358 CHEMICAL PROBLEMS 2019 no. 3 (17) ISSN 2221-8688 UDC 546:544.35:538.95 CALCULATION OF STANDARD THERMODYNAMIC FUNCTIONS OF ARGYRODIT Ag8GeSe6

F.S. Ibrahimova Institute of Catalysis and ANAS, H.Javid Ave.,113, AZ 1134, Baku, Azerbaijan, e-mail: [email protected]

Received 12.06.2019

Abstract : Based on literature data, with the additional calculations are selected most reliable data for the thermodynamic parameters of crystal silver selenide, and silver selenogermanate: 0 0 0 0 ∆H298 (α-Ag2Se)= −43.5, ∆H298 (GeSe,cr)=−82.9, ∆H298 (GeSe2,cr)=−103.7, ∆H298 (α- 0 0 0 Ag8GeSe6,cr)=−290.4, ∆G298 (α-Ag2Se)=−50.3, ∆G298 (GeSe, cr)=−84.2, ∆G298 (GeSe2,cr)= −103.1, 0 −1 0 0 0 ∆G298 (α-Ag8GeSe6,cr)=−306.3 kJ·mol , S298 (α-Ag2Se)=150.3, S298 (GeSe,cr)=78.3, S298 (GeSe2, cr)=112.6, 0 (α-Ag GeSe , cr)=711.6 J·mol−1.К-1, =377.1 J·mol−1.К-1. It was revealed that the S298 8 6 C p,298

compound Ag2GeSe3 is formed in the amorphous state, unstable and decomposed into the Ag8GeSe6 and GeSe2 compounds. The applicability of the Debye method based on quantum concepts of atomic oscillations in the crystal lattice of a solid in the Magnus-Lindemann and Eastmen-Tsagareishvili approximations for calculating the heat capacity and entropy of a ternary compound with a common chalcogenide anion is revealed. Keywords: Ag8GeSe6, thermodynamic functions, Debye method. DOI: 10.32737/2221-8688-2019-3-358-365 Introduction

Ag8GeSe6 refers to Argurodites with a confirmed. Proceeding from phase diagrams of general of A8BX6 (A = Cu, boundary binary systems and the results of the Ag; B = Si, Ge, Sn; and X = S, Se, and Te). differential thermal analysis of a number of Some of these compounds, including samples of the ternary system, equations were Ag8GeSe6, have ionic conduction and can be obtained for calculation and 3D modeling of used as electrochemical sensors, electrodes the liquidus Ag8GeSe6 [6]. and electrolyte materials in solid-state batteries The thermodynamic parameters of the and displays, etc [1-5]. In view of the Ag8GeSe6 compound are necessary for the contradictoriness of the literature data, in [6] development of technology of obtaining the phase equilibria in the Ag–Ge–Se system were stoichiometric phase from simple substances restudied by differential thermal analysis and and from binary compounds. Enthalpy, Gibbs X-ray powder diffraction analysis. A number free energy of the formation and entropy of the of polythermal sections and an isothermal two Ag8GeSe6 modifications as set forth in [7, section at room temperature of the phase 8] were carried out within the ternary system diagram were constructed, and so was the study Ag-Ge-Se through measuring the projection of the liquids’ surface. The primary electromotive forces by means of silver solid crystallization fields of phases and types and electrolyte. The results of these studies differ coordinates of in- and monovariant in that the thermodynamic stability of the equilibriums were determined. It showed that a ternary compound Ag2GeSe3 synthesized in single ternary compound, Ag8GeSe6 was [8] was not confirmed in [7]. The isobaric heat formed in the system to have undergone capacity of Ag8GeSe6, estimated [2] by the congruent melting at 1175 K and polymorphic Debye method in line with Einstein modules, transformation at 321 K. The formation of the is not clearly approximated. Ag2GeSe3 and Ag8GeSe5,compounds Allowing for reasoning stated above, previously reported in the literature was not the objective of our work is to analyze

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F.S. IBRAGIMOVA 359 thermodynamic data for Ag8GeSe6 argyrodite calculations based on the Debye method. together with additional thermodynamic

Theoretical Part There are various methods for calculating Heat capacity. To calculate the heat capacity, the thermodynamic parameters of inorganic the Debye method is used in keeping with compounds which have been tested quantum concepts of atomic vibrations in the successfully in calculating heat capacity, crystal lattice of a solid. The equation for entropy, enthalpy and Gibbs free energy of the calculating the isochoric heat capacity Cv for a formation of binary and ternary chalcogenides three-atom compound is as follows [7]: [9-13]. Cv=9R⋅D(θD/T (1) Where 3 θD /T 3 T x dx3/θD T DT(θD / )= 12 − (2) ∫ x (/θD T θD 0 ee−−11 and θD is the Debye temperature defined as up according to the Neumann – Kopp rule, the θD=hν/k (3) isochoric heat capacity of the compound is In eqn. (2,3) h is the Planck’s constant, k is the determined. For compounds Ag8GeSe6: Boltzmann constant and ν is the vibrational Cv(Ag8GeSe6)=8Cv(Ag)+ Cv(Ag)+ 6Cv(Se) (5) frequency and the x-parameter is determined The values of the Debye temperature on the basis of the solid state theory. for silver, germanium, and selenium, together The calculation of the isochoric heat with their melting points and isochoric heat capacity is carried out in the sequence as capacities, are given in Table. 1. Recalculation follows. The initial data provide (Debye) of isochoric heat capacity to isobaric heat was temperatures of the elements forming the carried out according to the Magnus – compound, as well as the melting points of the Lindemann equation [11]: elements and compounds below: m 3/2 Сp=Cv+ 6,076 (nТ/Т ) (6) * m* m 1/2 θ D =θD(Т /Т ) (4) Here n is the number of atoms in the m * compound. T is the melting point of Here θ , θD are characteristic D Ag8GeSe6. In the equation (3): n=15, temperatures of the element in the compound Тm=1175 K [6], T=298K. m* m and the simple substance; Т , Т – melting The temperature dependence of the point of the compound and simple substance. isobaric heat capacity can be determined by * Based on θ D /Т function, the values of the equation: -2 the isochoric heat capacity (Cv) for each Сp=a+bТ-cТ (7) component are found, further summing them

5 5 m -2 m c=4,19⋅10 n; b=[25,64n+4,19⋅10 n(Т ) -Cp,298]/( Т -298); a=Cp,298 -298б+4,7n (8)

Table 1. Melting points (Тm), Debye temperature element in the compound and in a simple * substance (θ D , θD), isochoric heat capacities and standard entropies of silver, germanium, and selenium. С 0 v S 298 m * * element Т ,K θ θ θ -1 -1 D D D /298 J⋅ mol ⋅К

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360 CALCULATION OF STANDARD THERMODYNAMIC

Ag 1234 221 215.6 0.723 21.31 42.5 Ge 1210 403 397.1 1.332 22.87 31.1 Se 494 90 139.2 0.467 24.67 42.1

As a result of calculations of molar isochoric Entropy. Tsagareishvili [12] extended and isobaric heat capacity of Ag8GeSe6, the the range of applicability of the Eastman following values were obtained: equation [11] based on the Debye method to Cv(Ag8GeSe6) = 365.6 and Cp(Ag8GeSe6) = obtain the following equation for calculation 377.0 J.mol-1.K-1. of standard entropy of inorganic compounds: 4 / 3  200(M / n) 5 / 3  0 = S 298 0.75nRln 2 / 3 m  (9)   ρ T  n = 15- number of atoms in a molecule, R = compounds from simple substances we have: 8.31 J.mol-1.K-1, M = 1410 – molar mass, Тm 0 -1 -1 ∆ S 298 (Ag8GeSe6)=85.77 J.mol .K . =1175K [6] – melting temperature, ρ= 6.21 g. -3 Enthalpy of compound formation. sm [14] - density Ag8GeSe6. The value for Ag8GeSe6 was determined by As a result of the calculation, the calculation based on the data of binary following value was obtained for the standard compounds Ag2Se and GeSe2 (Table 2) in line 0 -1 -1 entropy S 298 (Ag8GeSe6)=711.6 J.mol .K . with a method described in [15,16] with due For the entropy of the formation of 0 regard for deviation from additivity ( / ∆H 298 ): 0 0 0 0 ∆H 298 (Ag8GeSe6,кр) = 4 ∆H 298 (Ag2Se,кр) + ∆H 298 (GeSe2,кр) + / ∆H 298 (10) The third term in (10) depends on the number The free energy of the formation of the of anion and the binding energy of metal – Ag8GeSe6 compound is calculated using the 0 Gibbs-Helmholtz equation: selenium (Me–Se). In (10): / ∆H 298 = –6 Е(Me–Se), where Е(Me–Se)= –2 kC 0 0 0 ∆GT ( Ag8GeSe6)= ∆H 298 ( Ag8GeSe6)+T∆S 298 ( Ag8GeSe6) (11) as is the case with the formation of (Eq. 10) compounds by the equation: enthalpy based on the data of binary 0 0 0 0 ∆G298 (Ag8GeSe6,cr) = 4 ∆G298 (Ag2Se,cr) + ∆G298 (GeSe2,cr) + / ∆G298 (12) In this work, they also calculated the free Equation (12) with respect to the compound energy of the formation of the compound Ag2GeSe3 has the form: Ag2GeSe3, the reliability of which is in doubt. 0 0 0 0 ∆G298 ( Ag2GeSe3,cr) = ∆G298 (Ag2Se,cr) + ∆G298 (GeSe2,cr) + / ∆G298 (13) Thermodynamic Calculations and Discussion

The results of the calculation of the time, the enthalpy of the formation of the thermodynamic parameters of Ag8GeSe6 GeSe2 obtained by different authors [19, 20] substantially depend on the reliability of these significantly differ. The following values were binary compounds Ag2Se, GeSe and GeSe2. obtained in [19] using the fluorine calorimetry Therefore we analyzed original sources from method for the standard enthalpy of the which the reference data are taken. formation of crystalline (cr) and glassy (gl) Thermodynamic data for Ag2Se and GeSe GeSe2 at 298 K, respectively: compounds quoted in various references are 0 −1 ∆H 298 (GeSe2,cr.) = − (103.7 ± 3.1) kJ·mol и consistent with each other [17,18]. At the same

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F.S. IBRAGIMOVA 361

0 −1 -1 (GeSe2,cr) = − (62.8 ± 3.1) kJ.mol , it seems ∆H 298 (GeSe2, gl) = − (91.6 ± 3.2) kJ·mol . Standard enthalpy of phase transition to be rather understated. The standard entropy values of Ag2Se, GeSe, and GeSe2 given in GeSe2(gl) = GeSe2 (cr) equals (-12.1 ± 4.2) kJ.mol-1. In [20] while the following values various papers [17, 18, 20] gave no rise to 0 were obtained by the method of direct doubt. Values S298 of these compounds are calorimetry in the standard enthalpy of the given in Table. 2. Standard free energies of the formation of crystalline and glassy formation of Ag8GeSe6 given in Table. 2 0 calculated by the Gibbs-Helmholtz equation. (amorphous) GeSe2: ∆H 298 (GeSe2,cr) = To analyze the dependence of the free −(84.4 ± 2)kJ·mol−1 and ∆H 0 (GeSe ,gl) = 298 2 energy of the formation of compounds on the −1 −(76.5 ± 1) kJ·mol . Standard enthalpy of composition in Fig. 1, we first calculate the phase transition GeSe2 (gl) → GeSe2 (cr) free energy of the reaction: -1 0 equals (-7.9 ± 2.1) kJ.mol . Value ∆H 298 0 GeSe(cr) + Se (cr) → GeSe2(cr) + ∆G298 (14)

Fig. 1. Dependence of the free energy of formation of selenide and germanium disulfide in the crystalline state on the composition: 1- [19], 2- [20], 3- [18]

0 0 0 According to [19]: ∆G298 = ∆G298 (GeSe2,cr)- follows that the values ∆G298 (Ag2GeSe3) 0 given in the work are below additive values ∆G298 (GeSe,cr)= –103.7-(-84.2)= –19.5 kJ.mol-1 (Fig. 1, curve 1). According to [8]: that indicate the thermodynamic instability of the Ag GeSe compound. In this work, an ∆G0 = -83.6-(-84.2 = 0.6 kJ. mol-1 (Fig. 1, 2 3 298 alloy of this composition was synthesized and 0 curve 2). According to [20]: ∆G298 = -62.8-(- investigated. Based on the X-ray diffraction -1 84.2 = 21.4 kJ.mol (Fig. 1, curve 3). The last analysis, it revealed that the Ag2GeSe3 two values for the free energy of reaction (14) compound is obtained in the glassy state with are not consistent with reality (Fig.1, curve rapid cooling of the melt. After annealing of 2,3). Note that GeSe is a peritectic compound, the obtained alloy, there was no line in the and GeSe2 is a congruently melting compound. XRD diffractogram for the Ag2GeSe3 The results of the calculation of the compound. The value of the standard entropy standard thermodynamic functions of the Ag8GeSe6, calculated by equation (9), nearly ternary compound Ag8GeSe6, as well as those coincides (Table 2) with the results of of Ag2GeSe3 are shown in Fig.2. From Fig. 2 it measuring EMF [7].

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362 CALCULATION OF STANDARD THERMODYNAMIC

Fig.2. Dependences of the free energy in the formation of ternary compounds in the crystalline 0 state on the composition: 1-additive calculation by Eq. (12.13 with / ∆G298 =0), 2-[7], 3-[8].

Table 2. Thermodynamic functions of compounds in the crystalline state

0 Compound 0 0 S298 C – ∆GT – ∆HT p,298 T,K -1 -1 -1 kJ.mol J.mol .К

α-Ag2Se 298 50.3±2[18] 43.5±0.5[18] 150.3±1.5[18] 81.8[21] GeSe 298 84.2±5[18] 82.9±5[18] 78.3±1[18] 50.0[21]

GeSe2 298 103.1±2.0[19] 103.7±3.1 [19] 112.6±2[19] 71.2[21]

α-Ag8GeSe6 298 306.3±3[7] 285.7±6[7] 694.1±19[7] 298 288.6±5[8] 261.8±5[8] 714.4±10[8] 298 316.1±5 290.4±5 711.6±10 377.1 calculation by calculation by calculation by Debye Eq.(12) Eq.(10) Eq.(9) calculation method β-Ag8GeSe6 400 316.6±3[7] 270.7±4[7] 740.9±14[7] 249.0±3[8] 240.9±3[8]

Ag8GeSe6 320 15.0±5[7] 46.9±15[7] α→ β

Conclusion A comparative analysis of the related to Argurodites allowed us to choose the experimental and calculated thermodynamic most reliable information about the free data for the ternary compound Ag8GeSe6 energy, formation of enthalpy, standard

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F.S. IBRAGIMOVA 363 entropy, and heat capacity. The work revealed Lindemann and Eastmen-Tsagareishvili applicability of the Debye method based on approximations for calculation of heat capacity quantum concepts of atomic oscillations in the and entropy of ternary compound with a crystal lattice of a solid in the Magnus- common chalcogenide anion.

Acknowledgement This work was carried out in conformity with the grant No EİF-BGM-3-BRFTF-2+/2017- 15/05/1-M-13).

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Ag8GeSe6 ARQİRODİTİN STANDART TERMODİNAMİKİ FUNKSİYALARININ HESABLANMASI

F.S. İbrahimova AMEA-nın akad. M.Nağıyev adına Kataliz və Qeyri-üzvi Kimya İnstitutu AZ 1143 Bakı, H. Cavid pr.113, e-mail: [email protected]

Nəzəri hesablamalar və ədəbiyyat məlumatlarının təhlili əsasında kristal halı üçün gümüş, germanium selenidləri və gümüş selenogermanatlarının termodinamik parametrlərinin ən etibarlı qiymətləri 0 0 0 0 seçilmişdir: ∆H298 (α-Ag2Se)= −43.5, ∆H298 (GeSe,cr)=−82.9, ∆H298 (GeSe2,cr)=−103.7, ∆H298 (α- 0 0 0 Ag8GeSe6,cr)=−290.4, ∆G298 (α-Ag2Se)=−50.3, ∆G298 (GeSe,cr)=−84.2, ∆G298 (GeSe2,cr)=−103.1, 0 −1 0 0 0 ∆G298 (α-Ag8GeSe6,cr)=−306.3 kJ·mol , S298 (α-Ag2Se)=150.3, S298 (GeSe,cr)=78.3, S298 (GeSe ,cr)=112.6, 0 (α-Ag GeSe ,cr)=711.6 J·mol−1.К-1, =377.1 J·mol−1.К-1. Amorf halında 2 S298 8 6 C p,298 mövcud olan Ag2GeSe3 birləşməsi qeyri-sabit olduğu üçün Ag8GeSe6 və GeSe2 birləşmələrinə parçalanır. Ag8GeSe6 birləşməsinin misalında müəyyən edildi ki, Magnus-Lindemann və Eastmen-Tsagareishvili yaxınlaşmaları əsasında Debay metodu ümumi xalkogenid anionlu üçlü birləşmənin istilik tutumu və entropiyasını hesablamaq üçün istifadə oluna bilər. Açar sözlər: argyrodite Ag8GeSe6, termodinamiki funksiyalar, Debay metodu

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F.S. IBRAGIMOVA 365

РАСЧЕТ СТАНДАРТНЫХ ТЕРМОДИНАМИЧЕСКИХ ФУНКЦИЙ АРГИРОДИТА Ag8GeSe6

Ф.С. Ибрагимова Институт Катализа и Неорганической Химии им. акад. М. Нагиева Национальной АН Азербайджана AZ 1143 Баку, пр.Г.Джавида, 113, e-mail: [email protected]

На основании анализа литературных данных с проведением дополнительных расчетов выбраны наиболее достоверные данные для термодинамических параметров 0 кристаллических селенидов серебра, германия и селеногерманата серебра: ∆H298 (α- 0 0 0 Ag2Se)= −43.5, ∆H298 (GeSe,кр)=−82.9, ∆H298 (GeSe2,кр)=−103.7, ∆H298 (α-Ag8GeSe6,кр) 0 0 0 =−290.4, ∆G298 (α-Ag2Se)=−50.3, ∆G298 (GeSe,кр)=−84.2, ∆G298 (GeSe2,кр)=−103.1, 0 −1 0 0 0 ∆G298 (α-Ag8GeSe6,кр)=−306.3 kJ·mol , S298 (α-Ag2Se)=150.3, S298 (GeSe,кр)=78.3, S298 0 α −1 -1 −1 -1 (GeSe2,кр)=112.6, S298 ( -Ag8GeSe6,кр)=711.6 Дж·мол .К , C p,298 =377.1 Дж·мол .К . Выявлено, что соединение Ag2GeSe3 образуется в аморфном состоянии, неустойчиво и распадается на соединения Ag8GeSe6 и GeSe2. Показана применимость метода Дебая, основанного на квантовые представления о колебаниях атомов в кристаллической решетке твердого тела в приближениях Магнуса-Линдемана и Истмена-Цагарейшвили, для расчета теплоемкости и энтропии тройного соединения с общим халькогенид анионом. Ключевые слова: аргиродит Ag8GeSe6, термодинамические функции, метод Дебая

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