THERMODYNAMIC PROPERTIES OF SOME TERNARY COMPOUNDS OF THE ARGYRODITE FAMILY Текст научной статьи по специальности «Химические науки»

ISSN 2522-1841 (Online) ISSN 0005-2531 (Print)

UDC 544.31:546.5723

THERMODYNAMIC PROPERTIES OF SOME TERNARY COMPOUNDS OF THE

ARGYRODITE FAMILY

I.J.Alverdiyev1, S.Z.Imamaliyeva2, E.LAkhmedov3, Yu.A.Yusibov1, M.B.Babanly2'3

1Ganja State University

2 M.Nagiyev Institute of Catalysis and Inorganic Chemistry, Ministry of Science and Education

of the Republic of Azerbaijan 3Baku State University

[email protected]

Received 17.02.2023 Accepted 01.03.2023

Compounds of the argyrodite family are valuable environmentally friendly functional materials with mixed ion-electronic conductivity, thermoelectric, photovoltaic, optical, and other properties. This paper presents the results of a thermodynamic study of the Cu8GeS6 and Cu8GeSe6 compounds - representatives of this family using the EMF method with Cu4RbCl3I2 solid electrolyte in the 295-430 K temperature range. From the EMF measurement data, the partial molar functions of copper were calculated in both crystal modifications of the Cu8GeS6 and Cu8GeSe6 compounds, undergoing polymorphic transformations at 330 and 335 K, respectively. Based on solid-phase equilibria diagrams of the Cu-Ge-S(Se) systems, the potential-forming reactions responsible for the partial molar functions of copper in the alloys were determined and the thermodynamic functions of formation and standard entropies of both modifications of these compounds, as well as the thermodynamic functions of their polymorphic transitions, were calculated. The work also presents and analyzes the thermodynamic data for compounds of the argyrodite family available in the literature.

Keywords: Cu8GeS6, Cu8GeSe6 argyrodites, phase transition, thermodynamic functions, EMF method, Cu4RbCl3I2 solid electrolyte.

doi.org/10.32737/0005-2531-2023-4-21-30 Introduction

Complex chalcogenides of copper and silver, due to their interesting functional properties, are good environmentally friendly materials for a wide range of applications, for example, as thermoelectrics, photovoltaics, ionic conductors et al [1-6]. Recent investigations showed the promise of using them also in bio-medicine [7] and for photocathodic applications in solar-driven water splitting [9, 10]

Among these materials, an important place is occupied by argyrodite family compounds with the general formula AI8BIVX6 (A-Cu, Ag; BIV-Si, Ge, Sn; X-S, Se, Te) [11-13]. All of these compounds crystallize in a tetrahe-dral close-packed structure that contains weakly bound A+ cations. B4+ cations are coordinated

8 x

by 4 anions and form [BX4] - polyanions. These polyanions and X2- anions, form a rigid framework with vacancies for A+ cations. A characteristic feature of compounds of the argy-

rodite family is the presence of polymorphic phase transitions at relatively low temperatures (<530 K) [11, 14]. Low-temperature modifications (ghetto type) have various ordered low-symmetry structures, which are described in detail in the literature [12-14]. An increase in temperature leads to distortion of the anionic framework of the crystal lattice, which leads to the transition of low-temperature ordered modifications to high-temperature disordered ones. Moreover, unlike low-temperature phases, all high-temperature phases are isostructural (aris-totype) and crystallize in a cubic lattice (Sp. Gr. F-43m) [11, 12, 15-17]. Unlike low-temperature modifications, where A+ cations are or-deredly located in certain positions, in high-temperature phases A+ cations are mobile as in a liquid [13].

In addition, compounds of this family, despite the diversity of composition, demonstrate anomalously low lattice thermal conduc-

tivity, as in glasses [12, 13]. On the other hand, the rigid anion framework provides electron transport as in semiconductors. Therefore, all high-temperature modifications of argyrodites are mixed ion-electronic conductors [18, 19]. Thus, the presence of two independent structural units (a rigid anionic framework and weakly bound Cu+ or Ag+ cations) makes them good matrix compounds for the development of highperformance thermoelectric materials by separately tuning the electrical and thermal properties. Thanks to this feature of argyrodites, it was possible to obtain materials with fairly high values of thermoelectric figure of merit (up to ZT=1.6) [13, 20, 21].

In addition, these compounds are of great interest as photovoltaic and optical materials as well as photoelectrodes in various processes, including the catalytic decomposition of water [22-25].

A set of reliable data on phase equilibria and thermodynamic data plays an important role in choosing the conditions for the directed synthesis of new complex materials [26-28].

An important role in obtaining reliable, mutually consistent data on phase equilibria and thermodynamic properties of complex phases is played by one of the high-precision methods of chemical thermodynamics - the EMF method [29-31]. The presence of superionic conductors with pure Cu+ and Ag+ conductivity allows for this purpose to use the EMF method with a solid electrolyte [31-38].

In this work, we continued ther-modynamic studies of argyrodite compounds and presented new data for Cu8GeS6 and Cu8GeSe6 compounds by EMF method with a solid Cu+-conducting electrolyte Cu4RbCl3I2

Experimental part

It is known that in thermodynamic studies of various compounds or phases using the EMF method in concentration cells, not pure compounds or solid solutions are used as right (cathode) electrodes, but equilibrium alloys from certain phase regions of the corresponding systems [30, 31]. Therefore, to rationally select the compositions of alloys -electrodes, we used

solid-phase equilibria diagrams of Cu-Ge-X systems in the Cu2X-GeX2-X composition regions (X-S, Se). Figure 1 shows a schematic phase diagram of the Cu2S-GeS2-S subsystem, constructed taking into account literature data [39, 40].

From Figure 1 it is easy to establish that the ray line coming from the copper corner of the Cu-Ge-S concentration triangle and passing through the composition of the studied compound Cu8GeS6 enters the Cu8GeS6-Cu2GeS3-S three-phase region. This means that Cu2GeS3 and elemental sulfur should be formed during the equilibrium copper extraction from the composition of this compound. Therefore, the equilibrium alloys from the above three-phase region are the most convenient for studying by the EMF method.

According to available literature data, the character of solid-phase equilibria in the Cu-Ge-Se system is qualitatively similar to the sulfide system, i.e. it contains a similar Cu8GeSe6-Cu2GeSe3-Se three-phase region [39, 41].

Taking this into account, for research by the EMF method we prepared 2 alloys for each of the three-phase regions with the addition of 1-2 at% of excess sulfur or selenium (red circles in Figure 1). The synthesis of alloys was carried out by fusing elemental components of a high degree of purity (copper, registration №7440-50-8, purity, 0.99999; germanium, 7440-56-4, 0.99999; sulfur, 7704-34-9, 0.999; selenium, 7782-49-2, 0.9999) in evacuated (10- Pa) quartz ampoules. Considering the high vapor pressure of sulfur and selenium at the interaction temperature, the synthesis was carried out in a two-zone inclined furnace. The temperature of the lower high-temperature zone was 1000-1100 K, and the upper low-temperature zone was 50-100 K below the boiling point of chalcogen (the boiling points of sulfur and selenium are 720 and 960 K, respectively [42]). After the interaction of the main mass of chalco-gen, the ampoule was completely transferred to a high-temperature zone and kept for 2-3 hours.

Samples obtained were subjected to longtime homogenizing annealing at 800 K for 500

hours and then cooled in the turned-off mode sents the powder diffractogram of alloy #1 from

furnace. the Cu8GeS6-Cu2GeS3-S three-phase region as

The equilibrium of the obtained alloys an example. and their conformity to the phase diagram was controlled by the XRD method. Figure 2 pre-

Fig. 1. Solid-phase equilibria diagram at 300 K of the Cu-Ge-S system in the Cu2S-GeS2-S three-phase region.

4 3 2 1.9 1.8 1.7 1.6 1.5 1.4

d - Scale

Fig. 2. Powder diffraction pattern of alloy #1 in Figure 1.

For experiments, the concentration cells

of the

(-) Cu (sol.) Cu4RbCl3I2 (sol.) (Cu in alloy) (sol.) (+) (1)

type were assembled. Here, solid superion conductor Cu4RbCl3I2 was taken as an electrolyte.

The right electrodes were prepared by pressing the powdered annealed alloys into pel-

lets with a diameter of ~0.6 cm and a thickness of 0.3 cm. A high-purity copper plate with a diameter of ~0.6 cm and a thickness of 0.1 cm was used as the left electrode.

The solid electrolyte (Cu4RbCl3I2) was synthesized by the procedure described in [29, 30] by melting chemically pure anhydrous CuCl, CuI, and RbCl in ampules evacuated to

-10 2 Pa at 900 K followed by cooling to 450 K and homogenizing annealing at this temperature for 100 h. Pellets with a thickness of -0.4 cm were cut from the obtained cylindrical ingot with a diameter of -0.8 cm, which were used as a solid electrolyte in (1)-type cells.

An electrochemical cell was assembled, the construction of which is described in [29, 30]. The EMF was measured in the 295-390 K (sulfides) and 300-430 K (selenides) temperature intervals by using a Keithley 2100 6 V digital multimeter with an accuracy of ±0.1 mV. At these temperature intervals, the studied alloys were in a solid state, and the compositions of the equilibrium phases were almost independent of temperature [39-41]. EMF measurements of alloys were first carried out in the temperature interval of the existence of high-temperature modifications Cu8GeS6 and Cu8GeSe6, and then - low-temperature ones as in works [33, 34].

The chromel-alumel thermocouple and a mercury thermometer with an accuracy of ±0.5 K were used for measurements of the temperature of the electrochemical cells.

After holding the electrochemical cell at -400 K for 50-60 h, the first equilibrium EMF values were obtained. The subsequent ones were obtained every 4-6 hours after a certain temperature. The EMF values that did not differ from each other during repeated measurements

at a given temperature by more than 0.2 mV, regardless of the direction of temperature change, were recorded as equilibrium values. The reversibility of the composed concentration chains was controlled by the constancy of the masses and phase compositions of the electrodes.

Results and discussions

The EMF measurements of type (1) cells for both systems are shown in Figure 3. As can be seen from Figure the EMF temperature dependence for both compounds is represented by two straight lines with different slopes, intersecting at 330 or 335 K. The intersection points correspond to the temperatures of the polymorphic transformation of the Cu8GeS6 and Cu8GeSe6 compounds [39-41].

Since the EMF temperature dependencies for both crystalline modifications of the studied compounds are linear, thermodynamic calculations can be made based on them [29, 30]. For this, the experimental results were obtained by the method of least squares using a special computer program, and corresponding linear equations were obtained in the form recommended in the modern scientific literature [29, 30]: E = a + bT ± t[(S2 /n) + S2 • (T - T)2J12 (2)

—1_1_

380 420 T, K

Fig. 3. EMF temperature dependences of the (1)-type concentration cells.

Table 1. EMF dependences of the (1)-type concentration cells for Cu8GeS6 and Cu8GeSe6 compounds

Phase Temperature interval, K E, MB = a + bT ± 2SE(T)

a-Cu8GeS6 295-320 379.1 + 0.049T + 2. il/2 2 0,04 + 2.9 • 10~5(T - 307.7)2 15 J

ß-Cu8GeS6 330-390 357, 8 + 0,116T ± 2 °'45 +6,2-10-6(T 360,5)2 24 1/2

a-Cu8GeSe6 300-330 254,8 + 0,075T±2,2 °'02+9,M0-6(T 314,4)2 15 ■1/2

ß-Cu8GeSe6 340-430 234, 3 + 0,136T ± 2 0 21 ' +1,3-KT6(T 378,0)2 24 1/2

Table 2. Partial molar thermodynamic functions of copper in the crystalline modifications of the Cu8GeS6 and

Cu8GeSe6 compounds

Phase T, K -AGcu — Hcu A Scu

kC • mol-1 C • mol—1 • K—1

a-Cu8GeS6 298 37.99+0.02 36.58+0.32 4.73+1.04

ß-Cu8GeS6 400 -39.00+0.10 34.52+0.55 11.19+1.52

a-Cu8GeSe6 298 26.74+0.01 24.59+0.19 7.21+0.59

ß-Cu8GeSe6 400 27.86+0.06 22.61+0,27 13.12+0.70

In equation (2), a and b are coefficients, n is the number of pairs of values E and T; T -average temperature in K, t is Student's test, and SE and Sb are the variances of individual EMF values and the constant b. With the number of experimental points n = 30, and the confidence level equal to 95%, the Student's test is t < 2.

For each compound, 2 equations corresponding to high- and low-temperature modifications were obtained (Table 1).

From the equations given in Table 1 based on thermodynamic relations,

AG. =-zFE

AHcu = -z

E - T

SE ST

= -zFa

(3)

(4)

AScu = zF

SH (5)

(here z- is the charge of potential forming ion, F-Faraday number) the partial thermodynamic functions of copper in both modifications of the Cu8GeS6 and Cu8GeSe6 compounds were calculated (Table 2).

Since sulfur and selenium are in a crystalline state in the temperature range of

EMF measurements, and the content of all phases in solid-phase equilibria diagrams is constant, the integral thermodynamic functions of the studied compounds were calculated by the method of potential-forming reactions. As can be seen from the phase diagram (Figure 1), the separation of 1 mole of pure copper from the Cu8GeS6 compound under equilibrium conditions would lead to its decomposition into a Cu2GeS3+S heterogeneous mixture. In the same hypothetical process, a similar Cu2GeSe3+Se two-phase mixture would be obtained for the selenide compound. This shows that [29, 30] for opposite processes occurring in (1)-type cells, the equations responsible for the potential difference forming have the following form

Cu(s.)+0,167Cu2GeS3+0.5S (s.)=0.167 Cu^GeS6 (s.) (6) Cu(s.)+0,167Cu2GeSe3+0.5Se (s.)=0.167Cu8GeSe6 (s.) (7)

So, the Gibbs free energies and enthalpies of formation of these ternary compounds can be calculated using formulas Af Z(CusGeS6) = 6AZcu + Af Z(Cu2GeS3) (8) Af Z(CusGeSe6) = 6A Zcu +Af Z(Cu2GeSe3) (9)

p

(here Z - are G or H functions), while the absolute entropies - by using formulas

S°(Cu8GeS6) = 6[AScu + S°(Cu)] + 3S°(S) +

+S°(Cu2GeS3) (10)

S°(Cu GeSe ) = 6[ASCu + S°(Cu)] + 3S°(Se) +

+S° (Cu GeSe

(11)

Based on expressions (8)-(10), the integral thermodynamic functions were calculated for both modifications of the Cu8GeS6 and Cu8GeSe6 compounds (Table 3). Errors were calculated using the error accumulation method.

In the calculations, we used the standard entropies of elemental copper, sulfur and selenium given in the literature

(( S0(Cu) = 33,15 ± 0,08 C-mol-1-K-1; S0(S) = 42,44 ± 0,50 C-mol-1-K-1, (S°(Se)= 42.13±0.21 J-mol-1-K-1) [49], as well as the following values of the standard integral thermodynamic functions of the Cu2GeS3 and Cu2GeSe3 compounds determined by the EMF method

Cu2GeS3 [37]: AG0 =-211.3+2.4 kJ-mol-1; A H0 =-213.7+2.3 KJ-mol-1; S0 =190.3+5.5 J-K-1-mol-1; Cu2GeSe3 [50]: A G0 =-176.8+3.1 kJ-mol-1;

A H0 =-173.9+3.1 KJ-mol-1; S0 =233.3+5.1 J-K^-mol-1. The experimental results obtained made it possible to calculate the thermodynamic functions of polymorphic transformations, as well as the thermodynamic functions of the formation and standard entropies of both modifications of the studied compounds. Considering that the values of the heats of formation of both modifications of ternary compounds remain almost constant in the temperature range of the studies, we can write:

AH = A H0 (HT) - A H0(RT)

(12)

where AHpt. - is the enthalpy of the polymorphic transformation of the compound, A H0(HT) and A H0(RT) - are the enthalpy of formation of its high- and low-temperature modifications, respectively. On the other hand, expressions (8) and (9) show the fractions of the Cu8GeS6 va Cu8GeSe6 compounds in potential forming reactions for both modifications of the Cu8GeS6 and Cu8GeSe6 compounds are the same. Therefore, the enthalpy of formation in (12) can be replaced by the corresponding partial molar function of copper:

AHt. = 6[AHcu(HT) - AHCU(RT)] (13)

Table 3. Standard integral thermodynamic functions of the argyrodite family compounds

Phase - ag0 - AH0 S0 J-K-1 -mol-1 Source

KJ-mol-1

RT-CusGeS6 439.2+2.6 433.2+4.3 515.4+12.9 Present work

HT-Cu8GeS6 *450.9+3.1 420.8+5.6 554.2+15.7 Present work

RT-CusGeSe6 337.2+3.7 321.4+6.4 604.0+9.8 Present work

105.1+1.9 114.5+9.2 143+2 [43]

HT-Cu8GeSe6 *345.0+3.5 309.6+4.8 639.4+10.4 Present work

HT-Ag8SiSe6 388,7±4,4 369,9±6,4 675±12 [44]

Ag8SiTe6 235,3±5,4 229,4±6,6 676±11 [44]

RT-Ag8GeSe6 306.0+3.1 285.7+5.7 694.0+19.2 [33]

HT-AgsGeSe6 *316.6+3.4 249.0 270.7+4.2 240.9 740.9+13.8 [33] [35]

Ag8GeTe6 234.8+0.5 217.5+2.7 726.0+10.0 [45]

266 ± 2 221 ± 1 - [36]

RT-Ag8SnSe6 335.3+2.9 320.4+6.4 695.5+10.5 [34]

HT-Ag8SnSe6 *342.4+3.2 305.0+6.8 738.8+10.6 [34]

352.5+1.9 323.1+1.6 - [46]

350.3+1.8 320.4+8.1 736.6+23.8 [47]

347.6+27.2 336.2+19.2 [48]

Note: data marked with an asterisk (*) refer to 400 K.

Table 4. Temperatures and thermodynamic functions of phase transitions of the A 8B X6 compounds

Compound Tp.t. AHp.t, kJ-mol"1 ASp.t., J-mol"1 -K"1 Source, method

Cu8SiS6 336 14.85±0.59 44.20±1.77 [51], DSC

Cu8SiSe6 325 14.73±0.59 45.32±1.81 [52], DSC

Cu8GeS6 330 12.4±5.1 37.8±14.1 Present work, EMF

15.54±0.62 47.09±2.88 [51], DSC

Cu8GeSe6 330 11.9±2.8 35.5±8.4 Present work, EMF

11. 23±0.45 34.03±1.36 [52], DSC

8.1±0,5 [54], calorim.

6.2 [55], DTA

Ag8GeS6 495 9.46±0.38 19.11±0.76 [53], DSC

Ag8GeSe6 320 15.4±4.7 46.9±14.8 [33], EMF

321 16.95±0.68 52.80±2.11 [53], DSC

Ag8SnS6 446 8.77±0.35 19.66±0.79 [53], DSC

Ag8SnSe6 355 15.4±4.3 43.4±12.1 [34], EMF

19.67±0.60 55.41±2.22 [53], DSC

Expression (13) is more convenient for calculations since the final result obtained in this case does not take into account the errors in the enthalpies of formation of the Cu2GeS3 and Cu2GeSe3 compounds.

The enthalpies of polymorphic transformations of the CugGeS6 and Cu8GeSe6 compounds according to expression (13) and the entropies of polymorphic transformations can be calculated from the expression ASp,=AHp,/Tp,

The results are shown in Table 4.

Tables 3 and 4 present the results of this work as well as thermodynamic functions for other argyrodite compounds known from the literature.

In this work and [34, 35], the EMF of concentration cells were measured in temperature ranges covering the regions of existence of both modifications of the Cu8GeS6, Cu8GeSe6, Ag8GeSe6 u Ag8SnSe6. This made it possible to calculate the partial molar functions of copper (silver), as well as standard integral ther-modynamic functions of both high-temperature and low-temperature modifications of these compounds (Table 3), as well as the enthalpy and entropy of their phase transitions (Table 4).

From Table 3 it follows that the standard integral thermodynamic functions obtained by Moroz et al. and by us are in good agreement. It should also be noted the a good agreement between the data for HT- Ag8SnSe6 obtained by EMF measurements of concentration cells

relative to tin [48] and silver [35, 47, 49] electrodes. At the same time, the data from [44] for RT- Cu8GeSe6 are greatly underestimated. They are lower in absolute value even than the sum of the corresponding values of the Cu2Se and GeSe2 starting binary compounds, which is thermodynamically impossible.

Thermodynamic functions of phase transitions of the A!8BIVX6 compounds (Table 4) were determined by the DSC [52-54] and by the EMF method in the present work and also [34, 35]. Calorimetric data are the results of direct measurements of heat flow and have a fairly high accuracy (error no more than 6-7%). The relatively high errors in the data obtained by the EMF method are because they are calculated indirectly from the differences in the temperature coefficients of the EMF for two modifications of the compounds under study.

Table 4 also shows anomalously high values of enthalpy and entropy of phase transformations of argyrodite compounds compared to conventional polymorphic transitions for chalcogenides. Apparently, this is because the transition from low-temperature ordered structures to high-temperature ones is accompanied by strong disorder in the cation sublattice, leading to the mobility of Cu+ and Ag+ cations, as in liquids.

Conclusion

We continued the thermodynamic study of argyrodite family compounds and presented new data for the Cu8GeS6 and Cu8GeSe6 com-

pounds - representatives of this family, obtained by the EMF method with the C^RbC^ solid electrolyte in the 295-430 K temperature range. From the EMF measurements, the partial molar functions of copper and the integral thermodynamic functions of both modifications of these compounds, as well as the thermody-namic functions of their polymorphic transitions were calculated. The work also presents the thermodynamic data available in the literature for other representatives of this family and carries out their comparative analysis.

Acknowledgment

This work is supported by the Azerbaijan Science Foundation - Grant No AEF-MCG-2022-1(42)- 12/10/4-M-10.

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ARGÏRODÏT AiLOSÎNÎN BOZÏ BiRLO§MOLORlNiN TERMODÏNAMÏK XASSOLORl

i.C.Alverdiyev, S.Zjmamaliyeva, E.LOhmadov, Y.O.Yusibov, M.B.Babanli

Argirodit ailasi birlaçmalari qançiq ion-elektron keçiriciliyina, maraqli termoelektrik, fotoelektrik, optik va s. xassalara malik qiymatli ekoloji tahlükasiz funksional materiallardir. içda bu ailaya aid olan Cu8GeS6 va Cu8GeSe6 birlçmalarinin Cu+ keçiriciliya malik Cu4RbCl3I2 bark elektrolitli qatiliq dövralarinin elektrik harakat qüvvasinin (EHQ) ôlçûlmasi ila termodinamik tadqiqinin naticalari taqdim olunur. EHQ ôlçmalari asasinda müvafiq olaraq 330 va 335 K -da polimorf çevrilmaya maruz qalan bu birlaçmalarin har iki kristallik modifikasiyalannda misin parsial molyar funksiyalari hesablanmiçdir. Cu-Ge-S(Se) sistemlarinin barkfaza tarazliqlan diaqramlan asasinda bu parsial molyar kamiyyatlara uygun potensialamalagatirici reaksiyalar müayyan edilmiç, Cu8GeS6 va Cu8GeSe6 birlçmalarinin har iki kristallik modifikasiyalarinin amalagalma termodinamik funksiyalari va mütlaq entropiyalari, hamçinin bu birlaçmalarin polimorf çevrilma termodinamik funksiyalari hesablanmiçdir. içda hamçinin argirodit ailasi birlaçmalarinin termodinamik xassalarina aid adabiyyat malumatlari verilmiç va araçdinlmiçdir.

Açar sözlzr: CusGeS6, Cu8GeSe6, argirodit, faza keçidi, termodinamik funksiyalar. EHQ üsulu, Cu4RbCl3I2 bark elektroliti.