The Co-Sb-Ga System: Isoplethal Section and Thermodynamic Modeling

Abstract

The Co-Sb-Ga ternary system is an important thermoelectric material system, and its phase equilibria are in need of further understanding. The CoSb₃-GaSb isoplethal section is experimentally determined in this study. Phase equilibria of the ternary Co-Sb-Ga system are assessed, and the system’s thermodynamic models are developed. In addition to the terminal phases and liquid phase, there are six binary intermediate phases and a ternary Co₃Sb₂Ga₄ phase. The Ga solution in the CoSb₃ compound is described by a dual-site occupation (Ga_VF) _x Co₄Sb_12−x/2(Ga_Sb) _x/2 model. Phase diagrams are calculated using the developed thermodynamic models, and a reaction scheme is proposed based on the calculation results. The calculated results are in good agreement with the experimentally determined phase diagrams, including the CoSb₃-GaSb isoplethal section, the liquidus projection, and an isothermal section at 923 K (650 °C). The dual-site occupation (Ga_VF) _x Co₄Sb_12−x/2(Ga_Sb) _x/2 model gives good descriptions of both phase equilibria and thermoelectric properties of the CoSb₃ phase with Ga doping.

1 Introduction

Thermoelectric materials and devices have attracted substantial research interest, primarily in waste heat recovery and efficiency enhancement of energy usage. Various studies have been carried out to develop materials with better thermoelectric properties.[1–5] Skutterudite compounds have a body-centered cubic structure, and there are two major voids per unit cell. When a third atom is incorporated into the voids, the compound is described as RM₄X₁₂, and is referred to as filled skutterudite. CoSb₃ is a skutterudite compound;[6–10] it has been reported that filled CoSb₃ skutterudites have promising thermoelectric properties, and Ga is one of the suitable filling atoms.[6–10]

Phase equilibria information is fundamentally important for materials’ development, processing-route selection, and related products’ reliability assessment. Although Co-Sb-Ga is of great interest in thermoelectric applications, there are only limited phase equilibria results.[10–12] Markovski et al.[11] determined the Co-Sb-Ga isothermal section at 773 K (500 °C). Qiu et al.[10] reported the solubility of Ga in the CoSb₃ phase and the equilibrium phase relationships around the CoSb₃ phase at 923 K (650 °C). Chen et al.[12] determined the liquidus projection including the invariant reaction temperatures and the isothermal section at 923 K (650 °C) of the Co-Sb-Ga ternary system.

The phase diagrams of the three binary constituent systems have been determined,[13–15] but the CoSb₃ phase has been described as a line compound in all previous studies.[15–17] Since ternary solubility in the CoSb₃ phase is critical, a thermodynamic model of the CoSb₃ phase which can properly describe its ternary solubility needs to be developed. This study remodels the Co-Sb binary system using a defect model, and also experimentally determines the CoSb₃-GaSb isoplethal section due to the insufficiency of ternary phase equilibria data.[10–12] The thermodynamic models of the Co-Sb-Ga system are then reassessed with the new constituent binary models and the ternary Co-Sb-Ga phase equilibria results.

2 Experimental Procedures

Ternary Co-Sb-Ga alloys were prepared using pure Co foil (99.95 wt pct purity, Alfa Aesar, USA), Sb shots (99.9999 wt pct purity, Alfa Aesar, USA), and Ga shots (99.9 wt pct purity, Alfa Aesar, USA). A total amount of about one gram was weighed. These elements were encapsulated in a quartz tubes at a vacuum of 10⁻⁵ bar. The sample capsule was placed at 1273 K (1000 °C) for 3 days to ensure complete melting and mixing of the elements, and then quenched in water. The samples were heat treated at different temperatures for various lengths of reaction time. The compositions, temperatures, and heat-treatment times of the alloys are summarized in Table I.

Table I Nominal Compositions and Equilibrium Phases of Ternary Co-Sb-Ga Alloys

After the predetermined lengths of reaction time, the sample capsule was removed from the furnace and quenched in water. The quenched ingots were then cut into halves. One half was meant for powder X-ray diffraction analysis (XRD, Rigaku Ultima IV/ED2802N, Japan) using Cu-K _α radiation. The other half was mounted and metallographically examined. The microstructures were analyzed using optical microscopy (Olympus, BH, Japan) and scanning electron microscopy (SEM, Hitachi, s-2500, Japan). The phase compositions were determined using electron probe microanalyzer (EPMA, JOEL, JXA-8600SX, Japan).

3 Experimental Results

Figure 1(a) shows the BEI micrograph of the as-quenched alloy #4(Co-70.0 at. pct Sb-10.0 at. pct Ga). The alloy was heat treated at 1123 K (850 °C) for 1 month, and it was then quenched in water. Two major phase regions can be observed. The large gray phase region is a single-phase region. Its composition is Co-66.6 at. pct Sb-0.8 at. pct Ga, and it is the CoSb₂ phase. The other region is not a single-phase region. According to its microstructure, it was the liquid phase prior to its removal from the furnace. Figure 1(b) shows the XRD diffractogram, which confirms the existence of the CoSb₂ phase. Alloy #4 is in the CoSb₂ + liquid two-phase region at 1123 K (850 °C). It should be mentioned that thermal analysis is usually a much more efficient technique for the determination of isoplethal section. However, significant undercooling is observed in this system, and the liquidus temperatures determined by thermal analysis are not consistent, which is why tedious and time-consuming phase equilibria experiments were necessary for this study.

Fig. 1

(a) BEI micrograph of the as-quenched alloy #4(Co-70.0 at. pct Sb-10.0 at. pct Ga) heat treated at 1123 K (850 °C). (b): XRD diffractogram of the as-quenched alloy #4

Figure 2(a) shows the BEI micrograph of the as-quenched alloy #8(Co-70.0 at. pct Sb-10.0 at. pct Ga). Its nominal composition is the same as that of alloy #1, and it was heat treated at 1073 K (800 °C) for 1 month. Three different phase regions are found. The composition of the bright phase is Co-74.1 at. pct Sb-0.8 at. pct Ga, and it is the CoSb₃ phase. The composition of the gray phase region is Co-66.1 at. pct Sb with negligible Ga, and it is the CoSb₂ phase. The region with finer microstructure was the liquid phase prior to its removal from the furnace. Figure 2(b) shows the XRD diffractogram, which confirms the existence of the CoSb₃ and CoSb₂ phases. The alloy #8 at 1073 K (800 °C) is in the CoSb₃ + CoSb₂ + liquid three-phase region. Since alloys #4 and #8 have different equilibrium phases, there should be a phase boundary between alloy #4 (CoSb₂ + liquid) and alloy #8 (CoSb₃ + CoSb₂ + liquid).

Fig. 2

(a) BEI micrograph of the as-quenched alloy #8(Co-70.0 at. pct Sb-10.0 at. pct Ga) heat treated at 1073 K (800 °C). (b) XRD diffractogram of the as-quenched alloy #8

Figures 3(a) through (d) show the BEI micrographs of the as-quenched alloys #13(Co-65.0 at. pct Sb-20.0 at. pct Ga), #2(Co-70.0 at. pct Sb-10.0 at. pct Ga), #22(Co-52.5 at. pct Sb-45.0 at. pct Ga), and #23(Co-70.0 at. pct Sb-10.0 at. pct Ga). Following similar analytic procedures as mentioned for alloys #4 and #8, the equilibrated phases of these alloys at the heat-treated temperatures were determined to be in the liquid + CoSb₃, liquid + CoSb, liquid + GaSb, and liquid + CoSb₃ + GaSb phase regions, respectively. Figure 4 shows the BEI micrograph of alloy #5(Co-65.0 at. pct Sb-20.0 at. pct Ga). Compared with the micrographs as shown in Figure 3, there is no large solid which co-exists c the alloy #5 is in the liquid state at 1123 K (850 °C). The results of the determined equilibrium phases are summarized in Table I.

Fig. 3

(a) BEI micrograph of the as-quenched alloy #13(Co-65.0 at. pct Sb-20.0 at. pct Ga) heat treated at 1023 K (750 °C). (b) BEI micrograph of the as-quenched alloy #2(Co-70.0 at. pct Sb-10.0 at. pct Ga) heat treated at 1193 K (920 °C). (c) BEI micrograph of the as-quenched alloy #22(Co-52.5 at. pct Sb-45.0 at. pct Ga) heat treated at 953 K (680 °C). (d): BEI micrograph of the as-quenched alloy #23(Co-70.0 at. pct Sb-10.0 at. pct Ga) heat treated at 923 K (650 °C)

Fig. 4

BEI micrograph of the as-quenched alloy #5(Co-65.0 at. pct Sb-20.0 at. pct Ga) heat treated at 1123 K (850 °C)

The isoplethal section along the CoSb₃-GaSb region can be constructed based on these ternary experimental results and the phase diagrams of Co-Sb[15] and Ga-Sb[14] systems. Along the CoSb₃ terminal, the invariant reactions encountered are the melting of CoSb (the liquidus temperature at CoSb₃), melting of CoSb₂ (the liquid + CoSb = CoSb₂ peritectic reaction), melting of CoSb₃ (the liquid + CoSb₂ = CoSb₃ peritectic reaction), and the liquid = Sb + CoSb₃ eutectic reaction. Their reaction temperatures are at 1363 K, 1209 K, 1147 K, and 902 K (1090 °C, 936 °C, 874 °C, and 629 °C),[15] respectively. Along the GaSb terminal, there are encountered the congruent melting of GaSb at 984.7 K (711.7 °C),[14] and liquid = GaSb + Sb eutectic reaction at 862.3 K (589.3 °C).[15] The CoSb₃-GaSb isoplethal section is thus determined as shown in Figure 5.

Fig. 5

Isoplethal section along the CoSb₃-GaSb region

4 Thermodynamic Modeling

In the temperature range of interest, the Co-Sb-Ga system has 12 phases: HCP_A3 (Co_LT), FCC_A1(Co_HT), CoGa, CoGa₃, Orthorhombic_Ga(Ga), GaSb, Rhombohedral_A7(Sb), CoSb, CoSb₂, CoSb₃, Co₃Sb₂Ga₄, and liquid phases.

The Gibbs energies of pure elements with respect to temperature $^{0} G_{i} (T) = G_{i} (T) - H_{i}^{\text{SER}}$ are represented by Eq. [1]:

$$ {^{0}} G_{i} (T) = a + bT + cT\ln(T) + {dT^{2}} + {eT^{ - 1}} + {fT^{3}} + {iT^{4}} + {jT^{7}} + {kT^{ - 9}} . $$

(1)

The $^{0} G_{i} (T)$ data refer to the constant enthalpy values of the standard element reference $H_{i}^{\text{SER}}$ at 298.15 K (25.15 °C) and 1 bar as recommended by the Scientific Group Thermodata Europe (SGTE).[18] The reference states are HCP_A3 (Co), Orthorhombic_Ga(Ga), and Rhombohedral_A7(Sb). The $^{0} G_{i} (T)$ expressions may be given for several temperature ranges, where the coefficients a, b, c, d, e, f, i, j, k are with different values. The $^{0} G_{i} (T)$ functions are taken from SGTE Unary (Pure elements) TDB v5.0.[18]

Liquid, HCP_A3 and FCC_A1(Co) phases are described by the substitutional solution model[19]:

$$ G_{\text{m}} = \sum\limits_{i} {x_{i} {}^{0}G_{i} \left( T \right) + RT} \sum\limits_{i} {x_{i} ln\left( {x_{i} } \right)} + \sum\limits_{i} {\sum\limits_{i > j} {x_{i} x_{j} \left( {\sum\limits_{\nu } {{}^{\nu }L_{ij} \left( {x_{i} - x_{j} } \right)^{\nu } } } \right)} } + x_{i} x_{j} x_{k} \left( {\sum\limits_{i} {x_{i}^{i} L_{ijk} } } \right), $$

(2)

where x _i is a mole fraction of element, L _ij is the binary interaction parameter, and L _ijk is the ternary interaction parameter.

The intermetallic compounds are described by the compound energy formalism (CEF).[19] The Gibbs energies of the intermetallic compounds are given by Eq. [3]

$$ G_{\text{m}} = \sum\limits_{I0} {P_{I0} \left( Y \right){}^{0}G_{I0} + RT\sum\limits_{\text{s}} {N^{\text{s}} } } \sum\limits_{i} {y_{i}^{\text{s}} \ln \left( {y_{i}^{\text{s}} } \right)} + \sum\limits_{Z > 0} {\sum\limits_{IZ} {P_{IZ} \left( Y \right)L_{IZ} } } , $$

(3)

where the first term of Eq. [3] represents Gibbs energy of pure elements, the second term represents mechanical mixing, and the third one indicates excess Gibbs energy. The ternary intermetallic compound Co₃Sb₂Ga₄ does not exhibit homogeneity range, so its description is reduced to the line compound case. Under this circumstance, Eq. [3] is shown as

$$ G_{m} = \sum\limits_{i} {x_{i} {}^{0}G_{i} } + A + B \times T $$

(4)

Equation [4] does not have terms connected with mechanical mixing and excess Gibbs energy, and the Gibbs energy is described as a linear function of temperature.

Thermodynamic descriptions of the binary Co-Ga system by Chari et al.,[13] Ga-Sb by Ansara et al.,[14] and Co-Sb by Zhang et al.[15] are adopted in this study. However, the CoSb₃ phase has been described as a line compound in all the previous studies.[15–17] Since the CoSb₃ phase is of primary interest and the Ga solubility in the CoSb₃ phase is critical to its thermodynamic properties, a thermodynamic model of the CoSb₃ phase which can properly describe its ternary solubility needs to be developed even though the Ga solubilities in the CoSb₃ phase are small. The (Ga_VF) _x Co₄Sb_12−x/2(Ga_Sb) _x/2 description is used for the CoSb₃ phase in this study according to the report of Qiu et al.[10]

The parameters of these thermodynamic models are determined by an optimization procedure. The optimization has been performed using Pandat[20] and Thermocalc[21] software following the guidelines proposed by Schmid-Fetzer et al.[22] The invariant reactions and phase equilibrium data of the Co-Ga-Sb ternary system are used. All parameters are finally evaluated together to provide the best descriptions of the Co-Sb-Ga ternary system, and the results are summarized in Table II.

Table II Phases Stabilities, Thermodynamic Functions, and Parameters of the Co-Sb-Ga Ternary System

5 Thermodynamic Modeling Results and Discussion

The calculated isothermal section of the Co-Ga-Sb system at 923 K (650 °C) is superimposed with the experimental results by Chen et al.[12] as shown in Figure 6, and the calculation reproduces experimental data well. There are nine tie-triangles at the 923 K (650 °C) isothermal section: Liquid + CoSb₃ + GaSb, Liquid + CoGa₃ + GaSb, CoGa + CoGa₃ + GaSb, CoGa + GaSb + Co₃Sb₂Ga₄, CoSb₃ + GaSb + Co₃Sb₂Ga₄, CoGa + Co₃Sb₂Ga₄ + CoSb₃, CoGa + CoSb₂ + CoSb₃, CoGa + CoSb + CoSb₂, and CoGa + CoSb+(Co). Due to experimental difficulties, there are no experimental phase equilibria data with a Co concentration higher than 34 at. pct. However, the phase relationships at the Co-rich corner can be determined by calculation based on the developed thermodynamic models. As shown in Figure 6, the CoGa phase has tie lines with most of the compounds.

Fig. 6

Calculated isothermal section at 923 K (650 °C) superimposed with data given by Chen et al.[12]

Figure 7 shows an enlarged portion of the 923 K (650 °C) isothermal section around CoSb₃ along with the experimental data by Qiu et al.[10] The calculation results are in good agreement with experimental data. Although the solubility of Ga in the CoSb₃ is around 1 at. pct and is not significant from the aspect of phase equilibria study, it has been demonstrated that the defect type and the Ga solubility are critical to the thermoelectric properties of the CoSb₃(Ga) phase. The (Ga_VF) _x Co₄Sb_12−x/2(Ga_Sb) _x/2 dual site occupancy leads to effective scattering of a wide range of lattice phonons, and shows nearly intrinsic semiconductor behavior with low electron concentration and a large Seebeck coefficient.[10] The compositions of Ga at two different sites, i.e., the vacancy site and the Sb site, can be computed directly from the model. For example, when x is 0.1, the Ga solubility in the compound is 0.93 at. pct, then 0.62 at. pct of the Ga is at the vacancy site and 0.31 at. pct Ga is at the Sb site. This defect model also successfully describes the tilt solubility range of the CoSb₃(Ga) phase, as shown in Figure 6, and provides good understanding for both the phase equilibria and the thermoelectric properties.[10,12]

Fig. 7

Zoomed part of the isothermal section at 923 K (650 °C) together with experimental data given by Qiu et al.[10]

In addition to the isothermal section, the liquidus projection and the CoSb₃-GaSb isoplethal section are also calculated. As shown in Figures 8 and 9, the calculated liquidus projection and the isoplethal section are in good agreement with experimental determinations.[12] The regimes of primary solidification phases and the temperature descending directions of all the univariant lines are the same. The invariant reactions are summarized in Table III. Except for the 5 degree difference of the reaction, L + CoGa = CoGa₃ + GaSb, all the other reactions are reproduced very well. It should be mentioned that the experimental uncertainties of thermal analysis could be significant due to kinetic effects such as undercooling in this system. Furthermore, there are no thermodynamic properties of Co-Sb-Ga alloys and no phase equilibria data at the Co-rich corner, and the properties of the ternary intermetallic compound Co₃Sb₂Ga₄ are unknown. Further valid refinement of these thermodynamic descriptions should require at least some properties of Co₃Sb₂Ga₄ compound, thermodynamic properties of Co-Sb-Ga alloys, and Co-rich Co-Sb-Ga phase equilibria data.

Fig. 8

Calculated liquidus projection of the Co-Ga-Sb system superimposed with experimental data given by Chen et al.[12]

Fig. 9

Calculated isoplethal section CoSb₃-GaSb superimposed with experimental data given in this study

Table III The Invariant Reactions of the Ternary Co-Sb-Ga System

The reaction scheme is shown in Figure 10. Solidification paths of ternary Co-Sb-Ga alloys could be predicted according to the liquidus projection and the reaction scheme if equilibrium solidification is followed. For example, according to the reaction scheme and the liquidus projection, CoSb₃ is the primary solidification phase of the Co-78.0 at. pct Sb-18.0 at. pct Ga alloy,[12] GaSb is the secondary phase, and the alloy completely solidifies at the L = CoSb₃ + GaSb + Sb invariant reaction. The results of the solidified phases are in good agreement with the prediction.[12]

Fig. 10

The calculated reaction scheme of the Co-Ga-Sb ternary system

Similarly, according to the liquidus projection and the reaction scheme, CoGa and GaSb are the primary and secondary solidification phases of the Co-30.0 at. pct Sb-30.0 at. pct Ga alloy,[12] respectively. The Co₃Sb₂Ga₄ ternary phase should form after GaSb, and then the CoSb₃ phase forms after the ternary phase. However, the Co₃Sb₂Ga₄ ternary phase is not found. The reason could be simply because either it is not formed or could not be detected due to very weak signals resulting from the small amount of Co₃Sb₂Ga₄ phase. Furthermore, solidification paths could penetrate through instead of staying on the univariant lines in some peritectic type reactions.[23] Even though phase diagrams are important, it still should be mentioned that phase transformation is a combined result of both thermodynamic and kinetic driving forces, and inconsistencies could be encountered if only thermodynamic factors are considered.

6 Conclusions

In addition to the terminal phases and the liquid phase, there are six intermediate binary phases: CoGa, CoGa₃, CoSb, CoSb₂, CoSb₃, and GaSb, together with one ternary phase Co₃Sb₂Ga₄ in the Co-Ga-Sb ternary system in the temperatures ranging from 700 K to 1300 K (427 °C to 1027 °C). Liquid and terminal solid solution phases are described by the substitutional solution model. Most of the intermetallic compounds are described by the compound energy formalism—except for the Ga solution in the CoSb₃ compound, which is described by a dual-site occupation (Ga_VF) _x Co₄Sb_12−x/2(Ga_Sb) _x/2 model and the ternary Co₃Sb₂Ga₄ phase described by line compound. As mentioned above, there are no ternary thermodynamic properties and no phase equilibria data at the Co-rich corner, and the description of the ternary intermetallic compound is predicted based on only the liquidus projection and the existence of this phase at 923 K (650 °C). Although the calculated results show quite good agreement with most of the experimental measurements, the thermodynamic descriptions could be further improved with more experimental results regarding the Co₃Sb₂Ga₄ ternary compound as well as phase equilibria information at the Co-rich corner.