Quasi-Ternary System Ag₂Se–GeSe₂–As₂Se₃

Abstract

Phase equilibria in the quasi-ternary system Ag₂Se–GeSe₂–As₂Se₃ were investigated by direct synthesis, x-ray phase, differential thermal and microstructural analysis methods. Isothermal section of the system at 513 K (240 °C) was constructed, the existence of ternary compounds Ag₈GeSe₆, Ag₃AsSe₃, AgAsSe₂, AgAs₃Se₅ was confirmed, and the existence of quaternary compounds was not found. Three quasi-binary phase diagrams Ag₂Se–As₂Se₃, Ag₈GeSe₆–AgAsSe₂, GeSe₂–AgAsSe₂, three vertical sections Ag₈GeSe₆–Ag₃AsSe₃, Ag₈GeSe₆–As₂Se₃, GeSe₂–AgAs₃Se₅, and the liquidus surface projection onto the concentration triangle were constructed. The regions of primary crystallization of phases, character, temperature, and coordinates of mono- and invariant equilibria were determined.

1 Introduction

The binary compounds Ag₂Se, GeSe₂, As₂Se₃ melt congruently at 1170 K (897 °C), 1013 K (740 °C), and 648 K (375 °C)^[1], respectively, possess insignificant homogeneity regions and may serve as components of the quasi-ternary system Ag₂Se–GeSe₂–As₂Se₃. The study of this quasi-ternary system is of current interest because it is formed by binary compounds with important semiconducting properties. Complex chalcogenide semiconductors attract growing interest in materials science due to their prospects for use as materials in the fields of nonlinear optics, optoelectronics, and acousto-optics.^[2,3,4,5,6]

Phase equilibria in the quasi-binary system Ag₂Se–GeSe₂ were studied in Ref 7,8,9,10. The authors of Ref 10 confirmed the existence of one ternary compound Ag₈GeSe₆ which melts congruently at 1175 K (902 °C) and undergoes two polymorphous transformations at 269 K (–4 °C)^[7] and 321 K (48 °C),^[7,9,10] respectively. The eutectic points coordinates were ascertained as 1103 K (830 °C), 15 mol.% GeSe₂ and 843 K (570 °C), 56 mol.% GeSe₂,^[10] and agree well with Ref 7. γ-Ag₈GeSe₆ which is stable at room temperature crystallizes in space group, S.G. Pmn2₁, with lattice parameters a = 0.7823 nm, b = 0.7712 nm, c = 1.0885 nm.^[11]

The Ag₂Se–As₂Se₃ phase diagram was described in Ref 12,13,14. According to Ref 14, the existence of three compounds, Ag₃AsSe₃, AgAsSe₂ and AgAs₃Se₅, was established in the system. The AgAs₃Se₅ compound forms incongruently at 643 K (370 °C) and has a eutectic with As₂Se₃ at 87 mol.% As₂Se₃ and 630 K (357 °C). The AgAsSe₂ compound melts congruently at 673 K (400 °C) and does not have a polymorphous transformation (whereas according to Ref 13 there is a polymorphous transformation of AgAsSe₂ at 658 K (385 °C)). The peritectic reaction L + Ag₂Se ↔ Ag₃AsSe₃ takes place at 663 K (390 °C). The coordinates of the eutectic of Ag₃AsSe₃ − AgAsSe₂ are 33 mol.% As₂Se₃ and 653 K (380 °C).

The crystal structure of the Ag₃AsSe₃ compound was determined in Ref 13, 15. The compound is an analogue of the proustite mineral (Ag₃AsS₃), crystallizes in S.G. R3c; and has lattice parameters a = 1.1285 nm, c = 0.8803 nm ^[13], or a = 1. 1298 nm, c = 0.8757 nm^[15]. For the high-temperature modification (HTM) of AgAsSe₂, the authors of Ref 13 determined the crystal structure S.G. R $\overline{3}$ m, structure type NaCrS₂, a = 0.3915 nm, c = 2.0375 nm. The diffraction pattern of the low-temperature modification (LTM) of AgAsSe₂ was indexed by the authors of Ref 13 in the primitive tetragonal cell with a = 1.2548 nm, c = 1.1140 nm. The compound AgAs₃Se₅ crystallizes in S.G. R $\overline{3}$ m, a = 0.38195(1) nm, c = 5.0082(2) nm^[16].

Phase diagram of the GeSe₂–As₂Se₃ system of the eutectic type, with the eutectic point at 20 mol.% GeSe₂ and 618 K (345 °C)^[17].

2 Experimental Methods

Phase equilibria in the quasi-ternary system Ag₂Se–GeSe₂–As₂Se₃ were studied using 122 samples. The alloys were synthesized by direct single-temperature method from high-purity elements (Ag 99.995, Ge 99.99, Se 99.9997, As 99.9999 wt.%) in quartz containers that were evacuated to a residual pressure of 0.133 Pa and sealed. The synthesis was performed in a shaft-type furnace with temperature control with an accuracy of ± 5 K (± 5 °C). The maximum synthesis temperature was 1373 K (1100 °C), the heating and cooling rate was 10 K/h (10 °C/h). Homogenization annealing at 513 K (240 °C) was held for 600 h, after which the samples were quenched into 25% aqueous NaCl solution.

The as-obtained samples were investigated by x-ray diffraction (XRD) method (DRON 4–13 diffractometer, CuK_α radiation, 10(20)° < 2θ < 90°, 0.05° scan step, 1–5 s exposure in each point) and differential thermal analysis (DTA) ("Thermodent H307/1" furnace with a PDA-1 XY-recorder, Pt/Pt–Rh thermocouple). The two-phase or three-phase composition of the samples was also checked by the microstructure analysis (MSA), which was performed on a PMT-3 M microhardness tester.

3 Results and Discussion

3.1 Isothermal Section of the Quasi-Ternary System Ag ₂ Se–GeSe ₂ –As ₂ Se ₃ at 513 K (240 °C)

According to XRD and MSA results of 122 samples (Fig. 1), isothermal section of the Ag₂Se – GeSe₂ – As₂Se₃ system at 513 K was plotted (Fig. 2). Diffraction patterns of the binary compounds were indexed (Fig. 3): GeSe₂ by S.G. P2₁/c, a = 0.7007(2) nm, b = 1.6819(5) nm, c = 1.1806(3) nm, β = 90.74(2)º; As₂Se₃ in S.G. P2₁/n, a = 1.2794(7) nm, b = 0.9874(5) nm, c = 0.4267(2) nm, α = 90.96(4)º, and agree well with the literature data from Ref 18,19,20, respectively. The existence of the four ternary compounds Ag₈GeSe₆, Ag₃AsSe₃, LTM-AgAsSe₂, AgAs₃Se₅ was confirmed (Fig. 3). The diffraction pattern of the Ag₈GeSe₆ compound was indexed with the orthorhombic S.G. Pmn2₁, a = 0.78443(5) nm, b = 0.77372(5) nm, c = 1.09141(7) nm, which is consistent with Ref 11. The diffraction pattern of Ag₃AsSe₃ was indexed with the hexagonal S.G. R3c, structural type proustite Ag₃AsS₃, a = 1.1270(6) nm, c = 0.8765(9) nm, which agrees with Ref 13. The LTM-AgAsSe₂ was identified by comparing our diffraction pattern with the one indexed with a tetragonal structure (a = 1.2548 nm, c = 1.1140 nm) presented in Ref 13. The crystal structure of the AgAs₃Se₅ compound was determined by the powder diffraction method. It was found that the compound crystallizes in S.G. R $\overline{3}$ m, a 0.38195(1) nm, c = 5.0082(2) nm)^[16]. Ag₂Se was obtained as a LTM (S.G. P2₁2₁2₁, a = 0.4337(5) nm, b = 0.7072(5) nm, c = 0.7773(5) nm).

Fig. 1

Chemical and phase compositions of the Ag₂Se–GeSe₂–As₂Se₃ system samples at 513 K

Fig. 2

Isothermal section of the quasi-ternary system Ag₂Se–GeSe₂–As₂Se₃ at 513 K

Fig. 3

Experimental diffractograms of the binary and ternary compounds of the quasi-ternary system Ag₂Se–GeSe₂–As₂Se₃

The presence of the four two-phase equilibria, Ag₈GeSe₆–Ag₃AsSe₃, Ag₈GeSe₆–AgAsSe₂ (Fig. 4), GeSe₂–AgAsSe₂, and GeSe₂–AgAs₃Se₅, was established in the studied quasi-ternary system according to x-ray phase analysis and MSA of the synthesized samples. They divide the system into the respective regions of three-phase equilibria Ag₂Se + Ag₈GeSe₆ + Ag₃AsSe₃, Ag₃AsSe₃ + Ag₈GeSe₆ + AgAsSe₂, AgAsSe₂ + Ag₈GeSe₆ + GeSe₂, AgAs₃Se₅ + AgAsSe₂ + GeSe₂ and As₂Se₃ + AgAs₃Se₅ + GeSe₂. No significant solid solubility ranges were found for the binary compounds or intermediate ternary compounds.

Fig. 4

Experimental diffractograms of the samples of the Ag₈GeSe₆–AgAsSe₂ system (compositions are given in mol.%)

3.2 The Quasi-Binary System Ag ₂ Se–As ₂ Se ₃

Due to somewhat differing literature data in Ref 12,13,14, we re-investigated the Ag₂Se–As₂Se₃ system (Fig. 5). The compositions of the samples for the investigation are given in Table 1. Phase diagram of the system was plotted from the results of XRD, DTA (Table 1) and MSA. The existence and formation mechanism of three compounds Ag₃AsSe₃, AgAsSe₂ and AgAs₃Se₅, and the polymorphous transformation of AgAsSe₂ were confirmed. Ag₃AsSe₃ melts incongruently at 660 K (387 °C), AgAsSe₂ melts congruently at 683 K (410 °C), and AgAs₃Se₅ melts incongruently at 644 K (371 °C). The horizontal line at 635 K (362 °C) corresponds to the eutectic reaction L_e1 ↔ AgAs₃Se₅ + As₂Se₃ with the eutectic point at 88 mol.% As₂Se₃. The temperatures of invariant reactions practically do not differ from Ref 15. The phase diagram of the Ag₂Se – As₂Se₃ system shows a horizontal line at 630 K (357 °C) which indicates a polymorphous transformation of the AgAsSe₂ compound; obtained temperature value is slightly lower than indicated in Ref 12, 13.

Fig. 5

Phase diagram of the Ag₂Se–As₂Se₃ system: 1–L; 2–L + Ag₂Se, 3–L + Ag₃AsSe₃, 4–L + HTM-AgAsSe₂, 5–L + AgAs₃Se₅, 6–L + As₂Se₃, 7–Ag₃AsSe₃ + HTM-AgAsSe₂, 8–HTM-AgAsSe₂ + AgAs₃Se₅, 9–Ag₂Se + Ag₃AsSe₃, 10–Ag₃AsSe₃ + LTM-AgAsSe₂, 11–LTM-AgAsSe₂ + AgAs₃Se₅, 12–AgAs₃Se₅ + As₂Se₃

Table 1 Compositions of the samples of the Ag₂Se–As₂Se₃ quasi-binary system and their DTA results

3.3 The Quasi-Binary System Ag ₈ GeSe ₆ –AgAsSe ₂

Phase diagram of the Ag₈GeSe₆ – AgAsSe₂ system (Fig. 6) is based on DTA, XRD and MSA results. The axes of the isothermal section (Fig. 1 and 2) and the liquidus projection (Fig. 12) are in mol.% of the components, Ag₂Se, As₂Se₃ and GeSe₂, while the axes of the vertical sections (Figs. 6-11) are in mol.% of the compounds constituting these sections. For easier correlation with the isothermal section and the liquidus projection, a secondary axis with mol.% of As₂Se₃ is added to the diagram. The compositions of the synthesized samples as well as DTA results are given in Table 2. Some of the DTA curves are shown in Fig. 7. They were measured from and till the temperature of annealing of the samples, 513 K. The investigated system is of the eutectic type. The eutectic point coordinates were determined by plotting the Tammann triangle according to Ref 21. Point e₅ corresponds to the composition of 4 mol.% Ag₈GeSe₆–96 mol.% AgAsSe₂ (55.2 mol.% Ag₂Se–3.4 mol.% GeSe₂–41.4 mol.% As₂Se₃), 660 K (387 °C), where the invariant reaction L_e5 ↔ Ag₈GeSe₆ + HTM-AgAsSe₂ takes place. The liquidus is represented by the curves of the primary crystallization of Ag₈GeSe₆ and the solid solution HTM-AgAsSe₂. The eutectoid reaction HTM-AgAsSe₂ ↔ LTM-AgAsSe + Ag₈GeSe₆ takes place at 590 K (317 °C). Below this temperature the samples are two-phase, Ag₈GeSe₆ + LTM-AgAsSe₂, which was established by XRD (Fig. 4) and MSA methods. No significant solid solubility based on the starting compounds was observed.

Fig. 6

Phase diagram of the Ag₈GeSe₆–AgAsSe₂ system: 1–L, 2–L + Ag₈GeSe₆, 3–L + HTM-AgAsSe₂, 4–Ag₈GeSe₆ + HTM-AgAsSe₂, 5–HTM-AgAsSe₂, 6–HTM-AgAsSe₂ + LTM-AgAsSe₂, 7–Ag₈GeSe₆ + LTM-AgAsSe₂

Table 2 Compositions of the samples of the Ag₈GeSe₆–AgAsSe₂ quasi-binary system calculated through the ternary, binary compounds and their DTA results

Fig. 7

DTA curves of some alloys of the Ag₈GeSe₆–AgAsSe₂ system: 1–AgAsSe₂, 2–97 mol.% AgAsSe₂ − 3 mol.% Ag₈GeSe₆, 3–85 mol.% AgAsSe₂ − 15 mol.% Ag₈GeSe₆, 4–Ag₈GeSe₆

3.4 The Vertical Section Ag ₈ GeSe ₆ –Ag ₃ AsSe ₃

The compositions and DTA data of the alloys are given in Table 3. Based on these the vertical section was built. The liquidus (Fig. 8) crosses the primary crystallization regions of Ag₈GeSe₆ (field 2) and Ag₂Se (field 4). The regions of the secondary crystallization of the monovariant eutectic reaction L_e3-U1 ↔ Ag₂Se + Ag₈GeSe₆ (field 3) and the peritectic reaction L_p2-U1 + Ag₂Se ↔ Ag₃AsSe₃ (field 5) descend to the plane of the invariant reaction L_U1 + Ag₂Se ↔ Ag₈GeSe₆ + Ag₃AsSe₃ which occurs at 650 K (377 °C) and ends with the exhaustion of L and Ag₂Se. Therefore, below 650 K (377 °C) the samples are two-phase Ag₈GeSe₆ + Ag₃AsSe₃ (field 6), which was determined by XRD and MSA data. No solid solubility based on the starting compounds was found.

Table 3 Compositions of the samples of the Ag₈GeSe₆ – Ag₃AsSe₃ vertical section calculated from the compositions of the ternary, binary compounds and their DTA results

Fig. 8

The vertical section Ag₈GeSe₆–Ag₃AsSe₃: 1–L, 2–L + Ag₈GeSe₆, 3–L + Ag₂Se + Ag₈GeSe₆, 4–L + Ag₂Se, 5–L + Ag₂Se + Ag₃AsSe₃, 6–Ag₈GeSe₆ + Ag₃AsSe₃

3.5 The Quasi-Binary System GeSe ₂  – AgAsSe ₂

Phase diagram of the GeSe₂–AgAsSe₂ system (Fig. 9) is based on DTA (Table 4), XRD and MSA results for 16 samples, compositions of which are given in Table 4. Phase diagram is of the eutectic type, the liquidus consists of the curves of the primary crystallization of GeSe₂ (ab) and the solid solution HTM-AgAsSe₂ (bc), respectively. The horizontal line at 670 K (397 °C) corresponds to the invariant eutectic reaction L_e6 ↔ GeSe₂ + HTM-AgAsSe₂. The coordinates of the eutectic point e₆ are 7.7 mol.% GeSe₂–92.3 mol.% AgAsSe₂ (46 mol.% Ag₂Se–8 mol.% GeSe₂–46 mol.% As₂Se₃) as determined by plotting the Tammann triangle. The eutectoid reaction HTM-AgAsSe₂ ↔ LTM-AgAsSe₂ + GeSe₂ takes place at 610 K (337 °C). Below this temperature, the samples are two-phase GeSe₂ + LTM-AgAsSe₂ that is consistent with Fig. 2. No significant solid solubility based on the starting compounds was detected.

Fig. 9

Phase diagram of the GeSe₂–AgAsSe₂ system: 1–L, 2–L + GeSe₂, 3–GeSe₂ + HTM-AgAsSe₂, 4–L + HTM-AgAsSe₂, 5–HTM-AgAsSe₂, 6–HTM-AgAsSe₂ + LTM-AgAsSe₂, 7–GeSe₂ + LTM-AgAsSe₂

Table 4 Compositions of the samples of the GeSe₂–AgAsSe₂ quasi-binary system calculated from the compositions of the ternary, binary compounds and their DTA results

3.6 The Vertical Section Ag ₈ GeSe ₆ –As ₂ Se ₃

The Ag₈GeSe₆ – As₂Se₃ section (Fig. 10) is based on XRD, MSA and DTA results of 20 samples. Their compositions and DTA data are shown in Table 5. The liquidus of the vertical section is represented by the primary crystallization curves of Ag₈GeSe₆ (ab), GeSe₂ (bcd), HTM-AgAsSe₂ (df), AgAs₃Se₅ (fg) and As₂Se₃ (gj). The section crosses two subsystems of the studied quasi-ternary system, AgAsSe₂ + Ag₈GeSe₆ + GeSe₂ (II) and AgAsSe₂ + GeSe₂ + As₂Se₃ (III). The section crosses the plane of the invariant eutectic reaction L_E2 ↔ HTM-AgAsSe₂ + Ag₈GeSe₆ + AgAs₃Se₅ at 630 K (357 °C) in subsystem II. This ends with the exhaustion of liquid, therefore the alloys are three-phase (field 12) below 630 K (357 °C) in the region between 2 and 75 mol.% As₂Se₃. The horizontal at 590 K (317 °C) represents the reaction HTM-AgAsSe₂ ↔ LTM-AgAsSe₂ + Ag₈GeSe₆ + GeSe₂ in the subsolidus region, and alloys below 590 K contain LTM-AgAsSe₂ and are three-phase (LTM-AgAsSe₂ + Ag₈GeSe₆ + GeSe₂).

Fig. 10

The vertical section Ag₈GeSe₆–As₂Se₃: 1–L, 2–L + Ag₈GeSe₆, 3–L + GeSe₂, 4–L + HTM-AgAsSe₂, 5–L + AgAs₃Se₅, 6–L + As₂Se₃, 7–L + Ag₈GeSe₆ + GeSe₂, 8–L + HTM-AgAsSe₂ + GeSe₂, 9–L + HTM-AgAsSe₂ + AgAs₃Se₅, 10–L + GeSe₂ + AgAs₃Se₅, 11–L + AgAs₃Se₅ + As₂Se₃, 12–Ag₈GeSe₆ + HTM-AgAsSe₂ + GeSe₂, 13–GeSe₂ + HTM-AgAsSe₂, 14–GeSe₂ + HTM-AgAsSe₂ + LTM-AgAsSe₂, 15–HTM-AgAsSe₂ + GeSe₂ + AgAs₃Se₅, 16–Ag₈GeSe₆ + LTM-AgAsSe₂ + GeSe₂, 17–GeSe₂ + LTM-AgAsSe₂, 18–LTM-AgAsSe₂ + GeSe₂ + AgAs₃Se₅, 19–GeSe₂ + AgAs₃Se₅, 20–GeSe₂ + AgAs₃Se₅ + As₂Se₃

Table 5 Compositions of the samples of the Ag₈GeSe₆ – As₂Se₃ vertical section calculated from the compositions of the ternary, binary compounds and their DTA results

The sample with 80 mol.% As₂Se₃ is two-phase at the annealing temperature (LTM-AgAsSe₂ + GeSe₂) because it falls on the quasi-binary section GeSe₂–AgAsSe₂. The section in subsystem III crosses the reaction plane at 634 K (361 °C) which reflects the invariant reaction L_U2 + HTM-AgAsSe₂ ↔ AgAs₃Se₅ + GeSe₂. This reaction ends in samples with higher Ag₈GeSe₆ content with the disappearance of the liquid, so that the alloys of this subsystem below 634 K (361 °C) are three-phase (field 15). The horizontal line at 630 K (357 °C) corresponds to the reaction HTM-AgAsSe₂ + AgAs₃Se₅ ↔ LTM-AgAsSe₂ + GeSe₂ in the subsolidus region, thus the alloys below 630 K (357 °C) contain LTM-AgAsSe₂ and are three-phase (AgAs₃Se₅ + LTM-AgAsSe₂ + GeSe₂). This reaction ends in point k with the exhaustion of both L and HTM-AgAsSe₂, so that the alloys are two-phase GeSe₂ + AgAs₃Se₅ below 630 K (357 °C) (field 19). Samples with higher As₂Se₃ content end in the invariant reaction at 634 K (361 °C) with the exhaustion of HTM-AgAsSe₂. Therefore, the alloys below 634 K (361 °C) are three-phase L + GeSe₂ + AgAs₃Se₅ (field 10). This field together with the region of the secondary crystallization L + As₂Se₃ + AgAs₃Se₅ (field 11) descends to the plane of the invariant reaction L_E3 ↔ GeSe₂ + As₂Se₃ + AgAs₃Se₅ at 600 K (327 °C). This reaction ends with the exhaustion of the liquid; thus, the alloys are three-phase (GeSe₂ + As₂Se₃ + AgAs₃Se₅) below 600 K (327 °C). This agrees with the results shown in Fig. 2. The phase composition of the samples was determined by XRD and MSA results.

3.7 The Vertical Section GeSe ₂  – AgAs ₃ Se ₅

The section (Fig. 11) was investigated by DTA, XRD and MSA of 17 samples with compositions given in Table 6. The liquidus consists of the curves of the primary crystallization of GeSe₂ (ab) and HTM-AgAsSe₂ (bc). The section crosses the plane of the invariant reaction L_U2 + HTM-AgAsSe₂ ↔ AgAs₃Se₅ + GeSe₂ at 634 K (361 °C), which ends with the exhaustion of both L and HTM-AgAsSe₂, so that the alloys are two-phase below 634 K (361 °C) as confirmed by XRD and MSA results.

Fig. 11

The vertical section GeSe₂–AgAs₃Se₅: 1–L, 2–L + GeSe₂, 3–L + HTM-AgAsSe₂ + GeSe₂, 4–L + HTM-AgAsSe₂, 5–L + HTM-AgAsSe₂ + AgAs₃Se₅, 6–GeSe₂–AgAs₃Se₅

Table 6 Compositions of the samples of the GeSe₂–AgAs₃Se₅ vertical section calculated from the compositions of the ternary, binary compounds and their DTA results

3.8 Liquidus Surface Projection of the Quasi-Ternary System Ag ₂ Se–GeSe ₂ –As ₂ Se ₃

The liquidus surface projection of the quasi-ternary system Ag₂Se–GeSe₂–As₂Se₃ (Fig. 12 and Table 7) is based on literature data and our own results from studies of three phase diagrams Ag₂Se–As₂Se₃, Ag₈GeSe₆–AgAsSe₂ and GeSe₂–AgAsSe₂ and three vertical sections Ag₈GeSe₆–Ag₃AsSe₃, Ag₈GeSe₆–As₂Se₃ and GeSe₂–AgAs₃Se₅, as well as the isothermal section of the system at 513 K (240 °C).

Fig. 12

Liquidus surface projection of the quasi-ternary system Ag₂Se–GeSe₂–As₂Se₃

Table 7 Character, temperatures of invariant reactions and coordinates of invariant points in the quasi-ternary system Ag₂Se–GeSe₂–As₂Se₃

The system’s liquidus consists of the fields of the primary crystallization of Ag₂Se (Ag₂Se-p₂-U₁-e₃-Ag₂Se), Ag₃AsSe₃ (e₂-E₁-U₁-p₂-e₂), HTM-AgAsSe₂ (p₁-U₂-e₆-E₂-e₅-E₁-e₂-p₁), AgAs₃Se₅ (e₁-E₃-U₂-p₁-e₁), As₂Se₃ (As₂Se₃-e₇-E₃-e₁-As₂Se₃), Ag₈GeSe₆ (e₃-U₁-E₁-e₅-E₂-e₄-e₃) and GeSe₂ (GeSe₂-e₇-E₃-U₂-e₆-E₂-e₄-GeSe₂). The largest fields correspond to the primary crystallization of Ag₈GeSe₆ and GeSe₂. The fields of the primary crystallization are separated by 13 monovariant curves of binary eutectic and peritectic reactions and 14 invariant points (Table 7).

The system undergoes five quaternary invariant reactions (Table 7): transition L_U1 + Ag₂Se ↔ Ag₈GeSe₆ + Ag₃AsSe₃ at 650 K (377 °C), eutectic L_E1 ↔ Ag₈GeSe₆ + Ag₃AsSe₃ + HTM-AgAsSe₂ at 640 K (367 °C), eutectic L_E2 ↔ Ag₈GeSe₆ + GeSe₂ + HTM-AgAsSe₂ at 630 K (357 °C), transition L_U2 + HTM-AgAsSe₂ ↔ AgAs₃Se₅ + GeSe₂ at 634 K (361 °C) and eutectic L_E3 ↔ GeSe₂ + As₂Se₃ + AgAs₃Se₅ at 600 K (327 °C).

4 Conclusions and Future Work

Phase equilibria in the Ag₂Se–GeSe₂–As₂Se₃ system were investigated for the first time by XRD and MSA. At 513 K (240 °C) four ternary compounds Ag₈GeSe₆, Ag₃AsSe₃, AgAsSe₂, AgAs₃Se₅ were identified and an isothermal section of Ag₂Se–GeSe₂–As₂Se₃ system was constructed. The liquidus surface projection of the quasi-ternary system Ag₂Se–GeSe₂–As₂Se₃ was plotted according to the investigation of the vertical sections Ag₈GeSe₆–Ag₃AsSe₃, Ag₈GeSe₆–As₂Se₃, GeSe₂–AgAs₃Se₅ and phase diagrams Ag₂Se–As₂Se₃, Ag₈GeSe₆–AgAsSe₂, GeSe₂ – AgAsSe₂. There are seven fields of the primary crystallization of Ag₂Se, Ag₃AsSe₃, HTM-AgAsSe₂, AgAs₃Se₅, As₂Se₃, Ag₈GeSe₆ and GeSe₂ on the liquidus surface projection with the largest fields of Ag₈GeSe₆ and GeSe₂ compounds. In the investigated system there are two transition reactions: L_U1 + Ag₂Se ↔ Ag₈GeSe₆ + Ag₃AsSe₃ at 650 K (377 °C), L_U2 + HTM-AgAsSe₂ ↔ AgAs₃Se₅ + GeSe₂ at 634 K (361 °C) and three eutectic ones: L_E1 ↔ Ag₈GeSe₆ + Ag₃AsSe₃ + HTM-AgAsSe₂ at 640 K (367 °C), L_E2 ↔ Ag₈GeSe₆ + GeSe₂ + HTM-AgAsSe₂ at 630 K (357 °C) and L_E3 ↔ GeSe₂ + As₂Se₃ + AgAs₃Se₅ at 600 K (327 °C).

This work was performed as part of the effort to gather more data for a thermodynamic assessment of the Ag₂Se–B^IVSe₂–As₂Se₃ systems, where B^IV–Si, Ge, Sn, which is still in progress.