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358 CHEMICAL PROBLEMS 2019 No. 3 (17) ISSN 2221-8688 CALCULATION of STANDARD THERMODYNAMIC FUNCTIONS of ARGYRODIT A

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358 CHEMICAL PROBLEMS 2019 No. 3 (17) ISSN 2221-8688 CALCULATION of STANDARD THERMODYNAMIC FUNCTIONS of ARGYRODIT A 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 Inorganic Chemistry 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, germanium 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: argyrodite 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 chemical formula 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 CHEMICAL PROBLEMS 2019 no. 3 (17) 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. 0 С v S 298 m * * element Т ,K θ θ θ /298 -1 -1 D D D J⋅ mol ⋅К CHEMICAL PROBLEMS 2019 no. 3 (17) 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 0.75nRln 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].
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