Experimental investigation of the 3Tl2Se + Sb2Te 3 ? 3Tl2Te + Sb2Se3 phase diagram

Article abstract of DOI:10.1016/j.jallcom.2012.11.202

Phase equilibriums were established in the 3Tl₂Se + Sb ₂Te₃ ? 3Tl₂Te + Sb₂Se ₃ mutual system mainly by the X-ray powder diffraction and differential thermal analyses, with the aid of microhardness and EMF measurements applied to equilibrated alloys. According to the obtained experimental results the phase diagrams in form of the polythermal section and isothermal section at 300 K as well as the projection of the liquids surface have been constructed. It was found experimentally that the system is mutually reversible and is characterized by a wide solid solubility fields along the TlSbSe₂-TlSbTe₂ subsystem and within the Tl ₂Se-Tl₉SbSe₆-Tl₉SbTe ₆-Tl₂Te subsystem. The homogeneity and primary crystallization fields as well as the types and coordinates of non- and monovariant equilibriums were determined. The dependencies of crystallographic parameters, microhardness and EMF values upon the composition are discussed. From the EMF measurements, the partial molar functions of thallium (ΔG?,ΔH?,ΔS?) were calculated for the revealed nonstoichiometric quaternary phases.

Full text of DOI:10.1016/j.jallcom.2012.11.202

Journal of Alloys and Compounds 555 (2013) 184–192
Contents lists available at SciVerse ScienceDirect
Journal of Alloys and Compounds
journal homepage: www.elsevier.com/locate/jalcom
Experimental investigation of the 3Tl2Se + Sb2Te3 M 3Tl2Te + Sb2Se3 phase diagram
b,
a
Yasin I. Jafarov a, Mahammad B. Babanly a, , Andrei V. Shevelkov , Ziya S. Aliev
⇑
⇑
a Baku State University, General and Inorganic Chemistry Department, Azerbaijan
b Moscow Lomonosov State University, Chemistry Department, Russia
a r t i c l e i n f o
a b s t r a c t
Article history:
Phase equilibriums were established in the 3Tl2Se + Sb2Te3 M 3Tl2Te + Sb2Se3 mutual system mainly by
the X-ray powder diffraction and differential thermal analyses, with the aid of microhardness and EMF
measurements applied to equilibrated alloys. According to the obtained experimental results the phase
diagrams in form of the polythermal section and isothermal section at 300 K as well as the projection
of the liquids surface have been constructed. It was found experimentally that the system is mutually
reversible and is characterized by a wide solid solubility fields along the TlSbSe2–TlSbTe2 subsystem
and within the Tl2Se–Tl9SbSe6–Tl9SbTe6–Tl2Te subsystem. The homogeneity and primary crystallization
fields as well as the types and coordinates of non- and monovariant equilibriums were determined. The
dependencies of crystallographic parameters, microhardness and EMF values upon the composition are
Received 18 September 2012
Received in revised form 26 November 2012
Accepted 30 November 2012
Available online 21 December 2012
Keywords:
Quaternary system
Thallium selenide
Antimony telluride
Phase diagram
Thermodynamic properties
Electro-motive force
discussed. From the EMF measurements, the partial molar functions of thallium ð
DG;
D
H;
D
SÞ were calcu-
lated for the revealed nonstoichiometric quaternary phases.
Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction
of known ternary phases but with complex substitutional patterns
and wide homogeneity ranges. In many cases these phases repre-
sent certain interest as objects for varying and tuning properties
of their parent compounds.
Here, we report the results of the complete investigation of
phase equilibriums in the 3Tl2Se + Sb2Te3 M 3Tl2Te + Sb2Se3 qua-
ternary mutual system hereafter denoted (A). We open this paper
with reviewing the necessary literature data on the border systems
and compounds in them, follow with the experimental procedure,
and then discuss our data on the phase equilibriums, polythermal
sections, liquidus surface, and partial molar thermodynamic
functions.
Complex chalcogenides of heavy p metals exhibit properties
that make them a good base for creating various functional mate-
rials, including thermoelectrics [1–3] and three-dimensional (3D)
topological insulators [4,5]. These properties open the opportunity
to realize a number of new applications in thermoelectrics, spin-
tronics and quantum computing.
In recent years, phase diagrams of several ternary and quater-
nary systems consisting of chalcogenides of thallium, antimony
and bismuth have been investigated. These systems include Tl2S–
Sb2S3–Bi2S3 [6], Tl2Se–Sb2Se3–Bi2Se3 [7], Tl2Te–Sb2Te3–Bi2Te3 [8],
3Tl2S + Sb2Se3 M 3Tl2Se + Sb2S3 [9], 3Tl2S + Bi2Se3 M Tl2Se + Bi2S3
[10], 3Tl2S + Bi2Te3 M 3Tl2Te + Bi2S3 [11] and 3Tl2Te + Bi2Se3 -
M 3Tl2Se + Bi2Te3 [12]. In these systems, new quaternary phases
with sizable homogeneity ranges were found and subsequently
studied for their physicochemical properties.
1.1. Binary compounds
Initial binary compounds Tl2Se, Tl2Te, Sb2Se3 and Sb2Te3 form-
ing the 3Tl2Se + Sb2Te3 M 3Tl2Te + Sb2Se3 quaternary mutual sys-
tem all melt congruently at 663, 698, 863 and 895 K, respectively
[13,14]. Tl2Se crystallizes in the tetragonal system, space group
P4/n, a = 8.54, c = 12.71 Å, z = 10 [15], whereas Tl2Te forms the
monoclinic lattice with the following unit cell parameters:
a = 15.662, b = 8.987, c = 31.196 Å, b = 100.761°, z = 44 and the
space group C2/c [16]. Sb2Se3 has the orthorhombic crystal struc-
ture, space group Pbnm: a = 11.633; b = 11.780; c = 3.985 Å; z = 4,
whereas Sb2Te3 crystallizes in the rhombohedral tetradymite type
of structure with the unit cell parameters: a = 4.25; c = 30.2 Å, z = 9
[15].
Understanding the phase relationships in the corresponding
systems is always helpful for the development of relative materi-
als. Specifically, the synthesis and growth of the large single crys-
tals from the melt requires the knowledge of the respective phase
diagrams. Quaternary phases are much more complex than ternary
ones; at the same time they frequently contain quaternary analogs
⇑
Corresponding authors. Addresses: Z. Khalilov Str. 23, Baku, AZ 1148, Azerbaijan
(M.B. Babanly), Leninskie Gory 1-3, Moscow 119991, Russia (A.V. Shevelkov).
E-mail addresses: babanly_mb@rambler.ru (M.B. Babanly), shev@inorg.chem.-
msu.ru (A.V. Shevelkov).
0925-8388/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.jallcom.2012.11.202

Y.I. Jafarov et al. / Journal of Alloys and Compounds 555 (2013) 184–192
185
1.2. Quasi-binary border subsystems and ternary compounds
1.2.1. The section Tl2Se–Tl2Te
This quasi-binary section relates to the eutectic type with the
limited solid solubility fields based on the initial compounds. The
eutectic composition lies at 20 mol% Tl2Te and 648 K [17].
1.2.2. The section Tl2Se–Sb2Se3
In our previous work [18], the refined phase diagram of this sys-
tem was reported. Four ternary compounds, namely Tl9SbSe6, Tl3-
SbSe3, TlSbSe2 and TlSb3Se5 were confirmed in this system. Two
of them Tl9SbSe6 and TlSbSe2 melt congruently at 725 and 730 K,
respectively, whereas Tl3SbSe3 and TlSb3Se5 are formed by peritec-
tic reactions at 625 and 740 K, respectively. The compositions of
the peritectic points lie at 26 and 70 mol% Sb2Se3, respectively.
The eutectic composition between TlSbSe2 and Tl3SbSe3 has the
melting point of 610 K at 28 mol% Sb2Se3, whereas the eutectic
composition formed by TlSb3Se5 and TlSbSe2 crystallizes at 705 K
and 64 mol% Sb2Se3.
TlSbSe2 undergoes a phase transition at 665 K. The low temper-
ature modification crystallizes in the monoclinic system, space
group P21 with the following unit cell parameters: a = 9.137,
b = 4.097, c = 12.765 Å, b = 111.75° [19], whereas the high temper-
ature modification has the orthorhombic crystal structure with the
unit cell parameters a = 9.138; b = 23.735; c = 4.107 Å [20]; it pre-
sents a disordered variant of the TlI structure type. Olsen and co-
authors [21] reported that Tl3SbSe3 crystallizes in the Na3AsS3-type
cubic structure with the unit cell parameter a = 9.435 Å (space
group P213). Tl9SbSe6 has the Tl5Te3 type tetragonal crystal struc-
ture, space group P4/n, with the unit cell parameters a = 8.539
and c = 12.69 Å [22].
Fig. 2. Phase diagram (a), concentration relations of microhardnesses (b) and EMF
of the chains of type (1) at 300 K (c) of the system Tl9SbSe6–Tl9SbTe6.
ently at 798 K and forms a continuous solid solution field with Tl2-
Te. The solubility in the solid phase based on Sb2Te3 was found to
be about 5 mol% at 753 K. According to the literature [23], TlSbTe2
has the hexagonal crystal structure of the NaCrS2 type with the
unit cell parameters a = 4.425 and c = 23.303 Å. Tl9SbTe6 is the
1.2.3. The section Tl2Te–Sb2Te3
This section is characterized by formation of two intermediate
ternary compounds TlSbTe2 and Tl9SbTe6. The former decomposes
by a peritectic reaction at 753 K, whereas the latter melts congru-
Fig. 1. Crystal structures of low-temperature TlSbSe2 (a), Tl3SbSe3 (b), TlSb3Se5 (c), Tl9SbTe6 (d), Tl9SbTe6 (e), and TlSbTe2 (f). Shown are polyhedra around antimony: square
pyramids in (a), pyramids with Sb in a vertex (b), octaherda in all the rest. Thallium atoms are shown as large light spheres.

186
Y.I. Jafarov et al. / Journal of Alloys and Compounds 555 (2013) 184–192
Fig. 3. XRD patterns for different compositions in the Tl9SbSe6–Tl9SbTe6 system: entire 2h range (bottom), from 19° to 39° 2h (top).
system (A) were prepared by melting the stoichiometric quantities of the pre-syn-
ternary analog of Tl5Te3 and has the tetragonal unit cell, space
group I4/m, a = 8.828 Å and c = 13.001 Å [22,24].
thesized binary and ternary compounds in sealed silica tubes. After determining the
corresponding solidus temperatures, all alloys were annealed at 20–50 K below the
solidus for 800–1000 h in order to achieve complete homogenization.
XRD and DTA analyses and microhardness measurements were employed to
analyze the samples. The XRD analysis was performed with a Bruker D8 ADVANCE
1.2.4. The section Sb2Se3–Sb2Te3
This section is of eutectic type with limited solid solubility
fields based on initial compounds [25]. The eutectic composition
was found at 18 mol% Sb2Te3 and 833 K. The solid solubility based
on Sb2Te3 and Sb2Se3 is achieved at 63 and 5 mol%, respectively, at
room temperature.
diffractometer using the Cu-K radiation. DTA was performed using an NTR-74 de-
a
vice with two chromel–alumel thermocouples. Microhardness measurements were
done with a microhardnesmeter PMT-3, the typical loading being 20 g. For the elec-
tro-motive force (EMF) measurements, the following concentration chains were
used:
Fig. 1 compiles the crystal structures of the above discussed ter-
nary compounds.
ðꢁÞTl ðsolidÞ=glycerin þ KCL þ TlCl=Tl in alloys ðsolidÞ ðþÞ
ð1Þ
2. Experimental
In the chains of type (1), metallic thallium was the left (negative) electrode, while
equilibrium alloys of the system (A) were exploited as the right (positive) electrode.
A saturated glycerin solution of KCl with the addition of 1 mol% of TlCl was used as
the electrolyte. The assembly of an electrochemical cell and measurements were
similar to those reported elsewhere [26]. EMF was measured by the compensation
method in the temperature range of 300–450 K using the high-resistance universal
B7-34A digital voltmeter with the accuracy of 0.1 mV.
The starting binary Tl2Se, Tl2Te, Sb2Se3 and Sb2Te3 as well as ternary TlSbSe2,
TlSbTe2, Tl9SbSe6, Tl9SbTe6, Tl3SbSe3, TlSb3Se5 compounds were synthesized by
melting stoichiometric amounts of the respective high purity grade elements (not
less than 99.999%) in evacuated (ꢀ10ꢁ2 Pa) sealed silica tubes. The quality of the
synthesized compounds was checked by the differential thermal analysis (DTA)
and X-ray diffraction analysis (XRD), which confirmed their purity. Alloys of the

Y.I. Jafarov et al. / Journal of Alloys and Compounds 555 (2013) 184–192
187
3. Results and discussion
The combined analysis of all our experimental data and the
results found in the literature on the phase equilibria in the
Tl2Se–Tl2Te [17], Tl2Se–Sb2Se3 [18], Tl2Te–Sb2Te3 [27,28] and Sb2-
Se3–Sb2Te3 [25] systems enabled us to construct the self-consistent
diagram of the phase equilibriums in the mutual system (A).
3.1. Quasi-binary and partly quasi-binary sections
3.1.1. The section Tl9SbSe6–Tl9SbTe6
This is the only quasi-binary section of the system (A). Accord-
ing to the DTA results its phase diagram belongs to type I within
the Roseboom’s classification (Fig. 2a) though both initial com-
pounds have different crystal structure. The XRD data shows
(Fig. 3) that in the wide composition area (P15 mol% Tl9SbTe6)
the solid solution has the Tl9SbTe6 type of the crystal structure,
whereas the phase with 10 mol% Tl9SbTe6 is isostructural to Tl9-
SbSe6. The results of the microhardness measurements confirm
that all samples contain just a single phase. The maximum values
of microhardness are observed at 10–20 mol% Tl9SbTe6 (Fig. 2b).
Further confirmation of the XRD and microhardness analysis re-
sults comes from the EMF data. (Fig. 2c) clearly shows that the
dependence of the EMF values on the composition is expressed
by the monotonous curve that confirms continuous changes of
the composition of the investigated phases, which are the right
electrode of the chains of type (1).
Taking into account these results we assume that the heteroge-
neous region a1
15 mol% Tl9SbTe6 and the a1
+
a2 degenerate nearest of the composition with
a2 phase transition can be consid-
?
ered as morphotropic. This can be explained by comparing the
crystal structures of Tl9SbSe6 and Tl9SbTe6 (Fig. 1, panels d and
e). Having almost the same metrics they differ slightly by the ori-
entation of the [SbE6] octahedra (E = Se, Te) and a degree of dis-
placement of the thallium atoms from their ideal positions.
Fig. 4. Phase diagram (a), concentration relations of microhardnesses (b) and EMF
of the chains of type (1) at 300 K (c) of the system TlSbSe2–TlSbTe2.
75, 50 and 20 mol% TlSbSe2 are qualitatively similar to pure
TlSbTe2. Upon increasing the TlSbSe2 content in alloys the corre-
sponding peak positions are shifted towards higher angles. Com-
bined, this confirms that the sample with 90 mol% TlSbSe2
belongs to the solid solution based on TlSbSe2, whereas the sam-
ples having 75, 50 and 20 mol% TlSbSe2 are the solid solution based
on TlSbTe2. As can be seen in Fig. 5, the sample with 80 mol%
TlSbSe2 is the only two-phase alloy, and on the XRD pattern there
3.1.2. The section TlSbSe2–TlSbTe2
This is the non quasi-binary section (Fig. 4) due to the incongru-
ent character of TlSbTe2, but it behaves as a quasi-binary system
below 730 K. Liquidus consists of three parts corresponding to
the primary crystallization of the c10
; c2 and b2-phase, which are
the solid solutions based on the high-temperature modification
of TlSbSe2, TlSbTe2 and Sb2Te3, respectively.
Below the liquidus curve of b2-phase there is a curve corre-
sponding to the secondary crystallization of the
are reflections from the
c2-phase and the most intensive reflec-
c2-phase, which
tions of the c01-phase.
occurs by a peritectic reaction L + b2 2. The eutectic contains
?
c
The EMF measurements further confirm the phase diagram
(Fig. 4c). Apparently, the EMF value is the linear function of the
approximately 17 mol% TlSbTe2 and crystallizes at 710 K. The
eutectoid point (E⁄) lies at 635 K and 13 mol% TlSbTe2. Wide solid
solubility fields are formed in this system based on the initial ter-
nary compounds.
composition in the homogeneity fields of the c1 and
(with different increments), whereas in the two-phase area of
c2 it remains constant independent of the relative content of
c2-phases
c1
+
The c01-phase and
c
2-phase have maximum homogeneity fields
at the temperature of eutectics with 13 and 80 mol%, respectively.
The homogeneity field of the 1-phase based on low temperature
the phases. The powder XRD patterns of the samples on the sec-
tions Tl9SbSe6–Tl9SbTe6 and TlSbSe2–TlSbTe2 were indexed by
means of the TopasV3.0 software and the calculated unit cell
parameters are listed in Table 1.
c
modification of TlSbSe2 has its maximum at the eutectoid temper-
ature. The observed homogeneity fields of c1 and c2 at 400 K are
achieved at about 10 and 76 mol%, respectively.
The results of the microhardness measurements confirmed the
constructed phase diagram (Fig. 4b). Microhardness values of the
solid solutions based on TlSbSe2 and TlSbTe2 increase monoto-
nously upon increasing concentration of the second component,
whereas in the two-phase area they remain constant.
The XRD data on the alloys air-quenched after annealing for
about 600 h at 670 K are presented in Fig. 5. Apparently, the sam-
ple containing 90 mol% TlSbSe2 displays a diffraction pattern that
qualitatively similar to pure TlSbSe2 whereas the alloys having
3.2. Solid-state phase equilibriums in the system (A)
The sections Tl9SbSe6–Tl9SbTe6 and TlSbSe2–TlSbTe2 divide the
system (A) into three independent subsystems: Tl2Se–Tl2Te–Tl9-
SbTe6–Tl9SbSe6, Tl9SbSe6–Tl9SbTe6–TlSbTe2–TlSbSe2 and TlSbSe2–
TlSbTe2–Sb2Te3–Sb2Se3 (Fig. 6).
The first subsystem is fully covered by the fields of the solid
solutions with the Tl2Se (a1), Tl9SbTe6 (a2) and Tl2Te (a3) structure
types. The borders of the a1 and a2 phases as well as two-phase

188
Y.I. Jafarov et al. / Journal of Alloys and Compounds 555 (2013) 184–192
Fig. 5. XRD patterns for different compositions in the TlSbSe2–TlSbTe2 system: entire 2h range (bottom), from 21° to 45° 2h (top).
Table 1
Crystal structure parameters of the solid solutions in the TlSbSe2–TlSbTe2 and Tl9SbSe6–Tl9SbTe6 subsystems.
Section
Composition
Crystal system
Lattice parameters, Å
a
b
c
TlSbSe2–TlSbTe2
TlSbSe2
Orthorhombic
Orthorhombic
Rhombohedral
Rhombohedral
Rhombohedral
Rhombohedral
11.9146(5)
12.009(3)
4.2195(3)
4.2117(7)
4.3695(15)
4.3372(9)
4.145(2)
4.213(1)
4.5414(14)
4.5409(11)
22.716(2)
22.709(2)
23.211(4)
23.324(4)
TlSbSe1.8Te0.2
TlSbSe1.5Te0.5
TlSbSeTe
TlSbSe0.4Te1.6
TlSbTe2
Tl9SbSe6–Tl9SbTe6
Tl9SbSe6
Tetragonal
Tetragonal
Tetragonal
Tetragonal
Tetragonal
Tetragonal
Tetragonal
8.5334(2)
8.5347(1)
8.5365(1)
8.6923(3)
8.7639(2)
8.8352(1)
8.8352(1)
12.6944(3)
12.7741(3)
12.9509(3)
13.0157(3)
13.0217(8)
13.0434(4)
13.0270(2)
Tl9SbSe5.4Te0.6
Tl9SbSe4.8Te1.2
Tl9SbSe3.6Te2.4
Tl9SbSe2.4Te3.6
Tl9SbSe1.2Te4.8
Tl9SbTe6

Y.I. Jafarov et al. / Journal of Alloys and Compounds 555 (2013) 184–192
189
Table 2
Invariant equilibriums in the 3Tl2Se + Sb2Te33Tl2Te + Sb2Se3 system.
Point in Fig. 7
Equilibrium
Composition, mol%
t, K
3Tl2Se
3Tl2Te
Sb2Se3
D1
D2
D3
e1
e2
e3
LMTl9SbSe6
LMTlSbSe2
LMTl9SbTe6
75
25
25
75
725
730
798
648
610
705
75
20
LMa1
LMTl3SbSe3
LMTlSb3Se5+ c01
+
a3
80
46
17
+
c1
54
83
e4
e5
e6
p1
p2
p3
p4
U1
U2
U3
E1
E2
LMa2
LMb1 + b2
LMc01
L + 1MTl3SbSe3
L + b1MTlSb3Se5
L + b2Mc2
+
c2
50
17
685
833
710
625
740
753
700
605
705
690
600
685
82
75
51
87
+
c2
8
49
13
a
28
97
13
10
13
15
11
L +
L +
a
2Ma3
c
1MTl3SbSe3
+
c2
29
3
5
30
8
58
87
82
55
81
L + b1MTlSb3Se5 + b2
L + b2MTlSb3Se5
+
+
+
c2
c2
c2
LMTl3SbSe3
LMTlSb3Se5
+
+
a2
c1
Fig. 6. Isothermal section at 300 K of the phase diagram of the 3Tl2Se + Sb2Te3-
M3Tl2Te + Sb2Se3 mutual system.
Table 3
Monovariant equilibriums in the 3Tl2Se + Sb2Te3M3Tl2Te + Sb2Se3 system.
Curve in Fig. 7
Equilibrium
L + 2Ma3
Temperature interval, K
p4K1
K1e1
p1K2
K2E1
e2U1
U1E1
e6U1
e6E2
e3E2
p2U2
e5U2
U2U3
U3E2
e4E1
p3U3
a
700–660
660–648
625–610
610–600
610–605
605–600
710–605
710–685
705–685
740–705
833–705
705–690
690–685
685–600
753–690
LMa3
L + a1
+ a1(a2)
(a2)MTl3SbSe3
LM
LM
LM
a2 + Tl3SbSe3
c
c
1 + Tl3SbSe3
2 + Tl3SbSe3
LMc1
LMc1c2
LM 1 + TlSb3Se5
+ c2
c
L + b1MTlSb3Se5
LMb1 + b2
LMb2 + TlSb3Se5
LM
LMa2
L + b2Mc2
c2 + TlSb3Se5
+
c2
We were unable to accurately differentiate the fields of primary
crystallization of the 1 and 2 phases. They together occupy a very
wide area in Fig. 6. The primary crystallization fields of the b2 and
2 phases are also having a wide extension, which allows the vari-
a
a
c
ety of the compositions of alloys for growing of single crystals of
the solid solutions.
Fig. 7. Projection of the liquidus surface of the 3Tl2Se + Sb2Te33Tl2Te + Sb2Se3
system. Primary crystallization fields are shown: 1,
c1Þ; 5, 2; 6, TlSb3Se5 (C2); 7, b1; 8, b2.
a3; 2, a1 (a2); 3, Tl3SbSe3 (C1); 4,
Table 2 summarizes the types and coordinates of nonvariant
equilibriums, including border systems, whereas Table 3 compiles
the types and temperature intervals for the monovariant equilibri-
ums. The interesting feature of the given system is the transitions
of two peritectic equilibriums into the corresponding eutectics
(Fig. 7, Table 3). The approximate points of these transitions (K1
and K2) are labeled on the p4e1 and p1E1 curves.
c10
ð
c
regions of C1 + a1 and C1 + a2 are shown by dashed lines in Fig. 6.
The two-phase area a1 a2 is degenerated, whereas the a2
+
+ a3
area is continuously narrowed with increasing the tellurium con-
tent and practically degenerated at the M point (Fig. 6).
Two other subsystems consist of different two- and three-phase
regions formed from various combinations of the a1
, a2, a3, b1, b2,
c1 and 2-phases as well as ternary compounds Tl3SbSe3 (C1) and
c
3.4. Several polythermal sections of the phase diagram of the system
(A)
TlSb3Se5 (C2). The borders of these regions were determined by
means of analyzing the XRD patterns and from the comparison of
the DTA results for certain polythermal sections.
In order to achieve the self-consistent phase diagram of the sys-
tem (A), we studied the polythermal sections 3Tl2Se–Sb2Te3, 3Tl2-
Te–Sb2Se3, 2Tl2Se–TlSbTe2, 2Tl2Te–TlSbSe2, 1.5TlSbTe2–Sb2Se3
and 1.5TlSbSe2–Sb2Te3 as well as a number of samples which
compositions positioned out of these sections. Below, the diagonal
sections 3Tl2Se–Sb2Te3 and 3Tl2Te–Sb2Se3 are discussed and are
3.3. The liquidus surface of the system (A)
The liquidus surface of the system (A) (Fig. 7) consists of eight
fields corresponding to primary crystallization of various phases.

190
Y.I. Jafarov et al. / Journal of Alloys and Compounds 555 (2013) 184–192
3.4.2. The section 3Tl2Te–Sb2Se3
This section (Fig. 9) is characterized by a complex reaction pat-
tern. It intersects four single-phase (b1, c2 3), five two-phase
3) and three three-phase
2) fields in the subsolidus area.
,
a2, a
(b1 + C2, b2 + c2
,
c
2 + C1, a2
+
c2,
a2
+
a
(b1 + b2 + C2, b2 +
c2 + C2, C1 + a2
+
c
Concentration and temperature ranges of primary crystallization of
phases and monovariant equilibriums are in good agreement with
Fig. 7.
This section clearly features four horizontals lines at 705, 690,
605 and 600 K, respectively, according to invariant transition (U2,
U3, U1) and eutectic (E1) equilibriums (Table 2).
3.5. Thermodynamic properties of the solid solutions
The results of the EMF measurements of the chains of type (1)
allowed calculating thermodynamic properties of alloys of the sec-
tions Tl9SbSe6–Tl9SbTe6 and TlSbSe2–TlSbTe2. The analysis showed
the linearity of the EMF dependences upon temperature for all al-
loys. Accordingly, the linear least-square treatment of the data was
performed [26] and the results were expressed according to the lit-
erature recommendations [29] as:
Fig. 8. Polythermal section 3Tl2Se–Sb2Te3 of the 3Tl2Se + Sb2Te33Tl2Te + Sb2Se3
phase diagram.
"
#
1=2
SE2
n
2
E ¼ a þ bT ꢂ t
þ S2bðT ꢁ TÞ
ð2Þ
where n is the number of pairs of E and T values; SE and Sb are the
error variances of the EMF readings and b coefficient, respectively; T
is the average of the absolute temperature; t is the Student’s test. At
the confidence level of 95% and n P 20, the Student’s test is t 6 2
[26]. The composed equation of the mode (2) is presented in
Table 4.
ꢀ
ꢀ
ꢀ
The partial molar functions of thallium ð
DG;
D
H;
D
SÞ (Table 5) in
the a2 1 and 2- phase, as well as in c1 2 two-phase alloys were
,
c
c
+ c
calculated by known thermodynamic relations [26] taking into ac-
count the phase state of alloys by using data from the Table 4. The
graphical dependences of the partial molar functions of thallium of
the composition for the sections Tl9SbSe6–Tl9SbTe6 and TlSbSe2–
TlSbTe2 are plotted based on Table 5 (Fig. 10a and b). As can be
Fig. 9. Polythermal section 3Tl2Te–Sb2Se3 of the 3Tl2Se + Sb2Te33Tl2Te + Sb2Se3
phase diagram. Phase areas: 1, L + b1 + C2; 2, L + b1 + b2; 3, L + b2; 4, L + C2 + b2; 5, 6,
L + b2 + c2; 7, L + c1 + c2, 8, L + C1 + c2.
ꢀ
ꢀ
ꢀ
seen from Fig. 10, the isotherms of
ous and monotonous functions of the composition in the homogo-
nous range of the 1 and 2 phases. In the two-phase region c1 + c2
DGTl, DHTl and DSTl are continu-
c
c
their values remain constant regardless of the common composi-
tion, which is due to the constant composition of both phases in
this area.
compared with the general T-x-y diagram of the quaternary mu-
tual system.
It should be noted that the monotonous character of the con-
centration dependences of the partial thermodynamic functions
of thallium in the homogeneity regions of the a2, c1 and c2 phases
indicates that formation of the solid solutions in the systems Tl9-
SbSe6–Tl9SbTe6 and TlSbSe2–TlSbTe2 is accompanied by minor
3.4.1. The section 3Tl2Se–Sb2Te3
This section (Fig. 8) crosses the primary crystallization field of
the a1
25 mol% Sb2Te3 the liquid phase completely crystallizes to form
pure 1-phase or 2-phase. The border of these phases is found
, a2, c2 and b2 phases. In the composition range of 0–
structural and energetic changes. Besides, it confirms that the a2
,
c1 and c2 phases belong to the substitutional type of solid
solutions.
a
a
to have the composition corresponding to ꢀ 16 mol% Sb2Te3.
After primary crystallization of the b2-phase from the melt con-
taining more than 75 mol% Sb2Te3, the TlSbTe2 based
crystallizes by the monovariant peritectic reaction (Table 3, the
curve p3U3) and forms the two-phase field 2 + b2.
In the composition range of 25–40 mol% Sb2Te3, after primary
crystallization of 2-phase, observed is the formation of Tl3SbSe3
by the monovariant peritectic reaction (Table 3, Fig. 7, the curve
p1K2), the latter transforms into a eutectic equilibrium (the curve
K2E1) nearest of E1.
c
2-phase
4. Conclusions
c
We have shown that Tl2Se + Sb2Te3MTl2Te + Sb2Se3 is a mutual
quaternary system that features wide solubility fields along the
TlSbSe2–TlSbTe2 non quasi-binary section and within the Tl2Se–
Tl9SbSe6–Tl9SbTe6–Tl2Te subsystem. The only quasi-binary section
Tl9SbSe6–Tl9SbTe6 shows a morphotropic phase transition between
the solid solutions based on the Se and Te derivatives. The liquidus
surface of the system consists of eight fields occupying very wide
compositional area. The calculated partial molar thermodynamic
functions of thallium prove that the formation of the solid solu-
tions is accompanied by minor energetic changes, reflecting minor
a
In the region of 40–75 mol% Sb2Te3, crystallization of the two-
phase mixture a2
+ c2 occurs. The crystallization process finishes
with the quadriphase eutectic reaction (E1) in the region of 40–
50 mol% Sb2Te3.

Y.I. Jafarov et al. / Journal of Alloys and Compounds 555 (2013) 184–192
191
Table 4
Temperature dependencies of the EMF for the chains of type (1) in the TlSbSe2–TlSbTe2 and Tl9SbSe6–Tl9SbTe6 system (T = 300–430 K).
h
i
Phase area, mol% TlSbTe2 (Tl9SbTe6)
1=2
SE2
n
2
E; mV ¼ a þ bT ꢂ t þ S2bðT ꢁ TÞ
ꢀ
ꢁ
1=2
TlSbSe2–TlSbTe2
0 (TlSbSe2) [25]
33; 4
40
2
685; 1 ꢁ 0; 091T ꢂ 2
661; 7 ꢁ 0; 074T ꢂ 2
638; 7 ꢁ 0; 046T ꢂ 2
620; 2 ꢁ 0; 017T ꢂ 2
580; 2 þ 0; 032T ꢂ 2
533; 6 þ 0; 084T ꢂ 2
489; 7 þ 0; 134T ꢂ 2
468; 8 þ 0; 111T ꢂ 2
þ 5 ꢃ 10ꢁ4ðT ꢁ 366; 4Þ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢁ
ꢁ
ꢁ
ꢁ
ꢁ
ꢁ
ꢁ
1=2
1=2
1=2
1=2
1=2
1=2
1=2
5 (c1
)
5; 6
28
2
2
2
2
2
2
2
þ 7 ꢃ 10ꢁ4ðT ꢁ 367; 2Þ
10–24 (c1+ c2)
4; 8
28
þ 6 ꢃ 10ꢁ4ðT ꢁ 367; 2Þ
þ 5 ꢃ 10ꢁ4ðT ꢁ 367; 2Þ
þ 4 ꢃ 10ꢁ4ðT ꢁ 367; 2Þ
þ 2 ꢃ 10ꢁ5ðT ꢁ 367; 2Þ
þ 4 ꢃ 10ꢁ4ðT ꢁ 367; 2Þ
þ 7 ꢃ 10ꢁ4ðT ꢁ 368; 6Þ
25 (c2
40 (c2
60 (c2
80 (c2
)
)
)
)
4; 2
28
5; 4
28
3; 6
28
5; 2
28
100 (TlSbTe2) [25]
0 (Tl9SbSe6) [25]
4; 7
40
ꢀ
ꢁ
1=2
Tl9SbSe6–Tl9SbTe6
22; 5
40
1; 3
2
486; 2 ꢁ 0; 052T ꢂ 2
468; 7 ꢁ 0; 018T ꢂ 2
þ 0; 0003ðT ꢁ 366; 5Þ
þ 4 ꢃ 10ꢁ5ðT ꢁ 368; 4Þ
ꢀ
ꢁ
1=2
20(a2
40(a2
60(a2
80(a2
)
)
)
)
2
20
ꢀ
ꢀ
ꢀ
ꢁ
1=2
1; 8
20
2
450; 4 þ 0; 016T ꢂ 2
426; 4 þ 0; 058T ꢂ 2
405; 9 þ 0; 097T ꢂ 2
þ 1; 3 ꢃ 10ꢁ4ðT ꢁ 368; 4Þ
ꢁ
1=2
1; 1
20
2
þ 3 ꢃ 10ꢁ5ðT ꢁ 368; 4Þ
ꢁ
1=2
2; 4
20
2
þ 1; 8 ꢃ 10ꢁ4ðT ꢁ 368; 4Þ
ꢀ
ꢁ
1=2
100 (Tl9SbTe6) [25]
34; 7
40
2
402; 7 þ 0; 094T ꢂ 2
þ 5 ꢃ 10ꢁ4ðT ꢁ 367; 8Þ
Table 5
Relative partial thermodynamic functions of thallium in the solid solutions of the TlSbSe2–TlSbTe2 and Tl9SbSe6–Tl9SbTe6 systems at 298 K.
Section
Composition mol% TlSbTe2 (Tl9SbTe6)
ꢀ
ꢀ
ꢀ
ꢁ
D
GTl
ꢁ
D
HTl
DSTl
(kJ molꢁ1
)
(JꢃKꢁ1 molꢁ1
)
TlSbSe2–TlSbTe2
0 (TlSbSe2) [25]
5 (c1
10–24 (c1
63,49 0,34
61,72 0,36
60,30 0,34
59,35 0,31
56,90 0,28
53,90 0,20
51,10 0,28
48,42 0,35
45,42 0,27
44,71 0,10
43,92 0,17
42,81 0,40
41,95 0,19
41,56 0,35
66,10 1,59
63,85 1,88
61,63 1,74
55,98 1,59
55,98 1,42
51,49 1,00
47,25 1,42
45,23 1,89
46,91 1,20
45,2 0,45
ꢁ8,8 4,31
ꢁ7,1 5,1
ꢁ4,4 4,7
ꢁ1,6 4,3
3,1 3,9
)
+
c2)
25 (c2
40 (c2
60 (c2
80 (c2
)
)
)
)
8,1 2,7
12,9 3,9
10,7 5,1
ꢁ5,0 3,4
ꢁ1,7 1,2
1,5 2,2
5,6 1,1
9,4 2,7
9,1 4,3
100 (TlSbTe2) [25]
0 (Tl9SbSe6) [25]
Tl9SbSe6–Tl9SbTe6
20(a2
40(a2
60(a2
80(a2
)
)
)
)
43,46 0,81
41,14 0,39
39,16 0,96
38,85 1,60
100(Tl9SbTe6) [25]

192
Y.I. Jafarov et al. / Journal of Alloys and Compounds 555 (2013) 184–192
Acknowledgment
This work was supported by Science Development Foundation
under the President of the Republic of Azerbaijan, grant no EIF-
2011-1(3)-82/69/4-M-50.
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