Thermodynamic properties of selected compounds of the Ag–In–Se system determined by the electromotive force method

The equilibrium phase space of the Ag–In–Se system in the part AgInSe 2 –InSe–Se below 500 K consists seven three-phase regions In 2 Se 3 –AgIn 11 Se 17 –Se (I), AgIn 11 Se 17 –AgIn 5 Se 8 –Se (II), AgIn 5 Se 8 –AgInSe 2 –Se (IІІ), In 2 Se 3 – In 6 Se 7 –AgIn 11 Se 17 (ІV), In 6 Se 7 –AgIn 11 Se 17 –AgIn 5 Se 8 (V), InSe–In 6 Se 7 –AgIn 5 Se 8 , and InSe–AgIn 5 Se 8 – AgInSe 2 (VI). Division of the AgInSe –InSe–Se into separate phase regions was performed based on electromotive vs temperature dependences + The Ag + act as the small nucleation centers for stable phases. Based on the temperature dependences of the electromotive force of ECCs with PE of the (I)–(VI) phase regions, the standard thermodynamic functions of the binary In 6 Se 7 and three ternary compounds in the adjacent phase regions were calculated for the first time. The agreement of the calculated values of the standard Gibbs energies of the AgIn 5 Se 8 compound in two different phase regions (II) ∆ f 𝐺 (ІІ)○ = −(819.6 ± 8.9) kJ·mol −1 and ∆ 𝐺 (V)○ = −(820.0 ± 8.9) kJ·mol −1 characterizes the phase composition of the .


Introduction
The T-x diagram Ag2Se-In2Se3 of the Ag-In-Se system features the formation of AgInSe2, AgIn5Se8, and AgIn11Se17 compounds with congruent 1060 K, 1088 K, and incongruent 1077 K type of melting, respectively [1]. The AgInSe2 and AgIn5Se8 compounds crystallize from the melt as phases of variable composition, undergo polymorphic transformations at 968 K and 1013 K, respectively. The homogeneity ranges of these compounds are equal ~3 and ~4 mol.% In2Se3 at the room temperature. The isothermal cross-section of the Ag-In-Se system at 723 K is characterized by the Ag3In, Ag2Se, In4Se3, InSe, In6Se7, In2Se3, AgInSe2, and AgIn5Se8 compounds [2]. The existence of AgIn11Se17 compound has not been established. The ternary AgInSe2 and AgIn5Se8 compounds are evaluated as promising for use in nonlinear optics, manufacturing of visible and infrared LEDs, infrared detectors, solar cells, and other electrooptical devices [3,4]. Information on the main thermodynamic properties of the ternary phases AgInSe2 and AgIn5Se8, which are important for the analysis of uncontrolled changes in the operation of scientific and technological equipment, is currently lacking. Presented in [5,6] data on the standard Gibbs energy of the formation of AgInSe2 and AgIn5Se8 compounds Δ f ○ = −188 kJ·mol −1 and Δ f ○ = −850 kJ·mol −1 are approximate because they do not take into account the Gibbs energy of the synthesis reactions Δ r ○ from the calculated amounts of Ag2Se and In2Se3.
The purpose of this work was to establish the values of standard thermodynamic functions (Gibbs energy, enthalpy, and entropy) of the AgInSe 2 , AgIn 5 Se 8 , AgIn11Se17, and In6Se7 compounds by using the EMF method [7][8][9] and literature data on the thermodynamic properties of the InSe and In2Se3 compounds [10]. The results of calculations of thermodynamic functions of compounds can be used to analyze the reasons for changes in the performance of equipment manufactured with their participation and modeling the phase diagrams of multicomponent systems, including Ag-In-Se, by the CALPHAD methods [11,12].

I. Experimental
The high purity elements Ag, In, and Se (>99.99 wt.%, Alfa Aesar, Germany) were used for synthesis of the compounds. The evacuated melts of the calculated amounts of the elements were well-mixed for 20 min and followed by cooling to the room temperature at a rate of ~5 K·min −1 . Crushed to a particle size of ~5 μm polycrystalline samples were used for X-ray analysis and preparation of positive electrodes of electrochemical cells (ECCs). An 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 to establish the phase composition of the samples. The following programs STOE WinXPOW [13], PowderCell [14], FullProf [15], as well as databases [16,17] were used for X-ray phase analysis.
Synthesis of a thermodynamically equilibrium set of compounds below 500 K from a phase non-equilibrium mixture of compounds obtained by cooling the melts and the EMF (E) measurements were performed in ECCs type (A): where C is the graphite (inert electrode), Ag is the left (negative) electrode, SE is the solid-state electrolyte (Ag3GeS3Br glass), PE is the right (positive) electrode, R(Ag + ) is the buffer region of PE that contacts with SE. The process of forming of the thermodynamically stable set of phases from phase non-equilibrium mixture of finely dispersed compounds is carried out in the R(Ag + ) region. The Ag + ions act as the small nucleation centers for stable phases [18].
Components of the ECCs in powder form were pressed at 10 8 Pa through a 2 mm diameter hole arranged in fluoroplast matrix up to density ρ = (0.93 ± 0.02)•ρ0, where ρ0 is the experimentally determined density of cast samples [19,20]. The experiments were performed in a horizontal resistance furnace, similar to that described in [21]. As the protection atmosphere we used a flow of highly purified (99.99 volume fraction) Ar (g) at P = 1.210 5 Pa. The gas flow of Ar at the rate of 10 -5 m 3 min -1 from the right to the left electrodes of the ECCs. The temperature was maintained with an accuracy of ± 0.5 K. The EMF values of the cells were measured using high-resistance (input impedance of >10 12 Ω) the Picotest M3500A universal digital multimeter. The equilibrium in ECCs at each temperature was achieved within 2 h. During equilibrium the EMF values were constant or their variations were not exceed ±0.2 mV [22]. The dependences of the EMF of the cells on temperature E(T) were analyzed by the method described in [23][24][25]. The ratios of initials components of PE of ECCs were determined from the equations of potential-forming reactions in respective phase regions.
The cooled melts of the binary and ternary compounds mentioned in reactions (R1)-(R6) are thermodynamically non-equilibrium. In particular, according to results of Xray analysis, the cooled melt of the formula composition In2Se3 is characterized by two modifications of In2Se3 with closely related structures (space groups (SG) P63 for the In2Se3 phase, stable under normal conditions, and SG P61 for the high-temperature modification of In2Se3), and the InSe sample, apart from the InSe compound (SG R3m), contains impurities of the In 6 Se 7 phase (SG P2 1 /m), Fig. 2, a, b. The crystallized AgIn11Se17 melt contains a set of lines of the AgIn11Se17 compound with an uncertain structure and the AgIn5Se8 (SG P-42m), Fig. 2, c. The crystallized AgIn5Se8 contains impurities of the AgInSe2, Fig. 2 equations (R1)-(R6) are the combination of thermodynamically nonequilibrium phases, which cause the formation of the R(Ag + ) region in the ECC. The process of forming of the thermodynamically stable set of phases from phase non-equilibrium mixture of finely dispersed compounds for the participation of Ag + ions as a catalyst end in 48 hours at 500 K. The criterion for attaining phase equilibria in the R(Ag + ) region of PE is the reproducibility of the E(T) relations of ECCs during the heating-cooling cycles. The measured EMF values as a function temperature of ECCs are presented in Table 1.

* Data point not included in treatment
The linear dependencies E(T) between 430 K and 494 K provided that ∆ r = const and equal zero [23] were calculated by the least squares method and expressed as: The temperature dependences the EMF of ECCs is presented in Fig. 3. The correctness of presented in Fig. 1 division of the Ag-In-Se system in the AgInSe2-InSe-Se part below 500 K is confirmed by the following provisions: E vs T dependences of ECCs with PE of the (I)-(VI) phase regions are characterized by different EMF values at T=const and the intercept and slope coefficients; the phase regions that are more distant from the point of Ag are characterized by higher EMF values at T = const.
where is the number of electrons involved in the reactions (R1)-(R6), F = 96485.33289 С·mol -1 is Faraday's constant, and E is the EMF of ECCs.
The values of thermodynamic functions of the reactions (R1)-(R6) at 298 K and p=10 5 Pa were calculated using Eqs. (7)- (9). The determined results are listed in Table 2.
The Gibbs energy, enthalpy, and entropy of reaction (R1) are related to the Gibbs energy, enthalpy, and entropy of the AgInSe2 compound and pure elements of Ag and Se by Eqs. (10)-(12): Table 2 The values of standard thermodynamic functions of the reactions (R1)-(R6).
Combining Eqs. (13)-(15), using thermodynamic data of the pure elements Ag, In, Se and binary compounds InSe, In2Se3 [10], the standard thermodynamic data of selected compounds in the Ag-In-Se system were calculated for the first time. A comparative summary of the calculated values together with the available literature data is listed in Table 3.
The Considering data presented in Table 3, the temperature dependences of the Gibbs energy of formation of the AgIn11Se17, AgIn5Se8, AgInSe2, In6Se7, AgIn5Se8, and AgInSe2 compounds in the phase regions (І)-(VI) are described by Eqs.

Conclusions
The phase composition and triangulation of the equilibrium T-x space of the Ag-In-Se system in the part of AgInSe2-InSe-Se below 500 K have been established. The AgInSe2-InSe-Se concentration space contains seven three-phase regions formed by the InSe, In6Se7, In2Se3, AgInSe2, AgIn5Se8, and AgIn11Se17 compounds. Equations of the temperature dependences of the Gibbs energy as well as the values of standard thermodynamic functions of the In6Se7, AgInSe2, AgIn5Se8, and AgIn11Se17 compounds were established for the first time. The phase composition of the InSe-AgIn5Se8-In6Se7, In6Se7-AgIn11Se17-AgIn5Se8, In2Se3-AgIn11Se17-In6Se7, In2Se3-AgIn11Se17-Se, and AgIn11Se17-AgIn5Se8-Se regions is a combination of stochiometric compounds.