TherModynaMIc re-aSSeSSMenT of The al-Sn-Zn Ternary SySTeM

In this paper, a thermodynamic re-assessment of the Al-Sn-Zn ternary system was performed by means of the CALculation of PHAse Diagram (CALPHAD) approach. The thermodynamic descriptions of the binary Al-Sn, Al-Zn, and Sn-Zn systems from the literature were directly adopted, and the newly reported experimental phase equilibria, enthalpies of mixing, and activities of Al in the ternary liquid phase were taken into account. A set of self-consistent thermodynamic parameters for the ternary Al-Sn-Zn system were finally obtained. A comprehensive comparison between the presently calculated phase equilibria/thermodynamic properties and the experimental data indicates that the present thermodynamic descriptions of the ternary Al-Sn-Zn system show very good agreement with most of the experimental data. The further direct comparison with the calculated results due to the previous assessment demonstrates that a significant improvement was achieved by the present assessment though fewer ternary interaction parameters were utilized.


Introduction
The alloy systems containing lead (Pb) have been generally used as solders in electronics due to their low cost, superior mechanical properties, and excellent physical and chemical performances [1]. However, the Pb containing materials have been restricted by legislation worldwide because of their harmfulness to the environment and human health [2,3]. In the recent years, development of the lead-free solder materials has attracted more attention among researchers [4][5][6][7][8][9][10]. To replace conventional Pb-Sn solders, the new lead-free solders should meet some requirements, such as the excellent electrical conductivity, optimal melting temperature, as well as good wetting joining surfaces [11]. Additional properties of the solder materials, such as high strength, corrosion resistance, and low cost have to be considered in design of the new lead-free solders [12,13]. Among all the lead-free candidates, the melting temperature of Sn-Zn system (472.15 K) is very close to the eutectic temperature of Sn-Pb (456.15 K) [14]. In addition, the Sn-Zn solders have better mechanical strength than the conventional Sn-Pb solders [15]. However, Zn is well known for the problems related to wettability and corrosion and is very prone to oxidation [16]. The addition of aluminum can improve the corrosion resistance of the binary Sn-Zn alloys, even with very small amounts [17]. Therefore, the ternary Al-Sn-Zn system is considered as an important candidate in the lead-free solder systems. In order to promote the development of the lead-free solders, knowledge of the phase equilibria and thermodynamic properties of the ternary Al-Sn-Zn system is of fundamental importance and indispensable for design of the novel solders in the framework of the CALculation of PHAse Diagram (CALPHAD) approach [18,19].
Until now, only Fries et al. [20] performed a thermodynamic assessment of the Al-Sn-Zn ternary system using the CALPHAD approach. Their thermodynamic descriptions have been included in the COST 507 database [21]. Moreover, the new experimental enthalpies of mixing of the ternary liquid phase, activities of Al in the liquid phase and phase equilibria data along different sections were reported recently [22][23][24][25][26][27]. Hence, it is necessary to reassess the Al-Sn-Zn ternary system in order to construct the self-consistent thermodynamic database for the quaternary and higher-order lead-free systems. Moreover, there are three sub-binary systems i.e. Al-Sn, Al-Zn, and Sn-Zn in the Al-Sn-Zn ternary system. The Al-Sn binary system was first assessed by Fries et al. [20]. Later, Kang and Pelton [28] re-assessed the Al-Sn binary system by modeling the liquid phase with the modified quasi-chemical model (MQM). However, neither of the two groups [20,28] considered the solubility of Sn in (Al) fcc during their thermodynamic assessments. Furthermore, the new experimental data on enthalpies of mixing of the Al-Sn binary liquid phase were recently reported by Flandorfer et al. [29]. Hence, Cheng et al. [30] thermodynamically re-assessed the Al-Sn binary system by considering the solubility of Sn in (Al) fcc, as well as the new experimental enthalpies of mixing in the liquid phase. The calculated results by Cheng et al. [30] showed better agreement with more experimental information than those in the previous assessment [20,28]. Therefore, the thermodynamic parameters from Cheng et al. [30] were directly utilized in the present work. The Al-Zn binary system was first assessed by Murray [31]. However, the calculated phase diagram was not in good agreement with the experimental data available in the literature. Later, Mey and Effenberg [32] re-assessed this system, but the calculated phase boundaries of the (Al) fcc in the two-phase region ((Al) fcc +(Zn) hcp ) and those for the miscibility gap of the (Al) fcc were different from the experimental data in the literature. After that, a thermodynamic assessment of this system was again performed by Mey [33], Chen and Chang [34], and Mathon et al. [35]. The three thermodynamic assessments gave very similar results. Recently, Wasiur-Rahman and Medraj [36] reoptimized the Al-Zn system with MQM. The thermodynamic descriptions of Al-Zn system reported by Mey [33] was used to establish the thermodynamic databases for the Al-Mg-Zn [37], Al-Cu-Zn [38], and Al-Zn-Ti [39] systems. In consideration of the compatibility of thermodynamic database in multicomponent systems, the thermodynamic parameters of the Al-Zn system from Mey [33] were adopted in the present work, while the Sn-Zn binary system was thermodynamically assessed by several other authors [40][41][42]. It should be noted that Lee [40] assessed the Sn-Zn binary system based on more experimental data. The calculated results by Lee [40] show good agreement with most of the experimental data. Thus, the thermodynamic description by Lee [40] was adopted in the present work. The calculated phase diagrams of the Al-Sn, Al-Zn, and Sn-Zn binary systems from Refs. [30,33,40] are shown in Fig. 1.
Consequently, a CALPHAD re-assessment of the Al-Sn-Zn ternary system is to be performed by considering all the experimental data available in the literature and also the newly updated thermodynamic descriptions of boundary binaries. An accurate set of thermodynamic descriptions of the ternary Al-Sn-Zn system will be then established for the future development of the new Sn-Zn-Albased solders.

Literature review
All the experimental phase equilibria and thermodynamic properties of the Al-Sn-Zn ternary system available in the literature are strictly reviewed, and also concisely summarized in Table 1.
The liquidus temperatures of the Al-Sn-Zn ternary system over the entire concentration triangle were initially investigated by Plumbridge [43] using thermo analysis (TA). Afterwards, the liquidus surface of the Al-Sn-Zn ternary system was studied again by several authors [44][45][46] using TA. In 1980s, Vincent [47], Vincent and Sebaoub [48], and Vincent [49] experimentally studied several vertical sections (i.e., Al x Sn 1-x -Sn y Zn 1-y and Al x Zn 1-x -Sn) in the Al-Sn-Zn ternary system using differential thermal analysis (DTA). Besides, Lin et al. [22] investigated the cooling curves of the Al-Sn-Zn solders with different compositions by measuring the temperature variations using thermocouple. In 2011, Sidorov et al. [23] studied the physical properties (i.e., density, electrical resistivity, and magnetic susceptibility) of the Al-Sn-Zn alloys at high temperatures. Moreover, liquidus temperatures of the several ternary Al-Sn-Zn alloy samples were also reported in Ref. [23]. In 2012, Smetana et al. [24] smelted 20 different Al-Sn-Zn alloys and measured their phase transition temperatures (including liquidus, solidus, and invariant reactions) using DTA. Recently, Drápala et al. [25] experimentally investigated the multiple Al-Sn-Zn alloys with various contents of elements. The phase transition temperatures (like liquidus, solidus, and invariant reactions) of these samples were determined by means of DTA method. Besides, the microstructures of partial sample were also studied by optical metallography (OM) and energy dispersive X-ray spectroscopy (EDX). All the experimental data in Refs. [22][23][24][25][43][44][45][46][47][48][49] were employed in the present optimization.
The chemical potentials of Al in the Al-Sn-Zn liquid phase at 973 K and 1073 K along the Sn 0.5 Zn 0.5 -Al join were experimentally determined by Tikhomirov and Sryvalin [50] using the electromotive force (EMF) method. In 2002, the enthalpies of mixing and activities of Al in the ternary liquid Al-Sn-Zn alloys at 973 K along different vertical sections (i.e., Sn 0.33 Zn 0.66 -Al, Sn 0.5 Zn 0.5 -Al and Sn 0.66 Zn 0.33 -Al) were measured by Knnot and Mikula [26] using the EMF method. However, the enthalpies of mixing reported by Ref. [26] were not directly measured, but evaluated from the EMF values. In order to perform direct determination of the experimental data, the enthalpies of mixing of the liquid at 973 K along Sn 0.33 Zn 0.66 -Al, Sn 0.5 Zn 0.5 -Al and Sn 0.66 Zn 0.33 -Al joins were again investigated by Knott et al. [27] by means of calorimetric method. Hence, the enthalpies of mixing of the ternary liquid phase from Ref. [27] were taken into account during optimization of the thermodynamic parameters, while the enthalpies of mixing by Knnot and Mikula [26] were not.

Thermodynamic models
The thermodynamic parameters of pure elements Al, Sn, and Zn were directly taken from SGTE compilation by Dinsdale [54]. The liquid and (Al) fcc phases were modeled as the completely disordered solution. Thus, the molar Gibbs energy of ϕ phase (ϕ = liquid, or (Al) fcc ) can be expressed as follows: (1) where R is the gas constant, T is the absolute temperature, ϕ is the indicator of the liquid phase, x i and are the mole fraction and the molar Gibbs energy of the elements i (i=Al, Sn and Zn), and represents the excess Gibbs energy, which can be expressed by Redlich-Kister polynomial: (2) where and s are the binary and ternary interaction parameters, respectively. The interaction parameter can be expressed in turn as the linear function of temperature, i.e., a+bT, with the coefficients a and b to be optimized.

results and discussion
In the present work, the thermodynamic parameters of the ternary Al-Sn-Zn system were optimized through the PARROT module [55] incorporated in Thermo-Calc software package on the basis of the available experimental data from the literature. The principle of the optimization is based on the minimizing square sum of the differences between the measured and calculated values. During the optimization, each piece of experimental data was firstly given a fixed weight. Then, the weights were changed systematically during the optimization until most of the selected experimental data can be reproduced in the limits of the set uncertainty. In the first step of the assessment, only the enthalpies of mixing in the liquid phase from different vertical sections were considered to determine the ternary interaction parameters (especially for a values) for the liquid phase. Secondly, the activities and chemical potentials of Al in the ternary Al-Sn-Zn liquid alloys were considered. The obtained ternary parameters for the liquid phase in the first step were then modified. Finally, the ternary interaction parameters for liquid phase have been optimized by the experimental phase equilibria information related to liquid phase. In addition, the contribution to Gibbs energy of the (Al) fcc solid solution phase from the Zn-Sn binary system is missing, because the (Sn-Zn) fcc phase is thermodynamically unstable. Hence, the was set and fixed to avoid the existence of the unstable (Sn-Zn) fcc phase during the optimization. A self-consistent set of thermodynamic parameters of the ternary Al-Sn-Zn system were finally obtained by considering all the experimental data, and they are listed in Table 2.
The calculated vertical sections in the ternary Al-Sn-Zn system using the presently established thermodynamic descriptions are shown in Figs. 2 to 9, compared with the experimental data by Refs. [22][23][24][25][26][27][43][44][45][46][47][48][49][50].   [20] are also superimposed in the plots for a direct comparison. The solid blue lines represent the calculated results in the present work, while the red dashed lines are from Fries et al. [20]. As shown in Fig. 2, most of the experimental data can be well reproduced by the present thermodynamic modeling. Furthermore, a significant improvement can be clearly observed, compared with the previous one [20]. Figure 3 gives the comparison between the calculated vertical sections (i.e., Al 0.1198 Sn 0.8802 -Al 0.0697 Zn 0.9303 and Sn 0.949 Zn 0.051 -Al) with the experimental data by Refs. [23][24][25]43] and the calculated results due to the previous assessment by Fries et al. [20]. As shown in Fig. 3 (a), the calculated result shows a good agreement with most of the experimental data [23][24][25]. Compared with the previous one [20], the present work can better reproduce the experimental data [23][24][25]. Similarly, Fig. 3(b) shows the presently calculated result is in good agreement with the experimental data [43] and

T. Cheng and L.-J. Zhang / JMM 55 (3) B (2019) 439 -449
443 Figure 2. Calculated vertical sections along Al x Sn 1-x -Al y Zn 1-y joins, compared with the experimental data [24] and the previous assessment [20]:   [23][24][25]43] and the previous assessment [20] also the previous assessment [20]. The vertical sections along the Al 0.1131 Zn 0.8869 -Sn and Al 0.4852 Zn 0.5148 -Sn joins were calculated and displayed in Fig. 4. As shown in Fig. 4(a), the experimental data [22] can be well reproduced by the present thermodynamic calculations. A meaningful improvement is achieved in comparison with the previous assessment by Fries et al. [20]. However, Fig. 4(b) shows some deviations between the present calculation and the calculation based on the previous assessment by Fries et al. [20] and the experimental data [47], which exist in the liquidus. As shown in Fig.  4(b), the largest deviation is located around 40-70 at.% Sn. One of the possible reasons for such deviation is that the mass loss of Sn occurred during the experimental melting process for the alloys with high content of Sn. Therefore, further accurate experiments are necessary for validation. Figure 5 shows the calculated vertical sections along Al 0.9754 Sn 0.0246 -Sn 0.0577 Zn 0.9423 and Al 0.6534 Sn 0.3466 -Sn 0.5624 Zn 0.4376 , in comparison with the experimental data [43-46, 48, 49] and also the previous assessment [20]. The presently calculated results are in good agreement with the experimental data [43-46, 48, 49] and the calculated results by Fries et al. [20]. Figure 6 presents the calculated vertical sections along Al 0.902 Sn 0.098 -Sn 0.098 Zn 0.902 , Al 0.8 Sn 0.2 -Sn 0.2 Zn 0.8 and Al 0.6 Sn 0.4 -Sn 0.4 Zn 0.6 joins, respectively. Again, as can be seen, the presently calculated results agree well with the experimental data [25], and also the previous assessment by Ref. [20]. Figure 7 shows the calculated enthalpies of mixing of the ternary Al-Sn-Zn liquid phase (reference states: liquid Al, liquid Sn and liquid Zn) at 973 K along the Sn 0.33 Zn 0.67 -Al, Sn 0.5 Zn 0.5 -Al, and Sn 0.67 Zn 0.33 -Al joins, compared with the experimental data [27] and the calculated results due to the previous assessment by [20]. The presently calculated results show perfect agreement with all the measured experimental data [27]. Furthermore, there is a significant improvement, compared with the calculated results by [20], especially close to the Sn-Zn boundary binary. Figure  8 represents the calculated activities of Al (reference state: liquid Al) in the ternary Al-Sn-Zn liquid alloys at 973 K, compared with the experimental data [26] and also the calculated results due to the previous T. Cheng  compared with the experimental data [22,47] and the previous assessment [20] [43-46, 48, 49] and the previous assessment [20] assessment by [20]. As can be seen, the presently calculated results agree well with the experimental data [26], and also the calculated results by Fries et al. [20]. Figures 9(a) and (b) display the calculated chemical potentials of Al (reference state: liquid Al) in the ternary Al-Sn-Zn liquid alloys at 973 K and 1073 K, respectively. It should be noted that most of the experimental data [50] can be well reproduced by the present thermodynamic calculations, which are also consistent with the previous assessment by Fries et al. [20]. Figures 10(a) and (b) represent the calculated isothermal sections of the ternary Al-Sn-Zn system at 523.15 K from the present work and the previous assessment [20], compared with the same experimental data [25]. In the plots, the alloys No. 1, 2, and 3 represent the initial components of experimental alloys. The No. 1', 2', and 3' represent the phase compositions of (Al) fcc after long-time homogenization of the alloys No. 1, 2, and 3, respectively, while the No. 1", 2", and 3" represent the phase compositions of (Zn) hcp . As can be seen, the calculated results from both the present work and the previous assessment [20] show perfect agreement with the experimental data by [25]. Similarly, Figs. 11(a) and (b) show the calculated isothermal sections of the ternary Al-Sn-Zn system at 573.15 K from the present assessment and the previous one by Fries et al. [20], respectively. Again, the calculated results from both the present work and the previous assessment [20] can well reproduce the experimental data [25] Figure 12 shows the calculated liquidus projection of the ternary Al-Sn-Zn system over the entire composition range (a) and in the Sn-rich corner (b) according to the presently obtained thermodynamic descriptions. As can be clearly seen in Fig. 12, there are three primary crystallization fields, i.e. (Al) fcc , (Sn) bct , and (Zn) hcp . The E 1 represents the eutectic reaction (L↔(Al) fcc +(Sn) bct +(Zn) hcp ), while the U 1 represents the peritectic reaction (L+(Al) fcc2 ↔(Al) fcc1 +(Zn) hcp ). Table 3 summarizes the invariant equilibria associated with the liquid phase in the ternary Al-Sn-Zn system from different sources. As can be clearly seen in Table 3 [27] and the previous assessment [20]. The reference states are liquid Al, liquid Sn and liquid Zn  [26] and the previous assessment [20].     [20], compared with the experimental data [25]

conclusions
All the experimental phase equilibria and thermodynamic properties of the ternary Al-Sn-Zn system available in the literature were critically reviewed.
A CALPHAD-type thermodynamic assessment of the Al-Sn-Zn ternary system was performed by taking all the experimental data, and the thermodynamic descriptions for the boundary binaries into account. A set of self-consistent thermodynamic parameters of the Al-Sn-Zn ternary system was finally obtained.
Various phase equilibria and thermodynamic properties were calculated according to the obtained thermodynamic parameters, and comprehensively compared with the experimental data, and also the calculated results due to the previous assessment. The calculated results due to the present thermodynamic descriptions can reproduce most of the experimental data. Moreover, though with fewer ternary interaction parameters, a significant improvement was achieved in the present assessment, in comparison with the previous one.