DSC Investigation and Thermodynamic Modeling of the Al–Sb–Sn System

Abstract

The Al–Sb–Sn ternary system was studied by combining experimental measurement and thermodynamic modeling. The three vertical cross-sections of Al–SnSb, Sn–AlSb, and Sb–AlSn were measured by Differential Scanning Calorimetry (DSC). Based on the Calculation of Phase Diagram (CALPHAD) method, the thermodynamic modeling of the Al–Sb–Sn ternary system was carried out based on the evaluated experimental data by FactSage. A set of thermodynamic model parameters consistent with the experimental data was obtained.

1. Introduction

Babbitt metals have recently attracted much attention among researchers because of their excellent mechanical properties [1,2,3,4,5]. Babbitt metals are commonly used for making sliding bearings and liners that operate in rotating parts in equipment and/or machineries such as diesel engines, turbines, and compressors [6]. Babbitt metals are either tin- or lead-based alloys having excellent embedding ability and conformability characteristics [7,8,9,10,11,12]. Despite their higher cost, tin Babbitt alloys are often used in preference to lead Babbitt alloys due to their excellent corrosion resistance, easy bonding, and lesser tendency towards segregation [13,14,15]. Tin-base Babbitt commonly contain antimony and copper [16,17,18,19,20].

Tin–antimony alloy is one of the most important types of tin-based alloys. Tin-based Babbitt metals are called bearing alloys due to the intermetallic compound (SbSn), which is harder than the matrix [21]. Resistance to wear is the most significant property of bearing alloys, as they are typically used for sliding bearings to transmit loads between moving surfaces because of their lubrication property, and they also have a good combination of strength and surface properties, referring to Wang et al. [22].

For the tin–antimony binary alloy, the effects of adding different ratios of aluminum on the structural, mechanical, electrical, and thermal properties of tin–antimony bearing alloy Sn₈₇Sb₁₃ were investigated [21]. The hardness and minimum shear stress of the base alloy increased after adding the Al proportions. Moreover, the internal friction of the origin alloy significantly decreased after adding the different fractions of Al. Therefore, it is important to have a better understanding of the enhancement of mechanical properties with the addition of aluminum, as well as the relationship between the phase composition and their thermodynamic properties in the Al–Sb–Sn system.

In this work, the thermodynamic model of the Al–Sb–Sn system was established based on the experimental results reported before and conducted by Differential Scanning Calorimetry (DSC) in this work, respectively. All calculations were performed using the FactSage software (8.2, Thermfact Ltd. (Montreal, QC, Canada) and GTT-Technologies (Aachen, Germany)) [23]. Thermodynamic modeling the Al–Sb–Sn system is helpful for the reasonable design of alloy composition for a higher-performance bearing alloy.

2. Literature Review

2.1. Binary System

In a good thermodynamic assessment, existing binary assessments are used as first approximations, and then ternaries are modeled. Sometimes, a conclusion can be made that binaries worked reasonably well, so no modification was necessary [24]. The assessments of the Al–Sb and Al–Sn binary systems by Paliwal et al. [25] and Kang et al. [26] were accepted in the present work. The Sb–Sn binary system was the latest assessed by Zhang et al. [27] based on available experimental data in 2021. Hence, the previous assessment of experimental data for the Sb–Sn binary system is not repeated here. Since the thermodynamic model of liquid used in the Sb–Sn system was an associate solution model [28], the thermodynamic model of liquid was remodeled by the Modified Quasichemical Model (MQM) [29,30,31] to be consistent with Al–Sb and Al–Sn binary systems which were described in Section 4.

2.2. Ternary System

For the Al–Sb–Sn ternary system, only a few experimental studies of phase diagrams and thermodynamic properties are available. The thermodynamic assessment has not been reported so far.

In 1942, Hirosi et al. [32] studied the vertical sections of the Al–Sb–Sn system in different compositions by means of thermal analysis and the microscopic test. Two eutectic–peritectic reactions were reported: one of them occurs between Rhombohedral–Sb and liquid phase at 425 °C and the other between SnSb and liquid at 246 °C, resulting in the formation of Sb₃Sn₄ and AlSb in the former, and of Bct-Sn and AlSb in the latter. A ternary eutectic among Bct-Sn, AlSb, and Al was reported at 229 °C, but the composition of the eutectic point was not determined.

In 1981, Gerdes et al. [33] studied the vertical section of AlSb–Sn by DTA. Using a high-temperature calorimeter, the change δ (Δ H) in the enthalpy on mixing the molten AlSb with Sn in the entire concentration range was determined [34]. It was shown that the concentration dependence of the δ (Δ H) values is positive over the whole concentration range, which is in close accordance with the regular solution behavior [35].

In 1994, Li et al. [36] utilized the equilibrium cooling technique to determine the isothermal section of the Al–Sb–Sn system at room temperature. They observed the section was composed of five single-phase regions, Al, Sb, Sn, AlSb, and SnSb, and seven two-phase regions, Al + AlSb, Al + Sn, AlSb + Sn, AlSb + Sb, AlSb + SnSb, Sb + SnSb, and SnSb + Sn, and three three-phase regions, Al + AlSb + Sn, AlSb + Sb + SnSb, and AlSb + SnSb + Sn. The solid solubility range in the Rhombohedral–Sb and SnSb was reported as 0–10 mol% Sn, 0–2 mol% Al, and 39–56 mol% Sn, 0–4 mol% Al, respectively.

3. Materials and Methods

The three adjacent binary systems are relatively simple systems. Only two binary compounds, AlSb and Sb₃Sn₄, are observed. The ternary system involves one liquid phase and only three solid phases, no ternary compound is mentioned in the literature. In such a case, the only questions that remain are: what are the temperatures of the invariants and what are the limits in the composition of certain domains [37]. The DSC characterization is a feasible method to answer these two questions. The compositions of the studied alloys are represented in

Table 1. Nominal Composition of Al–Sb–Sn samples.

Vertical Section	Sample Number	Elemental Composition (at.%)
		Al	Sn	Sb
Al–SnSb	1	5	47.5	47.5
	2	10	45	45
	3	15	42.5	42.5
	4	20	40	40
	5	30	35	35
	6	35	32.5	32.5
	7	40	30	30
	8	45	27.5	27.5
	9	60	20	20
	10	70	15	15
	11	80	10	10
Sn–AlSb	12	40	20	40
	13	25	50	25
	14	15	70	15
Sb–AlSn	15	40	40	20
	16	30	30	40
	17	20	20	60
	18	15	15	70
	19	10	10	80

.

The starting materials are high-purity Sn (99.99%), high-purity Sb (99.99%), and high-purity Al (99.99%), produced by Guangzhou Metal Metallurgical Materials Company (Guangzhou, China). The total mass of each initial sample was approximately 3 g. Arc melting was used to melt the samples weighed in the corresponding ratio. Since Sb is easy to evaporate at high temperatures, Cai et al. [38] added 2 wt.% Sb to the rich chromium alloy during melting when studying the Cr-Pb-Sb system. Therefore, 2 wt.% excess Sb was added in each sample to compensate for the loss during melting. In order to reduce the oxidation of metals, pure titanium was placed in the arc melting stove as an oxygen absorber and argon gas (99.999%) as a protective gas. The mass loss of each sample was less than 1%, and a 20–40 mg sample was used in DSC.

The vertical sections of the Al–Sb–Sn ternary system were determined by differential thermal analysis using a synchronous thermal analyzer, Labsys Evo (SETARAM, Caluire, France). Before any DSC experiment, temperature calibration was carried out. The calibration metals used in this work are Zn, Pd, Au, Ag, Al, In, Ni, Sn, and Pb. The measured melting point of all metals is compared with the known melting point temperature; the temperature uncertainty in this work is ±3 °C, and the temperature detection sensitivity of DSC is 0.01 °C.

The weighed sample was placed in an alumina crucible with a cover for DSC. The rate of heating is very important in DSC experiments [39], so the setting of the heating rate must be determined first. A too-fast heating rate will lead to serious thermal lag, resulting in the measured temperature being too high; although the peak shape is sharper, it may cause similar two peaks to overlap. Too-slow heating will make the reaction signal insensitive. In this work, the heating rate was set at 10 °C/min. When the two peaks are too close to distinguish, the heating rate was appropriately reduced to 5 °C/min.

After the sample was placed, highly purified argon (99.999%) was used as protective gas with a flow rate of 20 mL/min. Before the experiment, the protective gas was passed for 10 min to remove air and prevent oxidation of the alloy. During the experiment, the sample was first held at 30 °C for 10 min, then heated to 600 °C at 10 °C/min, and finally cooled to room temperature at 10 °C/min. The evaporation of the sample during the experiments was observed by the change in the TG curve. All tabulated temperatures are determined by extrapolating the observed temperatures at a heating and cooling rate equal to zero, which corresponds to an equilibrium state.

4. Thermodynamic Model

The stoichiometric compounds existing in the Al–Sb–Sn ternary system are Al–FCC–A1, AlSb, and Sb₃Sn₄ in the Al–Sb and Sn-Sb binary system, respectively. Liquid, Bct-Sn, Rhombohedral–Sb, and SnSb are present as solution phases in the Al–Sb–Sn ternary system. In the current modeling, the thermodynamic data for AlSb and Sb₃Sn₄ were obtained from the modeling results of Paliwal and Jung [25] and Zhang et al. [27], respectively. The pure solid and liquid phase data for Al, Sb, and Sn were obtained from the SGTE database [40]. The gas phase was also taken into account in this work; all the thermodynamic data were taken from FactSage FACT Pure Substance database [22].

4.1. Stoichiometric Compounds

The stoichiometric compounds existing in the Al–Sb–Sn ternary system are Al–FCC–A1 and AlSb in the Al–Sb binary system and Sb₃Sn₄ in the Sb–Sn binary system. The expression for the standard Gibbs free energy of these stoichiometric compounds is as follows:

$$G^{°}={\mathsf{\Delta }}_f{H}_{298\mathrm{K}}^{°}+{\displaystyle {\int }_{298}^T{C}_p}dT-T\left[S_{298\mathrm{K}}^{°}+{\displaystyle {\int }_{298}^T{C}_p/TdT}\right]$$

(1)

where $C_p$ is the heat capacity; ${\mathsf{\Delta }}_f{H}_{298\mathrm{K}}^{°}$ is the standard enthalpy of formation at 298 K; $S_{298\mathrm{K}}^{°}$ is the standard entropy at 298 K.

4.2. Gas Phase

The ideal solution model was used to describe the gas phase in the Al–Sb–Sn ternary system (Al, Sb, Sn). The Gibbs energy of the gas phase is as follows:

$$G^{°}={\displaystyle \sum _i{x}_i}{}^{°}G{}_i^{Gas}+RT{\displaystyle \sum _i{x}_i\mathit{ln}{x}_i+RT\mathit{ln}(p/p^{°}})$$

(2)

where x_i is the mole fraction of gas species i, ${}^{°}G{}_i^{Gas}$ is the standard Gibbs free energy of gas species i taken from the FactSage FACT Pure Substance database [8], and $p^{°}$ is the standard pressure.

4.3. Liquid Phase

Paliwal and Jung [25] described the liquid phase of the Al–Sb binary system by using the MQM. Kang [26] described the liquid phase of the Al–Sn binary system by using the MQM [29,30,31], and Zhang et al. [27] modeled the liquid phase of the Sn–Sb binary system by using the associated solution model. In order to unify the liquid phase model, the liquid phase of Sn–Sb binary system was redescribed by the MQM in this work.

The MQM solution model has the following characteristics: (1) The short-range order in the liquid phase is described by the “pair approximation” method, and the excess Gibbs free energy caused by configurational energy is described by the “pair” fraction of components; (2) Components in the liquid phase exist in the form of “pairs” and are randomly mixed; (3) The coordination number of each unit in the liquid phase can be the same or different. More details about the MQM are presented by Pelton et al. [29,30,31], and were not discussed in this work.

For the Sn–Sb binary system, one parameter was added in the modeling of the liquid phase. The expression for this parameter is:

$$\mathsf{\Delta }{g}_{AB}=\mathsf{\Delta }{g}_{AB}^0+{\displaystyle \sum _{i\ge 1}\mathsf{\Delta }{g}_{AB}^{i0}}{X}_{AA}^i+{\displaystyle \sum _{j\ge 1}\mathsf{\Delta }{g}_{AB}^{0j}}{X}_{BB}^j$$

(3)

where $\mathsf{\Delta }{g}_{AB}^0$, $\mathsf{\Delta }{g}_{AB}^{i0}$ and $\mathsf{\Delta }{g}_{AB}^{0j}$ are model parameters, all of which can be written in the a + bT form, and A and B are Sn and Sb. The pairs (Sn–Sn) and (Sb–Sb) have the most content on the Sn-rich side and Sb-rich side, and $\mathsf{\Delta }{g}_{\mathrm{SnSb}}^{i0}$ and $\mathsf{\Delta }{g}_{\mathrm{SnSb}}^{0j}$ affect the liquid phase of the Sn-rich side and Sb-rich side, respectively. The pair (Sn–Sb) has the most content near SnSb, so $\mathsf{\Delta }{g}_{\mathrm{SnSb}}^0$ mainly affects the liquidus near SnSb. The Gibbs free energy of liquid phase could be adjusted by changing the $\mathsf{\Delta }{g}_{\mathrm{SnSb}}^0$, $\mathsf{\Delta }{g}_{\mathrm{SnSb}}^{i0}$, $\mathsf{\Delta }{g}_{\mathrm{SnSb}}^{0j}$, i and j at the same time. The coordination number z is an important parameter in the phase diagram modeling, which ratio determines the position of the maximum short-range order. In this work, the short-range order was not taken into account and the coordination numbers were all set to 6.

The binary terms were extrapolated into higher-order liquid by the symmetric Kohler extrapolation [41], due to the components in the liquid phase all being separated into one group with similar chemical properties. Ternary term $\mathsf{\Delta }{g}_{\mathrm{AlSb}(\mathrm{Sn})}^{001}$, which is the effect of the third component Sn upon the binary interaction between Al and Sb, was also used to describe the ternary liquid phase better.

4.4. Solid Solution Phase

Zhang et al. [27] used a substitution solution model to describe Bct (Sn) and Rhombohedral (Sb), and the Compound Energy Formalism (CEF) model [42] to describe SnSb solid solution phase. This modeling result was adopted in this work without any modification. Kang et al. considered the solubility of Al in Bct (Sn), which was also taken into account in this work.

The expressions for Gibbs free energies of phases described by the substitution solution model and CEF model are Equations (4) and (5) as listed below, respectively.

$$G_m^{\phi }={\displaystyle \sum x_i}{}^{°}G{}_i^{\phi }+RT{\displaystyle \sum x_i\mathit{ln}{x}_i}+x_i{x}_j{\displaystyle \sum _{\nu =0}^n{}^{\nu }L{}_{i.j}^{\phi }{\left(x_i-x_j\right)}^{\nu }}$$

(4)

$$G_m-{\displaystyle \sum n^s(1-y_{Va}^s)}{\displaystyle \sum x_I^0{G}_I^{stst}={\displaystyle \sum {\mathsf{\Delta }}_f^0{G}_{end}\prod y_J^s}}+RT{\displaystyle \sum {\displaystyle \sum n^s{y}_J^s\mathit{ln}(y_J^s)}}+{}^{E}G{}_m$$

(5)

For Equation (4), where R is the gas constant, x_i and x_j (i, j = Al, Sn, Sb) are the mole fractions. ${}^{°}G{}_i^{\phi }$ are Gibbs free energies of pure phases (i, j = Al, Sn, Sb). ${}^{\nu }L{}_{i.j}^{\phi }$ are binary interaction parameters in the Al–Sn, Al–Sb and Sn–Sb binary systems, respectively.

For Equation (5), the left hand side represents the mixing Gibbs energy, ${}^{M}G{}_m$. Additionally, numerical values of ${}^{°}G{}_{end}$ were given relative to standard states (stst) of the components I. ${}^{E}G{}_m$ are regarded as excess terms [27].

5. Results and Discussion

5.1. DSC Results of the Al–Sb–Sn System

In order to get a reliable thermodynamic database of the Al–Sb–Sn ternary system, more DSC experiments were performed in this work. During the DSC measurements of the samples, the TG results of all samples indicated that there was no significant weight loss or gain during the entire heating process. The details of all samples measured by DSC are discussed below.

(1)

Al–SnSb system

Figure 1 shows a typical DSC curve for a sample (Sb_42.5Al₁₅Sn_42.5) in the Al–SnSb system. The DSC results of sample 1 show two endothermic peaks as the temperature increased, the first peak corresponding to the extrapolated starting point temperature of 242 °C, and the second peak corresponding to the temperature of 422 °C. The DSC results of sample 2 show three endothermic peaks as the temperature increased. The first peak had a sharp peak shape and the corresponding extrapolated starting point temperature was 244 °C, the second peak had a corresponding extrapolated starting point temperature of 327 °C, and the third peak was 403 °C. The DSC results of sample 3 also showed three endothermic peaks as the temperature increased. The first peak had a sharp peak shape and the corresponding extrapolated starting point temperature was 246 °C, the second peak had a corresponding extrapolated starting point temperature of 328 °C, and the third peak had a temperature of 380 °C. The DSC results of sample 4 also showed three endothermic peaks as the temperature increased. The first peak had a sharp peak shape and the corresponding extrapolated starting point temperature was 246 °C, the second peak had a corresponding extrapolated starting point temperature of 326 °C, and the third peak had a temperature of 379 °C. According to the DSC results of Al–SnSb vertical section samples, it can be found that the peak shape of the first peak of samples 2, 3, and 4 is very sharp, and the temperature is close to 245 °C, so it is inferred that there is an invariant reaction at about 245 °C in the vertical section of Al–SnSb. The temperature of the starting point corresponding to the second peak of samples 2, 3, and 4 is close. The temperature is about 327 °C, so it is speculated that there is a second invariant reaction around 327 °C.

The DSC results of sample 5 showed two endothermic peaks at 248 °C and 304 °C when the temperature increased, respectively. The DSC results of sample 6 showed an endothermic peak as the temperature increased, corresponding to 240 °C. The DSC results of sample 7 also showed an endothermic peak when the temperature increased, corresponding to the temperature of 234 °C. The DSC results of sample 8 also showed an endothermic peak as the temperature increased, corresponding to a temperature of 233 °C. The DSC results of sample 9 show two endothermic peaks when the temperature increased; the first peak is sharper in shape and corresponds to the extrapolated starting point temperature of 231 °C, and the second peak corresponds to the temperature of 579 °C. The DSC results of sample 10 show two endothermic peaks as the temperature increased; the first one has a sharp shape, which corresponds to the starting point temperature of extrapolation of 229 °C, and the second one corresponds to the temperature of 590 °C. The DSC results of sample 11 showed an endothermic peak with a sharp peak shape when the temperature increased, which corresponded to the extrapolated starting point temperature of 230 °C. Therefore, it is speculated that there should be a third invariant reaction in this Al–SnSb system with a temperature of about 230 °C.

(2)

Sn–AlSb system

Figure 2 shows a typical DSC curve for a sample (Sb₄₀Al₄₀Sn₂₀) in the Sn–AlSb system. The heat-flux curve of sample 12 showed an endothermic peak with a sharp peak shape, which corresponded to an extrapolation starting point temperature of 246 °C. The DSC results of sample 13 showed an endothermic peak with a sharp peak shape when the temperature increased, corresponding to the starting point temperature of the extrapolation of 237 °C. The DSC results of sample 14 showed an endothermic peak with a sharp peak shape as the temperature increased, corresponding to the starting point temperature of extrapolation of 251 °C.

(3)

Sb–AlSn system

Figure 3 shows a typical DSC curve for a sample (Sb₄₀Al₃₀Sn₃₀) in the Sb–AlSn system. The DSC results of sample 15 showed two endothermic peaks when the temperature increased. The first peak was sharper, corresponding to the starting point temperature of extrapolation of 233 °C, and the second peak was 530 °C. The DSC results of sample 16 showed three endothermic peaks as the temperature increased. The first peak was sharper in shape, corresponding to the extrapolated starting point temperature of 248 °C, the second peak was 327 °C, and the third peak was 352 °C. The DSC results of sample 17 showed two endothermic peaks when the temperature increased. The first peak was sharper in shape, corresponding to the starting point temperature of the extrapolation of 420 °C, and the second peak was 512 °C. The DSC results of sample 18 showed two endothermic peaks as the temperature increased; the first peak was sharper in shape, corresponding to the extrapolated starting point temperature of 425 °C, and the second peak was 560 °C. The DSC results of sample 19 showed two endothermic peaks when the temperature increased. The first peak was sharper, corresponding to the starting point temperature of the extrapolation of 424 °C, and the second peak was 593 °C. Since the temperature of the first extrapolated starting point measured for the three samples is close to that of about 423 °C, it is assumed that there is an invariant reaction in the Sb–AlSn vertical cross section at about 423 °C.

All the transition temperatures of these 19 samples mentioned above in the vertical section of the Al–Sb–Sn ternary system were summarized in

Table 2. Transition temperatures of Al–Sb–Sn samples by DSC.

Vertical Section	Elemental Composition (X, Mole Fraction)			Transition Temperature (°C)
Sn–AlSb	XAl	XSn	XSb	AlSb + L↔AlSb + BCT (I)
	0.4	0.2	0.4	246
	0.25	0.5	0.25	237
	0.15	0.7	0.15	251
Sb–AlSn	XAl	XSn	XSb	AlSb + L↔AlSb + L + Al (M)	AlSb + L + Al↔AlSb + Al + BCT (I)
	0.4	0.4	0.2	530	233
				AlSb + L↔AlSb + L + SnSb (M)	AlSb + L + SnSb↔AlSb + L + Sn4Sb3 (I)	AlSb + L + Sn4Sb3↔AlSb + Sb3Sn4 + BCT (I)
	0.3	0.3	0.4	352	327	248
				AlSb + L↔AlSb + RHOM + L (M)	AlSb + RHOM + L↔AlSb + SnSb + RHOM (I)
	0.2	0.2	0.6	512	420
	0.15	0.15	0.7	560	425
	0.1	0.1	0.8	593	424
Al–SbSn	XAl	XSn	XSb	AlSb + L↔AlSb + L + SnSb (M)	AlSb + L + SnSb↔AlSb + L + Sb3Sn4 (I)	AlSb + L + Sb3Sn4↔AlSb + Sb3Sn4 + BCT (I)
	0.05	0.475	0.475	422
	0.1	0.45	0.45	403	327	244
	0.15	0.425	0.425	380	328	246
	0.2	0.4	0.4	379	326	246
				AlSb + L↔AlSb + L+Sb3Sn4 (M)	AlSb + L + Sb3Sn4↔AlSb + Sb3Sn4 + BCT (I)
	0.3	0.35	0.35	304	248
				AlSb + L↔AlSb + L + Al (M)	AlSb + L + Al↔AlSb + BCT + Al (I)
	0.35	0.325	0.325		240
	0.4	0.3	0.3		234
	0.45	0.275	0.275		233
	0.6	0.2	0.2	579	231
	0.7	0.15	0.15	590	229
	0.8	0.1	0.1		230

Note: The markings “(M)” and “(I)” means Monovariant and Invariant, respectively.

. The reactions mentioned in Table 2 are corresponding with the phase change between two adjacent phase regions.

5.2. Thermodynamic Modeling of the Al–Sb–Sn System

Table 3. Thermodynamic model parameters used in the Al–Sb–Sn system.

Phase	Thermodynamic Parameters	Reference
Al-FCC_A1	$\begin{array}{l}-7976.15+137.093038T-24.3671976T\mathit{ln}(T)\\ -1.884662E-3T^2-0.877664E-6T^3+74,092T^{-1}(298.15\mathrm{K} < T < 700\mathrm{K})\end{array}$	[40]
	$\begin{array}{l}-11,276.24+223.048446T-38.5844296T\mathit{ln}(T)\\ +18.531982E-3T^2-5.764227E-6T^3+74,092T^{-1}(700\mathrm{K} < T < 933.47\mathrm{K})\end{array}$
	$\begin{array}{l}-11,278.378+188.684153T-31.748192T\mathit{ln}(T)-1.231E28T^{-9}\\ (933.47\mathrm{K} < T < 2900\mathrm{K})\end{array}$
Al-BCC_A2	$\begin{array}{l}-7976.15+137.093038T-24.3671976T\mathit{ln}(T)\\ -1.884662E-3T^2-0.877664E-6T^3+74,092T^{-1}(298.15\mathrm{K} < T < 700\mathrm{K})\end{array}$	[40]
	$\begin{array}{l}-1193.24+218.235446T-38.5844296T\mathit{ln}(T)\\ +18.531982\mathrm{E}-3T^2-5.764227E-6T^3+74,092T^{-1}(700\mathrm{K} < T < 933.47\mathrm{K})\end{array}$
	$\begin{array}{l}-1195.378+183.871153T-31.748192T\mathit{ln}(T)-1.231\mathrm{E}28T^{-9}\\ (933.47\mathrm{K} < T < 2900\mathrm{K})\end{array}$
Al-LIQUID	$\begin{array}{l}3028.879+125.251171\mathrm{T}-24.3671976T\mathit{ln}(T)-1.884662E-3T^2\\ -0.87764E-6T^3+74,092T^{-1}(298.15\mathrm{K} < T < 700\mathrm{K})\end{array}$	[40]
	$\begin{array}{l}-271.21+211.206579T-38.5844296T\mathit{ln}T+18.531982E-3T^2\\ -5.764227E-6T^3+74,092T^{-1}+7.934E-20T^7(700\mathrm{K} < T < 933.47\mathrm{K})\end{array}$
	$-795.996+177.430178T-31.748192T\mathit{ln}T(933.47\mathrm{K} < T < 2900\mathrm{K})$
Sb-BCT_A5	$\begin{array}{l}-8242.858+156.154689\mathrm{T}-30.5130752T\mathit{ln}(T)+7.748768\mathrm{E}-3T^2\\ -3.003415E-6T^3+100,625T^{-1}(298.15\mathrm{K} < T < 903.78\mathrm{K})\end{array}$	[40]
	$\begin{array}{l}-10,738.83+169.485872\mathrm{T}-31.38T\mathit{ln}(T)+1.6168E27T^{-9}\\ (930.78\mathrm{K} < T < 2000\mathrm{K})\end{array}$
Sb-RHOMBO_A7	$\begin{array}{l}-9242.858+156.154689\mathrm{T}-30.5130752T\mathit{ln}(T)\\ +7.748768\mathrm{E}-3T^2-3.003415E-6T^3+100,625T^{-1}(298.15\mathrm{K} < T < 903.78\mathrm{K})\end{array}$	[40]
	$\begin{array}{l}-11,738.83+169.485872\mathrm{T}-31.38T\mathit{ln}(T)+1.6168E27T^{-9}\\ (930.78\mathrm{K} < T < 2000\mathrm{K})\end{array}$
Sb-LIQUID	$\begin{array}{l}10,579.47+134.231525\mathrm{T}-30.5130752T\mathit{ln}(T)\\ +7.748768\mathrm{E}-3T^2-3.003415E-6T^3+100,625T^{-1}(298.15\mathrm{K} < T < 903.78\mathrm{K})\end{array}$	[40]
	$8175.359+147.455986\mathrm{T}-31.38T\mathit{ln}(T)(930.78\mathrm{K} < T < 2000\mathrm{K})$
Sn-BCT_A5	$\begin{array}{l}-7958.517+122.765451\mathrm{T}-25.858T\mathit{ln}(T)+0.51185\mathrm{E}-3T^2-3.192767E-6T^3+18,440T^{-1}\\ (100\mathrm{K} < T < 250\mathrm{K})\end{array}$	[40]
	$\begin{array}{l}-5855.135+65.443315\mathrm{T}-15.961T\mathit{ln}(T)-18.8702\mathrm{E}-3T^2+3.121167E-6T^3-61,960T^{-1}\\ (250\mathrm{K} < T < 505.078\mathrm{K})\end{array}$
	$\begin{array}{l}2524.724+4.005269\mathrm{T}-8.2590486T\mathit{ln}(T)-16.814429\mathrm{E}-3T^2\\ +2.623131E-6T^3-1,081,244T^{-1}-1.2307\mathrm{E}25T^{-9}(505.078\mathrm{K} < T < 800\mathrm{K})\end{array}$
	$\begin{array}{l}-8256.959+138.99688\mathrm{T}-28.4512T\mathit{ln}(T)-1.2307E25T^{-9}\\ (800\mathrm{K} < T < 3000\mathrm{K})\end{array}$
Sn-RHOMBO_A7	$\begin{array}{l}-5923.517+122.765451\mathrm{T}-25.858T\mathit{ln}(T)\\ +0.51185\mathrm{E}-3T^2-3.192767E-6T^3+18,440T^{-1}(100\mathrm{K} < T < 250\mathrm{K})\end{array}$	[40]
	$\begin{array}{l}-3820.135+65.443315\mathrm{T}-15.961T\mathit{ln}(T)\\ -18.8702\mathrm{E}-3T^2+3.121167E-6T^3-61,960T^{-1}(250\mathrm{K} < T < 505.078\mathrm{K})\end{array}$
	$\begin{array}{l}4559.724+4.005269\mathrm{T}-8.2590486T\mathit{ln}(T)\\ -16.814429\mathrm{E}-3T^2+2.623131E-6T^3-1,081,244T^{-1}-1.2307\mathrm{E}25T^{-9}\\ (505.078\mathrm{K} < T < 800\mathrm{K})\end{array}$
	$\begin{array}{l}-6221.959+138.99688\mathrm{T}-28.4512T\mathit{ln}(T)-1.2307E25T^{-9}\\ (800\mathrm{K} < T < 3000\mathrm{K})\end{array}$
Sn-LIQUID	$\begin{array}{l}-855.425+108.677684\mathrm{T}-25.858T\mathit{ln}(T)\\ +0.51185\mathrm{E}-3T^2-3.192767E-6T^3+18,440T^{-1}+1.47031E-18T^7(100\mathrm{K} < T < 250\mathrm{K})\end{array}$	[40]
	$\begin{array}{l}1247.957+51.355548\mathrm{T}-15.961T\mathit{ln}(T)\\ -18.8702\mathrm{E}-3T^2+3.121167E-6T^3-61,960T^{-1}+1.47031E-18T^7(250\mathrm{K} < T < 505.078\mathrm{K})\end{array}$
	$\begin{array}{l}9496.31-9.809114\mathrm{T}-8.2590486T\mathit{ln}(T)\\ -16.814429\mathrm{E}-3T^2+2.623131E-6T^3-1,081,244T^{-1}(505.078\mathrm{K} < T < 800\mathrm{K})\end{array}$
	$-1285.372+125.182498\mathrm{T}-28.4512T\mathit{ln}(T)(800\mathrm{K} < T < 3000\mathrm{K})$
Liquid (Al,Sb,Sn)(Va)	GAl:Va = GAl-LIQUID, GAl:Va = GAl-LIQUID, GAl:Va = GAl-LIQUID	[40]
	$\mathsf{\Delta }{g}_{\mathrm{AlSb}}^{°}=-5768.40+1.674T$	[25]
	$g_{\mathrm{AlSb}}^{01}=1334.70$	[25]
	$g_{\mathrm{AlSb}}^{10}=5836.68$	[25]
	$\mathsf{\Delta }{g}_{\mathrm{AlSn}}^{°}=5439.2-1.8830T$	[26]
	$g_{\mathrm{AlSn}}^{01}=-836.8+0.8368T$	[26]
	$g_{\mathrm{AlSn}}^{10}=2510.4-0.4184T$	[26]
	$\mathsf{\Delta }{g}_{\mathrm{SnSb}}^{°}=-1700-T$	This work
	$g_{\mathrm{SnSb}}^{10}=550$	This work
	$g_{\mathrm{AlSb}(\mathrm{Sn})}^{001}=-500$	This work
Bct (Al,Sb,Sn)	GAl =GAl-BCC_A2, GSb = GSb-BCT_A5, GSn = GSn-BCT_A5	[40]
	${}^{0}L{}_{\mathrm{Al},\mathrm{Sn}}=14,136.95-4.7123T$ ${}^{0}L{}_{\mathrm{Sn},\mathrm{Sb}}=-5200+12.5\cdot T$	[26,27]
Rhombohedral (Sb,Sn)	GSb = GSb-RHOMBO_A7, GSn = GSn-RHOMBO_A7	[27]
	${}^{0}L{}_{\mathrm{Sb},\mathrm{Sn}}=6400-5T$	[27]
	${}^{1}L{}_{\mathrm{Sb},\mathrm{Sn}}=-5000$	[27]
SnSb (Sn,Sb,Va)4(Sb)3	$G_{\mathrm{Sn}:\mathrm{Sb}}^{}=390+8.5T+G_{{\mathrm{Sn}}_4{\mathrm{Sb}}_3}$	[27]
	$G_{\mathrm{Sb}:\mathrm{Sb}}^{}=88,000+42T+7G_{\mathrm{R}\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{B}\mathrm{O}\_\mathrm{A}7}$ $G_{\mathrm{Va}:\mathrm{Sb}}^{}=12,100-2T+3G_{\mathrm{R}\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{B}\mathrm{O}\_\mathrm{A}7}$ ${}^{0}L{}_{\mathrm{Sn},\mathrm{Sb}}=86,000+25.5T$ ${}^{1}L{}_{\mathrm{Sn},\mathrm{Sb}}=-48,000$	[27]
AlSb	$\begin{array}{l}{G}_{\mathrm{AlSb}}^{°}=-71,309.3454+247.2924T-46.13T\mathit{ln}(T)\\ -0.003855T^2+800T^{-1}(298\mathrm{K} < T < 1335\mathrm{K})\end{array}$	[25]
	$\begin{array}{l}{G}_{\mathrm{AlSb}}^{°}=-78,273.5346+321.9495T-56.494T\mathit{ln}(T)\\ (1335\mathrm{K} < T < 3000\mathrm{K})\end{array}$
Sb3Sn4	$\begin{array}{l}{G}_{{\mathrm{Sb}}_3{\mathrm{Sn}}_4}^{°}=-80,789.114+735.4373T-155.3832T\mathit{ln}(T)\\ -0.052234496T^2+3.474423E-6T^{-3}+54,035T^{-1}(298\mathrm{K} < T < 505\mathrm{K})\end{array}$	[27]
	$\begin{array}{l}{G}_{{\mathrm{Sb}}_3{\mathrm{Sn}}_4}^{°}=-47,269.677+489.6854T-124.5754T\mathit{ln}(T)-0.044011T^2\\ +1.482279E-6T^{-3}-4,023,101T^{-1}-4.9228E25T^{-9}(505\mathrm{K} < T < 800\mathrm{K})\end{array}$
	$\begin{array}{l}{G}_{{\mathrm{Sb}}_3{\mathrm{Sn}}_4}^{°}=-90,396.408+1029.651T-205.344T\mathit{ln}(T)-0.02324T^2\\ -9.0102E-6T^{-3}-301,875T^{-1}-4.9228E25T^{-9}(800\mathrm{K} < T < 903\mathrm{K})\end{array}$
	$\begin{array}{l}{G}_{{\mathrm{Sb}}_3{\mathrm{Sn}}_4}^{°}=-97,884.322+1069.645T-207.9448T\mathit{ln}(T)\\ +4.80131E27T^{-9}(903\mathrm{K} < T < 2000\mathrm{K})\end{array}$
	$\begin{array}{l}{G}_{{\mathrm{Sb}}_3{\mathrm{Sn}}_4}^{°}=-97,884.322+1069.645T-207.9448T\mathit{ln}(T)\\ -4.9228E25T^{-9}(2000\mathrm{K} < T < 3000\mathrm{K})\end{array}$

Note: Gibbs energies and enthalpy are expressed in J/mol, entropy and heat capacity are expressed in J/mol·k.

presents all the parameters for the compounds and solution phases used in the modeling of the Al–Sb–Sn system. The assessments of the Al–Sb and Al–Sn binary systems by Manas et al. [25] and Kang et al. [26] were accepted in the present work without any modifications. The thermodynamic model of the liquid phase in the Sb–Sn binary system was remodeled by the MQM to be consistent with the liquid phases in the Al–Sb and Al–Sn binary systems. A ternary parameter in the liquid phase was added to describe the ternary liquid phase better. The Gibbs energies of all pure liquid and solid Al, Sb, and Sn were taken from the SGTE database [40].

The calculated Sn–Sb binary system phase diagram along with the experimental data [43,44,45,46,47,48] are presented in Figure 4. The parameter $\mathsf{\Delta }{g}_{\mathrm{SnSb}}^{°}=-2200$ J/mol in the liquid phase was given a small negative value to fit the liquid phase region. The calculated activities of the end-member Sn in the liquid Sb phase at 905 °C compared with the experimental data [49] are shown in Figure 5. The calculated results of mixing enthalpy for Sn–Sb at 700 °C compared with the experimental data [50,51] are shown in Figure 6. The available phase diagram and thermodynamic data mentioned above were reproduced well within experimental uncertainty limits.

The calculated vertical sections of the Al–Sb–Sn ternary system compared with the experimental results are shown in Figure 7, Figure 8, Figure 9 and Figure 10. The solid lines represent the calculated results, and the dots represent the experimental results. By comparing the optimized results with the experimental data of the vertical sections in Figure 7, Figure 8, Figure 9 and Figure 10, most experimental data are reproduced well within experimental uncertainty limits. The experimental results of Li et al. [36] were not taken into account due to the inconsistency with binary system experimental results. The calculated enthalpy on mixing the molten AlSb with Sn at 1072 °C compared with the experimental results is shown in Figure 11. The calculated results in the low Sn content range are lower than the experimental results.

According to the calculated thermodynamic parameters, the projection diagram of the liquid from 300 °C to 2000 °C was calculated, as shown in Figure 12 below. As shown in Figure 12, five primary phase regions are observed in this liquidus projection, where the AlSb phase composed most of the primary phase regions due to its high stability in the Al–Sb binary system. All ternary invariant reactions in the Al–Sb–Sn system are presented in

Table 4. Calculated invariant reactions in the Al–Sb–Sn ternary system.

T (°C)	Liquid Composition (X, Mole Fraction)			Reaction
	XAl	XSn	XSb
240.20	1.009 × 10−6	0.943	0.057	Liquid + Bct$\leftrightarrow$Sb3Sn4 + AlSb
425.38	2.372 × 10−4	0.476	0.524	Liquid + SnSb$\leftrightarrow$Rhombohedral + AlSb
229.67	0.019	0.981	1.579 × 10−6	Liquid$\leftrightarrow$Al + AlSb + Bct
319.08	1.157 × 10−5	0.810	0.190	Liquid + Sb3Sn4$\leftrightarrow$SnSb + AlSb

.

6. Conclusions

The vertical sections of Sn–AlSb, Al–SnSb, and Sb–AlSn in the Al–Sb–Sn ternary system are determined by DSC. The thermodynamic model of the Al–Sb–Sn ternary system is obtained by remodeling the liquid phase of the Sn–Sb binary system by MQM and adding a ternary parameter. Most experimental results agree well with the calculated results based on the database of the Al–Sb–Sn ternary system. Thermodynamic studies and modeling of the Al–Sb–Sn ternary system can be integrated into the thermodynamic database of bearing alloys.