97 20:17125T
ð1Þ
E 0 (Au)0.15:(Zn)0.85 hcp fcc GAu:Zn ¼ 0:15 0 GAu þ 0:85 0 GZn 12620 þ 0:166T 0
Au5Zn3 (Au)0.625:(Zn)0.375 hcp fcc Au 5 Zn 3 GAu:Zn ¼ 0:625 0 GAu þ 0:375 0 GZn 24049:09 þ 4:01927T 0 0 fcc a 0 G Au ¼ 4250 1:1T þ 0 G hcp Zn , G Zn ¼ 2969:82 1:56968T þ G Zn , 0 hcp where 0 G fcc and G . For other solution phases, lattice stabilities of pure Zn Au elements, Au and Zn, are those of same status of the studied phase, which 0 fcc 0 bcc 0 hcp are taken from Dinsdale [23]. In summary, 0 G Liq Au , G Au , G Au , G Au , 0 Liq 0 hcp 0 bcc 0 fcc G Zn , G Zn , G Zn and G Zn are taken from Dinsdale [23].
H.S. Liu et al. / Intermetallics 11 (2003) 987–994
tions, formulae of these phases are given as Au0.75Zn0.25, Au0.25Zn0.75, Au0.15Zn0.85, Au0.44Zn0.56, and Au0.625Zn0.375, respectively. Under the assumption of the Neumann- Kopp rule, Gibbs energies of these compounds may be expressed as hcp fcc G Aud Zne ¼ d 0GAu þ e 0GZn þ E þ FT
ð13Þ
where d and e are atomic ratios in the formula; E and F are also parameters to be optimized.
991
phases has been obtained as listed in Table 2. Good agreement has been reached between calculation and reported experimental data as demonstrated later. 4.1. Thermodynamic property 4.1.1. Liquid Fig. 1 shows the enthalpy of mixing of liquid, demonstrating a good agreement between calculated values and experimental data given by Hayer [17] but it deviates from those reported by Gerling and Predel [13] in the composition range from 40 to 60at.% Zn. Even
4. Results and discussion The lattice stabilities of elements Au and Zn in different states are taken from the database for pure elements given by Dinsdale [23]. By using CALPHAD method, the Au–Zn binary system has been assessed and a set of thermodynamic parameters of various Table 3 Heats of formation of some phases in the Au–Zn binary system Phase
Atomic percent of Zn
Temperature (K)
H (J/mol)
Reference
fcc(Au)
25.0 25.0 50.0 50.0 50.0 50.0 25.0 25.0 25.0 25.0
798 798 322 322 800 800 594 594 322 322
14,411 15,268 25,711 26,274 25,816 25,810 16,730 16,944 17,061 19,009
[20] this [20] this [20] this [20] this [20] this
b’
a1 a2
work work work work work
Fig. 2. Calculated activity of Zn in liquid Au–Zn alloys in comparison with experimental data (Ref. state: liquid Zn).
Fig. 1. Heat of mixing of liquid: comparison of calculated values with experimental data.
Fig. 3. Calculated activity of Au in liquid Au–Zn alloys compared with experimental data (Ref. state: liquid Au).
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H.S. Liu et al. / Intermetallics 11 (2003) 987–994
so, the calculated values are acceptable. In addition, assessed enthalpy of mixing of liquid appears to be weakly temperature dependent. Such dependence is usually observed in Zn-based and other low meltingpoint systems, e.g. Sn-base systems. The activities of Zn in liquid alloys are also assessed as illustrated in Fig. 2, and those of Au are calculated as shown in Fig. 3. Clearly the assessed activities of Zn are in good agreement with the corresponding data at different temperatures from different resources, while calculated activities of Au are only in good agreement with
those reported by Ipser et al. [15] and by Yazawa and Gubcova [16] but do not match the extrapolated values obtained by Prasad et al. [11]. It should be noted here that only activities of Zn were utilized in the optimization because they were measured directly by EMF or vapor pressure and were much more reliable. Even so, the predicted activities of Au in liquid Au–Zn alloys are in agreement with those extrapolated by Ipser et al. [15] and those experimentally determined values by EMF by Yazawa and Gubcova [16]. Hence activities of both Au and Zn in liquid are reasonable.
Fig. 4. Activity of Au in fcc alloys: comparison between calculated values and experimental data (Ref. state: fcc Au).
Fig. 6. Calculated activity of Zn in solids at 700, 900 and 923 K in comparison with experimental data (Ref. state: hcp Zn).
Fig. 5. Calculated activity of Zn in solids at different temperatures compared with experimental data (Ref. state: liquid Zn).
Fig. 7. Heats of formation of solid phases: comparison between calculated values and experimental data referred to fcc Au and hcp Zn.
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H.S. Liu et al. / Intermetallics 11 (2003) 987–994
4.1.2. Solid The calculated values of activity of Au do not fit well to the extrapolated data reported by Prasad et al. [11] as illustrated in Fig. 4. However, predicted activities of Zn in all solid phases (shown in Figs. 5 and 6) demonstrate excellent agreement with almost all experimental data at different temperatures. Even so, calculated activities of both Au and Zn in all solids including fcc are acceptable if deviations in extrapolated values of the activity of Au [11] are taken into account. The heats of formation of these solids at different temperatures are further calculated to compare with corresponding experimental data [20] as listed in Table 3 and shown in Fig. 7. It is clear that almost all calculated data fit well to reported experimental data with only one exception for a2. This is presumably due to the simple stoichiometric compound model in this study. When more reliable information about a2 can be obtained, relatively complete optimization will be possible for a2.
Fig. 8. Phase diagram of the Au–Zn binary system in the present work.
Table 4 Invariant reactions in the Au–Zn binary system Reaction
Atomic Percent of Zn in phases in order
Temperature (K)
Reaction type
Reference
(Au)+a1)a3
18.0 21.5 19.0 16.0 22.0 18.6 25.0 25.6 25.0 25.0 29.5 27.0 38.0 29.2 27.5 38.3 36.0 33.5 39.5 34.0 – – 36.0 34.5 39.5 29.0 40.5 37.5 29.1 41.5 37.5 50.0 48.5 49.1 52.5 65.5 56.0 54.5 64.1 56.0 63.0 57.0 62.5 61.5 btq btq 62.5 57.2 64.6 84.5 76.0 79.5 82.1 74.1 79.3 74.0 78.0 75.0 74.2 79.0 75.0 92.0 83.5 88.0 91.7 83.3 87.5 – 82.5 – – – 85.0
573 572 693 681 543 540 676 670 956 957 955 573 578 1024 1031 1008 453 455 927 932 946 858 855 793 794 763 763 443 458 711 718 954
Peritectoid Peritectoid Congruent Congruent Congruent Congruent Eutectoid Eutectoid Eutectic Eutectic Eutectic Peritectoid Peritectoid Congruent Congruent Congruent Peritectoid Peritectoid Peritectic Eutectic Eutectic Peritectic Peritectic Peritectoid Peritectoid Peritectic Peritectic Peritectoid Peritectoid Peritectic Peritectic Congruent
[5] this work [5] this work [5] this work [5] this work [5] [7] this work [5] this work [5] [7] this work [5] this work [5] [7] this work [5] this work [5] this work [5] this work [5] this work [5] this work this work
(Au))a1 a1)a2 (Au))a1+b’ L)(Au)+ b’
a1+b’)Au5Zn3 L)b’
b’+g)d L +b’ )g (L)b’+g)
L+g)g3 g+g3)g2 L+g3)E E+g3E’ L+E)(Zn) Lg
96.0 89.0 92.5 95.8 89.8 94.8 66.7
994
H.S. Liu et al. / Intermetallics 11 (2003) 987–994
assessed phase diagram of the Au–Zn binary system in this work is acceptable.
5. Conclusion Thermodynamic assessment of the Au–Zn binary system has been performed based on reported thermodynamic properties and phase boundaries. By considering the homogeneities and crystal structures of all phases, different thermodynamic models are adopted for various phases. Through the CALPHAD method, reasonable consistency is reached between the calculated and experimental data, and a set of parameters describing all phases has been obtained.
Acknowledgements Fig. 9. Comparison of calculated phase diagram of the Au–Zn binary system with experimental boundaries.
4.2. Phase diagram All invariant reactions occurring in this system are calculated as listed in Table 4. It can be seen that most reactions were well reproduced with two exceptions. Firstly, according to Okamoto and Massalski [5], the g phase is formed through a peritectic reaction: L+b0 )g, which was deduced from the liquidus of g measured by Vogel [10], but was not confirmed by DTA results [12]. In light of Ref. [12], a eutectic type, L)b0 +g, is proposed. The present calculation supports the latter type of reaction, i.e. L)b0 +g. Secondly, the reaction E)g3+E0 given by Okamoto and Massalski [5] is doubtful. In fact, it might be more reasonable to attribute this reaction to g3+E)E0 with temperature lowering when considering the phase boundaries of g3, E and E0 measured by Pearson [6]. If the type E) g3+E0 is true, E0 must be richer in Zn than E when such a reaction happens. Unfortunately compositions of E0 and E do not show such characteristics [5]. Fig. 8 gives the phase diagram of the Au–Zn binary system assessed in this work, and comparison of calculated phase diagram with reported experimental boundaries is illustrated in Fig. 9. Apparently, except for the boundaries of the a2 and g phases, most phases are well reproduced. This has partly resulted from simplification of a2 and g2 to stoichiometric compounds. Although the boundaries of g3, especially g2+g3/g3, has not been well optimized, it is still acceptable at present because sufficient information about this phase is not available. In summary, considering the consistency between thermodynamic properties and phase relations, the
One of the authors, H.S. Liu, would like to thank for the support (Project No.76089) from Scientific Research Foundation of Central South University, ChangSha, Hunan, People0 s Republic of China, and the support from Grant-in-aids for Scientific Research from Ministry of Education, Science, Sports and Culture, Japan. Helpful suggestions from Prof C.T. Liu is also appreciated.
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