The Co-Sb-Ga System: Isoplethal Section and Thermodynamic Modeling WOJCIECH GIERLOTKA, SINN-WEN CHEN, WEI-AN CHEN, JUI-SHEN CHANG, G. JEFFREY SNYDER, and YINGLU TANG 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 (GaVF)xCo4Sb12x/2(GaSb)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 (GaVF)xCo4Sb12x/2(GaSb)x/2 model gives good descriptions of both phase equilibria and thermoelectric properties of the CoSb3 phase with Ga doping. DOI: 10.1007/s11661-015-2763-1 Ó The Minerals, Metals & Materials Society and ASM International 2015 I. 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-SbGa isothermal section at 773 K (500 °C). Qiu et al.[10] WOJCIECH GIERLOTKA, Assistant Professor, is with the Department of Materials Science and Engineering, National Dong Hwa University, Hualien, Taiwan R.O.C. SINN-WEN CHEN, Professor, WEI-AN CHEN, Master Student, and JUI-SHEN CHANG, Doctoral Student, are with the Department of Chemical Engineering, National Tsing Hua University, Hsinchu, Taiwan R.O.C. Contact e-mail: swchen@mx.nthu.edu.tw G. JEFFREY SNYDER, Professor, is with the Materials Science, California Institute of Technology, Pasadena, CA, and also with the Department of Materials Science and Engineering, Northwestern University, Evanston, IL. YINGLU TANG, Doctoral Student, is with the Materials Science, California Institute of Technology. Manuscript submitted October 22, 2014. Article published online 10 February 2015 1488—VOLUME 46A, APRIL 2015 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. II. 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 105 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 heattreatment times of the alloys are summarized in Table I. METALLURGICAL AND MATERIALS TRANSACTIONS A Table I. Nominal Compositions and Equilibrium Phases of Ternary Co-Sb-Ga Alloys Nominal Composition No. CSG-1 CSG-2 CSG-3 CSG-4 CSG-5 CSG-6 CSG-7 CSG-8 CSG-9 CSG-10 CSG-11 CSG-12 CSG-13 CSG-14 CSG-15 CSG-16 CSG-17 CSG-18 CSG-19 CSG-20 CSG-21 CSG-22 CSG-23 CSG-24 CSG-25 CSG-26 at. pct Co at. pct Sb at. pct Ga Heat-Treated Temp. T [K (°C)] 22 20 22 20 15 10 22 20 18 15 10 20 15 10 7 22 20 18 15 10 7 2.5 20 15 10 5 72 70 72 70 65 60 72 70 68 65 60 70 65 60 57 72 70 68 65 60 57 52.5 70 65 60 55 6 10 6 10 20 30 6 10 14 20 30 10 20 30 36 6 10 14 20 30 36 45 10 20 30 40 1223 (950) 1193 (920) 1123 (850) 1123 (850) 1123 (850) 1123 (850) 1073 (800) 1073 (800) 1073 (800) 1073 (800) 1073 (800) 1023 (750) 1023 (750) 1023 (750) 1023 (750) 973 (700) 973 (700) 973 (700) 973 (700) 973 (700) 973 (700) 953 (680) 923 (650) 923 (650) 923 (650) 923 (650) 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-Ka 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). III. 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 twophase 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. METALLURGICAL AND MATERIALS TRANSACTIONS A Equilibrated Phases liquid + CoSb liquid + CoSb liquid + CoSb2 liquid + CoSb2 liquid liquid liquid + CoSb3 liquid + CoSb2 + CoSb3 liquid + CoSb2 liquid + CoSb2 liquid liquid + CoSb3 liquid + CoSb3 liquid liquid liquid + CoSb3 liquid + CoSb3 liquid + CoSb3 liquid + CoSb3 liquid + CoSb3 liquid liquid + GaSb liquid + CoSb3 + GaSb liquid + CoSb3 + GaSb liquid + CoSb3 + GaSb liquid + CoSb3 + GaSb 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. 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). Figures 3(a) through (d) show the BEI micrographs of the as-quenched alloys #13(Co-65.0 at. pct Sb20.0 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 liqVOLUME 46A, APRIL 2015—1489 Fig. 1—(a) BEI micrograph of the as-quenched alloy #4(Co70.0 at. pct Sb-10.0 at. pct Ga) heat treated at 1123 K (850 °C). (b): XRD diffractogram of the as-quenched alloy #4. uid + CoSb3 + GaSb phase regions, respectively. Figure 4 shows the BEI micrograph of alloy #5(Co65.0 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. 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 GaSb[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 1490—VOLUME 46A, APRIL 2015 Fig. 2—(a) BEI micrograph of the as-quenched alloy #8(Co70.0 at. pct Sb-10.0 at. pct Ga) heat treated at 1073 K (800 °C). (b) XRD diffractogram of the as-quenched alloy #8. isoplethal section is thus determined as shown in Figure 5. IV. 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 are represented by temperature 0 Gi ðTÞ ¼ Gi ðTÞ HSER i Eq. [1]: 0 Gi ðTÞ ¼ a þ bT þ cT lnðTÞ þ dT2 þ eT1 þ fT3 þ iT4 þ jT7 þ kT9 : ½1 The 0 Gi ðTÞ data refer to the constant enthalpy values at 298.15 K of the standard element reference HSER i (25.15 °C) and 1 bar as recommended by the Scientific METALLURGICAL AND MATERIALS TRANSACTIONS A 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). Fig. 5—Isoplethal section along the CoSb3-GaSb region. [18] Group Thermodata Europe (SGTE). The reference states are HCP_A3 (Co), Orthorhombic_Ga(Ga), and Rhombohedral_A7(Sb). The 0 Gi ðTÞ 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 METALLURGICAL AND MATERIALS TRANSACTIONS A 0 Gi ðTÞ 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]: VOLUME 46A, APRIL 2015—1491 Fig. 6—Calculated isothermal section at 923 K (650 °C) superimposed with data given by Chen et al.[12]. Fig. 8—Calculated liquidus projection of the Co-Ga-Sb system superimposed with experimental data given by Chen et al.[12]. Fig. 7—Zoomed part of the isothermal section at 923 K (650 °C) together with experimental data given by Qiu et al.[10]. Gm ¼ X xi 0 Gi ðTÞ þ RT X i þ xi lnðxi Þ i XX i xi xj m i>j þ xi xj xk X X m m Lij xi xj ! ½2 ! xii Lijk ; i where xi is a mole fraction of element, Lij is the binary interaction parameter, and Lijk 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] X X X PI0 ðYÞ0 GI0 þ RT Ns ysi ln ysi Gm ¼ s I0 þ XX PIZ ðYÞLIZ ; i ½3 Z>0 IZ 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 X xi 0 Gi þ A þ B T ½4 Gm ¼ i 1492—VOLUME 46A, APRIL 2015 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 (GaVF)xCo4Sb12x/2(GaSb)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. V. 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 METALLURGICAL AND MATERIALS TRANSACTIONS A METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 46A, APRIL 2015—1493 [13] [13] [13] [13] [13] [13] GCoGa Ga:Co ¼ GGACO GCoGa Sb:Co ¼ 13; 000 þ 0:5 GHSERSB þ 0:5 GHSERCO GCoGa Ga:Sb ¼ 8000 þ 0:5 GHSERGA þ 0:5 GHSERSB GCoGa Co:Va ¼ GCOCO þ GGAVA GGACO GCoGa Ga:Va ¼ GGAVA LCoGa Co;Ga:Co ¼ 11752 þ 3:505 T LCoGa Co:Co;Va ¼ 6847 þ :6913 T LCoGa Ga:Co;Va ¼ 24462 þ 9:677 T LCoGa Co;Ga:Va ¼ 7557 0:3907 T 0 0 0 0 298 to 4000 (25 to 3763) 298 to 4000 (25 to 3763) 298 to 4000 (25 to 3763) 298 to 4000 (25 to 3763) 298 to 4000 (25 to 3763) 298 to 4000 (25 to 3763) 298 to 4000 (25 to 3763) 298 to 4000 (25 to 3763) 298 to 3000 (25 to 2727) 298 to 3000 (25 to 2727) CoGa3 CoSb 298 to 4000 (25 to 3763) [13] GCoGa Co:Co ¼ GCOCO [15] [15] this study this study [15] GCoSb Sb:Co:Va ¼ 15; 370 3:95 T þ 0:4920984 T LNðTÞ þ 0:002260266 T 2 1:0735435E 06 T 3 20074 T ð1Þ þ 1:5E 21 T 7 þ 0:3333 GHSERCO þ 0:3333 GHSERSBL GCoSb Ga:Co:Va ¼ 4:99997817E þ 02 þ 0:3333 GHSERCO þ 0:3333 GHSERGA GCoSb Ga:Co:Co ¼ 105:196221þ:6666 GHSERCO# + :3333 GHSERGA# GCoSb Sb:Ga:Co ¼ 105:196221þ:3333 GHSERCO# + :3333 GHSERGA# þ:3333 GHSERSB# this study GCoSb Sb:Co:Co ¼ 12; 044:4 þ 3:2 T þ 0:6667 GHSERCO þ 0:3333 GHSERSBL 3 LCoGa Co:Ga;Sb ¼ 8272:47406 þ 2:6880078E 02 T this study 3 GCoGa Co:Sb ¼ 500 þ 0:25 GHSERCO þ 0:75 GHSERSB 0 [13] 3 GCoGa Co:Ga ¼ 30; 770 þ 3:043 T þ 0:25 GHSERCO þ 0:75 GHSERGA [13] [13] [13] this study 298 to 3000 (25 to 2727) ¼ 24989:4441 3:60764371 T þ 0:35 GHSERCO# + 0:23 GHSERSB# + 0:42 GHSERGA# CoGa References 298 to 3000 (25 to 2727) Function Co3Sb2Ga4 3 Sb2 Ga4 GCo Co:Ga:Sb Temperature Range [K (°C)] Phases Stabilities, Thermodynamic Functions, and Parameters of the Co-Sb-Ga Ternary System Phase Table II. 1494—VOLUME 46A, APRIL 2015 METALLURGICAL AND MATERIALS TRANSACTIONS A 298 to 4000 (25 to 3763) 903.78 to 3000 (630.78 to 2727) 298 to 903.78 (25 to 630.78) 302.91 to 4000 (73 to 3727) 0 A1 GFCC ¼ 17;512:331þ575:063691 T 108:228783 T LNðTÞþ:227155636 Ga T 2 1:18575257E 04 T 3 þ 439;954 T ð1Þ A1 GFCC ¼ 3255:643þ122:53019 T 26:0692906 T LNðTÞþ1:506E 04 T 2 Ga 4:0173E 08 T 3 118332 T ð1Þþ1:64547E þ 23 T ð9Þ A1 GFCC ¼ þ10631:142þ142:454689 T 30:5130752 T LNðTÞþ:007748768 T 2 Sb 3:003415E 06 T 3 þ 100625 T ð1Þ A1 ¼ þ8135:17þ155:785872 T 31:38 T LNðTÞþ1:616849E þ 27 T ð9Þ GFCC Sb FCC A1 LCo;Ga ¼ 12;5202 þ 54:131 T ¼ 1:35 200 to 302.91 (73 to 29.91) A1 FCC BMAGNCo 300 to 6000 (27 to 5727) 300 to 6000 (27 to 5727) 3 LCoSb Ga;Va:Co:Sb ¼ 1;850;000 1768 to 6000 (1495 to 5727) 298 to 1768 (25 to 1495) FCC_A1 0 [13] [18] [18] [18] [18] [18] [18] [18] [18] this study this study [15] this study 3 GCoSb Ga:Co:Ga ¼ 100 + 4*GHSERCO + 36*GHSERGA 3 GCoSb Va:Co:Sb ¼ 370;030:16þ842:02087 T 102:675938 T LNðTÞ + 4*GHSERCO + 12*GHSERSB 0 CoSb3 LVa:Co:Ga;Sb ¼ 750;000 this study this study [15] this study this study [15] References 2 GCoSb Co:Ga;Sb ¼ 52;035 þ 45 T A1 GFCC ¼ 737:832þ132:750762 T 25:0861 T LNðTÞ:002654739 Co T 2 1:7348E 07 T 3 þ 72527 T ð1Þ A1 GFCC ¼ 16; 770:075þ252:668487 T 40:5 T LNðTÞþ9:3488E Co þ30 T ð9Þ FCC A1 TCCo ¼ 1369 298 to 3000 (25 to 2727) 298 to 4000 (25 to 3763) CoSb3 LCoSb Ga;Sb:Co:Va ¼ 15; 258:117 0 298 to 4000 (25 to 3763) Function 2 GCoSb Co:Sb ¼ 25; 535 þ 5:3 T þ 2:0778578 T LNðTÞ 0:013091 T 2 þ 1:5696E 06 T 3 20142 T ð1Þ þ 2E 21 T 7 þ 0:333333 GHSERCO þ 0:6667 GHSERSBL 2 GCoSb Co:Ga ¼ 500 þ 0:333333 GHSERCO + :6667 GHSERGA LCoSb Sb;Ga:Co:Co ¼ 3000 0 298 to 4000 (25 to 3763) 298 to 3000 (25 to 2727) LCoSb Sb:Co:Co;Va ¼ 7522:5 + 4*T continued 0 Temperature Range [K (°C)] CoSb2 Phase Table II. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 46A, APRIL 2015—1495 Liquid HCP_A3 GaSb Phase 302.91 to 4000 (73 to 3727) 200 to 302.91 (73 to 29.91) 1768 to 6000 (1495 to 5727) 298 to 1768 (25 to 1495) 298 to 4000 (25 to 3763) 903.78 to 2000 (25 to 1727) 298 to 903.78 (25 to 630.78) 302.91 to 4000 (73 to 3727) 200 to 302.91 (73 to 29.91) A3 ¼ 1:35 HCP A3 LCo;Ga ¼ 87051 þ 22:438 T GLiquid ¼ 15;821:033þ567:189696 T 108:228783 T LNðTÞþ:227155636 T 2 1:18575257E Ga 04 T 3 þ 439954 T ð1Þ7:0171E 17 T 7 ¼ 1389:188þ114:049043 T 26:0692906 T LNðTÞþ1:506E 04 T 2 4:0173E GLiquid Ga 08 T 3 118332 T ð1Þ GLiquid ¼ þ15;395:278þ124:434078 T 25:0861 T LNðTÞ:002654739 T 2 1:7348E Co 07 T 3 þ 72527 T ð1Þ2:19801E 21 T 7 GLiquid ¼ 846:61þ243:599944 T 40:5 T LNðTÞ Co 0 A3 ¼ 16;812:331þ575:763691 T 108:228783 T LNðTÞþ:227155636 T 2 GHCP Ga 1:18575257E 04 T 3 þ 439954 T ð1Þ A3 GHCP ¼ 2555:643þ123:23019 T 26:0692906 T LNðTÞþ1:506E 04 T 2 Ga 4:0173E 08 T 3 118332 T ð1Þþ1:64547E þ 23 T ð9Þ A3 GHCP ¼ þ10;631:142þ143:154689 T 30:5130752 T LNðTÞþ:007748768 T 2 3:003415E Sb 06 T 3 þ 100625 T ð1Þ A3 GHCP ¼ þ8135:17þ156:485872 T 31:38 T LNðTÞþ1:616849E þ 27 T ð9Þ Sb BMAGNHCP Co ¼ 1396 298 to 6000 (25 to 5727) A3 TCHCP Co A3 GHCP ¼ þ310:241þ133:36601 T 25:0861 T LNðTÞ:002654739 T 2 1:7348E Co 07 T 3 þ 72527 T ð1Þ A3 ¼ 17;197:666þ253:28374 T 40:5 T LNðTÞþ9:3488E þ 30 T ð9Þ GHCP Co 298 to 6000 (25 to 5727) 1768 to 6000 (1495 to 5727) 298 to 1768 (25 to 1495) 298 to 4000 (25 to 3763) this study [18] [18] [18] [18] [13] [18] [18] [18] [18] [18] [18] [18] [18] this study [14] 298 to 4000 (25 to 3763) this study this study [13] References GGaSb Ga:Sb ¼ 21;738:110:53764 T + 2:692876 T LNðTÞ:00137791 T 2 þ 0:5 GHSERGA + 0:5 GHSERSB 0 GaSb LGa:Co;Sb ¼ 30;000 4:687707 T FCC A1 LCo;Ga;Sb ¼0 2 298 to 4000 (25 to 3763) Function this study FCC A1 LCo;Ga;Sb ¼ 15;229:4256 1 298 to 4000 (25 to 3763) continued GGaSb Ga:Co ¼ 300 þ 0:5 GHSERCO + 0:5 GHSERGA FCC A1 LCo;Ga;Sb ¼ 263;362:501 0 298 to 4000 (25 to 3763) ¼ þ30;657 25:625 T FCC A1 LCo;Ga 1 Temperature Range [K (°C)] Table II. 1496—VOLUME 46A, APRIL 2015 METALLURGICAL AND MATERIALS TRANSACTIONS A GCOCO Tetragonal_A6 Rhombohedral_A7 Orthorombic_Ga Phase [15] [15] [15] [14] [14] [14] this study this study this study LLiquid Co;Sb ¼ 8001:627:8 T LLiquid Co;Sb ¼ 23;400 þ 20:6 T LLiquid Co;Sb ¼ 13;708 4:5 T LLiquid Ga;Sb ¼ 13;953:8þ71:07866 T 9:6232 T LNðTÞ LLiquid Ga;Sb ¼ 1722:91:92588 T LLiquid Ga;Sb ¼ 2128:3 LLiquid Co;Ga;Sb ¼ 254;285:418268:922801 T LLiquid Co;Ga;Sb ¼ 327;367:684þ277:209828 T LLiquid Co;Ga;Sb ¼ 606;013:511640:916206 T 0 1 2 0 1 2 0 1 2 298 to 4000 (25 to 3763) 298 to 4000 (25 to 3763) 298 to 4000 (25 to 3763) 298 to 4000 (25 to 3763) 298 to 4000 (25 to 3763) 298 to 4000 (25 to 3763) 298 to 4000 (25 to 3763) 298 to 4000 (25 to 3763) 298 to 4000 (25 to 3763) 302.91 to 4000 (73 to 3727) 298 to 302.91 (25 to 29.91) 903.78 to 2000 (630.78 to 1727) 298 to 903.78 (25 to 630.78) 302.91 to 4000 (73 to 3727) 200 to 302.91 (73 to 29.91) Tetragonal A6 GGa ¼ 17;812:331þ575:263691 T 108:228783 T LNðTÞþ:227155636 T 2 1:18575257E 04 T 3 þ 439954 T ð1Þ Tetragonal A6 GGa ¼ 3555:643þ122:73019 T 26:0692906 T LNðTÞþ1:506E 04 T 2 4:0173E 08 T 3 118332 T ð1Þþ1:64547E þ 23 T ð9Þ GHSERCO + 2938 - :7138 T [13] [18] [18] [18] [18] [18] [18] [13] LLiquid Co;Ga ¼ 12;605:5 1 298 to 4000 (25 to 3763) Ga GOrthorombic ¼ 21;312:331þ585:263691 T 108:228783 T LNðTÞþ:227155636 T 2 Ga 1:18575257E 04 T 3 þ 439954 T ð1Þ Ga GOrthorombic ¼ 7055:643þ132:73019 T 26:0692906 T LNðTÞþ1:506E 04 T 2 Ga 4:0173E 08 T 3 118332 T ð1Þþ1:64547E þ 23 T ð9Þ Rhombohedral A7 ¼ 9242:858þ156:154689 T 30:5130752 T LNðTÞþ:007748768 T 2 GSb 3:003415E 06 T 3 þ 100625 T ð1Þ Rhombohedral A7 GSb ¼ 11;738:83þ169:485872 T 31:38 T LNðTÞþ1:616849E þ 27 T ð9Þ [13] LLiquid Co;Ga ¼ 61;807 þ 7:985 T 0 903.76 – 2000 (25 to 1727) 298 to 4000 (25 to 3763) [18] References [18] Function ¼ 10;579:47þ134:231525 T 30:5130752 T LNðTÞþ:007748768 T 2 3:003415E 06 T 3 þ 100625 T ð1Þ1:74847E 20 T 7 GLiquid ¼ þ8175:359þ147:455986 T 31:38 T LNðTÞ Sb GLiquid Sb 298 to 903.76 (25 to 630.76) Temperature Range [K (°C)] Table II. continued [18] Reaction Experiment[12] Calculation 1267 862 1091 1028 1017 959 973 969 A7 GRhombohedral Sb GHSERSB Ga L = Co + CoSb + CoGa — 861 L = CoSb3 + Sb + GaSb L + CoGa = CoSb + Co3Sb2Ga4 1091 L + CoSb = CoSb2 + Co3Sb2Ga4 1028 L + CoSb2 = CoSb3 + Co3Sb2Ga4 1020 L + Co3Sb2Ga4 = CoSb3 + GaSb 959 L + CoGa = Co3Sb2Ga4 + GaSb — L + CoGa = GaSb + CoGa3 960 Orthorombic GGa GHSERCO The Invariant Reactions of the Ternary Co-Sb-Ga System Temperature [K (°C)] GHSERGA [18] [18] Table III. 302.91 to 4000 (73 to 3727) 298 to 302.91 (25 to 29.91) GGAGA [13] [13] 9242:858þ156:154689 T 30:5130752 T LNðTÞþ:007748768 T 2 3:003415E 06 T 3 þ 100625 T ð1Þ 16;812:331þ573:563691 T108:228783 T*LN(T) + :227155636 T 21:18575257E 04 T 3 þ 439954 T ð1Þ 2555:643þ121:03019 T 26:0692906 T LNðTÞþ1:506E 04 T 2 4:0173E 08 T 3 118;332 T ð1Þ þ 1:64547E þ 23 T ð9Þ HCP A3 GCo GGHASERSBL [13] [13] 0:5 GHSERGA + 7250 - 6:35 T GGAVA [13] 0:5 GHSERCO + 0:5 GHSERGA - 42125 + 9:519 T Phase Temperature Range [K (°C)] GGACO References Function continued Table II. Fig. 9—Calculated isoplethal section CoSb3-GaSb superimposed with experimental data given in this study. METALLURGICAL AND MATERIALS TRANSACTIONS A (650 °C) isothermal section: Liquid + CoSb3 + GaSb, CoGa + CoGa3 + GaSb, Liquid + CoGa3 + GaSb, CoSb3 + GaSb + CoGa + GaSb + Co3Sb2Ga4, Co3Sb2Ga4, CoGa + Co3Sb2Ga4 + CoSb3, CoGa + CoGa + CoSb + CoSb2, and CoSb2 + CoSb3, 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. 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 (GaVF)xCo4Sb12x/2(GaSb)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, VOLUME 46A, APRIL 2015—1497 Fig. 10—The calculated reaction scheme of the Co-Ga-Sb ternary system. 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] 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. 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 1498—VOLUME 46A, APRIL 2015 solidifies at the L = CoSb3 + GaSb + Sb invariant reaction. The results of the solidified phases are in good agreement with the prediction.[12] 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 Sb30.0 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. VI. 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 (GaVF)xCo4Sb12x/2(GaSb)x/2 model and the ternary Co3Sb2Ga4 phase described by line compound. As mentioned above, there are no ternary thermodynamic METALLURGICAL AND MATERIALS TRANSACTIONS A 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. 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