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358
CHEMICAL PROBLEMS 2019 no. 3 (17) ISSN 2221-8688
UDC 546:544.35:538.95
CALCULATION OF STANDARD THERMODYNAMIC FUNCTIONS
OF ARGYRODIT AgsGeSe6
F.S. Ibrahimova
Institute of Catalysis and Inorganic Chemistry ANAS, H.JavidAve.,113, AZ1134, Baku, Azerbaijan, e-mail: ifs@,live.ru
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:
AH298 (a-Ag2Se) =
43.5,
AH
298
(GeSe,cr)=-82.9, AH098 (GeSe2,cr)=-103.7, AH2098 (a-
o
298 I
AgsGeSe6,cr)=-290.4, AG2°98 (a-Ag2Se)=-50.3, AG2°98 (GeSe, cr)=-84.2, AG2°98 (GeSe2,cr)= -103.1
AG2098 (a-Ag8GeSe6,cr)=-306.3 kJmol1, S298 (a-Ag2Se)=150.3, S2°98 (GeSe,cr)=78.3, S29)8 (GeSe2, cr)=112.6, S2098 (a-Ag8GeSe6, cr)=711.6 Jmol-1.K-1, Cp„_ =377.1 Jmol^.K1. It was revealed that the
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 general chemical formula of A8BX6 (A = Cu, Ag; B = Si, Ge, Sn; and X = S, Se, and Te). Some of these compounds, including Ag8GeSe6, have ionic conduction and can be used as electrochemical sensors, electrodes and electrolyte materials in solid-state batteries and displays, etc [1-5]. In view of the contradictoriness of the literature data, in [6] phase equilibria in the Ag-Ge-Se system were restudied by differential thermal analysis and X-ray powder diffraction analysis. A number of polythermal sections and an isothermal section at room temperature of the phase diagram were constructed, and so was the projection of the liquids' surface. The primary crystallization fields of phases and types and coordinates of in- and monovariant equilibriums were determined. It showed that a single ternary compound, Ag8GeSe6 was formed in the system to have undergone congruent melting at 1175 K and polymorphic transformation at 321 K. The formation of the Ag2GeSe3 and Ag8GeSe5,compounds previously reported in the literature was not
confirmed. Proceeding from phase diagrams of boundary binary systems and the results of the differential thermal analysis of a number of samples of the ternary system, equations were obtained for calculation and 3D modeling of the liquidus Ag8GeSe6 [6].
The thermodynamic parameters of the Ag8GeSe6 compound are necessary for the development of technology of obtaining the stoichiometric phase from simple substances and from binary compounds. Enthalpy, Gibbs free energy of the formation and entropy of the two Ag8GeSe6 modifications as set forth in [7, 8] were carried out within the ternary system study Ag-Ge-Se through measuring the electromotive forces by means of silver solid electrolyte. The results of these studies differ in that the thermodynamic stability of the ternary compound Ag2GeSe3 synthesized in [8] was not confirmed in [7]. The isobaric heat capacity of Ag8GeSe6, estimated [2] by the Debye method in line with Einstein modules, is not clearly approximated.
Allowing for reasoning stated above, the objective of our work is to analyze
o
thermodynamic data for Ag8GeSe6 argyrodite together with additional thermodynamic
calculations based on the Debye method.
Theoretical Part
There are various methods for calculating the thermodynamic parameters of inorganic compounds which have been tested successfully in calculating heat capacity, entropy, enthalpy and Gibbs free energy of the formation of binary and ternary chalcogenides [9-13].
Heat capacity. To calculate the heat capacity, the Debye method is used in keeping with quantum concepts of atomic vibrations in the crystal lattice of a solid. The equation for calculating the isochoric heat capacity Cv for a three-atom compound is as follows [7]:
Cv=9R-D(0d/T
Where
D(0D / T) = 12
3 °D / T 3
x dx ex -1
30D / T
,0 / t
-1
(1)
(2)
and 0D is the Debye temperature defined as
0D=hv/k (3)
In eqn. (2,3) h is the Planck's constant, k is the Boltzmann constant and vis the vibrational frequency and the x-parameter is determined on the basis of the solid state theory.
The calculation of the isochoric heat capacity is carried out in the sequence as follows. The initial data provide (Debye) temperatures of the elements forming the compound, as well as the melting points of the elements and compounds below: 0 D=0D(Tm*/Tm)1/2 (4)
Here 0 D, 0D are characteristic temperatures of the element in the compound and the simple substance; Tm , Tm - melting point of the compound and simple substance.
Based on 0 D /T function, the values of the isochoric heat capacity (Cv) for each component are found, further summing them
up according to the Neumann - Kopp rule, the isochori c heat capacity of the compound is determined. For compounds Ag8GeSe6: Cv(Ag8GeSe6)=8Cv(Ag)+ Cv(Ag)+ 6Cv(Se) (5)
The values of the Debye temperature for silver, germanium, and selenium, together with their melting points and isochoric heat capacities, are given in Table. 1. Recalculation of isochoric heat capacity to isobaric heat was carried out according to the Magnus -Lindemann equation [11]:
Cp=Cv+ 6,076 (nT/Tm )3/2 (6)
Here n i s the numb er of atoms in the compound. Tm is the melting point of Ag8GeSe6. In the equation (3): n=15, Tm=1175 K [6], T=298K.
The temperature dependence of the isobaric heat capacity can be determined by the equation:
Cp=a+bT-cT-2 (7)
c=4,19-105n; b=[25,64n+4,19-105n(Tm )"2-Cp,29s]/( Tm -298); a=Cp,298 -2986+4,7n (8)
Table 1. Melting points (Tm), Debye temperature element in the compound and in a simple substance (0 D, 0D), isochoric heat capacities and standard entropies of silver, germanium, and selenium.
Cv S0 0 298
element Tm,K 0d 0d* * 0d /298
J- mol-1 -K-1
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 and isobaric heat capacity of Ag8GeSe6, the following values were obtained: Cv(Ag8GeSe6) = 365.6 and Cp(Ag8GeSe6) =
377.0 J.mol"1.K"1
Entropy. Tsagareishvili [12] extended the range of applicability of the Eastman equation [11] based on the Debye method to obtain the following equation for calculation of standard entropy of inorganic compounds:
S2098 = 0.75nR< ln
200(M / n)
5/3
P
2/3
T m
4/3
(9)
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, Tn
=1175K [6] - melting temperature, p= 6.21 g.
3
sm [14] - density Ag8GeSe6.
As a result of the calculation, the following value was obtained for the standard entropy S2098 (Ag8GeSe6)=711.6 J.mol-1.K-1.
For the entropy of the formation of
A S2098 (Ag8GeSe6)=85.77 J.mol"1.K"1.
Enthalpy of compound formation.
The value for Ag8GeSe6 was determined by calculation based on the data of binary compounds Ag2Se and GeSe2 (Table 2) in line with a method described in [15,16] with due regard for deviation from additivity (/ AH 098 ):
AH 2098 (Ag8GeSe6,Kp) = 4 AH 298 (Ag2Se,Kp) + AH ^ (GeSe^p) + / AH0
298
(10)
The third term in (1o) depends on the number of anion and the binding energy of metal -selenium (Me-Se). In (10): /AH2098 = -6 E(Me-Se), where E(Me-Se)= -2 kC
The free energy of the formation of the Ag8GeSe6 compound is calculated using the Gibbs-Helmholtz equation:
AG0r ( Ag8GeSe6)= AH2098 ( Ag8GeSe6)+ TAS2098 ( Ag8GeSe6)
as is the case with the formation of (Eq. 10) enthalpy based on the data of binary
compounds by the equation:
AG2098 (Ag8GeSe6,cr) = 4 AG2098 (Ag2Se,cr) + AG2098 (GeSe2,cr) + / AG20
(11)
(12)
In this work, they also calculated the free energy of the formation of the compound Ag2GeSe3, the reliability of which is in doubt.
AG2098 ( Ag2GeSe3,cr) = AG2098 (Ag2Se,cr) + AG2098 (GeSe2,cr) + / AG0
Equation (12) with respect to the compound Ag0GeSe3 has the form:
(13)
Thermodynamic Calculations and Discussion
The results of the calculation of the thermodynamic parameters of Ag8GeSe6 substantially depend on the reliability of these binary compounds Ag2Se, GeSe and GeSe2. Therefore we analyzed original sources from which the reference data are taken. Thermodynamic data for Ag2Se and GeSe compounds quoted in various references are consistent with each other [17,18]. At the same
time, the enthalpy of the formation of the GeSe2 obtained by different authors [19, 20] significantly differ. The following values were obtained in [19] using the fluorine calorimetry method for the standard enthalpy of the formation of crystalline (cr) and glassy (gl) GeSe2 at 298 K, respectively: AH 2098 (GeSe2,cr.) = - (103.7 ± 3.1) kJ-mol-1 u
AH 2098 (GeSe2, gl) = - (91.6 ± 3.2) kJ-mol-1 . Standard enthalpy of phase transition GeSe2(gl) = GeSe2 (cr) equals (-12.1 ± 4.2) kJ.mol- . In [20] while the following values were obtained by the method of direct calorimetry in the standard enthalpy of the formation of crystalline and glassy (amorphous) GeSe2: AH °98 (GeSe2,cr) = -1
(84.4 ± 2)kJ-mol 1 and AH2098 (GeSe2,gl) = (76.5 ± 1) kJ-mol-1. Standard enthalpy of phase transition GeSe2 (gl) — GeSe2 (cr) equals (-7.9 ± 2.1) kJ.mol-1. Value AH098
GeSe(cr) + Se (cr) -
(GeSe2,cr) = - (62.8 ± 3.1) kJ.mol-1, it seems to be rather understated. The standard entropy values of Ag2Se, GeSe, and GeSe2 given in various papers [17, 18, 20] gave no rise to doubt. Values of these compounds are given in Table. 2. Standard free energies of the formation of Ag8GeSe6 given in Table. 2 calculated by the Gibbs-Helmholtz equation.
To analyze the dependence of the free energy of the formation of compounds on the composition in Fig. 1, we first calculate the free energy of the reaction:
GeSe2(cr) + AG.
0
298
(14)
-10
S -20 ea
o -g
i—a
-30
< -40
-50
l 1 I 1 1 < 1 1 1 1 1 < 1 < 1 I I 1 1 < 1
%/ //
t 1 O.SGeSe É . 1 . 1 r 1 . 1 . 1 .
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
mole fraction Se
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]
According to [19]: AG2098 = AG2098 (GeSe2,cr)-AG2098 (GeSe,cr)= -103.7-(-84.2)= -19.5 kJ.mol-1 (Fig. 1, curve 1). According to [8]: AG2°98 = -83.6-(-84.2 = 0.6 kJ. mol-1 (Fig. 1,
curve 2). According to [20]: AG2098 = -62.8-(-84.2 = 21.4 kJ.mol-1 (Fig. 1, curve 3). The last two values for the free energy of reaction (14) are not consistent with reality (Fig. 1, curve 2,3). Note that GeSe is a peritectic compound, and GeSe2 is a congruently melting compound.
The results of the calculation of the standard thermodynamic functions of the ternary compound Ag8GeSe6, as well as those of Ag2GeSe3 are shown in Fig.2. From Fig. 2 it
follows that the values AG298 (Ag2GeSe3)
given in the work are below additive values that indicate the thermodynamic instability of the Ag2GeSe3 compound. In this work, an alloy of this composition was synthesized and investigated. Based on the X-ray diffraction analysis, it revealed that the Ag2GeSe3 compound is obtained in the glassy state with rapid cooling of the melt. After annealing of the obtained alloy, there was no line in the XRD diffractogram for the Ag2GeSe3 compound. The value of the standard entropy Ag8GeSe6, calculated by equation (9), nearly coincides (Table 2) with the results of measuring EMF [7].
■30
0.0 0.1 0.2 0.3 OA Û.S 0.6 0.7 0.8 0.9 1.0 Ag2Se mole fraction GeSe2 GeSe?
Fig.2. Dependences of the free energy in the formation of ternary compounds in the crystalline state on the composition: 1-additive calculation by Eq. (12.13 with / AG298 =0), 2-[7], 3-[8].
Table 2. Thermodynamic functions of compounds in the crystalline state
Compound T,K - agT - ahT SO r 298 Cp,298
kJ.mol-1 J.mol-1.K-1
a-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]
a-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 calculation by Eq(12) 290.4±5 calculation by Eq(10) 711.6±10 calculation by Eq(9) 377.1 Debye calculation method
ß-Ag8GeSe6 400 316.6±3[7] 249.0±3[8] 270.7±4[7] 240.9±3[8] 740.9±14[7]
Ag8GeSe6 a^ ß 320 15.0±5[7] 46.9±15[7]
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
entropy, and heat capacity. The work revealed 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 calculation of heat capacity and entropy of ternary compound with a common chalcogenide anion.
Acknowledgement
This work was carried out in conformity with the grant No EiF-BGM-3-BRFTF-2+/2017-15/05/1-M-13).
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Ag8GeSe6 ARQiRODiTiNSTANDART TERMODiNAMiKi FUNKSiYALARININ
HESABLANMASI
F.S. ibrahimova
AMEA-nin akad. M.Nagiyev adina Kataliz va Qeyri-üzvi Kimya institutu AZ1143 Baki, H. Cavidpr.113, e-mail: asif.mammadov.47@mail.ru
Nazari hesablamalar va adabiyyat malumatlarinin tahlili asasinda kristal hali ûçûn gümü§, germanium selenidlari va gûmûç selenogermanatlarinin termodinamik parametrlarinin an etibarli qiymatlari
seçilmiçdir: AH°98 (a-Ag2Se)= -43.5, AH°98 (GeSe,cr)=-82.9, AH298 (GeSe2,cr)=-103.7, AH298 (a-
AgsGeSe6,cr)=-290.4, AG2098 (a-Ag2Se)=-50.3, AG2098 (GeSe,cr)=-84.2, AG2098 (GeSe2,cr)=-103.1,
S298 (a-Ag2Se) =150.3, S°98 (GeSe, cr)=78.3, S0
298
377.1 Jmol-1 .K1. Amorf halinda
AG2098 (a-Ag8GeSe6,cr)=-306.3 kJmol 1 (GeSe2,cr)=112.6, S2°98 (a-Ag8GeSe6,cr)=711.6 Jmol-1.K1, Cp
mövcud olan Ag2GeSe3 birlaçmasi qeyri-sabit oldugu ûçûn Ag8GeSe6 va GeSe2 birlaçmalarina parçalanir. Ag8GeSe6 birlaçmasinin misalinda müayyan edildi ki, Magnus-Lindemann va Eastmen-Tsagareishvili yaxinlaçmalari asasinda Debay metodu ümumi xalkogenid anionlu ûçlû birlaçmanin istilik tutumu va entropiyasini hesablamaq ûçûn istifada oluna bilar.
Açar sözldr: argyrodite Ag8GeSe6 termodinamiki funksiyalar, Debay metodu
РАСЧЕТ СТАНДАРТНЫХ ТЕРМОДИНАМИЧЕСКИХ ФУНКЦИЙ
АРГИРОДИТА AgsGeSee
Ф. С. Ибрагимова
Институт Катализа и Неорганической Химии им. акад. М. Нагиева
Национальной АН Азербайджана AZ1143 Баку, пр.Г.Джавида, 113, e-mail: asif.mammadov.47@,mail.ru
На основании анализа литературных данных с проведением дополнительных расчетов выбраны наиболее достоверные данные для термодинамических параметров кристаллических селенидов серебра, германия и селеногерманата серебра: АН298 (a-
Ag2Se)= -43.5, АН2098 (Ое8е,кр)=-82.9, АН2098 (0е8е2,кр)=-103.7, АН298 (a-AggGeSe^)
=-290.4, AG2098 (a-Ag2Se)=-50.3, AG2098 (GeSe,кр)=-84.2, AG2098 (GeSе2,кр)=-103Л,
AG2098 (a-Ag8GeSeб,кр)=-306.3 kJ-mof1, S(°98 (a-Ag2Se)=150.3, S098 (GeSe,кр)=78.3, S(°98
(GeSe2,кр)=112.6, S098 (a-Ag8GeSe6,кр) = 711.6 Дж-мол 1.K1, Cp =377.1 Дж-мол 1.K1.
Выявлено, что соединение Ag2GeSe3 образуется в аморфном состоянии, неустойчиво и распадается на соединения AggGeSeg 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 AggGeSeg, термодинамические функции, метод Дебая
