Thermodynamic assessment of the Au–Ni system

Computer Coupling of Phase Diagrams and Thermochemistry 29 (2005) 263–268 www.elsevier.com/locate/calphad

Thermodynamic assessment of the Au–Ni system Jianhua Wang a,∗ , Xiao-Gang Lu b , Bo Sundman b , Xuping Su a a Institute of Materials Research, School of Mechanical Engineering, Xiangtan University, Xiangtan 411105, Hunan, China b Department of Material Science and Engineering, Royal Institute of Technology, S-100 44 Stockholm, Sweden

Received 12 April 2005; received in revised form 15 September 2005; accepted 16 September 2005 Available online 3 October 2005

Abstract The phase diagram and thermodynamic properties of the Au–Ni system have been assessed from experimental thermodynamic and phase diagram data by means of the CALPHAD method. A consistent set of thermodynamic parameters for each phase was obtained. Good agreement is reached between the calculated and experimental results. The calculated congruent point is 1214.3 K and 42.6 at.% Ni and the critical point of the miscibility gap is 1089.5 K and 73.0 at.% Ni. c 2005 Elsevier Ltd. All rights reserved.  Keywords: Thermodynamic; Au–Ni system; Phase diagram; CALPHAD

1. Introduction The apparent simplicity of the phase diagram for the Au–Ni alloy system has stimulated much interest in this alloy, particularly in its aging behavior [1] and superparamagnetism [2]. It has also attracted much attention for many industrial purposes [3–5]. There are many thermodynamic data available for the Au–Ni systems as well as phase diagram data. But the consistency between thermodynamic data and phase diagram has not yet been checked. The spinodal decomposition in Au–Ni system has been investigated extensively by Hofer and Warbichler [6], Asai et al. [7] and Borelius [8,9]. In this work, by using proper models, a self-consistent description of the phase relations and thermodynamic properties of the Au–Ni system was derived by means of the CALPHAD technique [10].

fcc A1 phases. They were described using a substitutional solution model for which the Gibbs energy expression is: φ

φ

G φm = x Au 0 G Au +x Au 0 G Au + RT (x Au ln x Au + x Ni ln x Ni ) + E G φm φ

(1)

φ

where 0 G Au and 0 G Ni are the molar Gibbs energies of pure Au and Ni respectively with the structure φ in non-magnetic states, adopted from the work of Dinsdale [11]. The x Au and x Ni variables denote mole fraction of Au and Ni, respectively. φ R is the gas constant and T is the absolute temperature. E G m is the excess Gibbs energy, expressed as the Redlich–Kister polynomial [12] as:
φ i E φ G m = x Au x Ni L Au,Ni (x Au − x Ni)i (2) i

2. Thermodynamic models The Gibbs energies of the pure elements are described relative to the standard element reference (SER), i.e. the enthalpy of the pure elements in their stable states at 298.15 K [11]. There are only two phases in Au–Ni system: liquid and ∗ Corresponding author. Tel.: +86 732 8292213; fax: +86 732 8292210.

E-mail addresses: super [email protected], [email protected] (J. Wang). c 2005 Elsevier Ltd. All rights reserved. 0364-5916/$ - see front matter  doi:10.1016/j.calphad.2005.09.004

i Lφ Au,Ni

where are the binary interaction parameter evaluated in the present work. i Lφ Au,Ni can be temperature dependent and two terms are usually sufficient, i.e. i

φ

L Au,Ni = Ai + Bi T

(3)

where Ai and Bi are constants to be optimized. The nickel-rich fcc solid solution exhibits ferromagnetic ordering. According to Hillert and Jarl [13], the magnetic contribution to the Gibbs mg fcc + 1) f (τ ) with energy is described by G fcc m = RT ln(β

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τ = T /Tcfcc , Tcfcc is the critical Curie temperature and β fcc is the magnetic moment per mole of atoms. The term f (τ ) represents a polynomial obtained by Hillert and Jarl [9]. Tcfcc = fcc x + C x x , where T fcc is the ferromagnetic transition Tc,Ni Ni Au Ni c,Ni temperature for pure nickel and its value is 633 K, C is constant to be optimized. β fcc was assumed to decrease linearly from 0.52, the value of pure nickel. 3. Experimental information on phase diagram and thermodynamics The liquidus and solidus of the Au–Ni system were studied first by Levin [14], De Cesaris [15] and Fraenkel and Stern [16,17]. Later, Bienzle et al. [18], and Hall and Johnson [19] investigated the liquidus and solidus respectively. Esdaile and Mcadam [20] determined the activity–composition–temperature relations for both gold and nickel by application of the Margules equations and observed the phase boundaries of the system between 700 and 1725 K. Hansen and Anderko [21] reviewed the phase diagram of the system. The reviewed congruent point is at 42.5 at.% Ni and 954.8 ◦ C [21]. The result observed by Esdaile and Mcadam [20] is at 951 ◦ C. The miscibility gap was investigated firstly by Munster and Sagel [22], and Howard et al. [23]. The reviewed critical point of the miscibility gap is at 72.5 at.% Ni and 810.3 ◦ C [21]. The critical point of miscibility gap observed by Esdaile and Mcadam [20] is at 72.4 at.% Ni and 810 ◦ C. Later, Vesnin and Shebin [24] and Bienzle et al. [18] reinvestigated the miscibility gap curves. They confirmed that the effect of the onset of ferromagnetism on the phase boundaries is expected to be negligible [25], because the compositions of Au- and Ni-rich end of the miscibility gap below the apparent Tc of the two–phase alloys are very close to 0 and 100 at.% Ni, respectively. The calculated maximum displacement of the miscibility gap due to the ferromagnetic effect is only about 0.02 at.% Ni on the Au-rich branch at ∼473 K [26]. Oriani and Murphy [27] measured the enthalpies of formation of liquid Au–Ni alloys referring to liquid Au and solid Ni at 1100 ◦ C. Topor and Kleppa [28] reported the enthalpy of mixing data for the liquid alloys of Au–Ni by a Calvet-type calorimeter at 1378 K. Bienzle et al. [18] measured the integral molar enthalpies of formation of liquid Au–Ni alloys at 1373 K from their liquid components and deduced the enthalpies of formation of solid Au–Ni alloys at 1173 K from the activities of Ni. Predel and Zehnpfund [29] measured the enthalpies of solution of solid nickel in liquid gold at 1110 ◦ C in the concentration range between 0 and 42.2 at.% Ni, and the enthalpies of solution of Au–Ni solid solutions of the entire concentration range in liquid copper with the aid of a high temperature calorimeter. They obtained the enthalpies of liquid Au–Ni alloys and solid Au–Ni alloys at 1383 K from the liquid components and solid components respectively. In a later work, Oriani and Murphy [30] also measured the enthalpies of formation of solid Ni–Au alloys at 640 ◦ C by means of a differential solution calorimeter. Day and Hultgren [31] measured the enthalpy of Au–Ni alloys at 1150 K by liquid tin solution calorimetry.

Tomiska et al. [32] measured the activities of Ni in liquid Au–Ni alloys at 1820 K using the Knudsen effusion method in combination with a mass spectrometer. Berezutskii et al. [33] measured the activities of Au in liquid Au–Ni alloys at 1623 K, which deviate positively from Raoult’s law. Wang and Toguri [34] measured the activities of Ni in liquid alloys at temperatures from 1523 to 1608 K by equilibrating the alloy with the pure solid NiO under a CO + CO2 gas mixture of known partial pressure of O2 . The activities showed negative deviations from ideality, which were not used in the optimization because the results are not consistent with others. Grimsey and Biswas [35] measured the activities of Ni in Ni–Au alloys at 1450 K by use of galvanic cells with solid electrolyte, which also show a positive deviation from Raoult’s law. Sellars and Maak [36] measured the Ni activities in solid Ni–Au alloys at 1208, 1173, 1098 and 1048 K using galvanic cells with solid electrolyte. Bienzle et al. [18] measured the Ni activities in Ni–Au alloys at several temperatures using e.m.f. apparatus with an oxygen-ion conducting solid electrolyte. Seigle et al. [37] measured the Ni activities in Ni–Au alloys at 1173, 1123, 1073, 1023 and 973 K by electromotive force method. Hofer and Torkar [38] also measured the Ni activities in Ni–Au alloys at 1173, 1013 and 973 K using a galvanic cell with the solid electrolyte. All the Ni activities in solid exhibit positive deviations from Raoult’s law. The variation of the Curie temperature Tc as a function of concentration was described by Kuentzler and Kappler [39]. A linear behavior was obtained clearly for x Ni > 0.5 in their research work. The spinodal decomposition temperatures of Au–Ni alloys have been measured by Asai et al. [7] and Borelius [8,9]. 4. Assessment procedure Most of the experimental data mentioned above were used in the thermodynamic evaluation. The optimization was carried out by using Thermo-Calc [40]. Each piece of the selected information was given a certain weight by personal judgment, and changed by trial and error during the assessment, until most of the selected experimental information was reproduced within the expected uncertainty limits. The optimization was carried out step by step. The parameters for the solid phase were first optimized using the data of thermodynamic data of solid and the phase diagram data on the miscibility gap. The liquid phase was then investigated by considering the thermodynamic data of the liquid and liquidus as well as solidus. All the parameters were finally evaluated together to give the best description of the system. All evaluated parameters are listed in Table 1. 5. Results and discussion The assessed phase diagram is shown in Fig. 1. The calculated phase diagram is in good agreement with the experiments reported by [14–19] and [22–24]. The congruent point and the critical point of the miscibility gap in the system

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Table 1 The optimized parameters describing the thermodynamic properties of the Au–Ni systema liquid: 0 L Liq. = 9500 − 5.429 T Au,Ni 1 L Liq. = 1614 Au,Ni

fcc: 0 L fcc Au,Ni = 28 696 − 11.274 T 1 L fcc Au,Ni = −10 945 + 6.154 T 2 L fcc Au,Ni = 2519 Tcfcc = 633xNi − 500xAu xNi a The values are given in SI units per mole of atoms.

Fig. 2. The calculated enthalpy of formation of liquid Au–Ni alloys referring to liquid Au and solid Ni at 1378 K compared with various experimental measurements [27,28].

Fig. 1. The Au–Ni phase diagram (solid line) and spinodal line (broken line) calculated from the present thermodynamic description in comparison with experimental measurements [7–9], [14–19] and [22–24] respectively. Fig. 3. The calculated enthalpy of mixing of liquid Au–Ni alloys from liquid components at 1383 K compared with the experimental measurements [18,29].

Table 2 The congruent point and critical point in the Au–Ni system Point type

Present work

Ref. [20]

Ref. [21]

Congruent point Critical point

T, K (xNi ) 1214. 3 (0.426) 1089. 5 (0.73)

T, K (xNi ) 1224 (−) 1083 (0.724)

T, K (xNi ) 1228 (0.425) 1083.5 (0.725)

given by Esdiale and Mcadam [20] and Hansen and Anderko [21] are well reproduced by the assessment. The results are listed in Table 2. The spinodal line of the Au–Ni system was calculated from Gibbs free energy function in our assessment. It could be seen from the phase diagram that the decomposition temperatures of Au–Ni alloys agree well with most of the experimental data [7–9]. The calculated enthalpies of formation of liquid alloys from liquid Au and solid Ni are plotted in Fig. 2. Also shown in Fig. 2 are the experimental data measured by Oriani and Murphy [27], and Topor and Kleppa [28]. The assessed enthalpies of formation of liquid alloys from liquid components are plotted in Fig. 3, compared with the experimental data from Bienzle et al. [18], Predel and Zehnpfund [29]. The agreements between calculated results and the experiment data are satisfactory except some experimental data from Bienzle et al. [18].

Fig. 4. The calculated enthalpy of mixing of solid Au–Ni alloys from solid components at 1150 K compared with various experimental measurements [29–31].

Fig. 4 shows the assessed enthalpies of formation of solid Au–Ni alloys at 1150 K compared with the experimental measurements [29–31]. As can be seen, the calculation enthalpies agree well with experimental data.

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(a) At 1820 K [32].

(b) At 1450 K [35].

Fig. 6. The calculated activities of Au in liquid Au–Ni alloy at 1623 K compared with experimental measurements [33]. (Ref. state: liquid Au.)

liquid Au–Ni alloys at 1623 K with experimental measurements [33]. As can be seen, the calculated data are slightly larger than the experimental data. Fig. 7(a)–(e) show the calculated activities of Ni in solid Au–Ni alloys at 1173 K [18,36–38], 1123 K [37], 1098 K [36, 37], 1023 K [36–38], 973 K [18,37,38] together with various experimental data. The calculated activities fit well with the data measured by Bienzle et al. [18], but are lower than other experimental data [36–38]. Fig. 8 shows the calculated Curie temperature compared with the experimental measurements [39]. The calculated Curie temperatures of Au–Ni alloys agree well with the experimental data. 6. Conclusions Based on the experimental information available in the literature, the phase diagram and the thermodynamic properties in the Au–Ni system were evaluated. A consistent set of optimized thermodynamic parameters has been obtained to describe the Gibbs energies of liquid and fcc phases in this system. The calculated phase equilibria agree well with the data found in literature. Most of the experimental thermodynamic data agree well with the calculated results. Acknowledgements

(c) At 1373 K [18].

Fig. 5. The calculated activities of Ni in liquid Au–Ni alloy compared with experimental measurements. (Ref. state: liquid Ni.)

Fig. 5(a)–(c) show the calculated activities of Ni of liquid Au–Ni alloys compared with various experimental measurements at 1820 K [32], 1450 K [35] and 1373 K [18], respectively. Fig. 6 shows the calculated activities of Au of

One of the authors (Jianhua Wang) is grateful for the financial support by the China Scholarship Council and the Swedish Institute of the Swedish government for his visit to the Royal Institute of Technology, where the present work was conducted. He is also grateful for the earlier financial support of the National Natural Science Foundation of China (No. 50271059, No. 50471064) for his research work in thermodynamic computation. The authors are grateful to Dr. Huahai Mao and Dr. Lidong Teng for valuable discussion during this work.

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(a) At 1173 K [18,36–38].

(b) At 1123 K [37].

(c) At 1098 K [36,37].

(d) At 1023 K [36–38].

(e) At 1023 K [18,37,38].

Fig. 7. The calculated activities of Ni in solid Au–Ni alloy compared with various experimental measurements. (Ref. state: solid Ni.)

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Fig. 8. The calculated Curie temperature compared with the experimental measurements [39].

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