Phase equilibria in the Tl-TlI-Te system and thermodynamic properties of the Tl5Te3-xIx solid solution

Article abstract of DOI:10.1016/j.jallcom.2013.11.223

The Tl-TlI-Te ternary system was investigated by using the DTA and XRD analyses, microhardness and EMF measurements, leading to the construction of important polythermal and isothermal sections as well as the projection of the liquidus surface. Determined

Full text of DOI:10.1016/j.jallcom.2013.11.223

Journal of Alloys and Compounds 590 (2014) 68–74
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: www.elsevier.com/locate/jalcom
Phase equilibria in the Tl–TlI–Te system and thermodynamic properties
of the Tl Te I solid solution
5
3ꢀx x
Dunya M. Babanly a, , Ilham M. Babanly , Samira Z. Imamaliyeva , Vaqif A. Gasimov ,
⇑
b
b
a
c,
⇑
Andrei V. Shevelkov
a
Institute of Chemical Problems of ANAS, Baku, Azerbaijan
Department of Chemistry, Baku State University, Azerbaijan
Department of Chemistry, Lomonosov Moscow State University, Russia
b
c
a r t i c l e i n f o
a b s t r a c t
Article history:
The Tl–TlI–Te ternary system was investigated by using the DTA and XRD analyses, microhardness and
EMF measurements, leading to the construction of important polythermal and isothermal sections as
well as the projection of the liquidus surface. Determined were the fields of primary crystallization
and the types and coordinates of non- and monovariant equilibria. The system features the formation
Received 2 September 2013
Received in revised form 25 November 2013
Accepted 29 November 2013
Available online 13 December 2013
of continuous solid solutions (d-phase) between the Tl
of the d-phase completely covers the Tl Te I–Tl Te –Tl
functions ð G; H;
Tl
5
Te
3 5 2
and Tl Te I compounds. The homogeneity area
Te subsystem. The partial molar thermodynamic
5
2
5
3
2
Keywords:
Ternary system
Thallium tellurides
Thallium telluride-iodides
Solid solutions
D
D
D
SÞ of thallium as well as the standard integral thermodynamic functions of the
5
Te3ꢀx
I
x
solid solution (for various x) were calculated based on the results of the EMF measurements.
Ó 2013 Elsevier B.V. All rights reserved.
Phase diagram
Thermodynamic properties
1
. Introduction
Complex chalcogenides and chalcogen-halides of heavy p met-
toward the preparation of a required stoichiometry within a homo-
geneity range.
In our previous works, phase equilibria and thermodynamic
properties of the systems Tl–TlCl–S [5], Tl–TlBr–S [6], Tl–TlI–S
[7], Tl–TlCl–Se [8], Tl–TlBr–Se [9], Tl–TlCl–Te [10], and Tl–TlBr–Te
[11] were investigated. A number of polythermal and isothermal
sections as well as projections of liquidus surfaces were con-
structed. The homogeneity fields of the intermediate phases were
fixed and their fundamental thermodynamic functions were
calculated.
In this work, we report the results of the complete investigation
of phase equilibria and thermodynamic properties of the Tl–TlI–Te
system. The layout of this paper is as follows. We start with
reviewing the literature data on this system and compounds in
it, follow with the description of the experimental procedure,
and then discuss our results on the phase equilibria, polythermal
sections, liquidus surface, and thermodynamic properties of the
als are considered perspective functional materials. Many of them
exhibit semiconductor, thermoelectric, photoelectric, and mag-
netic properties [1,2]. According to recent investigations, Tl
6
SeI
-ray
4
and Tl Se I are promising materials for efficient X-ray and c
5
2
detection, outperforming the current state-of-the art material for
room temperature operation, CdZnTe (CZT) [3,4]. Given the prom-
ising performance of thallium-based chalcogenides and chalcogen-
ide-halide, these compounds continue to attract attention despite
of toxicity of thallium derivatives.
The synthesis and growth of the single crystals from the melt
requires the knowledge of the respective phase diagrams, which
makes the investigation of phase equilibria very important in
course of the material development. This is particularly true for
quaternary phases, which frequently present wide homogeneity
fields based on complex substitutional patterns. Typically, their
functional properties can be tuned by varying the composition,
which in turn calls for the development of a synthetic approach
5 x
Tl Te3ꢀxI solid solution.
1.1. Review of the literature data
⇑
Corresponding authors. Address: H. Javid 32, Baku, Azerbaijan (D.M. Babanly).
Leninskie Gory 1–3, Moscow 119991, Russia. Tel.: +7(495)9392074 (A.V. Shevel-
The ternary system Tl–Te–I was investigated along various
polythermal sections [12–15].
kov).
For the Tl–Te boundary system, 4 compounds have been re-
E-mail addresses: babanly_mb@rambler.ru (D.M. Babanly), shev@inorg.chem.
msu.ru (A.V. Shevelkov).
2 5 3 2 3
ported; they are Tl Te, Tl Te , TlTe, and Tl Te . The former two
0
925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.jallcom.2013.11.223

D.M. Babanly et al. / Journal of Alloys and Compounds 590 (2014) 68–74
69
Congruently melting compounds Tl
2
Te and Tl
5
Te
3
were prepared from the stoi-
melt congruently at 698 and 726 K, respectively, whereas the latter
two decompose upon melting at 573 and 511 K, respectively
chiometric amounts of the corresponding elements by one-step melting in vacuum-
ꢀ
2
sealed (ꢁ10 Pa) silica ampoules at 800 K, followed by cooling in a switched-off
furnace. For incongruently melting TlTe and Tl Te after fusing at 800 K the am-
poules were slowly cooled to 560 ± 5 K (TlTe) or 500 ± 5 K (Tl Te ), annealed for
[
16,17]. The quasi-binary system TlI–Tl
formation of a ternary compound Tl Te
reaction at 775 K [12]. The immiscibility area occupies the 20–
0 mol% TlI concentration interval at a synthectic temperature. Eu-
tectic is degenerated near TlI and crystallizes at 713 K. Authors of
12] assume the presence of the peritectic equilibrium between
Tl Te I and Tl Te I at
Te at ꢁ730 K. The homogeneity region of Tl
600 K is in the range ꢁ65–745 mol% Tl Te. The homogeneity
areas of TlI and Tl Te were not determined in that work.
This compound forms a continuous solid solution with Tl
13]. The polythermal sections TlI–TlTe and TlI–Tl Te [14] are sta-
2
Te is characterized by the
2
3
5
2
I that melts by a synthectic
2
3
500 h, and then slowly cooled in a switched-off furnace.
TlI was synthesized from the elements following a specially designed proce-
dure, which takes into account high volatility of iodine, describes in detail else-
where [27].
8
[
5 2
Ternary compound Tl Te I was synthesized by melting appropriate amounts of
5
2
2
5
2
the synthesized TlI and Tl Te in a vacuum-sealed quartz ampoule. This compound
2
ꢁ
2
decomposes by a synthectic reaction upon melting [12]. Accordingly, the ampoule
after fusing at 800 K was cooled slowly to 730 K and held at this temperature for
2
ꢁ
800 h.
Samples for the investigation of phase equilibria and thermodynamic properties
were prepared from Tl Te, Tl Te , TlTe, Tl Te , TlI, and Tl Te I. The total mass was
5
Te
3
[
2
3
2
5
3
2
3
5
2
ble in subsolidus, i.e., consist of heterogeneous mixtures of primary
compounds, but they are non-quasi-binary because of the peritec-
1 g. In most cases, after determining the solidus temperature, samples were an-
nealed at 20–30 K below the solidus for 800–1000 h.
2 3
tic decomposition of TlTe and Tl Te . There are wide areas of
immiscibility in the phase diagrams of both systems. The phase
diagram of the quasi-binary system TlI–Te is characterized by
monotectic and eutectic equilibria [15]. The T–x diagrams of the
boundary systems Tl–TlI [18] and TlI–Te [15] are of the monotectic
type. The binary compound TlI constituting one of the corners of
the ternary system Tl–TlI–Te melts congruently at 715 K and
2.2. Analysis
X-ray powder diffraction (XRD), differential thermal analysis (DTA), measure-
ment of microhardness, and electromotive force were used to characterize the
samples.
The XRD analysis was performed on a Bruker D8 ADVANCE diffractometer with
1
the Cu Ka radiation. The lattice parameters were refined using the Topas V3.0 soft-
ware. XRD confirmed that the pre-synthesized binary and ternary compounds were
phase-pure, and that the unit cell parameters perfectly matched the literature data
for binary compounds. The powder XRD pattern for Tl
V3.0 software. It was confirmed that Tl Te I crystallizes in the tetragonal Tl
structure type with the space group I4/mcm and the following unit cell parameters:
a = 9.026(1), c = 13.324(3) Å, z = 4, which perfectly matches the literature data (see
Table 1).
DTA was carried out with a Termoskan-2 device. The temperature was moni-
tored by a Chromel–Alumel thermocouple. The ramp rate was 5 K min . Temper-
atures of thermal effects were taken mainly from the heating curves. The melting
point of the ternary compound Tl
ature data [12,27].
undergoes the TlI
18]. Also, the preparation, stability regions, and properties of
Tl TeI were reported [19].
The following structural information is available from the liter-
I
, TlIII polymorph transformation at 451 K
[
5
Te
2
I was indexed using Topas
Te
3
2
6
5
2
5
ature regarding the binary and ternary compounds of the Tl–Te–I
system (see Table 1). The low-temperature modification of TlI crys-
tallizes in the orthorhombic symmetry and has a molecular-like
crystal structure, whereas the high-temperature modification be-
longs to the CsCl structure type [20,21].
ꢀ1
5 2
Te I was found to be in agreement with the liter-
2 2
Tl Te crystallizes in the monoclinic space group C /c with 44
Microhardness was measured with a PMT-3 tester, the typical loading being
0 g.
For the electromotive force (EMF) measurements, the following concentration
formulas per unit cell and has an unusually complex structure
2
1
+
2ꢀ
2 3
composed of Tl and Te [17]. TlTe and Tl Te possess less com-
plex crystal structures [22,23], however, they exhibit systems of
homonuclear Tl–Tl or Te–Te bonds that make their structure some-
what similar to cluster halides of bismuth and tellurium [24,25].
chains were assembled:
ðꢀÞTlðsolidÞ=glycerin þ KI þ TlI=½Tl ꢀ Te ꢀ IꢂðsolidÞðþÞ
ð1Þ
Tl
tallizing in the In
26,27]. Crystal structures of other thallium selenahalides and tel-
5
Te
3
and Tl
5
Te
2
I belong to a structural family of compounds crys-
In the chains of type (1), metallic thallium was used as the left electrode, while
equilibrium alloys of the system Tl–Te–I were exploited as the right electrode. A
saturated glycerin solution of KI with the addition of 0.1 mass% TlI was used as
an electrolyte. The electrodes were prepared by pressing the powdered alloys in
the form of pellets (0.5 g) in a molybdenum wire. The temperature was stabilized
at 350 K for 40–50 h. EMF was measured by the compensation method in the tem-
perature range of 300–400 K with the accuracy of ±0.1 mV, using a high-resistance
universal B7–34A digital voltmeter. The detailed description of the methods of
assembling the electrochemical cell and carrying out the EMF measurements are gi-
ven in [31,32].
5
Bi structure type and its less symmetric analogs
3
[
lurohalides of the 5:2:1 stoichiometry also belong to this structure
family [8–11,28,29].
2 6
Finally, the crystal structure of Tl TeI
features Te4+ cations in a
distorted octahedral environment of iodine atoms [30]. Note that
this compound does not belong to the ternary Tl–TlI–Te system
studied in this work.
3
. Results and discussion
2
. Experimental
2.1. Synthesis
To obtain complete a picture of phase equilibria in the system
Tl–TlI–Te we have prepared and investigated a number of samples
in the sections Tl Te–TlI, [Tl I]–Tl Te, and Tl Te I–Te(Tl), and also
several additional samples out of the given sections. The results
are given in Figs. 1–8 and Tables 2–6.
Elemental thallium (Tl-99.999%, Alfa Aesar), tellurium (Te-99.999%, Alfa Aesar)
2
2
2
5
2
and iodine (I-99% resublimed pearls, PA-ACS) were used as received. At the first
step, they were used for the preparation of binary compounds Tl Te, Tl Te , TlTe,
Tl Te , TlI, and Tl Te I.
2
5
3
2
3
5
2
Table 1
Structural data for compounds of the Tl–TlI–Te system.
Compound
TlI
Space group
Unit cell parameters
Ref.
Cmcm (LT) Pm–3m (HT)
a = 4.57, b = 12.92, c = 5.24 Å a = 4.201 Å
a = 15.662, b = 8.987, c = 31.196 Å, b = 100.76°
a = 8.929, c = 12.620 Å
[20,21]
[17]
[26]
Tl
Tl
2
Te
Te
C
2
/c
5
3
I4/mcm
TlTe
2
P4 /nmc
a = 18.229, c = 6.157 Å
[22]
Tl
Tl
Tl
2
5
2
Te
Te
TeI
3
2
Cc
I4/mcm
P2 /c
a = 17.413, b = 6.552, c = 7.910 Å, b = 133.6°
a = 9.026; c = 13.324 Å
a = 7.765, b = 8.174, c = 13.756 Å, b = 124.2°
[23]
[27]
[30]
I
a
6
1
a
Composition out of the Tl–TlTe–I system; see text.

7
0
D.M. Babanly et al. / Journal of Alloys and Compounds 590 (2014) 68–74
3.1. The polythermal section TlI–Tl
2
Te
The refined phase diagram of the system TlI–Tl
2
Te is shown in
Fig. 1. The compound Tl
reaction at 775 K (Fig. 1, segment SS on a bottom panel). The
5
Te
2
I melts incongruently by a synthectic
0
immiscibility field ranges from 20 to 75 mol% Tl
hectic temperature. Tl Te
Tl
Te (ꢁ99 mol% Tl
with TlI (5 mol% Tl Te, 710 K). There are wide areas of solid solu-
tion based on Tl Te I (d) and Tl Te ( ). The homogeneity regions
of d and -phases, defined using EMF and microhardness mea-
surements, are 66.5–90% and ꢁ97–100 mol% Tl Te, respectively
Fig. 1).
XRD analysis confirms the phase diagram of the system Tl
TlI (Fig. 2). Apparently, the samples in the 66.7–90 mol% Tl
composition range keep the Tl Te I structure type, however, the
shift of the peak positions point a the varying unit cell parameters.
The sample containing 95 mol% Tl Te contains the lines of reflec-
tion of -phase and d-phase. This is in agreement with the data
2
Te at the synt-
I is in a peritectic equilibrium (p ) with
Te, 705 K) and an eutectic equilibrium (e )
2 4
⁄
5
2
2
2
5
2
2
a
a
2
(
2
Te–
Te
2
5
2
Fig. 2. XRD patterns for different compositions of the TlI–Tl
2
Te system:
Te, 5-Tl Te.
1–66.7 mol.% Tl
2
Te, 2–80 mol.% Tl
2
Te, 3–90 mol.% Tl
2
Te, 4–95 mol.% Tl
2
2
2
a
of EMF and microhardness.
3.2. The isothermal section of the ternary system Tl–TlI–Te at 300 K
2
In general, the phase diagram of the system Tl Te–TlI (Fig. 1)
looks similar to one reported in the literature [12], but still some
important differences are noticeable. Firstly, according to our data
An isothermal section of the phase diagram at 300 K
demonstrates characteristics of solid-phase equilibria in the
system Tl–TlI–Te (Fig. 3), including the wide homogeneity area of
the homogeneity region of Tl
12] and occupies ꢁ66–90 mol% Tl
The solubility on the basis of Tl Te is no more than <5 mol%, but
Te
5 2
I is wider than the one given in
[
2
Te concentration intervals.
Tl
5
Te
2
I (d-phase). XRD analysis of the samples belonging to the
Te I–Tl Te confirms the formation of a continuous
2
subsystem Tl
5
2
5
3
on the basis of both modifications of TlI is very small. This is spe-
cifically testified by the constancy of the phase transformation
temperature (450 K) of TlI. We also verified the coordinates of eu-
tectic and peritectic equilibria that slightly differ from those re-
ported in the literature [12].
solid solution (Fig. 4). Apparently, the diffraction pattern for all
samples are qualitatively the same, but the peaks are systemati-
cally shifted to higher angles with increasing of the Tl Te content.
5 3
These results together with the data shown in Figs. 1 and 2 show
that the homogeneity area of the d-phase covers a very large part
of the subsystem Tl
Existence of wide homogeneity areas of
the formation of two-phase areas Tl , Tl
The subscript index I refers to the low-temperature modification
of thallium). Following three-phase areas exist in the system: Tl
5 2 5 3 2
Te I–Tl Te –Tl Te.
a- and d-phases leads to
I
+
a
I
+ d, + d, and TlTe + d.
a
(
I
+
(
(
TlI)
TlI)
I
+ d, Tl
I
+
+ Te.
a
+ d, (TlI)
I
+ TlTe + d, (TlI)
I
+ TlTe + Tl
2
Te
3
,
and
I
+ Tl Te
2
3
3.3. The liquidus surface of the system Tl–TlI–TeI
The liquidus surface (Fig. 5) consists of five fields corresponding
to primary crystallization of the d-phase, (TlI)II, Te, TlTe, and Tl Te
The liquidus surfaces of thallium and -phase are degenerate.
2
3
.
a
These fields are connected with different curves and points indicat-
ing non- and monovariant equilibria. Table 2 summarizes the types
and coordinates of all non-variant equilibria, whereas monovariant
equilibria are given in Table 3, temperature intervals of the latter
can be obtained from Fig. 5.
The two largest primary crystallization regions belong to
d-phase and (TlI)II. Both of these phases primarily segregate by
monotectic reactions in a wide composition area. The immiscibility
areas which are formed by 3 liquid phases on the basis of Tl (L
TlI)II (L ), tellurides and Te (L ) in different combinations (L + L
+ L , L + L , L + L + L ) cover a large part of the liquidus surface.
An interesting feature of the system Tl–TlI–Te is the existence of
1
),
(
2
3
1
2
,
L
1
3
2
3
1
2
3
/
//
T T T
triple aliquation (the triangle M M M ) with non-variant syntec-
tic equilibrium (#18 in Table 2). Coordinates of non-variant points,
particularly immiscibility regions, were refined by constructing the
above given polythermal sections of the phase diagram.
3.4. The non-quasi-binary polythermal sections
5 2
Phase diagrams of the non-quasi-binary systems Tl Te I–Te and
Fig. 1. Phase diagram (bottom), microhardnesses (middle), and EMF of the chains of
type (1) at 300 K (top) for the system TlI–Tl
2
Te.
2 2
[Tl I]–Tl Te are given in Figs. 6 and 7, respectively. These sections

D.M. Babanly et al. / Journal of Alloys and Compounds 590 (2014) 68–74
71
Fig. 3. The isothermal section of the phase diagram of the Tl–TlI–Te ternary system at 300 K.
3
.4.1. The polythermal section Tl
The polythermal section Tl Te
equilibria in the TlI–Tl Te–Te composition region. This section
crosses the following phase areas in the subsolidus region: d,
d + (TlI)II d + TlTe + (TlI) Tl Te + TlTe + (TlI) and Tl Te
Te + (TlI) . These areas completely conform with the solid-phase
diagram of the system (Fig. 3). The liquidus curve along the section
Tl Te I–Te consists of 3 parts corresponding to the primary crystal-
lization of Te, (TlI)II and d-phase. The immiscibility field ranges
between ꢁ65 and 100 mol% Tl Te I. From this two-phase field,
d-phase primary crystallizes in the ꢁ85ꢀ100 mol% Tl Te I compo-
sition range. Primary crystallization fields of (TlI)II and Te occupy
the 40–85 mol% and 0–40 mol% Tl Te I composition intervals,
respectively. The outgoing horizontal lines U , U and E conform
5
Te I–Te
2
5
2
I–Te (Fig. 6) illustrates the phase
2
,
I
,
2
3
I
,
2
3
+
I
5
2
5
2
5
2
5
2
1
2
to the four-phase transition and eutectic equilibria (Table 2), but
the line existing at 450 K reflects the polymorphic transition (TlI)II
Fig. 4. XRD patterns for different compositions of the Tl
-Tl Te I, 2–30 mol.% Tl Te , 3–50 mol.% Tl Te , 4–70 mol.% Tl
5
Te
Te
2
I–Tl
5
Te
3
system:
1
5
2
5
3
5
3
5
3
, 5-Tl
5
Te
3
.
, (TlI)
I
.
3
.4.2. The polythermal section [Tl
This polythermal section is characterized by formation of a
wide triple aliquation field L + L + L limited by the two-phase
+ L and L + L areas (Fig. 7). There are four or even five thermal
2 2
I]–Tl Te
intersect nearly all phase regions of the Tl–TlI–Te system and re-
flect the majority of non- and monovariant equilibria. A compari-
son of Figs. 6 and 7 with the data given in Figs. 3 and 5 and
Tables 2 and 3 shows the self-consistence of the obtained results
of phase equilibria.
1
2
3
L
1
2
2
3
effects on the DTA curves belonging to the samples of this section.
The horizontal lines at 575, 505 and 450 K conform to the melting
2 3
Fig. 5. Projection of the liquidus surface of the system. Primary crystallization fields are marked by numbers: 1-d, 2-(TlI)II, 3-Te, 4-TlTe, 5-Tl Te .

7
2
D.M. Babanly et al. / Journal of Alloys and Compounds 590 (2014) 68–74
the subsolidus region, this polythermal section crosses the follow-
ing phase fields: Tl , Tl + d, Tl + d, and Tl + (TlI) + d.
I
+
a
I
+
a
I
I
I
3.5. Thermodynamic properties of the solid solution Tl
5 x
Te3ꢀxI
The results of the EMF measurements of the chains (1) are con-
sistent with the solid-state phase diagram (Fig. 3).
It was found that EMF does not depend upon composition in the
2 3 2 3
three-phase areas TlI–TlTe–d, TlI–TlTe–Tl Te , and TlI–Tl Te –Te.
The EMF values change with drastically at each phase border. In
the two latter fields, the values of EMF are equal to those reported
2 3
for pure TlTe and Tl Te , respectively [33]. This proves the revers-
ibility of chains (1), as well as our results declaring the existence of
2 3
small homogeneity areas of TlTe and Tl Te in the system Tl–TlI–
Te.
The analysis showed the linearity of the EMF dependences upon
temperature for all alloys. Accordingly, the linear least-squares
treatment of the data was performed and the results were ex-
pressed according to the literature [31,32] as
5 2
Fig. 6. The polythermal section Tl Te I–Te of the Tl–TlI–Te system.
"
#
1
=2
2
E
S
2
2
b
E ¼ a þ bT ꢃ t
þ S ðT ꢀ TÞ
ð2Þ
n
where n is the number of pairs of E and T values; S
E
and S
b
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
[
32]. The composed equation of the mode (2) is presented in
Table 4.
The partial molar functions of thallium ð
the Tl solid solution were calculated by thermodynamic
relations [31,32] using the data given in Table 4 as follows:
ꢀ
ꢀ
ꢀ
D
G;
D
H;
D
SÞ (Table 5) in
Te3ꢀxI
5 x
D
GTl ¼ ꢀzFE
ꢀ
ꢁ
@
@
E
T
D
STl ¼ zF
¼ zFb
ð3Þ
P
ꢂ
ꢀ
ꢁ ꢃ
@
@
E
T
D
H
Tl ¼ ꢀzF E ꢀ T
¼ ꢀzFa
P
+
Fig. 7. The polythermal section [Tl
2
2
I]–Tl Te of the Tl–TlI–Te system.
where z is the charge of the potential-forming cation Tl and F is the
Faraday constant.
The graphical dependences of the partial molar functions of
thallium on the composition along the section Tl
plotted in Fig. 8. The isotherms of
5
ꢀ
Te
2
I–Tl
ꢀ
Tl
DG , DHTl and DSTl are continu-
5 3
Te are
ꢀ
ous and monotonous functions of the composition in the homoge-
neity range of the d-phase. The monotonous character of the
concentration dependences of the partial thermodynamic func-
tions of thallium in the homogeneity region of the d-phase indi-
cates that formation of the solid solution is accompanied by
minor structural and energetic changes. Besides, it confirms that
d-phase belongs to the substitutional type of solid solutions.
According to Fig. 3 the partial molar values of thallium in the
5 2
Tl Te I + TlI + TlTe phase area are the thermodynamic functions
of the following potential-forming reaction [31,32]:
TlðsÞ þ 0:5TlIðsÞ þ TlTeðsÞ ¼ 0:5Tl5Te2I
ð4Þ
Then, the standard thermodynamic functions of formation of
Tl
5
2
Te I were calculated as:
0
0
0
D
Z ðTl
5
Te
Z0 is the
phase, whereas
2
IÞ ¼ 2
D
Z
Tl þ 2
D
Z ðTlTeÞ þ
D
Z ðTlIÞ
ð5Þ
Fig. 8. Dependence of the relative partial thermodynamic functions of thallium on
the composition in the Tl Te I–Tl Te system.
0
0
5
2
5
3
where
D
D
G
and
D
H
values for the corresponding
298
298
D
Z
Tl is
D
H
Tl and
D
G
Tl. The standard entropy of
and polymorphic transition of thallium and polymorphic transition
of TlI, respectively. The thermal effects at 755 and 708 K reflect
Tl
5
Te
2
I was calculated as:
o
0
0
0
four-phase monotectic equilibria M
T
and M
1
(Fig. 5, Table 2). In
S ðTl5Te2IÞ ¼ 2
D
Z
Tl þ 2S ðTlÞ þ S ðTlIÞ þ 2S ðTlTeÞ
ð6Þ

D.M. Babanly et al. / Journal of Alloys and Compounds 590 (2014) 68–74
73
Table 2
Non-variant equilibria on the T–x–y diagram of the system Tl–TlI–Te.
No.
Points in Fig. 5
Equilibria
Composition, at.%
Tl
T, K
Te
1
2
3
4
5
6
7
8
9
D
D
1
2
L M Tl
L M Tl
2
Te(
a
(d)
)
66.7
62.5
65.5
30.0
12.5
50.8
30.0
43.0
35.0
41.0
29.0
69.5(97.0)
51.0(98.0)
48.0(15.0)
54.5(63.5)
51.5(97.0)
51.0(53.0)
57.0(69.0; 94.0)
33.3
37.5
34.5
70.0
75.0
1.7
68.0
57.0
65.0
57.5
70.0
30.5(3.0)
–
4.0(70.0)
9.0(27.5)
1.5(1.0)
8.0(40.0)
5.0(27.0;3.0)
698
723
695
497
707
710
491
573
511
568
505
680
714
712
775
708
695
755
5
Te
3
e
e
e
e
1
L M
L M Tl
a
+ d
Te
2
2
3
+ Te
3
4
L M (TlI)II + Te
L M (TlI)II + d
L M (TlI)II + Tl
L + d M TlTe
L + TlTe M Tl
L + d M (TlI)II + TlTe
L + TlTe M (TlI)II + Tl
E
p
p
2
Te
3
+ Te
1
2
2
Te
3
10
11
12
13
14
15
16
17
18
U
U
1
2
2
Te
3
‘
‘
‘
m
m
m
1
2
3
(m
(m
1
2
3
)
)
)
L
3
L
2
L
2
L
2
L
2
L
2
L
2
M L
M L
M L
1
1
3
+ Tl
+ (TlI)II
+ (TlI)II
2
Te
(m
‘
S(S )
+ L
3
M Tl
5
Te
+ (TlI)II + d
+ (TlI)II + d
+ d
2
I(d)
‘
‘
M
M
M
1
(M
(M
1
)
)
M L
M L
1
2
2
‘
3
(M
n
,M
n
‘‘)
+ L
3
M L
1
n
I
Indexes and II in the formulas are low- and high-temperature modifications.
Table 3
Table 5
Monovariant equilibria on T–x–y diagram of the system Tl–TlI–Te.
Relative partial thermodynamic functions of thallium in the solid solution Tl
at 298 K.
5
Te3ꢀx
I
x
No.
Curves in Fig. 5
Equilibria
Temperature intervals
’
’
1
2
3
4
5
6
7
8
9
SM
SM
n
; S M
n
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
2
2
2
3
2
2
2
2
3
3
3
3
3
3
3
+ L
+ L
M L
M L
M L
M L
M (TlI)II + d
M (TlI)II + d
M (TlI)II + d
+ d M TlTe
3
M d
M d
775–755
775–695
755–708
755–680
714–708
712–695
710–708
710–695
695–568
573–568
568–505
511–505
505–491
497–491
707–491
ꢀ
ꢀ1
ꢀ
ꢀ1
ꢀ
Tl
DS (J K mol
ꢀ1
ꢀ1
Phase
ꢀ
D
G
Tl
(kJ mol
)
ꢀ
D
H
(kJ mol
)
ꢀ
)
Tl
’
’
2
; S M
2
3
’
’
‘
Tl Te I
43.02 ± 0.08
42.49 ± 0.09
42.19 ± 0.09
41.49 ± 0.09
40.62 ± 0.09
39.99 ± 0.09
44.80 ± 0.44
43.76 ± 0.50
43.05 ± 0.47
42.72 ± 0.58
42.52 ± 0.55
42.46 ± 0.46
ꢀ5.98 ± 1.21
ꢀ4.25 ± 1.38
ꢀ2.89 ± 1.29
ꢀ4.15 ± 1.63
ꢀ6.37 ± 1.52
ꢀ8.30 ± 1.28
M
M
m
m
n
M
’m
1
; M
; M
; m
; m
T
M
m
1
1
+ d
5
2
’’
’
5
Tl Te
I
I
I
+ d
+ (TlI)II
+ (TlI)II
2.2 0.8
n
1
n
1
1
1
3
’
M ’
Tl Te
Tl Te
5
M
M
1
2
1
5
2.4 0.6
2.6 0.4
2
’
’
3
2
3
M
2
Tl
Tl
5
Te2.8I
0.2
e
e
M
4
ꢄM
1
;
5
Te
3
4
ꢄM
2
’
2
U
1
10
11
12
13
14
15
1 1
p U
1
U U
2
M (TlI)II + TlTe
Table 6
Standard integral thermodynamic functions of the solid solution Tl
p
2
U
2
+ TlTe M Tl
M (TlI)II + Tl
M Tl Te + Te
M (TlI)II + Te
2
Te
3
5
Te3ꢀx
I
x
at 298 K.
2
U E
2
Te
3
e
e
2
E
2
3
Phase
0
2
ꢀ1
0
ꢀ1
0
298
ꢀ1
ꢀ1
ꢀ
D
G
(kJ mol
)
ꢀ
DH
(kJ mol
)
S
(J K mol
)
98
298
3
E
Tl
Tl
Tl
Tl
Tl
Tl
5
5
5
5
5
5
Te
2
I
300.4 ± 1.3
288.0 ± 1.5
274.1 ± 1.6
257.3 ± 1.6
236.9 ± 1.7
213.5 ± 1.7
301.1 ± 2.3
287.8 ± 2.4
271.6 ± 2.5
253.9 ± 2.5
235.5 ± 2.6
216.6 ± 2.4
475.8 ± 6.6
477.0 ± 7.0
483.1 ± 7.4
484.3 ± 7.8
475.9 ± 8.2
459.1 ± 8.1
Te2.2
Te2.4
Te2.6
Te2.8
I
I
I
I
0.8
0.6
0.4
0.2
Table 4
Temperature dependencies of the EMF for the chains of type (1) for various phase
areas in the Tl
5
Te
3
–Tl
5
Te
2
I system (T = 300–400 K).
Te
3
h
i
1=2
Phase area
S
2
2
E
2
b
E; mV ¼ a þ bT ꢃ t þ S ðT ꢀ TÞ
n
h
h
h
h
h
h
i
i
i
i
i
i
Tl
Tl
Tl
Tl
Tl
Tl
5
5
5
5
5
5
Te
2
I + TlI + TlTe
þ 3:9 ꢄ 10ꢀ5ðT ꢀ 361:5Þ2
þ 5:1 ꢄ 10ꢀ5ðT ꢀ 363:1Þ2
þ 4:5 ꢄ 10ꢀ5ðT ꢀ 363:6Þ2
þ 7:1 ꢄ 10ꢀ5ðT ꢀ 368:2Þ2
þ 6:2 ꢄ 10ꢀ5ðT ꢀ 364:1Þ2
þ 4:4 ꢄ 10ꢀ5ðT ꢀ 362:7Þ2
1=2
1=2
1=2
1=2
1=2
1=2
4. Conclusions
1
2
:5
4
4
4
4
4
4
64:3 ꢀ 0:062T ꢃ 2
53:5 ꢀ 0:044T ꢃ 2
46:2 ꢀ 0:030T ꢃ 2
42:8 ꢀ 0:043T ꢃ 2
40:7 ꢀ 0:066T ꢃ 2
40:1 ꢀ 0:086T ꢃ 2
6
Te2.2
Te2.4
Te2.6
Te2.8
I
0.8
I
0.6
I
0.4
I
0.2
2
2
:0
6
Application of various experimental methods, including DTA,
XRD, as well as measurement of microhardness and EMF enabled
us to construct a self-consistent phase diagram of the system
1
2
:7
6
2
2
:6
6
5 2
Tl–TlI–Te containing only one ternary compound Tl Te I, which
2
2
:3
6
forms solid solution (d-phase) with a wide homogeneity range.
Several polythermal and isothermal sections and the projection
of the liquidus surface were constructed. The fields of primary
crystallization as well as types and coordinates of non- and mono-
variant equilibria were determined. From the electromotive force
measurements, the partial molar functions of thallium as well as
Te
3
1
2
:3
3
standard integral thermodynamic functions of Tl
5 2
Te I and the solid
Besides our own
namic functions of formation of TlTe [33] and TlI [34] and the stan-
DZTl data, we used the standard thermody-
solution Tl Te –Tl Te I were calculated.
5
3
5
2
0
ꢀ1 ꢀ1
dard entropy of thallium (S2 ¼ 64:2 ꢃ 0:2 J mol
K ) [34] for the
98
calculations.
Acknowledgment
The integral thermodynamic functions of the solid solutions
Te –Tl Te I were calculated by integration of the Gibbs–Duhem
equation [31]. Results are given in Table 6. Standard deviations
were calculated by accumulation of the errors.
Tl
5
3
5
2
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.

7
4
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