Experimental investigation and thermodynamic calculation of the Cu-Ge-Sb system

Article abstract of DOI:10.1016/j.jallcom.2017.08.051

Phase diagram of the Cu-Ge-Sb ternary system has been investigated experimentally and assessed thermodynamically by means of CALPHAD approach. Experimental results were obtained by using differential thermal analysis (DTA), scanning electron microscopy (SEM) with energy dispersive spectrometry (EDS), and X-ray powder diffraction (XRD) methods. Examined samples can construct two isothermal sections at 400 and 500 °C as well as three vertical sections of Cu-GeSb, Ge-CuSb, and Sb-CuGe. From equilibrated samples in Cu-rich part of the 500 °C isothermal section, one ternary compound was detected. Based on the present experimental data and available literature data, a thermodynamic description of the ternary Cu-Ge-Sb system has been developed. A reasonable agreement between experimental data and the calculated phase equilibria is obtained.

Full text of DOI:10.1016/j.jallcom.2017.08.051

Journal of Alloys and Compounds 726 (2017) 820e832
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: http://www.elsevier.com/locate/jalcom
Review
Experimental investigation and thermodynamic calculation of the
Cu-Ge-Sb system
,
b
,
*
b
c
ꢀ a
ꢁ
ꢀ a
ꢀ d
Milena Premovic
, Yong Du , Dusko Minic , Cong Zhang , Dragan Manasijevic ,
ꢁ
ꢀ d
ꢀ d
Ljubisa Balanovic , Ivana Markovic
a
ꢁ
University of Pristina, Faculty of Technical Science, Kneza Milosa 7, 40000, Kos. Mitrovica, Serbia
b State Key Laboratory of Powder Metallurgy, Central South University, Changsha, China
c Collaborative Innovation Center of Steel Technology, University of Science and Technology Beijing, Beijing, 100083, China
d University of Belgrade, Technical Faculty in Bor, VJ 12, 19210, Bor, Serbia
a r t i c l e i n f o
a b s t r a c t
Article history:
Phase diagram of the Cu-Ge-Sb ternary system has been investigated experimentally and assessed
thermodynamically by means of CALPHAD approach. Experimental results were obtained by using dif-
ferential thermal analysis (DTA), scanning electron microscopy (SEM) with energy dispersive spec-
trometry (EDS), and X-ray powder diffraction (XRD) methods. Examined samples can construct two
isothermal sections at 400 and 500 ꢀC as well as three vertical sections of Cu-GeSb, Ge-CuSb, and Sb-
CuGe. From equilibrated samples in Cu-rich part of the 500 ꢀC isothermal section, one ternary com-
pound was detected. Based on the present experimental data and available literature data, a thermo-
dynamic description of the ternary Cu-Ge-Sb system has been developed. A reasonable agreement
between experimental data and the calculated phase equilibria is obtained.
Received 22 April 2017
Received in revised form
6 August 2017
Accepted 7 August 2017
Available online 8 August 2017
Keywords:
Thermodynamic modeling
Cu-Ge-Sb
Scanning electron microscopy
Thermal analysis
X-ray diffraction
© 2017 Published by Elsevier B.V.
Contents
1.
2.
3.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 820
Materials and method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 822
Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 822
3.1.
3.2.
3.3.
Isothermal section at 400 ꢀC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 822
Isothermal section at 500 ꢀC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823
Vertical sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 826
4.
Thermodynamic modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 828
4.1.
4.2.
4.3.
Unary phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 828
Solution phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 828
Ternary compound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 828
5.
6.
Thermodynamic calculations and comparison with experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 829
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832
1. Introduction
In last decade phase-change memory (PCM) materials attracted
ꢁ
* Corresponding author. University of Pristina, Faculty of Technical Science, Kneza
Milosa 7, 40000, Kos. Mitrovica, Serbia.
a lot of attention [1e5]. The most commonly mass-produced PCM
ꢀ
E-mail address: milena.premovic@gmail.com (M. Premovic).
http://dx.doi.org/10.1016/j.jallcom.2017.08.051
0925-8388/© 2017 Published by Elsevier B.V.

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M. Premovic et al. / Journal of Alloys and Compounds 726 (2017) 820e832
821
materials are based on ternary Ge-Sb-Te system [6e9], which is
generally named as GST. Mostly promising alloy from GST system is
Ge2Sb2Te5. Due to a good performance such as large change in
optical constants and rapid phase transition between crystalline
and amorphous state, this material also has high piezoelectricity. A
possible application of GST alloy leads to the production of digital
video disk (DVD-RW) and compact disc re-writable (CD-RW)
[10e13]. In view of the limited materials of PCMs that have found
practical applications, future researcher work in this area is highly
needed. At a first stage as a basis for future investigations of PCMs,
knowledge of phase diagram is important.
Ternary phase diagram of the Cu-Ge-Sb system has not been
proposed in literature up to now. Ternary phase diagram has only
been subjected to limited investigations. According to the available
literature data up to now, just one ternary compound Cu6GeSb from
the ternary system has been reported by Lenz and Schubert [14]
who also determined its crystallographic data. In their work one
ternary alloy with composition Cu75Ge12.5Sb12.5 at. % was annealed
at 400 and 500 ꢀC for 2.5 days and quenched into water. According
to their investigation [14], the alloy annealed at 400 ꢀC consisted of
Fig. 1. Calculated Cu-Ge phase diagram [29].
the compounds are very close to each other in the Cu-Ge phase
diagram. The Cu-Ge binary system was thermodynamically
assessed by Wang et al. [29], and that thermodynamic parameter
was adopted in this study. Fig. 1 presents the calculated Cu-Ge
phase diagram based on the parameters given by Wang et al. [29].
The binary Ge-Sb system is a simple eutectic one with a visible
solubility of Ge in (Sb) [30] and a negligible solubility of Sb in (Ge)
[31,32]. The Ge-Sb system was thermodynamically optimized by
Chevalier [33] and Wang et al. [34] and re-optimized by Liu et al.
[35]. The calculated Ge-Sb phase diagram, as shown in Fig. 2, is
according to the recent optimized by Liu et al. [35]. The Ge-Sb phase
diagram assessed by Liu et al. [35] can reproduce experimental
information well [30,36e40], in particular the solubility of Ge in
(Sb) [30], which is not taken into account in the previous optimi-
zations [33,34].
The binary Cu-Sb system is complex, and it has been extensively
studied by several groups. Thermodynamic parameters of the sys-
tem have been determined by Liu et al. [41], Lee et al. [42] and
Gierlotka and Jendrzejczyk-Handzlik [43]. Thermodynamic pa-
rameters used in this study are from Liu et al. [41] and the calcu-
lated Cu-Sb phase diagram is shown in Fig. 3. In the work by Liu
et al. [41], more experiments data than those in the other optimi-
zation were taken into account, and a good agreement between
calculation and experiments was reached.
three phases:
h (Cu2Sb), h' (Cu3Ge) and x
(Cu5Ge). While at 500 ꢀC
only the Cu6GeSb ternary phase was discovered. Glasov and
Potemkin [15,16] investigated the interaction between copper and
antimony in a solid solution based on Ge with the formation of a
charged complex [15] and donoreacceptor interaction and mutual
solubility of the Cu and Sb components [16]. Solubility has been
measured at 500 and 600 ꢀC, and at both temperatures the detected
solubility was negligible.
In this work two isothermal sections at 400 and 500 ꢀC, three
vertical sections and liquid projection of the ternary Cu-Ge-Sb
system have been studied by using a combination of different
experimental techniques including differential thermal analysis
(DTA), scanning electron microscopy (SEM) with energy dispersive
spectrometry (EDS) and X-ray powder diffraction (XRD). Conse-
quently, based on the present experimental results and literature
data by using CALPHAD method [17,18] and Thermo-Calc software
package [19], thermodynamic parameters for the ternary Cu-Ge-Sb
system were systematically assessed.
The crystal structure data for the solid phases in the ternary
system are listed in Table 1.
The thermodynamic parameters for three binary sub-systems
are taken from literature. The binary Cu-Ge system consists of
(Cu), (Ge),
(Cu0.765Ge0.235),
x
(Cu5Ge) and three intermetallic compounds, ε'
' (Cu3Ge), (Cu0.735Ge0.265). The compositions of
h
q
Table 1
Crystal structure data for the solid phases in the Cu-Ge-Sb system [14,20e28].
Phase name
Common name
Space group
Strukturberichte
Pearson symbol
Lattice parameters/Ref.
designation/prototype
a
b
c
ꢁ
RHOMBO_A7
DIAMOND_A4
FCC_A1
(Sb)
(Ge)
(Cu)
b
A7/As
A4/C
hR6
cF8
4.50 [20]
R3ꢁm
5.65675 [21]
3.61 [22]
Fd3 m
ꢁ
A1/Cu
D03/BiF3
cF4
Fmꢁ3 m
BCC_A2
cF16
6.00 [23]
Fm3 m
CUSB_GAMMA
CUSB_DELTA
CUSB_EPSILON
CUSB_ZETA
g
d
(Cu85Sb15
(Cu4Sb)
ε(Cu3Sb)
(Cu77Sb23
)
P63/mmc
P63/mmc
A3/Mg
…/Mg
DOa/…
…/Cu10Sb3
hP2
hP2
oP8
2.68 [24]
2.752 [25]
5.504 [26]
9.92 [26]
4.30 [24]
4.320 [25]
4.853 [26]
4.397 [26]
Pmmn
4.431 [26]
4.20 [25]
ꢁ
z
)
hP26
p3
CUSB_ETA
EPSILON
CU3GE
h
(Cu2Sb)
P4/nmm
P63/mmc
Pmꢁnm
C38/Cu2Sb
…/Na3As
DOa/Cu3Sb
A2/Fe3Si
tP6
4.0006 [27]
4.169 [14]
5.29 [25]
6.1043 [27]
7.499 [15]
4.55 [25]
ε' (Cu0.765Ge0.235
h
q
)
' (Cu3Ge)
(Cu0.735Ge0.265
oP8
cI2
EPSILON2
)
5.906 [14]
Fm3 m
HCP_A3
CU6GESB
x
t
(Cu5Ge)
(Cu6GeSb)
P63/mmc
P63/mmc
A3/Mg
…/Na3As
hP2
hP8
2.612 [28]
4.165 [14]
4.231 [28]
7.475 [14]

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M. Premovic et al. / Journal of Alloys and Compounds 726 (2017) 820e832
822
elements bought from Alpha Acer) were used as a standard in
process of calibration.
Phase transition temperatures were determined by DTA
method. The DTA measurements were performed on an SDT Q600
(TA Instruments). The DTA instrument was calibrated to the
melting points of Au, Ag, Al, Bi, Cu, Ge, Sn, Sb, In, Ni and Zn. Alumina
crucibles were used and measurements were performed under
flowing argon atmosphere. Samples weighing between 20 and
30 mg were investigated at a heating rate of 5 ꢀC/min with three
cycles of heating and cooling. The sample masses and transition
temperatures were determined by analysis of one sample at
different testing conditions. The reference material was empty
alumina crucible. The overall uncertainty of the determined phase
transformation temperatures was estimated to be 1 ꢀC.
Phase transition temperatures were experimentally examined
on 13 samples. Twenty ternary alloys per isothermal section were
investigated with SEM-EDS and XRD method. The determined
composition of annealed samples was done by mapping entire
polished surface of the samples. The uncertainty of composition is
detected to be 0.2 at. %. Obtained compositions of the samples are
presented in Table 2 for both isothermal sections.
Fig. 2. Calculated Ge-Sb phase diagram [35].
2. Materials and method
All samples with total masses of about 3 g were prepared from
high purity (99.999 at. %) elements (Cu, Ge, and Sb) produced by
Alfa Aesar (Germany) in an induction furnace under high-purity
argon atmosphere. Since Sb is highly volatile, an additional
amount of Sb (about 1e2 at. %) was added to compensate for the
weight loss. The average weight loss of the samples during melting
was about 1 mass %.
After melting, samples for the SEMeEDS and XRD investigations
were put into quartz glass ampoules, sealed under vacuum and
annealed at 400 and 500 ꢀC for four weeks and quenched into ice
water in order to preserve the equilibrium compositions at desig-
nated temperature. The average weight loss of the samples during
annealing was less than 0.5 mass %.
3. Experimental results
3.1. Isothermal section at 400 ꢀC
In Table 3 are given results of SEM-EDS and XRD examination for
the alloys at 400 ꢀC. The compositions of the phases were deter-
mined by EDS, and lattice parameters of presented phases are
determined by using full Rietveld refinement, the goodness of
fitting was in the range from 1.5 to 2.0. Data for comparison of
lattice parameters were taken from literature for (Sb) [20], (Ge)
[21],
(Cu5Ge) [28] and (Cu) [22,44].
The same three phase region was detected in samples 1e4 (see
d(Cu4Sb) [25], h h(Cu2Sb) [27],
0(Cu3Ge) [25], ε(Cu3Sb) [26],
x
The compositions of samples and coexisting phases were
determined using JEOL JSM-6460 scanning electron microscope
and TESCAN VEGA3 scanning electron microscope both with en-
ergy dispersive spectroscopy (EDS) (Oxford Instruments X-act).
Powder XRD data for phase identification of samples were
recorded on a D2 PHASER (Bruker, Karlsruhe, Germany) powder
diffractometer equipped with a dynamic scintillation detector and
Table 3). Detected three phases are two solid solutions (Ge) and (Sb)
and one binary intermetallic compound Solid solution (Ge) dis-
solves a small amount of Cu and Sb, which is less than 1at. %, and
another solid solution (Sb) dissolves around 2 at. % Ge and Cu. The
solubility of Ge into (Sb) is higher than that of Cu, which is expected
according to the phases diagrams shown in Figs. 2 and 3.
ceramic X-ray Cu tube (KFL-Cu-2K) in a 2q
range from 10ꢀ to 75ꢀ
Samples 5, 6 and 7 (Table 3) show the existence of (Ge)þ
with a step size of 0.02ꢀ. The patterns were analyzed using the
Topas 4.2 software, ICDD databases PDF2 (2013). The instrument
was calibrated with Bruker standard, Korundprobe A26-B26-S.
Beside this standard, ten different powder elements (high purity
h
0(Cu3Ge)þ
h(Cu2Sb) three phases region. Detected solid solution
(Ge) has a small solubility of other two elements, and two inter-
metallic compounds are rich in copper. One is related to the binary
Cu-Ge side
side (Cu2Sb). Confirmation of
since it was hard to distinguish
(Cu0.765Ge0.235) by using composition measurements.
Next three samples 8, 9 and 10 from Table 3 confirmed the
three-phase region (Cu5Ge)þ
(Cu2Sb)þ
0(Cu3Ge). Three different
intermetallic compounds were detected (Cu2Sb), (Cu5Ge) and
0(Cu3Ge) and all these binary intermetallic compounds dissolve a
h
0(Cu3Ge), and the other is related to the Cu-Sb binary
h
h
0(Cu3Ge) was done by XRD analysis
(Cu0.735Ge0.265), ' (Cu3Ge), ε'
q
h
h
x
h
h
x
h
small amount of the third element. Sample 8 annealed indicates the
same composition as sample investigated by Lenz and Schubert
[14]. And the same three phases
are detected as in the literature [14].
Two-phase region (Cu2Sb) has been detected in
h(Cu2Sb), h' (Cu3Ge) and x (Cu5Ge)
x
(Cu5Ge)þ
h
samples 11 and 12, and a negligible solubility of the third element
into this two binary compound is detected. Sample 13 (see Table 3)
detected one solid solution (Cu) and two intermetallic compounds
x(Cu5Ge) and h(Cu2Sb). Solid solution (Cu) dissolves 10.5 0.4 at. %
of Ge and 0.7 0.4 at. % of Sb. A larger solubility of Ge into (Cu) solid
solution is expected according to the phases diagram shown in
Fig. 1 and the fact that Ge can be dissolved in (Cu) solid solution up
Fig. 3. Calculated CueSb phase diagram [41].

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M. Premovic et al. / Journal of Alloys and Compounds 726 (2017) 820e832
823
Table 2
List of experimentally examined alloys annealed at 400 and 500 ꢀC for four weeks.
Isothermal section at 400 ꢀC
Isothermal section at 500 ꢀC
Number of alloys
Number of alloys
Compositions of alloys detected with SEM-
EDS (at. %)
Compositions of alloys detected with SEM-
EDS (at. %)
x(Cu)
x(Ge)
x(Sb)
x(Cu)
x(Ge)
x(Sb)
1
2
3
4
5
6
7
8
19.3
15.0
10.1
41.0
60.6
70.0
59.8
75.0
78.5
80.1
81.5
85.8
83.0
80.1
85.0
80.4
86.0
88.5
91.0
91.0
23.2
68.4
9.1
57.5
16.6
80.8
29.7
7.7
13.1
20.6
12.5
10.3
4.0
8.7
1.9
7.8
13.5
7.0
1
2
3
4
5
6
7
8
10.1
20.0
63.3
71.2
73.0
70.5
81.2
73.0
74.6
78.7
81.67
79.2
83.1
88.7
79.7
78.1
64.9
71.2
86.8
73.6
9.8
1.8
80.1
78.2
5.2
31.5
22.9
15.4
9.5
16.7
6.5
29.3
31.7
16.9
19.6
12.5
11.2
15.9
9.8
12.3
9.2
6.4
8.0
3.9
5.9
11.6
20.0
2.1
20.5
16.3
8.0
5.2
8.6
11.1
9.2
2.7
13.1
13.2
26.6
12.2
17.7
9
9
9.1
10
11
12
13
14
15
16
17
18
19
20
10
11
12
13
14
15
16
17
18
19
20
13.3
13.14
12.2
5.8
2.1
17.6
8.8
21.9
2.2
1.0
15.7
6.4
4.5
4.1
6.6
7.6
7.0
4.9
2.4
8.7
to 12 at. %. Three different two-phases regions are detected with
samples 14, 16, 18, 19 and 20. The two-phase region (Cu)þ (Cu2Sb)
was detected with sample 14. In sample 16 showed the existence of
the solid solution (Cu) containing 10.6 0.5 at. % Ge, a small
amount of Sb and the binary intermetallic ε(Cu3Sb) phase. Next
three samples 18, 19 and 20 all showed the presence of the two-
Fig. 5 gives XRD patterns and microstructures of samples 9 and
h
13.
XRD pattern of sample 9 (Fig. 5a) as a results confirmed the
existence of three phases
conclusion was helpful in distinguishing
(Cu0.735Ge0.265) and ε' (Cu0.765Ge0.235). A microstructure of sample 9
is presented in Fig. 5c) where (Cu5Ge) is a dark phase, (Cu2Sb)
light phase and the phase with a composition of 75.1 0.1 at. % Cu,
24.5 0.4 at. % Ge and 0.4 0.3 at. % Sb is
0(Cu3Ge), which appears
as a fine grain gray phase. Fig. 5b) shows XRD patterns of sample 13
where three phases are detected (Cu5Ge), (Cu2Sb) intermetallic
h(Cu2Sb),
x
(Cu5Ge) and
h
0(Cu3Ge). This
h
0(Cu3Ge) phase from
q
phase region (Cu)þ
d
(Cu4Sb). The solid solution of (Cu) detected
x
h
in samples 19 and 20 shows a smaller solubility of Ge than that in
others samples where the (Cu) solid solution was detected. Two
different three-phase regions were detected in samples 15 and 17.
In both samples, two same phases occur, i.e. (Cu) and ε(Cu3Sb) and
one intermetallic compound that is different in each of the regions,
h
x
h
compounds and (Cu) solid solution. The same phases are detected
with composition analysis and micrograph of sample 13 is given in
Fig. 5d).
i.e.
h
(Cu2Sb) in sample 15 and
d(Cu4Sb) in sample 17).
According to the XRD results, determined lattice parameter is in
agreement with the literature [20,21,25e28,44]. Based on the
result, solid solution (Cu) dissolve significant amount of Ge (the
detected maximal solubility is 10.6 at. % of Ge into (Cu)), parameters
for determination of the lattice parameters, are used from Hume-
Rothery et al. [44]. In their work, the lattice parameters proposed
for the (Cu) solid solution with a maximum solubility of Ge 9.0 at. %
is 3.6456 Å. According to the results in Table 3, determined lattice
parameters for the solid solution (Cu) of sample 18 with a
composition close to the composition given by Hume-Rothery et al.
[44] is 3.6454 Å.
3.2. Isothermal section at 500 ꢀC
Compositions of investigated samples from the isothermal sec-
tion at 500 ꢀC are presented in Table 2. Most of the investigated
samples are in copper-rich part. Table 4 presents the determined
phase, compositions of the phases and their lattice parameters.
Based on the experimental results (Table 4), it is confirmed that
some of the samples detected same phase region (samples 4 and 17
are from two-phase region Lþ
from two-phase region
þ(Cu); samples 7 and 15 are from three-
phase region (Cu5Ge)þ
(Cu6GeSb)þ
0(Cu3Ge); samples 8, 18 and
20 are from three-phase region (Cu6GeSb)).
(Cu2Sb)þ
h
0(Cu3Ge); samples 13, 14 and 19 are
Fig. 4 presents four representative micrographs of the samples
b
annealed at 400 ꢀC.
t
x
h
In microstructure of sample 1 (see Fig. 4), three phases are
detected. The dark phase is a solid solution (Ge), lights phase is a
solid solution (Sb) and gray phase present intermetallic compound
b
þ
h
t
Based on the experimental results shown in Table 4, one ternary
compound is detected in copper-rich part with 12 samples (sam-
ples 5e12, 15, 16, 18 and 20). Composition of the ternary compound
is in range from 73.8 0.4 at.% to 76.4 0.2 at.% Cu,12.0 0.6 at.% to
15.0 0.2 at.% Ge and 11.00 0.6 at.% to 14.0 0.5 at.% Sb, which is
close to the composition of ternary compound Cu75Ge12.5Sb12.5 at.%
reported in the literature [14]. XRD analysis confirmed that the
ternary compound is same as reported by Lenz and Schubert [14],
and detected lattice parameters agree well with the literature data
h
(Cu2Sb). Three-phase region of (Ge)þ
h
0(Cu3Ge)þ
h(Cu2Sb) has
been detected in sample 5 and in microstructure of sample 5
(Fig. 4b). (Ge) solid solution is detected as dark phase distributed in
the surface of gray h(Cu2Sb) phase, while h
0(Cu3Ge) intermetallic
compound appears as a dark-gray phase. Fig. 4c) presents a
microstructure of sample 12 where two intermetallic compounds
x(Cu5Ge) and
h(Cu2Sb) appear. The last microstructure is related to
[14]. Besides the ternary compound, four
and (Cu5Ge) binary intermetallic compounds are detected in some
of the samples annealed at 500 ꢀC. Two
and (Cu2Sb), of four
h(Cu2Sb), b, h
0(Cu3Ge)
the sample 18, where two phases are visible, the (Cu) solid solution
as a large grains and one intermetallic
phase.
d(Cu4Sb) compound as a gray
x
b
h

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M. Premovic et al. / Journal of Alloys and Compounds 726 (2017) 820e832
824
Table 3
Experimentally determined phase composition in the ternary Cu-Ge-Sb system at 400 ꢀC annealed for four weeks.
N.
1
Determined phases
SEM-EDS
Compositions of phases (at. %)
Lattice parameters (Å)
XRD
Cu
Ge
Sb
a
b
c
(Ge)
(Sb)
(Ge)
(Sb)
0.0 0.3
0.6 0.2
66.2 0.3
0.0 0.5
0.5 0.6
65.2 0.3
0.3 0.5
0.7 0.6
65.2 0.3
0.6 0.6
0.4 0.7
67.0 0.8
0.6 0.3
65.3 0.6
75.6 0.1
0.1 0.3
66.1 0.4
75.0 0.1
0.1 0.7
65.2 0.1
76.0 0.1
75.6 0.2
66.0 0.8
85.0 0.7
86.5 0.3
75.1 0.1
68.2 0.6
65.2 0.4
85.0 0.5
75.0 0.1
86.1 0.6
68.1 0.2
86.9 0.7
67.7 0.2
88.8 0.5
87.4 0.8
67.6 0.1
68.1 0.3
88.5 0.2
88.7 0.3
75.7 0.1
67.3 0.4
76.03 0.3
89.0 0.2
89.2 0.7
79.4 0.7
75.0 0.2
90.5 0.3
79.8 0.4
81.0 0.5
93.1 0.3
95.0 0.2
81.0 0.1
99.8 0.3
2.6 0.2
1.8 0.5
99.8 0.5
1.9 0.8
1.1 0.1
98.7 0.2
2.0 0.6
0.0 0.4
98.7 0.2
0.6 0.6
0.5 0.1
98.4 0.2
1.2 0.5
23.2 0.4
98.6 0.2
1.7 0.4
24.9 0.2
99.2 0.3
0.9 0.1
23.5 0.4
23.3 0.1
1.1 0.3
14.5 0.7
13.2 0.3
24.5 0.4
0.3 0.5
1.8 0.6
14.6 0.7
24.2 0.3
13.2 0.3
0.2 0.8
12.9 0.2
0.5 0.1
10.5 0.4
12.5 0.5
0.9 0.4
0.9 0.2
10.6 0.5
10.4 0.1
0.3 0.8
0.6 0.3
0.47 0.4
10.0 0.1
9.7 0.2
1.0 0.4
0.5 0.5
8.7 0.3
0.6 0.7
1.0 0.1
6.0 0.3
3.0 0.2
0.4 0.4
0.2 0.4
96.8 0.3
32.0 0.8
0.2 0.5
97.6 0.7
33.7 0.2
1.0 0.4
97.3 0.8
34.8 0.1
0.7 0.8
99.0 0.4
32.5 0.3
1.0 0.5
33.5 0.7
1.2 0.3
1.3 0.5
32.2 0.2
0.1 0.8
0.7 0.1
33.9 0.4
0.5 0.5
1.1 0.3
32.9 0.2
0.5 0.5
0.3 0.2
0.4 0.3
31.5 0.4
33.0 0.7
0.4 0.1
0.8 0.3
0.7 0.5
31.7 0.2
0.2 0.3
31.8 0.6
0.7 0.4
0.1 0.2
31.5 0.3
31.0 0.1
0.9 0.3
0.9 0.6
24.0 0.2
32.1 0.5
23.5 0.1
1.0 0.2
1.1 0.3
19.6 0.4
24.5 0.7
0.8 0.3
19.6 0.5
18.0 0.8
0.9 0.1
2.0 0.3
18.6 0.4
5.6553(3)
4.4298(1)
3.9993(5)
5.6550(3)
4.4372(5)
4.0013(2)
5.6540(4)
4.4307(6)
3.9987(7)
5.6539(7)
4.4732(3)
3.9997(2)
5.6530(1)
3.9989(3)
5.2879(4)
5.6533(5)
3.9993(2)
5.2913(1)
5.6545(6)
3.9997(4)
5.2987(2)
5.2987(3)
3.9987(4)
2.6181(2)
2.6198(1)
5.2913(5)
3.9985(6)
3.9986(1)
2.6152(2)
5.2918(4)
2.6119(1)
3.9984(1)
2.6099(2)
3.9986(4)
3.6476(2)
2.6087(1)
3.9984(7)
4.0001(3)
3.6491(4)
3.6488(5)
5.5032(2)
4.0005(4)
5.5018(1)
3.6463(6)
3.6459(5)
2.7587(4)
5.5013(1)
3.6454(7)
2.7517(4)
2.7514(2)
3.6399(1)
3.6328(7)
2.7554(2)
6.1042(2)
h(Cu2Sb)
h(Cu2Sb)
2
(Ge)
(Sb)
(Ge)
(Sb)
6.1003(3)
6.1013(4)
6.1003(3)
h(Cu2Sb)
h(Cu2Sb)
3
(Ge)
(Sb)
(Ge)
(Sb)
h(Cu2Sb)
h(Cu2Sb)
4
(Ge)
(Sb)
(Ge)
(Sb)
h(Cu2Sb)
h(Cu2Sb)
5
(Ge)
(Ge)
4.1989(4)
4.1898(3)
4.2014(3)
4.2018(5)
4.2021(1)
4.2016(2)
h
h
(Cu2Sb)
h
h
(Cu2Sb)
6.1025(2)
4.4987(1)
0(Cu3Ge)
0(Cu3Ge)
6
(Ge)
(Ge)
h
h
(Cu2Sb)
h
h
(Cu2Sb)
6.1012(1)
4.5473(2)
0(Cu3Ge)
0(Cu3Ge)
7
(Ge)
(Ge)
h
h
h
h
(Cu2Sb)
h
h
h
h
(Cu2Sb)
6.1023(1)
4.5487(3)
4.5509(4)
6.1002(6)
4.2318(3)
4.2316(3)
4.5538(2)
6.1002(5)
6.1006(4)
4.2361(6)
4.5543(3)
4.2398(1)
6.1003(2)
4.2389(5)
6.1034(3)
0(Cu3Ge)
0(Cu3Ge)
(Cu2Sb)
0(Cu3Ge)
0(Cu3Ge)
(Cu2Sb)
8
x
x
h
h
h
(Cu5Ge)
(Cu5Ge)
x
x
h
h
h
(Cu5Ge)
(Cu5Ge)
9
0(Cu3Ge)
(Cu2Sb)
(Cu2Sb)
0(Cu3Ge)
(Cu2Sb)
(Cu2Sb)
10
x
(Cu5Ge)
0(Cu3Ge)
(Cu5Ge)
(Cu2Sb)
(Cu5Ge)
(Cu2Sb)
(Cu)
(Cu5Ge)
x
(Cu5Ge)
0(Cu3Ge)
(Cu5Ge)
(Cu2Sb)
(Cu5Ge)
(Cu2Sb)
(Cu)
(Cu5Ge)
h
x
h
x
11
12
13
h
x
h
x
h
h
x
x
4.2298(6)
6.1038(4)
6.1012(4)
h
h
(Cu2Sb)
(Cu2Sb)
h
h
(Cu2Sb)
(Cu2Sb)
14
15
(Cu)
(Cu)
ε(Cu3Sb)
(Cu)
(Cu)
ε(Cu3Sb)
h(Cu2Sb)
ε(Cu3Sb)
(Cu)
(Cu)
4.4289(2)
4.8517(5)
6.1007(4)
4.8541(6)
h(Cu2Sb)
16
17
ε(Cu3Sb)
(Cu)
(Cu)
4.4298(1)
4.4318(2)
d(Cu4Sb)
d(Cu4Sb)
4.3218(7)
4.8518(3)
4.3265(8)
ε(Cu3Sb)
(Cu)
ε(Cu3Sb)
(Cu)
18
19
20
d
d
(Cu4Sb)
(Cu4Sb)
d
d
(Cu4Sb)
(Cu4Sb)
4.3218(1)
4.3219(3)
(Cu)
(Cu)
(Cu)
(Cu)
d(Cu4Sb)
d(Cu4Sb)
compounds, are oriented to the binary Cu-Sb side. The experi-
mentally determined composition of this two compounds shows a
small solubility of the third element, (generally spiking less than
Determined lattice parameters of all the phases from XRD agree
well with the literature data [14,20,21,23,25,27,28,44].
Fig. 6 presents some of the representative microstructures of the
1.5 at. %) and XRD analysis confirmed that formed phases are
(Cu2Sb) binary intermetallic compound. Another two interme-
tallic compounds (Cu5Ge) and
0(Cu3Ge) are oriented to the binary
Cu-Ge side with maximum 1 at. % solubility of Sb. XRD analysis
confirmed that formed phases are (Cu5Ge) and
0(Cu3Ge). Three
b and
samples annealed at 500 ꢀC for four weeks.
h
Fig. 6a) presents microstructure of sample 2, where three phases
are detected and marked on micrograph. Solid solution (Sb) is
detected as a dominant light phase, intermetallic compound
x
h
x
h
h(Cu2Sb) as a dark phase and Liquid phase as a gray phase. The
solid solutions (Cu), (Sb) and (Ge) are detected with XRD and SEM-
EDS in some of the samples annealed at 500 ꢀC. It is detected that
solid solution (Cu) dissolve significant amount of Ge, for example in
sample 11 (see Table 4) solubility of Ge into (Cu) solid solution is
13.0 0.5 at. %, which is more than expected (based on Fig. 1). In
addition to solid phases, the liquid phase is detected in six samples.
microstructure of sample 3 is given at Fig. 6b), where in equilibrium
are three phases, solid solution (Ge), dominant intermetallic com-
pound
phase distributed between
detected in the microstructure of sample 5 (Fig. 6c)), ternary phase
(Cu6GeSb) (gray dominant phase), binary intermetallic compound
h
0(Cu3Ge) detected as a gray phase and Liquid phase as light
h
0(Cu3Ge) phase. Three phases are
t

ꢀ
M. Premovic et al. / Journal of Alloys and Compounds 726 (2017) 820e832
825
Fig. 4. SEM micrographs of the selected alloy samples annealed at 400 ꢀC for four weeks.
Fig. 5. Samples 9 and 13 annealed at 400 ꢀC: a) XRD pattern, sample 9, b) XRD pattern, sample 13, c) micrograph sample 9 and d) micrograph sample 13.
h
0(Cu3Ge) (dark phase) and Liquid phase (light gray phase). The
microstructure of sample 8 (Fig. 6d)) presents three phase region
(Cu6GeSb)þ (Cu2Sb)þ where is a light phase, (Cu6GeSb)
dominant gray phase and (Cu2Sb) dark phase. In microstructures
of samples 9 and 12 (see Fig. 6e) and f)) two different phas regions
are visible. In both micrographs ternary (Cu6GeSb) compound is
detected as a gray phase. Besides (Cu6GeSb) compound in sample
9, the binary intermetallic compound is detected, and in sample
12, solid solution (Cu) as an oval dark-gray phase.
Fig. 7 shows two XRD patterns and two micrographs of samples
15 and 19.
t
h
b
b
t
Fig. 7a) and c) presents XRD pattern and microstructure of
sample 15, respectively. Based on XRD experiments in sample 15,
h
three phases are stable
results help to conclude that phase with 74.6
23.8 0.3 at. % Ge and 1.6 0.3 at. % Sb is h
0(Cu3Ge), which on
x(Cu5Ge),
h
0(Cu3Ge), and
t(Cu6GeSb). XRD
t
0.2 at. % Cu,
t
b
micrograph appears as a dark phase (see Fig. 7c)). XRD pattern of
sample 19, on Fig. 7b) shows that two phases are detected, solid

ꢀ
M. Premovic et al. / Journal of Alloys and Compounds 726 (2017) 820e832
826
Table 4
Experimentally determined phase compositions in the ternary Cu-Ge-Sb system annealed at 500 ꢀC for four weeks.
N.
1
Determined phases
SEM-EDS
Compositions of phases (at. %)
Lattice parameters (Å)
XRD
Cu
Ge
Sb
a
b
c
(Sb)
(Ge)
L
(Sb)
L
(Sb)
(Ge)
e
0.5 0.1
0.9 0.3
38.1 0.5
0.3 0.5
48.1 0.3
66.1 0.8
58.2 0.1
73.6 0.2
0.8 0.3
3.9 0.3
98.6 0.1
21.2 0.3
0.8 0.1
7.6 0.4
0.4 0.5
25.0 0.2
25.6 0.3
98.3 0.3
17.4 0.5
24.4 0.7
14.7 0.2
23.9 0.1
13.4 0.4
11.7 0.2
0.9 0.3
12.0 0.6
24.4 0.6
13.5 0.5
15.2 0.4
12.3 0.6
0.8 0.2
0.7 0.3
12.0 0.1
0.5 0.3
14.9 0.2
12.9 0.3
12.5 0.2
13.9 0.4
13.0 0.5
11.7 0.4
12.4 0.5
1.2 0.2
8.7 0.4
0.3 0.6
1.9 0.1
12.4 0.7
15.3 0.4
23.8 0.3
13.1 0.5
0.3 0.7
11.3 0.2
25.1 0.1
21.9 0.4
1.1 0.5
1.2 0.2
15.0 0.2
0.4 0.5
1.4 0.4
0.3 0.1
0.7 0.2
12.2 0.1
95.6 0.3
0.5 0.3
40.7 0.4
98.9 0.7
44.3 0.6
33.5 0.2
16.8 0.2
0.8 0.3
0.9 0.4
18.7 0.5
0.9 0.6
11.0 0.6
1.5 0.4
17.0 0.3
20.0 0.1
32.6 0.5
14.0 0.1
1.0 0.4
11.0 0.4
0.5 0.3
13.4 0.1
32.1 0.3
27.1 0.2
13.8 0.3
25.8 0.7
0.5 0.7
11.7 0.4
13.0 0.6
1.2 0.1
1.2 0.2
2.2 0.4
11.2 0.3
24.5 0.6
2.1 0.5
24.9 0.3
3.2 0.2
13.8 0.6
1.1 0.7
1.6 0.3
12.6 0.2
26.2 0.4
2.5 0.6
0.7 0.2
19.7 0.6
31.6 0.3
26.0 0.2
11.0 0.5
26.5 0.7
3.5 0.1
27.4 0.3
32.8 0.4
14.0 0.5
4.4813(3)
5.6546(1)
e
2
(Sb)
e
4.4953(2)
e
6.1015(3)
4.5512(7)
4.5498(2)
h
L
h
(Cu2Sb)
h(Cu2Sb)
3.9983(4)
e
3
e
4.2018(6)
0(Cu3Ge)
h
0(Cu3Ge)
5.2981(2)
5.6542(3)
e
(Ge)
(Ge)
e
4
5
L
h
0(Cu3Ge)
63.9 0.4
74.7 0.6
74.3 0.6
74.6 0.3
69.6 0.1
68.3 0.2
66.5 0.2
74.0 0.3
74.6 0.1
75.5 0.3
84.3 0.3
74.3 0.1
67.1 0.6
72.2 0.6
74.2 0.2
73.7 0.3
84.6 0.4
75.4 0.2
74.5 0.2
84.9 0.3
85.8 0.6
86.1 0.3
76.4 0.2
74.3 0.1
89.2 0.4
74.8 0.2
94.9 0.2
73.8 0.5
83.6 0.1
74.6 0.2
74.3 0.4
73.5 0.3
86.2 0.3
74.2 0.5
58.4 0.6
67.3 0.3
72.8 0.2
74.0 0.3
73.1 0.4
95.1 0.5
72.3 0.2
66.5 0.6
73.8 0.4
4.1978(5)
4.1993(3)
h
0(Cu3Ge)
(Cu6GeSb)
5.2898(5)
4.1676(3)
5.2896(2)
e
t
h
L
(Cu6GeSb)
t
7.4795(6)
4.5498(3)
0(Cu3Ge)
h
0(Cu3Ge)
e
6
7
8
L
e
e
h
(Cu2Sb)
h(Cu2Sb)
3.9979(1)
4.1605(3)
5.2895(2)
4.1667(5)
2.6145(1)
4.1645(5)
3.9990(4)
5.9987(1)
4.1634(2)
5.9913(1)
2.6115(1)
4.1649(3)
4.1647(2)
2.6154(6)
3.6599(7)
3.6592(3)
4.1654(6)
5.9935(4)
3.6564(5)
5.9987(3)
3.6379(5)
4.1632(1)
2.6143(2)
5.2898(3)
4.1659(1)
5.9978(5)
3.6578(6)
5.2897(3)
e
6.1008(1)
7.4723(2)
4.5487(6)
7.4792(7)
4.2328(2)
7.4732(4)
6.1042(6)
t
h
t
x
(Cu6GeSb)
0(Cu3Ge)
(Cu6GeSb)
(Cu5Ge)
(Cu6GeSb)
t
h
(Cu6GeSb)
0(Cu3Ge)
4.1997(2)
t
(Cu6GeSb)
(Cu5Ge)
t(Cu6GeSb)
x
t
h
b
(Cu2Sb)
h(Cu2Sb)
b
9
t
(Cu6GeSb)
t(Cu6GeSb)
7.4714(7)
b
b
10
11
x
(Cu5Ge)
x(Cu5Ge)
4.2354(2)
7.4752(6)
7.4758(3)
4.2317(1)
t
t
(Cu6GeSb)
(Cu6GeSb)
t
t
(Cu6GeSb)
(Cu6GeSb)
x
(Cu5Ge)
x(Cu5Ge)
(Cu)
(Cu)
(Cu)
(Cu)
12
13
14
15
7.4765(4)
t
(Cu6GeSb)
t(Cu6GeSb)
b
(Cu)
b
b
(Cu)
b
(Cu)
(Cu)
t
(Cu6GeSb)
t(Cu6GeSb)
4.1899(1)
4.1993(4)
7.4784(3)
4.2352(2)
4.5467(6)
7.4765(5)
x
h
(Cu5Ge)
x
h
(Cu5Ge)
0(Cu3Ge)
0(Cu3Ge)
16
t
(Cu6GeSb)
t(Cu6GeSb)
b
b
(Cu)
(Cu)
17
18
h
L
0(Cu3Ge)
h
0(Cu3Ge)
4.5487(3)
6.1018(5)
7.4767(2)
e
h
b
(Cu2Sb)
h(Cu2Sb)
3.9989(1)
6.0001(5)
4.1687(3)
5.9963(2)
3.6392(6)
5.9982(7)
3.9989(4)
4.1643(4)
b
t
(Cu6GeSb)
t(Cu6GeSb)
19
20
b
(Cu)
b
b
(Cu)
b
h
(Cu2Sb)
h(Cu2Sb)
6.1005(2)
7.4744(3)
t
(Cu6GeSb)
t(Cu6GeSb)
solution (Cu) and intermetallic compound
visible from the micrograph of sample 19, presented at Fig. 7d).
b
. Same two phases are
reactions L/
h
þ(Sb)þ(Ge) and L/
h
þ
h
0þ(Ge). In Cu80Ge10Sb10
four transformations were recorded. Since the composition of al-
loys is closed to ternary compound it is expected that formation
temperature of this compound will be one of the detected tem-
peratures. At alloys annealed at 400 ꢀC, ternary compound do not
exist. Thus it is conclusive that the formation temperature of the
ternary compound should be second detected temperature
463.8 ꢀC. Third detected temperature is 493.3 ꢀC which can not be
temperature of disappearance of ternary compound since at sam-
ples annealed at 500 ꢀC, ternary compound was found and last
detected temperature present liquidus temperature.
3.3. Vertical sections
Thirteen ternary alloys from three vertical section Cu-Ge50Sb50
Ge-Cu50Sb50 and Sb-Ge50Cu50 are investigated by using DTA
method. Phase transition temperatures of 13 selected alloys are
summarized in Table 5. Solid state transition temperatures were
determined from the onset of the corresponding peak. The liquid
temperatures were evaluated from the peak maximum. Tempera-
tures presented in Table 5 are taken from the first heating cycle.
Based on DTA results it is visible that in all samples except for
Cu80Ge10Sb10 first detected phase transformation is in the range
from 415.8 ꢀC to 417.9 ꢀC, which should correspond to the eutectic
Since the temperature range of ternary compound is not found
by samples described in Table 5 additionally, sample 8 which has
been annealed at 400 ꢀC (Table 2) is examined with DTA method.
Sample 8 with a composition Cu75.03Ge12.43Sb12.54 at 400 ꢀC

ꢀ
M. Premovic et al. / Journal of Alloys and Compounds 726 (2017) 820e832
827
Fig. 6. SEM micrographs of the some selected alloy samples annealed at 500 ꢀC for four weeks.
Fig. 7. Samples 15 and 19 annealed at 500 ꢀC: a) XRD pattern, sample 15, b) XRD pattern, sample 19, c) micrograph sample 15 and d) micrograph sample 19.

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M. Premovic et al. / Journal of Alloys and Compounds 726 (2017) 820e832
828
Table 5
Phase transition temperatures along three vertical sections in the ternary Cu-Ge-Sb system.
Nominal composition (at.%)
Phase transition temperatures (ꢀC)
Other peak
Liquid
Vertical section CueGe50Sb50
Cu20Ge40Sb40
Cu40Ge30Sb30
Cu60Ge20Sb20
Cu80Ge10Sb10
417.8
416.8
417.9
329.7
537.1
475.3
705.3
616.5
505.1
747.3
463.8
493.3
Vertical section GeeCu50Sb50
Cu40Ge20Sb40
Cu30Ge40Sb30
Cu20Ge60Sb20
Cu10Ge80Sb10
416.7
415.8
417.4
416.9
504.3
720.2
806.3
863.5
505.1
502.1
498.7
Vertical section SbeCu50Ge50
Cu50Ge50Sb10
Cu40Ge40Sb20
Cu30Ge30Sb40
Cu20Ge20Sb60
417.4
417.3
417.6
415.8
416.3
550.1
511.3
523.1
747.3
729.9
633.4
554.0
580.7
Cu10Ge10Sb80
consists of the three phases (confirmed by EDS analysis and in
agreement with the literature [14]) (Cu2Sb), x
0(Cu3Ge) and
4.2. Solution phases
h
h
(Cu5Ge) phase. DTA results of sample Cu75.03Ge12.43Sb12.54 show
The ternary solution phases 4 (4 ¼ liquid and Fcc_A1 phase) are
treated as a substitutional solution. The Gibbs free energy is
expressed by Redlich-Kister polynomial [46]:
that first transformation of this sample appears at temperature
456.9 ꢀC which is described as
t
a
temperature of forming
(Cu6GeSb), and phase is stable until 504.7 ꢀC. Based on DTA results
the temperature stability of the ternary compound is in the range
Gfm ¼ xCuGf þ xGeGf þ xSbGf þ RTðxCu ln xCu þ xGe ln xGe þ xSb ln xSbÞ þ xCuxGeLf
Cu
Ge
Cu;Ge
SbLfGe;Sb þSebxGCfu;Ge;Sb
(2)
þxCu
x
SbLfCu;Sb þ xGe
x
from 457.9 ꢀC to 504.7 ꢀC. The last pick of this sample is at 626.8 ꢀC,
which is liquidus temperature.
where xCu, xGe and xSb are molar fractions of elements Cu, Ge, and
Sb, respectively. GCfu, GGfe and GSfb are the Gibbs energies of Cu, Ge,
and Sb in 4 phase. R is gas constant, T temperature, and
RTðxCu ln xCu þ xGe ln xGe þ xSb ln xSbÞ corresponds to the contribu-
4. Thermodynamic modeling
tion of the ideal entropy of mixing to the Gibbs energy. LfCu;Ge, Lf
Cu;Sb
and LfGe;Sb are interaction parameters from the corresponding bi-
nary systems [29,35,41]. The exGfCu;Ge;Sb term in Eq. (2) is the ternary
excess Gibbs energy, which is expressed as:
The Cu-Ge-Sb ternary system was thermodynamically assessed
by CALPHAD method [17,18] using Thermo-Calc software package
[19]. Thermodynamic parameters for constitutive binary systems
were taken from literature [29,35,41]. In this work, three phases
(Liquid, Fcc_A1, and ternary compound) are thermodynamically
assessed. All of the binary compounds are treated as pure binary
ones since the solid solubility for the third element is negligible.
Solid solutions (Ge) and (Sb) are not included in optimization since
the solubility of other two elements was in agreement with
extrapolated phase diagram.
ꢀ
ꢁ
0
1
2
exGfCu;Ge;Sb ¼xCuxGexSb xCu LCfu;Ge;Sb þxGe LfCu;Ge;Sb þxSb LCfu;Ge;Sb
(3)
0
2
where LfCu;Ge;Sb
,
1LfCu;Ge;Sb and LCfu;Ge;Sb are ternary interaction pa-
i
rameters expressed as LfCu;Ge;Sb ¼ ai þ biT and ai, bi are model pa-
rameters which need to be optimized from the experimental
phases diagram.
4.1. Unary phase
The thermodynamic parameters for Cu, Ge, and Sb were taken
from the literature published by Dinsdale [45], which are described
by Eq. (1).
4.3. Ternary compound
One ternary compound
Cu-Ge-Sb system. In view of a small homogeneity range, the ternary
(Cu6GeSb) compound is treated as a stoichiometric compound.
This ternary compound is described with the model (Cu)a(Ge)b(Sb)
c where sum of a, b and c is one (aþb þ c ¼ 1 follow as a ¼ 0.75,
b ¼ 0.125 and c ¼ 0.125). The Gibbs energy is described by an
equation of the form:
t(Cu6GeSb) is detected in the ternary
GiðTÞ ꢁ HiSER ¼ A þ B$T þ C$T ln T þ D$T2 þ E$Tꢁ1 þ F$T3
þ I$T7 þ J$Tꢁ9
(1)
t
where HiSER is the molar enthalpy of the elements i at 298.15 K and
1 bar in standard element reference (SER) state, T is absolute
temperature.

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M. Premovic et al. / Journal of Alloys and Compounds 726 (2017) 820e832
829
Table 6
Thermodynamic parameters of the Cu-Ge-Sb ternary system evaluated in this work.
Phase
Liquid
Model
Thermodynamic parameter (J/mol of atom)
0
1
2
0
(Cu,Ge,Sb)
Liq
Cu;Ge;Sb
L
L
L
L
¼ ꢁ19962 þ 28:1$T
¼ þ998
Liq
Cu;Ge;Sb
Liq
Cu;Ge;Sb
¼ ꢁ1990
Fcc_A1
(Cu,Ge,Sb)1(Va)1
Fcc A1
Cu;Ge;Sb:Va
¼ þ37000
0
0
t
(Cu6GeSb)
(Cu)0.75(Ge)0.125(Sb)0.125
GtCu:Ge:Sb ¼ 0:75 G
þ0:125 G
þ 0:125 G
Fcc A1
Diamond A4
Cu
Ge
0
Rhombo A7
ꢁ 2912 ꢁ 5:38,T
Sb
the experimental phases diagram.
5. Thermodynamic calculations and comparison with
experiments
Thermodynamic optimization of the ternary Cu-Ge-Sb system
Fig. 8. The calculated isothermal section at 400 ꢀC compared with the experimental
data.
0
0
0
Fcc A1
Diamond A4
Rhombo A7
Sb
Gt ¼ 0:75 G
þ 0:125 G
þ 0:125 G
þ A
Cu
Ge
þ B$T
Fig. 10. The calculated isothermal section at 500 ꢀC compared with the experimental
data.
(4)
where A, B are model parameters which need to be optimized from
Fig. 9. Magnified Cu-rich part of the calculated isothermal section at 400 ꢀC compared
Fig. 11. Magnified Cu-rich part of the calculated isothermal section at 500 ꢀC compared
with the experimental data.
with the experimental data.

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830
M. Premovic et al. / Journal of Alloys and Compounds 726 (2017) 820e832
Fig. 12. Calculated vertical sections of the Cu-Ge-Sb ternary system compared with the present experimental data: a) Cu-GeSb, b) Ge-CuSb and c) Sb-CuGe.
has been performed based on present experimental data of phase
presented in Table 4 and DTA measurements. Temperature inde-
pendent parameter presented in equation (4) as a A was firstly
modeled by using the experimental data from Table 4, about the
existence of ternary compound at 500 ꢀC, the temperature
dependent parameter B was estimated by using DTA results of
sample 8 (annealed at 400 ꢀC). Subsequently the parameters for the
solution phases (Fcc_A1 and Liquid) were optimized, and finally all
thermodynamic parameters were optimized simultaneously by
taking all the selected experimental data. The thermodynamic pa-
rameters obtained in this work are listed in Table 6 in the unit of J/
mol of the atom.
diagram and literature data [14]. Due to lack of thermodynamic
data related to this ternary system, the assessment was done just
based on data of phase diagram. The optimization of the parame-
ters was conducted using the PARROT module [19] based on a least
square procedure. The step-by-step optimization procedure
described by Du et al. [47] was utilized in the present assessment. In
the first step, the thermodynamic parameters for the ternary
compound were optimized based on experimentally results
Comparison between the calculated and the experimental phase
relations at 400 ꢀC is presented in Fig. 8. Fig. 9 presents magnified
Cu-rich part of the calculated isothermal section at 400 ꢀC
compared with the experimental data.
As shown in Figs. 8 and 9, the calculations reproduce the
experimental results of the samples annealed at 400 ꢀC very well.
Comparison of experimental date is also done for the isothermal
Table 7
Predicted invariant reactions involving the liquid phase in the Cu-Ge-Sb ternary
system.
Temperature (ꢀC) Invariant reaction Type at. %(Cu) at. %(Ge) at. %(Sb)
674.5
611.6
549.3
505.6
502.9
502.8
500.0
499.9
424.2
423.5
Lþ
q
q
þε0/h0
P1
U1
U2
U3
P2
U4
U5
U6
E1
E2
66.9
60.5
71.6
71.1
71.1
71.1
70.5
70.5
55.9
52.9
29.8
34.6
12.8
10.9
10.7
10.7
10.9
10.9
18.3
17.5
3.3
4.9
Lþ
/
h
0þ(Ge)
Lþε0/
h
h
0þ(Cu)/
0þ
x
15.6
18.0
18.2
18.2
18.6
18.6
25.8
29.6
Lþ
x
Lþ
/
0þ(Cu)
h
t
Lþ(Cu)/
bþt
Lþ
b
L þ
/
h t
þ
t
h
h
/
h
h0
þ
L/
þ
h
0þ(Ge)
L/
þ(Sb)þ(Ge)
Fig. 13. Predicted liquidus projection of the ternary Cu-Ge-Sb system.

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M. Premovic et al. / Journal of Alloys and Compounds 726 (2017) 820e832
831
section at 500 ꢀC. Fig. 10 presents calculated isothermal section of
the ternary Cu-Ge-Sb system at 500 ꢀC along with SEM-EDS data
from Table 4. Most alloys are concentrated in copper rich part.
Fig. 11 presents magnified Cu-rich part of the calculated isothermal
section at 500 ꢀC compared with the experimental data.
As shown in Figs. 10 and 11, a good agreement with most of the
experimental data is realized. Fig. 12 presents calculated three
vertical sections compared with experimentally determined tem-
peratures of the phase transformation. As can be seen from Fig. 12,
the calculations are in agreement with most of the experimental
data.
the other seven fields correspond to the intermetallic compounds
from which one is ternary (Cu6GeSb), and the other are binary
t
intermetallic compounds. Furthermore, from the presented liq-
uidus surface projection, the existence of ten invariant reactions is
suggested. The calculated temperatures of invariant equilibria and
the corresponding compositions of liquid phases are listed in
Table 7. Two reactions are P-type, six reactions are U-type and the
last two are E-type.
Both eutectic reactions are experimentally confirmed. All sam-
ples from Ge-CuSb vertical section, two samples from Cu-GeSb and
four samples from Sb-CuGe vertical section detect the existence of
Based on the optimized thermodynamic parameters given in
Table 6, the liquidus projection of the ternary Cu-Ge-Sb system was
calculated and present in Fig. 13.
the L/
h
þ(Sb)þ(Ge) eutectic reaction, and mean value from these
ten experimental data is 416.8 ꢀC which shows a good agreement
with a calculated temperature 423.5 ꢀC. Reaction E1 L/
has been confirmed with two alloy samples Cu60Ge20Sb20 and
Cu50Ge50Sb10 and detected temperature is 417.9 ꢀC and 417.4 ꢀC,
respectively. Detected temperature of the E1 reaction is also in close
hþ
h
0þ(Ge)
As can be seen in Fig. 13, these are ten primary crystallization
fields, i.e. (Ge), (Sb), (Cu),
crystallization fields are solid solutions of (Ge), (Sb) and (Cu), and
t, h, , q, x b. Three primary
h0 , ε0, and
Fig. 14. The reaction scheme for liquid phase of the Cu-Ge-Sb system according to the present calculations with temperature in ꢀC.

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M. Premovic et al. / Journal of Alloys and Compounds 726 (2017) 820e832
832
agreement with the calculation temperature which is 424.2 ꢀC.
Fig. 14 presents the reaction scheme for the system.
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The isothermal section at 400 ꢀC was investigated with 20
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