Experimental investigation and thermodynamic assessment of phase equilibria in the GaTe–AgGa5Te8–Te system below 600 K

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Introduction
Phase equilibria in the Ag-Ga-Te system have been investigated by several authors [1][2][3][4][5][6], using different experimental methods.In particular, Guittard et al. [1] divided the phase space of the Ag-Ga-Te system in the temperature range of 273-1000 K into 9 regions with the participation of binary and ternary compounds.In the binary systems Ag-Te, Ag-Ga, and Ga-Te, the temperature ranges for existence of the compounds Ag2Te, Ag1.9Te, Ag5Te3; phases of variable composition , ; compounds GaTe, Ga2Te3, Ga2Te5, have been established.Devision of the concentration space of the Ag-Ga-Te system was carried out with the participation of the mentioned binary compounds, phases of mixed composition, and ternary compounds of the quasi-binary system Ag2Te-Ga2Te3: Ag9GaTe6, AgGaTe2, and a phase AgxGa(4-x)/3(2-2x)/3Te2 which is a solid solution for 0.63 < x < 0.75 [3].
In Ref. [2] Deiseroth et al. synthesized the Ga7Te10 compound at 1020 K and determined its crystal structure.According to Ref. [4], there are four intermediate compounds in the Ga-Te system.The GaTe and Ga2Te3 compounds melt congruently at 1108 K and 1071 K, respectively; Ga3Te4 decomposes at 1057 K by the peritectic reaction on liquid L and compound Ga 2 Te 3 ; high-temperature modification of the Ga2Te5 forms by a eutectoid reaction at 681 K and decomposes by peritectic scheme at 757 K.The Ag2Te-Ga2Te3 cross-section of the Ag-Ga-Te system is characterized by three intermediate compounds: Ag9GaTe6, AgGaTe2, and AgGa5Te8 [3,5,6].According to Ref. [5], the orthorhombic compound AgGa5Te8 was obtained by cooling the melt of the calculated amounts of Ag2Te, Ga2Te3, and Te to 873 K, followed by annealing for 1 week.The minimum temperature of the of existence of this compound in the equilibrium T-x space of the Ag-Ga-Te system is unknown.Based on the a dimensionless figure of merit parameter ZT=(S 2 )T/k (where S is the Seebeck coefficient,  is the electrical conductivity, k is the thermal conductivity, and T is the absolute temperature), ternary compounds of the Ag-Ga-Te system belong to class of the thermoelectric materials [3,[5][6][7][8].
The effect of replacing part of the gallium cations of the compound p-Ag9GaTe6 according to the scheme Ag9Ga1-MTe6 (M = Cd, Zn, Mg, Nb;  = 0.05) on the ZT values is given in Ref. [6].In the case of Cd doping, the thermoelectric figure of merit parameter was achieved ZT  0.6 at 600 K.Such method of increasing the ZT value is ineffective in the case of a thermodynamically unbalanced state of the doping component in the crystal lattice of the compound.The action of such external factors as changes in temperature, pressure, radiation, etc. will contribute to the migration of impurities at the grain boundary, which will lead to a decrease in the ZT value of the sample over time.It is possible to avoid a decrease in the ZT value during the operation of a doped thermocouple by producing it in the form of an equilibrium solid solution based on a quaternary compound.As an example, for doping of the Ag9GaTe6, AgGaTe2, and AgGa5Te8, it is possible to use quaternary compounds of the Ag2Te-Ga2Te3-AgBr region.This region is part of the Ag-Ga-Te-AgBr system, where the formation of quaternary compounds Ag3Ga10Te16Br, Ag3Ga2Te4Br, and Ag27Ga2Te12Br9 is possible at the intersection points of the cross-sections AgGa 5 Te 8 -AgBr, AgGaTe 2 -AgBr, Ag 9 GaTe 6 -AgBr with the tie-line Ga 2 Te 3 -Ag 3 TeBr.There are no any previous reports on quaternary compounds of mentioned composition.The thermodynamic conditions for the formation of quaternary phases likely correspond to the temperature values T < 600 K, where there are kinetic obstacles to such a process.Kinetic obstacles to the synthesis of phases from pure substances and binary compounds can be overcome with the participation of a catalyst -Ag + ions, as small centers of nucleation of equilibrium phases [9,10].In order to establish the conditions for the existence of quaternary compounds in the Ag2Te-Ga2Te3-AgBr system, information on compounds in the GaTe-Te part of the Ga-Te system at T < 600 K is required.
The purpose of this work was to establish the phase equilibria of the GaTe-AgGa5Te8-Te system at T < 600 K and to determine the standard thermodynamic properties of compounds by the electromotive force (EMF) method.

I. Experimental
The high-purity substances Ag (>99.9 wt.%) and Ga, Te (>99.99 wt.%) were used to synthesize the binary and ternary compounds.Evacuated melts of the Ag2Te, GaTe, and Ga 2 Te 3 compounds, cooled to room temperature, were crushed to a particle size of ~110 -6 m for preparation of the positive electrodes (PE) of electrochemical cells (ECs).Melts of the Ga7Te10, AgGaTe2, and AgGa5Te8 compounds cooled to a temperature of 630 K were annealed for 2 weeks, followed by cooling to room temperature with the furnace turned off.The phase composition of the synthesized compounds was analyzed by an X-ray diffraction (XRD) technique.The STOE STADI P diffractometer equipped with a linear position-sensitive detector PSD, in a Guinier geometry (transmission mode, CuK1 radiation, a bent Ge(111) monochromator, and 2 scan mode) was used for these investigations.The following software programs STOE WinXPOW [11], PowderCell [12], FullProf [13], and databases [14,15] were applied to analyze the obtained results.
The modified EMF method [16] was used both to establish the phase equilibria in the GaTe-AgGa5Te8-Te region below 600 K and to determine the thermodynamic parameters of compounds.For these measurements, a certain number of ECs were assembled: where IE is the inert electrode (graphite powder), NE is the negative electrode (silver powder), SSE is the solidstate electrolyte (glassy Ag3GeS3Br), R{Ag + } is the region of PE that contacts with SSE.At the stage of cell preparation, PE is the nonequilibrium phase mixture of the well-mixed powdered binary compounds Ag2Te, GaTe, Ga2Te3, and pure substance tellurium.Compositions of these mixtures covered the entire concentration space of the GaTe-AgGa5Te8-Te system.An equilibrium set of phases was formed in the R{Ag + } region at 600 K for 48 h.The Ag + ions, displaced for thermodynamic reasons from the NE to the PE electrodes of the ECs, acted as catalysts, i.e., small nucleation centers of equilibrium phases [9,10].
The experiments were performed in a resistance furnace described in Ref. [17].A fluoroplastic base with a hole with a diameter of 2 mm was used to assemble the ECs.The powder components of ECs were pressed at pressure 10 8 Pa into the hole under a load of (2.0±0.1)tons to a density of ρ = (0.93±0.02)ρ0,where ρ0 is the experimentally determined density of cast samples.The assembled cells were placed in a quartz tube with nozzles for the purging of argon gas.The argon gas had a direction from the NE to PE of ECs at the rate of (10.0±0.2) cm 3 min -1 .The temperature of ECs was maintained by an electronic thermostat with ±0.5 K accuracy.The EMF (E) values of the cells (accuracy ±0.3 mV) were determined by a Picotest M3500A digital voltmeter with an input impedance of >10 12 Ohms.The reproducibility of the EMF versus temperature dependences (E(T)) of ECs in heating-cooling cycles was a criterion for completing the formation of the equilibrium set of phases in the R{Ag + } region.

II. Results and discussion
The AgGa5Te8 compound was not obtained by cooling the melt to 630 K followed by annealing for 2 weeks.The diffraction pattern of powder sample is shown in Fig. 1.
The presence of the AgxGa0.67Tephase (structure type (ST) ZnS, space group (SG) F-43m) and minor impurities of non-identified phase have been established by the XRD method.
The refined unit-cell parameter a = 0.59786 (5) nm is greater than a ~ 0.587÷0.590nm for Ga0.67Te, thus indicated the formation of solid solution.Such a metastable, for kinetic reasons, combination of the mentioned phases was confirmed by an attempt to implement the reaction AgGaTe2+2Ga2Te3=AgGa5Te8.For this reason, a well-mixed mixture of the AgGaTe2 and 2Ga2Te3 compounds was evacuated, kept for 2 weeks at 630 K and cooled to room temperature.According to the XRD results, the orthorhombic AgGa5Te8 compound also was not obtained, Fig. 2. The sample contained characteristic peaks of the phases AgxGa0.67Te(ST ZnS, SG F-43m), AgGaTe2 (ST CuFeS2, SG I-42d), and the pure Te (ST Se, SG P3121).
Thus, results of the XRD shown that the orthorhombic AgGa5Te8 compound decomposes at a certain value of the temperature in the range of 630-873 K.The existence of the AgGa5Te8 compounds in two temperature ranges was also established by the results of triangulation of the concentration space of the GaTe-AgGa5Te8-Te system by the EMF method and calculation of the thermodynamic properties of compounds.Other examples of the existence of silver-based ternary and quaternary compounds in two temperature ranges are presented in Ref. [18][19][20][21].
The division of the concentration space of the Ag- Ga-Te system in the GaTe-AgGa5Te8-Te part below 600 K into separate three-phase regions is shown in Fig. 3.
The following basic rules of the EMF method [22][23][24][25] were used for this triangulation: 1) within a specific phase region, the EMF value of the cell does not depend on the phase composition of the PE; 2) ECs with PE of different phase regions are characterized by different EMF values at T = const, Table . 1; 3) the three-phase region further away from the figurative point of Ag is characterized by a higher EMF value at a specific temperature.The spatial position of three-phase regions Ga2Te5-AgGa5Te8-Te (I), Ga2Te3-AgGa5Te8-Ga2Te5 (II), Ga7Te10-AgGa5Te8-Ga2Te3 (III), and Ga3Te4-AgGa5Te8-Ga7Te10 (IV) relative to the silver point was used to establish the overall potential-determining reactions: 2Ag + 5Ga2Te5 = 2AgGa5Te8 + 9Te, (R1) 4Ag + 9Ga2Te3 + Ga2Te5 = 4AgGa5Te8, (R2) Reactions (R1)-(R4) were carried out in the PE of ECs, the phase mixtures correspond to phase regions (I)-(IV), respectively.According to reactions (R1)-(R4), the ratios of binary compounds and pure tellurium for the assemble the PE of ECs were established.In particular, the compounds AgGa5Te8, Ga2Te5, Ga7Te10, and Ga3Te4 are present in the PE compositions in the following ratios of mixtures of the binary compounds and the simple substance Te: 0.5Ag2Te + 2.5Ga2Te3, Ga2Te3 + 2Te, GaTe + 3Ga2Te3, and GaTe + Ga2Te3, respectively.Processing of the E versus T experimental dependences was performed by the least squares method [26,27] and presented in the form of Eq. ( 1): where  and  are coefficients of linear equation,   is the Student's parameter [28],  is the number of experimental pairs   and   ,   2 and   2 are the statistical dispersions of the E and  quantities, respectively.Listed in the Table 1 the experimental values of E and T were used to calculate the coefficients and statistical dispersions of Eq. ( 1) in the phase regions (I)-(IV).The results of calculations are listed in the Table 2.
The Gibbs energies (Δ r ), enthalpies (Δ r ), and entropies (Δ r ) of the reactions (R1)-(R4) were calculated by the following thermodynamic equations: where  is the number of electrons involved in the reactions (R1)-(R4), F is the Faraday's constant, and E is the EMF of the ECs.The values of the thermodynamic functions of reactions (R1)-(R4) in the standard state (Т = 298 K and P = 10 5 Pa) were calculated according to Eqs. ( 2)-( 4) and are listed in the Table 3.
The Gibbs energies of reactions (R1) and (R2) are related to the Gibbs energies of compounds by Eqs. ( 5) and ( 6): By solving the system of equations ( 5) and ( 6) we obtained: Equations for determining the enthalpy of formation and entropy of the Ga2Te5 compound were obtained in a similar way: The corresponding reactions to determine the standard thermodynamic properties ∆ f  ○ , ∆ f  ○ , and  ○ of the AgGa5Te8, Ga7Te10, and Ga3Te4 compounds were written in a similar way using reactions (R2)-(R4) with the corresponding stoichiometric numbers.
For the first time, the standard thermodynamic quantities for compounds of the GaTe-AgGa5Te8-Te system were determined using Eqs.( 7)-( 9) and thermodynamic data of pure substances (Ag, Ga, Te) and the binary compound Ga2Te3 [29].The results of calculations are listed in the Table.4.

Fig. 1 .Fig. 2 .
Fig. 1.X-ray powder diffraction pattern of the sample with nominal composition AgGa5Te8, obtained by cooling the melt to 630 K. Compositions of the sample and identified phase (with structure type and space group indicated) are shown in the upper right corner.

Fig. 3 ..
Fig. 3. Division of the concentration space of the GaTe-AgGa5Te8-Te system at T<600 K. Red dots indicate compositions of the PE of ECs and EMF (mV) values of the ECs at 400.4 K. T a b l e .

Table 2 .
The coefficients and statistical dispersions of E versus T dependencies of the ECs.

Table 4 .
The values of standard (T=298 K and P=10 5 Pa) thermodynamic properties of compounds of the GaTe-AgGa5Te8-Te system.Uncertainties for Δ f  ○ , Δ f  ○ , and  ○ are standard uncertainties.