Thermodynamic reassessment of Au–Pt–Sn system

Au–Pt–Sn alloys are a novel class of materials with promising catalytic properties. This study provides updated information on phase equilibrium structures and thermodynamics of the Au–Pt–Sn ternary system. The formation enthalpies of Au–Sn and Pt–Sn binary subsystems were predicted by first principles calculations and these values were further refined by CALPHAD method. The results obtained accurately reproduced the experimental data. The reassessed phase diagram of the Au–Pt–Sn ternary system accurately described the phase composition of several Au–Pt–Sn alloys, which is essential for further modifications of these materials.


Introduction
Due to excellent physicochemical and biological properties, Au-Pt-based alloys are widely applied in microelectronics, catalysis, and biomedical fields. Among these materials, Au-Pt bimetallic catalysts draw particular attention in recent years [1,2]. Pt-Sn catalysts are highly active materials applied for catalytic reforming, electrocatalytic oxidation, and catalytic dehydrogenation of alkanes [3,4]. However, the main problems with these catalysts are low conversion rate and easy deactivation. Recent studies showed that the addition of Au in Pt-Sn alloys using a volume immersion method results in ternary Au-Pt-Sn catalysts with improved catalytic activity [5]. To find the optimum composition of a catalyst, the first step is the analysis of a phase diagram to determine all phases in the system and how the phases change with temperature and composition. Afterward, the thermodynamic parameters of each phase should be determined. This paper reassesses Au-Sn and Pt-Sn binary systems and uses these data for the reconstruction of the ternary Au-Pt-Sn system. The predicted data are compared with the experimental results for several Au-Pt-Sn alloys.

Literature review 2.1. Binary Au-Pt system
The phase diagram of Au-Pt system is highly complex due to the presence of a miscibility gap in a solid solution phase and the ambiguous shape of liquidus and solidus line [6]. Previous study found that the critical point of the miscibility gap in this system lies at 61 at.% Pt and at 1533 K, and that the shape of miscibility gap is highly asymmetric due to differences in enthalpies of formation in a solid state [7]. The cooling of Au-Pt alloy via miscibility gap results in a spontaneous separation into Au-rich and Pt-rich phases. Moreover, at 1223 K this alloy forms a single-phase region on the phase diagram between the miscibility gap and the solidus line [8]. This phase corresponds to the thermodynamically stable solid solution where the atoms are randomly positioned in the lattice. In another study by Xu et al [9], the phase diagram of a binary Au-Pt system was reevaluated using the combination of CALPHAD method and the most recent experimental data. In addition, the Gibbs free energies of face-centered cubic (FCC) and liquid phase have been studied using the Redlich-Kister mixing model. To accurately model the thermodynamic (TD) quantities of a solid phase and predict the experimental phase equilibrium data, the authors included the activity coefficients and the mixing enthalpy along with the constraints imposed by the Third Law of TD. This model revealed that the miscibility gap is slightly shifted to the Au-rich side compared with [7], with the critical point at about 1473K and Au-56% Pt (figure 1). Some TD data of binary Au-Pt system are listed in table 1.

Binary Au-Sn system
The phase diagram and thermodynamic (TD) data of binary Au-Sn system have been modeled by Chevalier [10], Liu et al [11], and Vincent Grolier [12] using the CALPHAD method. The work of Chevalier [10] was eliminated from further considerations in multicomponent systems as it did not use the data from Scientific Group Thermodata Europe (SGTE) unary compilation. Some shortages of the valuable work of Liu et al [11]    were clarified in Grolier et al [12] and Dong et al [13]. On the other hand, the results of Grolier's work [12] have been reassessed in [11] and [13] by taking into account the additional experimental data. The phase diagram of Au-Sn system reported in [11] was modified by Dong et al [13] using the ab initio method for the calculation of the enthalpies of formation of several phases. Furthermore, the work of Dong et al [13] provided more information on how liquid phase mixing enthalpy depends on the temperature of the optimization process. The TD parameters of Au-Sn system are given in table 2.
Other authors also studied the formation enthalpies (ΔH f ) of various stoichiometric Au-Sn systems. The ΔH f values obtained by Liu et al [11] are somewhat different from the experimental ones. This discrepancy is most pronounced for AuSn 2 which has a lower ΔH f value compared with the experimental one. Dong et al [13] also constructed a TD model for the Au-Sn system but these predictions were rough and significantly different from the experiment. Therefore, a novel methodology for the determination of ΔH f is presented in this study, where first principles predictions have been used as input values followed by the optimization of the weight of each phase.
Dong et al [13] calculated the ΔH f values of NiAs-type AuSn, AuSn 2 and AuSn 4 by ab initio method in order to evaluate the correlations in the binary systems and extrapolate data to ternary system. The calculated ΔH f of AuSn is −18.77 kJ mol −1 . This result deviates from the experimental value of −14.88 kJ mol −1 . The main reason for this deviation is an inconsistent selection of reference states. The experimental values in the previous papers selected diamond-type Sn as the reference state, while Dong et al [13] used body-centered tetragonal (BCT)-type Sn as the reference state to calculate the formation enthalpy. In order to compare the accuracy of two results, Dong et al [13] took BCT-type Sn as the reference state and the experimental value of AuSn at 78K was set to −15.69 kJ mol −1 but there was still a certain deviation from the calculated value of −18.77 kJ mol −1 . The reason for this deviation is further analyzed. Some studies [10] show that NiAs-type AuSn is a non-stoichiometric compound, but they do not consider the vacancies in the lattice or the substitution between atoms in the ab initio calculation process, and only build a simple atomic model due to the limited computing power. This is most likely the main reason for the observed differences between the calculated and the measured value of ΔH f for AuSn. Therefore, Dong et al [13] have taken the calculated enthalpy of formation as the initial value in the Table 3.

Phase
Experimental NiAs-type AuSn  process of Au-Sn optimization and set a small weight for these values to reduce the impact of calculation error on the optimization results. The formation enthalpy was finally optimized by Dong et al [13] and the results are listed in table 3. It can be seen from table 3 that the optimized ΔH f values of AuSn are very close to the experimental results. The phase diagram of Au-Sn system optimized by Dong et al [13] and compared with the data of Liu et al [11] is shown in figure 2. The diagram reveals the increase of decomposition and formation temperatures of HCP phase, which indicates that its stability decreased. Also, the formation temperature of AuSn 4 is decreased. The thermodynamic parameters predicted for several alloy phases are shown in table 2. The optimization process and the obtained results of two abovementioned models are analyzed and compared in detail. Due to the rough selection of the calculation model by Dong [13], the predicted formation enthalpies are quite different from the experimental values. The optimization parameters by Liu [11] are selected more precisely but the formation enthalpy of each compound still deviated from the experimental values. Therefore, the aim of this study was to use the results of high-accuracy first principles calculations as the input, fine-tune the thermodynamic parameters of Liu et al [11], re-optimize the thermodynamic data of Au-Sn binary system, and extrapolate to the ternary system.

Binary Pt-Sn system
The phase diagram of a binary Pt-Sn system optimized by Su et al [14] includes miscibility gap of the liquid phase. Recalculation of phase diagram in Pandat software revealed demixing of the liquid phase in the Sn-rich region above 900°C. This type of inverted miscibility gap of the liquid phase is not physically meaningful and has never been observed experimentally; the experimental phase diagram published by Su et al [14] did not show this artifact. However, this type of artifact has been observed in other systems and its origin is described in more detail in the literature [15]. A comprehensive thermodynamic (TD) characterization of the Pt-Sn system in  Table 4. TD data of Pt-Sn system. Reprinted from [16], Copyright (2008), with permission from Elsevier.

Phase type
Phase Thermodynamic parameters CALPHAD software has been described by Vincent Grolier [16]. Special attention was given to the artifacts observed in [14]. This reassessment was based on a critical evaluation of published experimental data on phase equilibria and TD properties of alloys. The formation of strong PtSn associates in the liquid phase was applied in model construction, and the possibility for short-range ordering or cluster formation was considered. The solution phase (Pt) was treated as a substitutional solution, which means that there was a possibility for the formation of intermediate Pt 3 Sn, PtSn, Pt 2 Sn 3 , PtSn 2 , PtSn 4 phases in a stoichiometric ratio. The absolute entropy and the entropy of fusion of intermetallic compounds were taken into consideration for the correct assignment of TD parameters. The phase diagram of Pt-Sn system reassessed by Grolier is shown in figure 3. Five intermetallic compounds identified in the system are listed in table 4.

Ternary Au-Pt-Sn system
The isothermal section of Au-Pt-Sn phase diagram in the Sn-rich region (50 at.% Sn) at 400°C was studied by Alexandra Neumann Torgersen [17]. The results given in figure 4 indicate the presence of a limited solidsolubility with the exchange between Au and Pt in the majority of binary phases. On the other hand, substantial homogeneity ranges are observed for AuSn and Pt 2 Sn 3 . The Au-to-Pt replacement is possible for up to 50% of gold in the AuSn phase, and Pt-to-Au exchange is allowed in Pt 2 Sn 3 phase until Pt content reaches 20%. Moreover, a new, ternary AuPt 2 Sn 4 phase is observed in the phase diagram and this phase was homogeneous between Au 137 Pt 293 Sn 570 and Au 196 Pt 241 Sn 563 .  Dong [18] reevaluated the TD description of the Au-Pt-Sn ternary alloy by remodeling the ternary compound, AuSn, PtSn, and the solubility of the third element in the corresponding binary phase. The authors calculated the isothermal sections of Au-Pt-Sn system at 150°C and 320°C and experimentally studied Au-20 wt%Sn-Pt reaction couples. Based on negligible changes in the microstructure of aged samples, it was concluded that the Au-20 wt%Sn-Pt system is stable at 150°C. The phase diagram reassessed by Dong [18] is given in figure 5 and the corresponding thermodynamic parameters are listed in table 5.
However, the Au-Pt-Sn phase diagram, particularly a part with low Au content (below 20 at.%) needs an additional investigation due to the lack of data about the high-temperature isothermal section of Au-Pt-Sn system and the influence of alloy components on the spinodal decomposition of Au-Pt system.

Calculation methods and thermodynamic modeling
In this study, the properties of solid-state species were calculated using density functional theory (DFT) implemented in the CASTEP module of Materials Studio 2016 software [19]. For the correct treatment of the exchange-correlation energy of electron-electron interactions, PW91 generalized gradient approximation (GGA) functional was used [20]. In the calculations, plane wave basis sets has been applied, and the kinetic energy cut-off was set to 380 eV for Au-Sn systems and 350eV for Pt-Sn systems. SCF convergence limit was 5.0×10 −7 eV/atom. Thermo-Calc and Pandat software were applied for the calculation and optimization of a phase diagram.

Pure element
The TD data of pristine Au, Pt, and Sn were obtained from the SGTE pure component database.

Liquid phase
Thermodynamics of the liquid and solution phase of Au-Pt-Sn ternary system is described using a substitutional solution model shown in (1): The excess G can be calculated according to (2): Table 5. TD parameters of Au-Pt-Sn system. Reprinted from [18], Copyright (2016), with permission from Elsevier.

In this equation,
The L θ terms represent binary (Au-Pt, Au-Sn, and Pt-Sn) or ternary (Au-Pt-Sn) interaction parameters of a solute phase. The ternary interaction parameter can decompose to the contributions of Au-rich, Pt-rich, and Snrich terms as represented in (3):

Intermetallic compounds
According to the literature data [18], solid-state structure is complex due to partial solid solubility of Au and Pt. In this case, the thermodynamics of binary intermetallic compounds in the ternary Au-Pt-Sn system can be determined from the sublattice model (Au,Pt) m :(Sn) n . The Gibbs free energy of this system can be calculated from the equation (4): , : , :

Ternary compound
The molar Gibbs free energy of ternary compound τ(AuPt 2 Sn 4 ) can be calculated from (5): Au Pt Sn Au

Results and discussion
The formation enthalpies (ΔH f ) of various intermetallic components are required for the optimization of a ternary phase diagram of Au-Pt-Sn. The crystal structure parameters and ΔH f are predicted using DFT The PARROT program within Thermo-Calc software is applied for further optimization of Au-Sn and Pt-Sn binary intermetallic systems to obtain agreement with the experiment for the ternary Au-Pt-Sn system. In the beginning, each ΔH f obtained either by ab initio calculations or taken from the literature is given a certain weight based on its importance and reliability. These weights change during the optimization until the predicted values are within the estimated experimental error range.   Other authors also studied the formation enthalpies of various stoichiometric Au-Sn systems. The ΔH f values obtained by Liu [11] are somewhat different from the experimental values. This discrepancy is most pronounced for AuSn 2 with a lower value compared with the experimental one. Dong [13] also constructed a TD model for the Au-Sn system but these predictions were rough and significantly different from the experiment. Therefore, the novel methodology for the determination of ΔH f is presented in this study, where first principles predictions served as input values and the appropriate weights of each phase were optimized. Because of the close relationship between HCP on one side and AuSn and Au 5 Sn on the other side, all three phases were optimized. The comparison between the optimized ΔH f values from this work and the previous literature reports for AuSn and Au 5 Sn is shown in figure 6. It should be noted that the optimized values for two binary compounds were in excellent agreement with the experiment (table 6). The results of this study for Au 5 Sn are lower than those of Liu and Dong [11,13], and the optimized ΔH f for AuSn 2 and AuSn 4 are between the values reported in these two studies. Therefore, the methodology applied in this study provided ΔH f values that better reproduce experimental data compared with the previous works [11,13].
The other optimized TD quantities of the Au-Sn system are given in table 7. Figure 6 shows a good agreement between the optimized phase diagram and the experimental values for the Au-Sn system. This graph also shows that the formation temperatures of Au 5 Sn and AuSn 4 are lower than the values found by   Liu [11], suggesting their stability at a lower temperature. The comparison between the optimized formation enthalpies and experimental values for various Au-Sn components (figure 7) further explains this result. The same methodology was applied for the optimization of thermodynamic quantities and the construction of phase diagram for a Pt-Sn binary system. The results are presented in table 8 and figure 8. Excellent agreement with the experimental phase diagram [16] confirms the reliability of calculated formation enthalpies.
The first principles-calculated ΔH f of various Pt-Sn components and the values refined by CALPHAD method are given in table 9. Very good agreement between two sets of data is observed, which confirms that the DFT results are a good starting point for further optimization.
As can be seen from figure 9, the optimized formation enthalpies of different Pt-Sn compounds are generally consistent with the previous literature reports [16].
After successful optimization of Au-Sn and Pt-Sn binary systems, we continued with the optimization of interaction parameters of the ternary system using Pandat software. The reassessment of Au-Pt-Sn system was done using the experimental data reported in literature [24]. The calculated TD parameters of Au-Pt-Sn alloys are listed in table 10.  The first step of ternary system optimization was to calculate the isothermal sections of Au-Pt-Sn system at 400°C and 700°C. When the calculated phases were approximately consistent with the experiment, the data on invariant reactions were optimized and fitted into the experimentally determined vertical sections. The result of this model is a set of self-consistent TD quantities that describe the system within the entire composition range. Starting from the data in table 10, vertical sections of the Au-Pt-Sn system were calculated at two temperatures and compared with the experimental values. Figure 10(b) shows that the optimized equilibrium junction lines of two-phase and three-phase regions (red line) for the system at 700°C match well the experimental data. The slight deviation was found only for the liquidus line most probably owing to partial oxidation of liquid observed in DTA analysis.  The isothermal section of the Au-Pt-Sn system at 400°C given in figure 11 shows good matching between the optimized and the experimental equilibrium junction lines for the two-phase and three-phase region near ternary phase τ (orange circle). Moreover, each of the phases fits well with the experimental data ( figure 11(b)).
To reproduce the vertical sections and construct the Au-Pt-Sn ternary phase diagram, we chose the alloy composition that matches the experimental data [24]. The atomic percentage of Au is fixed at 16%, and the composition of Pt and Sn varied between 0 and 84%. According to the results shown in figure 12, the calculated phase composition of alloy #1 is FCC+FCC+Pt 3 Sn, which is in line with the experimental data [24]. The predicted vertical sections for alloys 2-5 were also close to the experimental data, confirming the reliability and accuracy of the Au-Pt-Sn phase diagram optimized in this study.

Conclusions
This study provides new insights into the equilibrium phase structures and the character of phase transitions of the Au-Pt-Sn ternary system. Thermodynamics of binary Au-Sn and Pt-Sn subsystems is reassessed through the combination of first principles calculations and CALPHAD optimization. These data were further utilized to construct the optimized phase diagram of a ternary alloy. The optimized formation enthalpies were in better agreement with the experimental data compared with the previous studies [11][12][13]. The reassessed Au-Pt-Sn phase diagram is essential for further improvement of these alloys as catalysts and functional materials. Besides, this study provides a new methodology for the thermodynamic reassessment of other technologically important ternary alloys.