Electrochemical determination of thermodynamic properties of saturated solid solutions of Hg₂GeSe₃, Hg₂GeSe₄, Ag₂Hg₃GeSe₆, and Ag_1.4Hg_1.3GeSe₆ compounds in the Ag–Hg–Ge–Se system

Abstract

Triangulation of the Ag–Hg–Ge–Se system in the vicinity of GeSe₂, HgSe, Hg₂GeSe₃, Hg₂GeSe₄, Ag₂Hg₃GeSe₆, and Ag_1.4Hg_1.3GeSe₆ compounds and selenium was performed using X-ray diffraction and differential thermal analysis methods. The spatial position of the determined four-phase regions regarding figurative point of silver was used to write the equations of virtual potential-forming chemical reactions. Potential-forming processes were performed in electrochemical cells (ECCs) of the type (−) C | Ag | Ag₃GeS₃I glass | D | C (+) where C are the inert (graphite) electrodes, Ag and D are the electrodes of the ECCs, D represents equilibrium four-phase alloys, and Ag₃GeS₃I glass is a membrane with purely ionic Ag⁺ conductivity. The linear dependences of the EMF of galvanic cells on temperature in the range of 425–455 K were used to calculate the standard thermodynamic values of saturated solid solutions of Hg₂GeSe₃, Hg₂GeSe₄, Ag₂Hg₃GeSe₆, and Ag_1.4Hg_1.3GeSe₆ compounds.

Introduction

The phase space of the Ag–Hg–Ge–Se system features the existence of such chalcogenide compounds as Ag₂Se [1], GeSe, GeSe₂ [2], Ag₂GeSe₃ [3], Ag₈GeSe₆ [4, 5], and HgSe, Hg₂GeSe₃, Hg₂GeSe₄ [6, 7], as well as four-element phases of variable composition Ag_{∼7.12– ∼6.32}Hg_{∼0.44– ∼0.82}GeSe₆ (β), Ag_{∼6.08– ∼4.00}Hg_{∼0.96– ∼2.00}GeSe₆ (γ), Ag_3.4Hg_2.3GeSe₆ (δ), Ag_{∼2.24– ∼2.00}Hg_{∼2.88– ∼3.00}GeSe₆ (ε), and Ag_1.4Hg_1.3GeSe₆ [8]. Figurative points of most compounds and their solid solutions belong to the Hg–Ge–Se [7] and Ag₂Se–GeSe₂–HgSe [8] planes of Gibbs tetrahedron of the Ag–Hg–Ge–Se system. Two-phase alloys in the concentration plane Hg–Ge–Se at Т ≤ 600 К are found at the sections Hg₂GeSe₄–GeSe₂, Hg₂GeSe₄–HgSe, Hg₂GeSe₄–Se, Hg₂GeSe₄–HgGeSe₃, Hg₂GeSe₃–HgSe, Hg₂GeSe₃–GeSe, and Hg₂GeSe₃–GeSe₂ [7]. Two-phase equilibria in the Ag₂Se–GeSe₂–HgSe plane are the sections Ag₂Hg₃GeSe₆–Hg₂GeSe, Ag₂Hg₃GeSe₆–Ag_1.4Hg_1.3GeSe₆, Ag₂HgGeSe₆–HgSe, Ag_1.4Hg_1.3GeSe₆–GeSe₂, and Ag_1.4Hg_1.3GeSe₆–Hg₂GeSe₄ [8]. Hg₂GeSe₃ melts incongruently at 841 ± 5 K and has a polymorphous transformation at 810 K [6]. The homogeneity region of Hg₂GeSe₃ at 780 K lies within the range of 63.0–66.7 mol% HgSе. The solid solubility of HgSe in α- and β-phases of GeSe reaches 1 and 28 mol%, respectively. The solid solubility of GeSe in HgSe is negligible [7]. The crystal structure of Hg₂GeSe₄ based on powder diffraction data was reported in [8]. Re-investigation of Hg₂GeSe₄ based on single-crystal data was performed by Dong Y. et al. [9]. Details about four-element Т–х diagrams of the Ag–Hg–Ge–Se system are limited by the melting point of γ-phase of Ag₆HgGeSe₆ composition at 1220 K [10]. The thermodynamic properties of silver selenide [11, 12], germanium mono- and dichalcogenide saturated in silver [13], and Ag₂GeSe₃ and Ag₈GeSe₆ compounds [13, 14] were measured by EMF techniques. Thermodynamic properties of stoichiometric HgSe are given in [15].

This paper presents the results of the investigation by EMF method of the thermodynamic properties of silver-saturated Hg₂GeSe₃, Hg₂GeSe₄, and Ag_1.4Hg_1.3GeSe₆ compounds and ε-phase, i.e., Ag₂Hg₃GeSe₆, that is in equilibrium with selenium. The investigation method for assessing the thermodynamic properties was chosen due to the spatial position of the figurative points of the mentioned phases in regard to the points of selenium and silver, and the availability of data on the thermodynamic properties of the HgSe compound [15] as well as the GeSe₂ phase saturated by silver [13]. Thermodynamic properties of ternary and quaternary phases can be used for analytic modeling of р–Т–х diagrams of the Ag–Hg–Ge–Se system by CALPHAD methods [16, 17].

Experimental

The crystalline and glassy alloys were synthesized from pure elements (Ag 99.999 wt%, Alfa-Aesar, Germany; Ge 99.9999 wt%, Lenreactiv, Russia; Se 99.999 wt%, Lenreactiv, Russia) and previously prepared HgSe of at least 99.99 wt% purity in quartz ampoules evacuated to 1 Pa according to the procedure described in [18]. The mass of the synthesized alloys was 5 g. The maximum synthesis temperature of the crystalline alloys was 1050 K. Glassy Ag₃GeS₃I [19] was obtained by melt quenching from 1200 K into ice water. The alloys for the positive electrodes of electrochemical cells (ECCs) were ground to particle size of ≤5 μm and homogenized by annealing at 600 K for 48 h. The phase composition of the alloys was determined by X-ray diffraction (XRD) and differential thermal analysis (DTA) methods. DTA experiments were performed in evacuated quartz ampoules (p ≤ 1 Pa). The DTA curves of alloys were recorded using a Paulik-Paulik-Erdey derivatograph (Hungary) fitted with chromel-alumel thermocouples and an H307-1 XY recorder (Ukraine). The thermocouples were calibrated by the melting points of In (429 K), Sn (505 K), Cd (594 K), Te (723 K), Sb (904 K), NaCl (1074 K), Ge (1209 K), Ag (1236 K), and Cu (1357 К) [20]. The heating (cooling) rate of the DTA scans was 6–8 K min⁻¹. The temperature measurement error did not exceed ±5 K. XRD patterns were collected on a STOE STADI P diffractometer (Germany) equipped with a linear position-sensitive detector, in a modified Guinier geometry (transmission mode, CuKα₁ radiation, a bent Ge (111) monochromator, 2θ/ω scan mode). XRD data sets were processed using STOE WinX^POW (version 2.21) [21] and PowderCell (version 2.3) [22] software suits.

Potential-forming processes were performed in electrochemical cells of the type (−) C | Ag | Ag₃GeS₃I glass | D | C (+) where C are the inert graphite electrodes; Ag and D are the electrodes of ECCs; D represents equilibrium four-phase alloys, and Ag₃GeS₃I glass is a membrane with purely ionic Ag⁺ conductivity [19]. Ag₃GeS₃I glass, same as Ag₃GeS₃Br [23], belongs to the class of superionic materials [24]. The equilibrium in ECCs (E = const) was achieved during 4–6 h. The equilibria were considered when the EMF values were constant or their variations did not exceed ±0.2 mV.

Powdered cell components were pressed at 10⁸ Pa through the holes of 2-mm diameter arranged in the PTFE matrix up to density ρ = (0.93 ± 0.02)ρ ₀, where ρ ₀ is the experimentally determined density of cast alloys. To eliminate the possible defects of plastic deformation during the pressing of alloys, we performed five-fold thermal cycling of ECCs in the range of 400–480 K with heating and cooling rates of 2 K min ⁻¹. The ECCs were heated in a resistance furnace similar to that described in [25] filled with a mixture of H₂ and Ar (both supplied by Lviv chemical factory, Ukraine, 0.9999 volume fraction) in a molar ratio of 1:9, p = 1.2 × 10⁵ Pa. Spectrally pure hydrogen was obtained by the diffusion of the bottled gas through palladium foil. The flow of argon was purified from oxygen in a quartz tube by copper foil heated to 673 К. The flow of gas at the rate of 2·10⁻³ m³ h⁻¹ had the direction from the positive to the negative electrodes of the ECCs. The temperature was maintained with an accuracy of ±0.5 K. The EMF values of the cells were measured using the voltmeter of a U7–9 electrometric amplifier (Ukraine) with an input resistance of >10¹² Ω. The temperature dependences E(T) of the EMF of the cells were analyzed according to the technique in [26].

Results and discussion

The lines of two-phase alloys in Fig. 1 marked out four-phase regions Hg₂GeSe₄–Se–HgSe–Ag₂Hg₃GeSe₆ (I), Hg₂GeSe₄–HgSe–Hg₂GeSe₃–Ag₂Hg₃GeSe₆ (II), GeSe₂–Hg₂GeSe₄–Se–Ag_1.4Hg_1.3GeSe₆ (III), and Hg₂GeSe₄–Ag_1.4Hg_1.3GeSe₆–Ag₂Hg₃GeSe₆–Hg₂GeSe₃ (IV). The positions of the lines of two-phase equilibria were determined in Refs. [2, 6–8] and confirmed by our investigations. The spatial position of phase regions (I)–(IV) relative to the figurative point of silver allows us to apply the EMF method to determine the thermodynamic properties of involved ternary and quaternary phases [14]. The positive electrodes D were prepared by melting the mixture of elements taken in atomic ratio Ag/Hg/Ge/Se = 1.5/3/1/6, phase region (І); 1.5/5/2/9, region (ІІ); 1.1/1.3/1/6, region (ІІІ), and 2.4/10.2/5.1/20.4, region (ІV).

Fig. 1

Four-phase regions of the Ag–Hg–Ge–Se system in the GeSe₂–HgSe–Hg₂GeSe₃–Hg₂GeSe₄–Ag_1.4Hg_1.3GeSe₆–Ag₂Hg₃GeSe₆–Se phase region below 600 K: 1—figurative points of compounds and their saturated solid solutions; 2, 3—lines of two-phase equilibria; 4—sections of the concentration space connecting the figurative points of silver and positive electrodes D of ECCs; 5—figurative points of alloys of positive electrodes of ECCs of the phase regions (I)–(IV)

In accordance with Fig. 1, the virtual electrochemical reactions in the ECCs from the alloys D of regions (I)–(IV) are described by the equations:

$$ 2\mathrm{A}\mathrm{g}+{\mathrm{Hg}}_2{\mathrm{GeSe}}_4+\mathrm{S}\mathrm{e}+\mathrm{HgSe}\rightleftarrows {\mathrm{Ag}}_2{\mathrm{Hg}}_3{\mathrm{GeSe}}_6, $$

(1)

$$ 2Ag+2{Hg}_2{\mathrm{GeSe}}_4+\mathrm{HgSe}\rightleftarrows {\ Hg}_2{\mathrm{GeSe}}_3{+Ag}_2{Hg}_3{\mathrm{GeSe}}_6, $$

(2)

$$ 28\mathrm{A}\mathrm{g}+7{\mathrm{GeSe}}_2+13{\mathrm{Hg}}_2{\mathrm{GeSe}}_4+54\mathrm{S}\mathrm{e}\rightleftarrows 20{\mathrm{Ag}}_{1.4}{\mathrm{Hg}}_{1.3}{\mathrm{GeSe}}_6, $$

(3)

$$ 28\mathrm{A}\mathrm{g}+51{\mathrm{Hg}}_2{\mathrm{GeSe}}_4\rightleftarrows \kern0ex 10{\mathrm{Ag}}_{1.4}{\mathrm{Hg}}_{1.3}{\mathrm{GeSe}}_6+7{\mathrm{Ag}}_2{\mathrm{Hg}}_3{\mathrm{GeSe}}_6+34{\mathrm{Hg}}_2{\mathrm{GeSe}}_3 $$

(4)

Linear dependences E vs T in Fig. 2 are observed in the range of 425–455 K and are approximated by the equations:

$$ {E}_1/\mathrm{mV}=\left(306.238\pm 0.80464\right)+\left(0.16845\pm 0.00183\right)T/\mathrm{K}\left(420\le T/\mathrm{K}\le 460\right), $$

(5)

$$ {E}_2/\mathrm{mV}=\left(325.6806\pm 0.30895\right)+\left(0.08268\pm 0.000704\right)T/\mathrm{K}\left(422\le T/\mathrm{K}\le 460\right), $$

(6)

$$ {E}_3/\mathrm{mV}=\left(311.0379\pm 0.90231\right)+\left(0.15206\pm 0.00205\right)T/\mathrm{K}\left(423\le T/\mathrm{K}\le 457\right), $$

(7)

$$ {E}_4/\mathrm{mV}=\left(294.9613\pm 0.7310\right)+\left(0.16805\pm 0.00166\right)T/\mathrm{K}\left(423\le T/\mathrm{K}\le 463\right) $$

(8)

Fig. 2

The dependences of EMF (E) vs temperature (T) of electrochemical cells: 1–4 correspond to alloys D of the phase regions (I)–(IV)

The deviations from the linear dependences E _1–4(T) below 425 K result from the kinetic hindrances to achieving the equilibrium in ECCs. The non-linearity of E _1–4(T) above 460 K is likely due to the changes in the concentration regions of the existence of the phases. Eqs. (5)–(8) confirm the correctness of the triangulation of the concentration space of the Ag–Hg–Ge–Se system in the vicinity of the studied phases. Under the condition of T = const, the phase region more distant from the figurative point of silver is characterized by higher values of EMF [14]. Specifically, at Т = 430 К we observe Е ₁ = 378.7 mV, Е ₂ = 361.2 mV, Е ₃ = 376.4 mV, and Е ₄ = 367.2 mV.

Gibbs energies of reactions (1)–(4) can be calculated from the measured E(T) relations by using the basic thermodynamic equation:

$$ -{\varDelta}_{\mathrm{r}}{G}_T={n}_eFE(T), $$

(9)

where n _e  = 2, 2, 28, 28 is the number of electrons involved in the reactions (1)–(4), respectively; F = 96,485.3 С·mol ⁻¹ is Faraday’s number.

Applying Eq. (9) to reactions (1)–(4), we obtain

$$ {\varDelta}_{\mathrm{r}}{G}_{T,(1)}=\frac{1}{2}{\varDelta}_{\mathrm{f}}{G}_{T,{Ag}_2{Hg}_3{\mathrm{GeSe}}_6}-\frac{1}{2}{\varDelta}_{\mathrm{f}}{G}_{T,{Hg}_2{\mathrm{GeSe}}_4}-\frac{1}{2}{\varDelta}_{\mathrm{f}}{G}_{T,\mathrm{HgSe}}, $$

(10)

$$ {\varDelta}_{\mathrm{r}}{G}_{T,(2)}=\frac{1}{2}{\varDelta}_{\mathrm{f}}{G}_{T,{Ag}_2{Hg}_3{\mathrm{GeSe}}_6}+\frac{1}{2}{\varDelta}_{\mathrm{f}}{G}_{T,{Hg}_2{\mathrm{GeSe}}_3}-{\varDelta}_{\mathrm{f}}{G}_{T,{Hg}_2{\mathrm{GeSe}}_4}-\frac{1}{2}{\varDelta}_{\mathrm{f}}{G}_{T,\mathrm{HgSe}}, $$

(11)

$$ {\varDelta}_{\mathrm{r}}{G}_{T,(3)}=\frac{2}{2.8}{\varDelta}_{\mathrm{f}}{G}_{T,{Ag}_{1.4}{Hg}_{1.3}{\mathrm{GeSe}}_6}-\frac{0.7}{2.8}{\varDelta}_{\mathrm{f}}{G}_{T,{\mathrm{GeSe}}_2}-\frac{1.3}{2.8}{\varDelta}_{\mathrm{f}}{G}_{T,{Hg}_2{\mathrm{GeSe}}_4}, $$

(12)

$$ {\varDelta}_{\mathrm{r}}{G}_{T,(4)}=\frac{1}{2.8}{\varDelta}_{\mathrm{f}}{G}_{T,{Ag}_{1.4}{Hg}_{1.3}{\mathrm{GeSe}}_6}+\frac{0.7}{2.8}{\varDelta}_{\mathrm{f}}{G}_{T,{Ag}_2{Hg}_3{\mathrm{GeSe}}_6}++\frac{3.4}{2.8}{\varDelta}_{\mathrm{f}}{G}_{T,{Hg}_2{\mathrm{GeSe}}_3}-\frac{5.1}{2.8}{\varDelta}_{\mathrm{f}}{G}_{T,{Hg}_2{\mathrm{GeSe}}_4}, $$

(13)

where${\varDelta}_{\mathrm{f}}{G}_{T,\kern0.5em {\mathrm{GeSe}}_2,\mathrm{HgSe},\kern0.5em {Hg}_2{\mathrm{GeSe}}_3,\kern0.5em {Hg}_2{\mathrm{GeSe}}_4,{Ag}_{1.4}{Hg}_{1.3}{\mathrm{GeSe}}_6,{Ag}_2{Hg}_3{\mathrm{GeSe}}_6}$ are Gibbs energies of the formation of the appropriate phases from the elements at specified temperature T. In the approximation of small differences of the values of the thermodynamic functions of saturated solid solutions of the compounds in bordering phase regions, Eqs. (10)–(13) form a system of linear equations, from which the resulting Δ_f G _T were obtained as

$$ {\varDelta}_{\mathrm{f}}{G}_{T,\kern0.1em {\mathrm{Hg}}_2{\mathrm{GeSe}}_4}=-\frac{132}{7}{\varDelta}_{\mathrm{r}}{G}_{T,\kern0.1em (1)}+\frac{136}{7}{\varDelta}_{\mathrm{r}}{G}_{T,\kern0.1em (2)}+4{\varDelta}_{\mathrm{r}}{G}_{T,\kern0.1em (3)}--8{\varDelta}_{\mathrm{r}}{G}_{T,\kern0.1em (4)}+2{\varDelta}_{\mathrm{f}}{G}_{T,\kern0.1em \mathrm{HgSe}}+{\varDelta}_{\mathrm{f}}{G}_{T,\kern0.1em {\mathrm{GeSe}}_2}, $$

(14)

$$ {\varDelta}_{\mathrm{f}}{G}_{T,\kern0.1em {\mathrm{Hg}}_2{\mathrm{GeSe}}_3}={\varDelta}_{\mathrm{f}}{G}_{T,\kern0.1em {\mathrm{Hg}}_2{\mathrm{GeSe}}_4}+2\left({\varDelta}_{\mathrm{r}}{G}_{T,\kern0.1em (2)}-{\varDelta}_{\mathrm{r}}{G}_{T,\kern0.1em (1)}\right), $$

(15)

$$ {\varDelta}_{\mathrm{f}}{G}_{T,\kern0.1em {\mathrm{Ag}}_2{\mathrm{Hg}}_3{\mathrm{GeSe}}_6}=2{\varDelta}_{\mathrm{r}}{G}_{T,\kern0.1em (1)}+{\varDelta}_{\mathrm{f}}{G}_{T,\kern0.1em {\mathrm{Hg}}_2{\mathrm{GeSe}}_4}+{\varDelta}_{\mathrm{f}}{G}_{T,\kern0.1em \mathrm{HgSe}}, $$

(16)

$$ {\varDelta}_{\mathrm{f}}{G}_{T,\kern0.1em {\mathrm{Ag}}_{1.4}{\mathrm{Hg}}_{1.3}{\mathrm{GeSe}}_6}=1.4{\varDelta}_{\mathrm{r}}{G}_{T,\kern0.1em (3)}+0.35{\varDelta}_{\mathrm{f}}{G}_{T,\kern0.1em {\mathrm{GeSe}}_2}+0.65{\varDelta}_{\mathrm{f}}{G}_{T,\kern0.1em {\mathrm{Hg}}_2{\mathrm{GeSe}}_4} $$

(17)

Taking into account Eq. (9), Δ _f G _T , HgSe/ (kJ mol ⁻¹) = (−43.52 ± 0.05) + (17.33 ± 0.05) × 10⁻³ T/K (298 ≤ T / K ≤ 450) [15] and ${\varDelta}_{\mathrm{f}}{G}_{T,\kern0.1em {\mathrm{GeSe}}_2}/\kern0.1em \left(\mathrm{kJ}\kern0.28em {\mathrm{mol}}^{-1}\right)=\left(-102.6\pm 1.2\right)+\left(130.8\pm 3.5\right)\times {10}^{-3}T/\mathrm{K}$ (298 ≤ T / K ≤ 535) [13], Eqs. (14)–(17) result in:

$$ {\varDelta}_{\mathrm{f}}{G}_{T,{\mathrm{Hg}}_2{\mathrm{GeSe}}_4}/\kern0.1em \left(\mathrm{kJ}\kern0.28em {\mathrm{mol}}^{-1}\right)=\left(-146.3\pm 2.3\right)+\left(388.8\pm 5.3\right)\times {10}^{-3}T/\mathrm{K}\kern6em \left(420\le T/\mathrm{K}\le 460\right), $$

(18)

$$ {\varDelta}_{\mathrm{f}}{G}_{T,{\mathrm{Hg}}_2{\mathrm{GeSe}}_3}/\kern0.1em \left(\mathrm{kJ}\kern0.28em {\mathrm{mol}}^{-1}\right)=\left(-151.2\pm 2.9\right)+\left(405.3\pm 0.6\right)\times {10}^{-3}T/\mathrm{K}\kern6em \left(422\le T/\mathrm{K}\le 460\right), $$

(19)

$$ {\varDelta}_{\mathrm{f}}{G}_{T,{\mathrm{Ag}}_2{\mathrm{Hg}}_3{\mathrm{GeSe}}_6}/\kern0.1em \left(\mathrm{kJ}\kern0.28em {\mathrm{mol}}^{-1}\right)=\left(-247.8\pm 2.9\right)+\left(363.6\pm 5.4\right)\times {10}^{-3}T/\mathrm{K}\kern5em \left(423\le T/\mathrm{K}\le 457\right), $$

(20)

$$ {\varDelta}_{\mathrm{f}}{G}_{T,{\mathrm{Ag}}_{1.4}{\mathrm{Hg}}_{1.3}{\mathrm{GeSe}}_6}/\kern0.1em \left(\mathrm{kJ}\kern0.28em {\mathrm{mol}}^{-1}\right)=\left(-173.1\pm 2.0\right)+\left(278.0\pm 3.8\right)\times {10}^{-3}T/\mathrm{K}\kern4em \left(423\le T/\mathrm{K}\le 463\right) $$

(21)

Equations (18)–(21) express the temperature dependence of Gibbs energy of the formation of saturated solid solutions of corresponding phases from their elements. The values of the standard thermodynamic functions of phases calculated according to Eqs. (18)–(21) in the approximation ΔС _р  = 0 [27], are listed in Table 1. The values of entropy factor $T{\varDelta}_{\mathrm{r}}{S}_{298}^{\mathrm{o}}$ and enthalpy factor $\varDelta {H}_{298}^{\mathrm{o}}$ are listed for the comparison of their contribution to $\varDelta {G}_{298}^{\mathrm{o}}$. High negative values of ${\varDelta}_{\mathrm{r}}{S}_{298}^{\mathrm{o}}$ indicate the decrease of the grain dispersion and the increase of the symmetry of the crystal lattice of ternary and quaternary compounds upon the formation of solid solutions.

Table 1 Standard thermodynamic properties of saturated solid solutions of compounds in the Ag–Hg–Ge–Se system

Conclusions

• 1. The equations of the temperature dependence of Gibbs energy of the formation of saturated solid solutions of Hg₂GeSe₃, Hg₂GeSe₄, Ag₂Hg₃GeSe_6, and Ag_1.4Hg_1.3GeSe₆ compounds were obtained by EMF method.

• 2. The standard thermodynamic properties of the listed compounds were calculated in the approximation ΔС _р  = 0.

• 3. The formation of solid solutions of ternary and quaternary compounds is accompanied by the decrease of the grain dispersion and the increase of the symmetry of the crystal lattice as indicated by high negative values of ${\varDelta}_{\mathrm{r}}{S}_{298}^{\mathrm{o}}$.

• 4. The calculated values of the standard thermodynamic functions of the phases can be used in modeling the р–Т–х diagrams of the Ag–Hg–Ge–Se system by CALPHAD methods.