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.
ACKNOWLEDGMENT
The authors acknowledge the financial supports of
the National Science Council of Taiwan (NSC1013113-P-008-001 and NSC102-2221-E-259 -034).
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