Thermodynamic Study of Tl6SBr4 Compound and Some Regularities in Thermodynamic Properties of Thallium Chalcohalides

The solid-phase diagram of the Tl-TlBr-S system was clarified and the fundamental thermodynamic properties of Tl6SBr4 compound were studied on the basis of electromotive force (EMF) measurements of concentration cells relative to a thallium electrode. The EMF results were used to calculate the relative partial thermodynamic functions of thallium in alloys and the standard integral thermodynamic functions (−ΔfG0, −ΔfH0, and S0298) of Tl6SBr4 compound. All data regarding thermodynamic properties of thallium chalcogen-halides are generalized and comparatively analyzed. Consequently, certain regularities between thermodynamic functions of thallium chalcogen-halides and their binary constituents as well as degree of ionization (DI) of chemical bonding were revealed.


Introduction
Chalcohalides of p-elements are of considerable interest as promising functional materials of modern electronic engineering.Multitude of them exhibit semiconductor, thermoelectric, photoelectric, topological insulator, radiation detector, and magnetic properties [1][2][3].Tl 6 S(Se)I 4 ternary compounds are known as effective X-ray and -ray detectors, outperforming the current state-of-the-art material for room temperature operation, CdZnTe (CZT) [4,5].Given the promising performance of thallium-based chalcogenides and chalcogen-halides, these compounds continue to attract attention despite toxicity of thallium derivatives.
Knowledge of phase equilibria and thermodynamic properties of phases is of key importance in designing techniques and optimizing conditions for the fabrication, crystal growth of multicomponent inorganic materials.
The investigation of phase equilibria in Tl-X-Hal (X-S, Se, Te; Hal-Cl, Br, I) systems was started from the beginning of the 80th years of the last century.A special attention was paid to quasibinary systems Tl 2 X-TlHal because of possibility of formation of ternary compounds [6][7][8][9][10][11]. Existence of 11 ternary compounds was established in the Tl 2 X-TlHal systems: 6 ternary compounds of type Tl 5 X 2 Hal (all selenium and tellurium systems) and 4 ternary compounds of type Tl 6 XHal 4 (all sulphurous systems and Tl-Se-I system).Tl 2 TeHal 6 compounds were detected in the systems Tl-Te-Hal [12,13].
Physicochemical investigation of Tl-X-Hal (X-S, Se, Te; Hal-Cl, Br, I) systems was implemented in detail at a wide or full concentration range.A number of polythermal and isothermal sections as well as projections of liquidus surfaces were constructed.The primary crystallization and homogeneity areas of phases were fixed and the fundamental thermodynamic functions of ternary compounds and solid solutions were determined [20][21][22][23].
In this contribution, we present the thermodynamic study of Tl 6 SBr 4 compound, summarize all data on thermodynamic properties of thallium chalcohalides, and carry out a comparative review between the latter.At the end of the paper, we present some regularities detected in the thermodynamic properties of thallium chalcohalides.

Synthesis and Analysis.
For planning experiments, we have used the solid-phase diagram of the Tl-TlBr-S system [24] which allowed us to determine the relevant compositions of samples for thermodynamic studies and to select conditions for their synthesis and thermal treatment (Figure 1).We have composed electrochemical cell of the type in which the left electrode was pure metallic thallium and the right electrodes were samples from the mentioned region.
A saturated glycerin solution of KBr with the addition of 0.1 mass% TlBr was used as an electrolyte.Initial compounds Tl 2 S and TlBr were synthesized to prepare the right electrodes of the electrochemical cell of the type (1).Tl 2 S was synthesized by alloying of stoichiometric amounts of high-purity elemental components (Tl, 99.999 mass%, Alfa Aesar; S, 99.999 mass%, Alfa Aesar) in an evacuated silica ampoules at temperatures 30-50 K above the melting point.Tl 2 S, melting congruently at 728 K [17], readily crystallizes while slowly cooling the sample.
TlBr was prepared by an indirect method reported in [18].At first, metallic thallium was dissolved in the dilute sulphuric acid (7-10 mol%) at 350 K to get the Tl 2 SO 4 solution.Then diluted HBr was added to a hot 2% Tl 2 SO 4 solution until complete precipitation of TlBr.Yellowish green TlBr was separated from the mother liquor and washed with icy distilled water.The product was dried over KOH in a desiccator at 380-400 K and stored in the dark to prevent its decomposition.
The synthesized compounds were identified by differential thermal analysis DTA (NETZSCH 404 F1 Pegasus system) and X-ray powder diffraction XRD (Bruker D8 ADVANCE diffractometer, CuK 1 radiation) methods.
Alloys of the subsystem TlBr-Tl 2 S-Tl 2 S 3 were prepared by blending and interacting TlBr and Tl 2 S compounds and elemental sulphur in various ratios in evacuated quartz vessels.They were subjected to a long-term stepped homogenizing annealing under the conditions described in [24].The total mass of samples was 1 g and, after determining the solidus temperature, samples were additionally held at 20-30 K below the solidus for 500 h.

EMF Measurements.
To measure the EMF of the chains type (1), electrodes, electrolyte, and electrochemical cell were prepared.The left electrode was made by attaching metallic thallium to a molybdenum current collector.Taking into account oxidization of thallium even at room temperature, before assembling electrochemical cell, the left electrodes were kept in glycerin, since metallic thallium does not directly interact with it [19].
The right electrodes (see (1)) were prepared by pressing powdered equilibrium alloys of the system under study into current collectors in the form of cylindrical tablets with a weight of ∼0.5 g and placed in a tubular furnace; the temperature was stabilized at 350 K for 40-50 h.The wires were sealed in glass jackets to protect them from contact Table 1: Temperature dependences of EMF of the concentration chains type (1) in some phase regions of the subsystem TlBr-Tl 2 S-Tl 2 S 3 .

Number
Phase region in Figure 1 , mV =  +  ±  ⋅   () with the electrolyte.EMF was measured by the compensation method in the temperature range of 300-390 K with the accuracy of ±0.1 mV, using the high-resistance universal B7-34A digital voltmeter.In each experiment the first EMF reading was performed approximately 30 h after the start of the experiment and at least 2-3 h after reaching the desired temperature, which ensures the achievement of equilibrium.The EMF measurements were carried out 2-7 days or more in consideration of homogenization of the electrode alloys, after the cell had been assembled.Equilibrium values were considered the EMF readings that varied by no more than 0.5 mV irrespective of the direction of temperature change at repeated measurements at a given temperature.In order to eliminate the contribution of the thermopower, all contacts and leads were kept at the same temperature.Techniques of assembling the electrochemical cell and EMF measurements are described in detail in [25,26].

Thermodynamic Study of the Ternary Compound Tl 6 SBr 4 .
The solid-phase equilibrium diagram of the Tl-TlBr-S subsystem that had been constructed in [24] is given in Figure 1.As can be seen from Figure 1, there are 4 three-phase regions in the TlBr-Tl 2 S-Tl 2 S 3 subsystem: TlBr-TlS-Tl 2 S 3 (I), TlBr-TlS-Tl 6 SBr 4 (II), Tl 6 SBr 4 -Tl 4 S 3 -TlS (III), and Tl 2 S-Tl 6 SBr 4 -Tl 4 S 3 (IV).The EMF values measured in heterogeneous phase regions I-IV were processed by the least squares method [25,26] and presented as the following linear equations: where  2.
Our results of measuring the EMF of the cells type (1) in the TlBr-Tl 2 S-Tl 2 S 3 composition region were fully consistent with the solid-phase equilibrium diagram of the Tl-TlBr-S subsystem [24] (Figure 1).The EMF values at the given temperature, within I-IV three-phase regions, virtually coincide independently of the gross compositions of the right electrodes and vary discontinuously in transition from one of the regions to another.The EMF values at 300 K temperature for the phase areas showing in Table 1 are given in Figure 1.
It should also be noted that numerical values of EMF and equations of their temperature dependence in the phase regions I, III, and IV (Table 1) practically coincide with corresponding data [27] for the binary compounds TlS, Tl 4 S 3 , and Tl 2 S, respectively.This testifies reversibility of the electrochemical cells type ( 1) and therefore indirectly points to the absence of appreciable regions of solid solutions based on the aforementioned sulfides in the TlBr-Tl 2 S-Tl 2 S 3 subsystem.
The EMF values measured in the phase region II (Table 1) can be assigned to the compound Tl 6 SBr 4 and can be used in thermodynamic calculations.The calculation of the relative partial molar functions of thallium from the equation of the temperature dependence of the EMF in this phase region gave the quantities which are thermodynamic functions of the potential-forming reaction Tl + 4TlBr + TlS = Tl 6 SBr 4 according to Figure 1.

Comparative Review of Thermodynamic Properties of Thallium Chalcohalides.
Using obtained values of the standard integral thermodynamic functions of formation and standard entropies of thallium chalcohalides, other fundamental characteristics, standard thermodynamic functions of atomization of these compounds, were calculated.As is known, the atomization thermodynamic functions are quantities that characterize the change of relevant thermodynamic functions during decomposition of a compound to monatomic gas mixture.The atomization energy of ternary compounds was calculated using Δ at  (comp) = ∑ Δ at  (elem.)− Δ   (comp) , (7) where Δ   (comp) is the enthalpy of formation of a compound and ∑ Δ at  (elem.) is the sum of atomization  enthalpies of elements in a compound.The atomization entropy of ternary compounds was calculated on the following equation: Here  0 (comp) is the absolute standard entropy and ∑  0 (at.gas.) is the sum of the absolute entropies of elemental constituents of the considered compound in a monoatomic gas state.The Gibbs free energy of atomization of ternary compounds were calculated from Gibbs-Helmholtz equation using the data obtained from ( 7) and ( 8): Results are given in Table 4.The standard thermodynamic functions of atomization, formation, and formation from appropriate binary compounds (Tl 2 X and TlHal) of thallium chalcogen-halides are summarized in Table 5, for comparative analysis.
As can be seen from Table 5, the relationship between the standard thermodynamic functions of atomization, formation, and formation from appropriate binary compounds (Tl 2 X and TlHal) for all ternary compounds is as follows: where  is Gibbs free energy () or enthalpy ().
The atomization Gibbs free energies and enthalpies of all ternary compounds are very large positive quantities.The standard thermodynamic functions of formation of ternary compounds are 3-5 times smaller by absolute value than the proper atomization functions.This is associated with the fact that Δ at  0 is the minimal energy required to split up the crystal lattice into separate atoms.However, Δ at  0 is the driving force of the reverse process, combination of monatomic gases to form a crystal lattice.
The standard thermodynamic functions of formation of ternary compounds are much smaller than the Gibbs free energies and enthalpies of formation from binary constituents.The reason of such a sharp distinction can be explained by the fact that formation of a ternary compound from its binary constituents is not accompanied by a considerable energetic change in the system.Moreover, during Advances in Materials Science and Engineering the latter process the oxidation state numbers of elements, consequently the type of chemical bonding do not alter significantly.However, during formation of ternary compound from elemental components, quantities change significantly and therefore total energy of the system decreases sharply.
The high numerical values of the atomization entropy of all ternary chalcogen-halides can be explained by the dramatically increase in disorder during the decomposition of their crystal lattice (Table 5).

Some Regularities in Thermodynamic
Properties of Thallium Chalcogen-Halides.The comparative analysis of different thermodynamic functions of thallium chalcohalides with degree of ionization of the chemical bonding in those compounds as well as with the proper thermodynamic functions of binary compounds have shown the availability of some regularities.
The conformity between the standard Gibbs free energies and enthalpies of formation of ternary (Tl 6 XHal 4 and Tl 5 X 2 Hal) compounds and the sum of the proper functions of binary (TlHal and Tl 2 X) compounds is demonstrated in Figure 2. As shown in Figure 2, the absolute values of Δ   0 and Δ   0 functions of all ternary compounds are higher (∼3-7%) than the sum of the proper functions of binary compounds.
The correlations between Δ   0 298 and Δ   0 298 functions of ternary and binary TlHal compounds are represented in Figure 3.As can be seen, these dependencies are linear for all compounds of the type Tl 6 XHal 4 ; however the linear dependencies for Tl 5 Se 2 Hal and Tl 5 Te 2 Hal compounds with the same halogen atoms differ from each other.This is due to the fact that, TlHal compounds play a decisive role in the thermodynamic functions of the ternary compounds Tl 6 XHal 4 .Reversely, the main contribution in the thermodynamic functions of Tl 5 X 2 Hal compounds belongs to thallium chalcogenides Tl 2 X (X-Se, Te).Since the thermodynamic functions of formation of Tl 2 Se and Tl 2 Te compounds are considerably distinctive from each other, the values of relevant functions for Tl 5 Se 2 Hal and Tl 5 Te 2 Hal ternary compounds also differ by magnitude (Figure 3).
The dependence graphs of the standard thermodynamic functions (Gibbs free energy and enthalpy) of formation and atomization of the ternary compounds Tl 6 XHal 4 and Tl 5 X 2 Hal upon the ionization degree (ID) of chemical bonding are demonstrated in Figure 4.
The ID of a chemical bond in thallium chalcohalides was calculated by classical method [29].For this aim, the chemical bond in CsF compound with the highest value of ID was considered pure ionic type and the difference of the relative electronegativities of elements (Δ REN ) in this compound was found to be Δ REN = 3,2.Taking into account the equalities Δ REN = 0 and ID = 0% for nonpolar covalent bonds, the following equation was obtained.
Both thermodynamic properties of ternary compounds have a positive linear tendency with ID of bonding.Since the lattice energy of substance rises with an increase in the ID of chemical bond, the extension of the above-mentioned thermodynamic functions is natural (Figure 4).
It can be explained by the fact that the entropy of atomization is an indicator of the rise of irregularity during decomposition of crystal lattice into monatomic gas mixture.The same numerical value of atomization entropies of all  considered ternary compounds is the result of the transformation of the system from regular crystallic state with the lowest value of entropy into the irregular atomic gas mixture during the atomization process.The difference between the entropy of a substance (with the same formula) in a crystal state and the entropy of a monoatomic gas mixture is nearly two orders smaller than the value of the atomization entropy and therefore does not affect the magnitude of the latter.

Conclusion
By using electromotive force (EMF) measurements a regulated complex of thermodynamic properties for the Tl 6 SBr 4 compound was obtained.The data regarding the thermodynamic properties of thallium chalcogen-halides were systematized and comparatively analyzed.Some correlations between thermodynamic functions of thallium chalcogenhalides and their binary constituents as well as ionization degree of chemical bonding were revealed.

2 Advances 3 Figure 1 :
Figure1: Solid-phase equilibrium diagram of the system Tl-TlBr-S at 300 K[24].The compositions of the studied samples are given by hollow circles in the proper three-phase regions.

−Figure 2 :
Figure 2: The correlation between Δ   0 and Δ   0 functions of thallium chalcohalides and the sum of the proper functions of binary compounds.

Figure 3 :
Figure 3: The correlation between Δ   0 and Δ   0 functions of ternary and binary TlHal compounds.

Figure 4 :
Figure 4: The dependence of the standard thermodynamic Gibbs free energy and enthalpies of formation (a, b) and atomization (c) of the ternary compounds on the degree of ionization (ID) of chemical bonding.

Tl 5 Figure 5 :
Figure 5: The correlation between the atomization entropy of ternary compounds and the ionization degree (ID) of chemical bonding.
is the number of pairs of  and  values;   and   are the error variances of the EMF readings and  coefficient, respectively;  is the average of the absolute temperature;  is Student's test.At the confidence level of 95% and  ≥ 20, [25,26]'s test is  ≤ 2[25,26].The composed equation of the mode (2) is presented in Table 1.The experimental data of   and   and steps of calculation for the phase region II (Table 1), which is of special interest in terms of calculation of thermodynamic functions of the Tl 6 SBr 4 compound, are presented in Table 2.The values of , , ,  2  , and  2  quantities in (2) were calculated based on Table

Table 4 :
Standard thermodynamic functions of atomization of thallium chalcogen-halides.

Table 5 :
Comparison of thermodynamic functions of atomization, formation from elemental components, and formation from binary compounds of thallium chalcogen-halides.

Table 6 :
Δ REN and ID values for thallium chalcohalides.