Phase Equilibria in the Cu₂Se–GeSe₂–SnSe₂ System

Abstract

Phase equilibria in the Cu₂Se–GeSe₂–SnSe₂ quasi-ternary system were studied by differential thermal analysis (DTA) and X-ray powder diffraction analysis. A series of polythermal sections, the 750-K isothermal section of the phase diagram, and the liquid surface projection were plotted. Primary crystallization and homogeneity areas of phases were determined, as well as the characters and types of invariant and monovariant equilibria. Extensive Cu₂GeSe₃-base and Cu₂SnSе₃-base solid solutions were found to exist in the system along the Cu₂GeSe₃–Cu₂SnSe₃ section.

INTRODUCTION

Copper chalcogenides and their based phases are among the most popular subject matters of research in semiconductor materials science; they have many functional properties showing a potential for use in several fields, such as photoelectrochemical, photocatalytic, and solar cells [1–5]. These phases attract increasing attention as promising thermoelectric materials due to their high efficiency, tunable transport properties, as well as the low toxicity and availability of their constituents [6–11]. In addition, copper chalcogenides are mixed electron–ionic conductors and, due to the high mobility of “liquid-like” copper ions, they exhibit record-breaking values of cationic conductivity (up to ∼3 Ω^–1 cm^–1) and ion diffusion (~10^–5 cm²/s) [12–14]. This makes them promising materials for ion-selective electrodes or solid electrolytes in the development of various types of electric batteries, sensors, etc. [12–19].

It is well known that an efficient strategy for optimizing functional properties of the material is to modify its composition and structure. In order to search for and design new materials and for a better understanding of the relationships among the composition, structure, and properties, one needs to have reliable data on the phase equilibria and thermodynamic properties of the relevant multicomponent systems [19–22].

In our prior works [23–27], we carried out similar diligent studies of complex systems involving copper chalcogenides; we found new phases and determined their primary crystallization and homogeneity areas.

Here, we will present new experimental data on phase equilibria in the Cu₂Se–GeSe₂–SnSe₂ quasi-ternary system (system A). The ternary phases formed in this system (Сu₈GeSe₆, Cu₂SnSe₃, and Cu₂GeSe₃) have extensively been studied as thermoelectric materials [11–13].

The terminal compounds (Cu₂Se, GeSe₂, and SnSe) and boundary quasi-binary constituents (Cu₂Se–GeSe₂, GeSe₂–SnSe₂, and Cu₂Se–SnSe₂) of the title system have been well characterized.

Cu₂Se is a compound melting congruently at 1403 K and undergoing polymorphic transition at 396 K [28]. This compound has a homogeneity area extending toward an excess of selenium, which has the largest extent (33.3–36.6 at % Se) at 800 K.

Germanium diselenide GeSe₂ and tin diselenide SnSe₂ melt with an open maximum at 1015 [28] and 948 K [29] respectively.

Crystallographic data for the binary and ternary compounds of system A appear in Table 1.

Table 1. Crystal data for compounds of the Cu₂Se–GeSe₂–SnSe₂ system

System Cu₂Se–GeSe₂ forms ternary compounds Cu₈GeSe₆ and Cu₂GeSe₃ by a pertectic reaction (at 1083 K) and a dystectic reaction (at 1054 K), respectively [32]. Cu₈GeSe₆ experiences phase transition at 333 K [32] (or at 328 K [33]). Its low-temperature phase LT-Cu₈GeSe₆ crystallizes in hexagonal structure [32, 33], while the high-temperature phase HT-Cu₈GeSe₆ crystallizes in cubic structure [34] (Table 1). Cu₂GeSe₃ has two polymorphs with the phase transition at 893 K [35–38]. The high-temperature phase forms an orthorhombic lattice, and the low-temperature phase forms a tetragonal lattice. Two eutectics solidify in the system with the coordinates 1033 K, 38 mol % GeSe₂ and 973 K, 88 mol % GeSe₂ [32].

System Cu₂Se–SnSe₂ was studied in [39–41], and the results of those studies were summarized in the survey [42]. The system forms one compound, Cu₂SnSe₃, which melts congruently at 968 K [40, 41] and forms eutectics with the terminal binary components. The eutectic coordinates are 84 mol % SnSe₂, 853 K and 22 mol % SnSe₂, 983 K [40]. The solubility in the terminal compounds is within 3 mol % (SnSe₂) and 10 mol % (Cu₂Se) [41]. Cu₂SnSe₃ was reported to crystallize in a sphalerite-type cubic structure [43, 44]. However, the structural study of a single-crystal sample [45] showed that the compound has a monoclinic structure.

System GeSe₂–SnSe₂, which is a boundary quasi-binary system, has a eutectic phase diagram with limited reciprocal solubility in the terminal selenides [46]. The highest solubility in GeSe₂ and SnSe₂ is ∼9.6 and 6 mol %, respectively, at the eutectic temperature (823 K). The eutectic melt contains 49 mol % SnSe₂.

EXPERIMENTAL

The terminal binary compounds (Cu₂Se, SnSe₂, and GeSe₂) and the terminal compounds (Cu₂GeSe₃, Cu₈GeSe₆, and Cu₂SnSe₃) of system A were prepared to be used in experiments.

The constituent elements used in experiments were high-purity samples purchased from Evochem Advanced Materials: granulated copper (Cu-00029, 99.9999%), germanium chips (Ge-00003, 99.9999%), granulated tin (Sn-00005, 99.999%), and granulated selenium (Sе-00002, 99.999%). The binary and ternary compounds were prepared by alloying the constituent elements in stoichiometric proportions in evacuated (to ~10^–2 Pa) and then sealed-off silica glass ampoules at temperatures slightly above the melting temperatures of the compounds to be prepared. Cu₂Se, GeSe₂, Cu₂GeSe₃, and Cu₈GeSe₆, whose melting temperatures far exceed the selenium boiling point (958 K [47]), were prepared in two-zone syntheses. An ampoule with the reaction mixture was heated in an inclined tube furnace to a temperature ∼50 K higher than the melting point of the compound to be synthesized (a hot zone). A portion of the ampoule (~8 cm) was outside the furnace and cooled by water to control the selenium vapor pressure and avoid the ampoule explosion (a cold zone). The ampoule was rotated around its longitudinal axis and vibrated for speeding up the reaction. After most selenium was reacted, the ampoule was completely inserted into the furnace, exposed in the hot zone for 1 h, and then slowly cooled. In view of the deviation of Cu₂Se at low temperatures [28], the as-synthesized sample was quenched from 1300 K in cold water in order for it acquired a homogeneous stoichiometric composition.

DTA and X-ray powder diffraction were used to verify the identity of every compound prepared. The melting temperature and unit cell parameters for every prepared compound coincided with the above-cited literature data (Table 1) within the measurement error bars (DTA: ±3 K at high temperatures and ±2 at low temperatures; XRD: ±0.0003 Å).

More than 60 alloys to be used in experiments were prepared by direct in vacuo alloying of the terminal compounds; their compositions lie along Cu₂GeSe₃–Cu₂SnSe₃, Cu₈GeSe₆–“Cu₈SnSe₆,” 0.4Cu₈GeSe₆–Cu₂SnSe₃, GeSe₂–0.5Cu₂SnSe₃, 0.5Cu₂GeSe₃–SnSe₂, and Cu₂Se–“Ge_0.5Sn_0.5Se₂” sections; some additional alloys were prepared beyond these sections (Fig. 1). In order to provide the conditions as close to equilibrium as possible, cast alloys that were prepared by rapid melt cooling were then annealed at 750 K for 500 h.

Fig. 1.

Polythermal sections (lines) and alloys (dots) studied in the Cu₂Se–GeSe₂–SnSe₂ system.

DTA experiments were carried out on a 404 F1 Pegasus System (Netzsch) differential scanning calorimeter. The heating rate was 10 K/min. In some cases, cooling curves were measured in order to determine the liquidus temperature. The DTA results were processed in the Netzsch Proteus Software. The temperature measurement accuracy was ±2°.

X-ray powder diffraction experiments were carried out at room temperature on a D8 Advance (Bruker) diffractometer using CuK_α1 radiation. X-ray diffraction patterns were indexed in the Topas V3.0 Software (Bruker).

RESULTS AND DISCUSSION

The joint processing of the experimental data set using the literature data on the Cu₂Se–GeSe₂ [32], Cu₂Se–SnSe₂ [39–42], and GeSe₂–SnSe₂ [46] boundary binary systems provided a self-consistent pattern of phase equilibria in the Cu₂Se–GeSe₂–SnSe₂ system.

Hereinafter in the text, tables, and figures, the following phase notations will be used:

• α and δ stand for HT-Cu₂Se-base and HT-Cu₈GeSe₆-base solid solutions, respectively;

• β₁ and β₂ stand for GeSe₂-base and SnSe₂-base solid solutions, respectively; and

• γ₁ and γ₂ stand for Cu₂GeSe₃-base and Cu₂SnSe₃-base solid solutions, respectively.

Quasi-Binary Section Cu₂GeSе₃–Cu₂SnSe₃

The DTA and XRD results on the Cu₂GeSе₃–Cu₂SnSe₃ system appear in Table 2. This system is a quasi-binary section of the quaternary system and has a peritectic-type phase diagram (Fig. 2). Peritectic equilibrium L ↔ γ₁ + γ₂ is acquired at 985 K. The peritectic point is at 60 mol % Cu₂SnSe₃.

Table 2. DTA data and unit cell parameters in the Cu₂GeSe₃–Cu₂SnSе₃ system

Fig. 2.

Cu₂GeSе₃–Cu₂SnSe₃ phase diagram.

The X-ray powder diffraction patterns of homogenized Cu₂GeSe₃–Cu₂SnSe₃ alloys verified the formation of extensive substitutional solid solutions. One can see in Fig. 3 that the powder diffraction pattern of a 20 mol % Cu₂SnSe₃ alloy is qualitatively identical to the diffraction pattern of the compound Cu₂GeSе₃. This implies that this alloy is a solid solution based on this compound (γ₁). The 60 and 80 mol % Cu₂SnSe₃ alloys have diffraction patterns identiсal to that of pure Cu₂SnSe₃ with reflection angles slightly shifting in response to changing composition. The diffraction patterns of these alloys are fully indexed in the cubic crystal system (space group F$\bar {4}$3m) with reflection angles slightly shifting in response to changing composition. The 40 mol % Cu₂SnSe₃ alloy is comprised of two phases; its diffraction pattern is the sum of the diffraction lines from the γ₁ and γ₂ phases. Noticeable is some broadening of the diffraction peaks from the solid solutions compared to those of the parent compounds. This is apparently owing to the crystal distortion caused by nonuniform Ge ↔ Sn substitution despite the long-term annealing. Table 2 lists the unit cell parameters of the alloys and parent compounds of the Cu₂GeSe₃–Cu₂SnSe₃ system calculated in the Topas V3.0 program; Fig. 4 displays their concentration dependecies. Figure 4 implies that the unit cell parameters of the γ₁ and γ₂ phases vary linearly in the range 0–35 and 50–100 mol % Cu₂SnSe₃, respectively, and in intemediate alloys they remain unchanged regardless of the general alloy composition. This impies that the end-members of mutually saturated γ₁ and γ₂ phases are 35 ± 1 and 50 ± 1 mol %, respectively.

Fig. 3.

X-ray powder diffraction patterns of Cu₂GeSe₃–Cu₂SnSe₃ alloys.

Fig. 4.

Unit cell parameters versus concnetration in Cu₂GeSe₃–Cu₂SnSe₃ alloys.

Having indexed the powder diffraction patterns of Cu₂GeSe₃ and its base solid solutions and those of Cu₂SnSe₃ and its solid solutions, we found that the former were fully indexed in the tetragonal crystal system and the latter in the cubic crystal system.

Equilibrium Solid-Phase Diagram at 750 K

The equilibrium solid-phase diagram at 750 K was plotted using XRD data for some equilibrium alloys inside the Cu₂Se–GeSe₂–SnSe₂ concnetration triangle and the phase diagrams of boundary quasi-binary systems [32, 39–42, 46]. Figure 5 shows that the system features extensive solid solutions based on the terminal ternary compounds along the Cu₂GeS₃–Cu₂SnSe₃ quasi-binary section. The solid-solution homogeneity areas are shaped as bands with a width of ∼1–2 mol % (for the γ₁ phase) and ∼3–5 mol % (for the γ₂ phase). This correlates with the Cu₂Se–GeSe₂ and Cu₂Se–SnSe₂ phase diagrams [32, 42].

Fig. 5.

750-K isotherm of the Cu₂Se–GeSe₂–SnSe₂ system.

Limited solid solutions based on GeSe₂ (β₁), SnSe₂ (β₂), and НТ-Cu₈GeSe₆ (δ) also exist in the system at 750 K. The β₁ and β₂ phases form narrow bands extending along the GeSe₂–SnSe₂ boundary quasi-binary system ∼1 mol % wide and 8 and 6 mol % long, respectively. The δ phase homogeneity area extends to Cu₈Ge_0.9Sn_0.1Se₆ along the Cu₈GeSe₆–Cu₈SnSe₆ section. The solubility in the low-temeprature Cu₂Se phase is insignificant.

The interaction of coexisting phases in the system gives rise to two-phase areas (β₁ + γ₁, β₂ + γ₂, β₂ + γ₁, γ₁ + γ₂, γ₁ + δ, γ₂ + δ, γ₂ + α, and α + δ) and three-phase areas (β₁ + β₂ + γ₂, β₁ + γ₁ + γ₂, γ₁ + γ₂ + δ, α + γ₂ + δ). The phase compositions of samples in these fields were verified by XRD.

Figure 6 displays exemplary powder diffraction patterns of three alloys chosen from various phase areas (alloys 1, 2, and 3 in Fig. 5). An inspection of these diffraction patterns shows that they are the sums of diffraction lines from phases that are in equilibrium according to Fig. 5.

Fig. 6.

X-ray powder diffraction patterns and phase compositions of selected Cu₂Se–GeSe₂–SnSe₂ alloys. Alloy 1: 60 mol % Cu₂Se + 9 mol % GeSe₂; alloy 2: 15 mol % Cu₂Se + 75 mol % GeSe₂; and alloy 3: 35 mol % Cu₂Se + 35 mol % GeSe₂.

Liquids Surface Projection

Figure 7 images the liquidus surface projection of the Cu₂Se–GeSe₂–SnSe₂ system consisting of six primary crystallization fields of solid solutions based on binary compounds (α, β₁, and β₂) and ternary compounds (γ₁, γ₂, and δ). These fields are demarcated by eutectic and peritectic curves. On curve р₂U₁ at point K, peritectic equilibrium L + γ₁ ↔ γ₂ transforms to eutectic equilibrium L ↔ γ₁ + γ₂. These equilibria involve solid solutions. Therefore, in principle this transition must be accompanied by the formation of some surface in the relevant three-phase area, where three-phase equilibrium would become two-phase equilibrium with a passive role of the third phase [48, 49]. Since the γ₁ and γ₂ homogeneity areas almost do not go beyond the Cu₂GeSe₃–Cu₂SnSe₃ quasi-binary section, this surface is most likely degenerates into a point (K).

Fig. 7.

Liquidus surface projection for the Cu₂Se–GeSe₂–SnSe₂ system. Primary crystallization fields: (1) α (Cu₂Se), (2) δ (Cu₈GeSe₆), (3) γ₁ (Cu₂GeSe₃), (4) γ₂ (Cu₂SnSe₃), (5) β₁ (GeSe₂), and (60) β₂ (SnSe₂).

The types and coordinates of invariant equilibria and the types and temperature ranges of monovariant equilibria appear in Tables 3 and 4, respectively.

Table 3. Invariant equilibria in the Cu₂Se–GeSe₂–SnSe₂ system

Table 4. Monovariant equilibria in the Cu₂Se–GeSe₂–SnSe₂ system

The Cu₂GeSe₃–Cu₂SnSe₃ quasi-binary section divides the Cu₂Se–GeSe₂–SnSe₂ concnetration triangle into a pair of independent subsystems: Cu₂Se–Cu₂GeSe₃–Cu₂SnSe₃ and GeSe₂–Cu₂GeSe₃–Cu₂SnSe₃. The former features two invariant transition reactions (U₂ and U₃), and the latter features one invariant transition equilibrium (U₁) and one eutectic equilibrium (Е). Noteworthy, the latter can be regarded the reciprocal system 1.5GeSe₂ + Cu₂SnSe₃ ↔ 1.5SnSe₂ + Cu₂GeSe₃. Figure 7 implies that it is a reversibly reciprocal system, that is, it has not a quasi-binary diagonal. This is owing to the fact that the terminal compounds do not play a decisive role in the distrobution of phase areas, but their base extensive solid-solutions areas do.

Polythermal Sections of the Phase Diagram

Below we will consider some polythermal sections of the phase diagram of the title system in the context of the liquidus surface projection (Fig. 7; Tables 3 and 4) and the 750-K solid-phase equilibrium diagram (Fig. 5).

Section Cu₈GeSe₆–“Cu₈SnSe₆” (Fig. 8) entirely lies in the α phase primary crystallization area. The primary crystallization of the α phase is followed by crystallization of the HT-Cu₈GeSe₆-base δ phase by peritectic reaction L + α ↔ δ and the crystallziation of α + γ₂ two-phase mixtures by eutectic reaction L ↔ α + γ₂ (Table 4; Fig. 7, curves p₁U₃ and U₃e₃).

Fig. 8.

Polythermal section Cu₈GeSe₆–“Cu₈SnSe₆.”

The specificity of this section is in the δ phase homogeneity area lying on its plane, so that peritectic reaction L + α ↔ δ fully consumes both initial phases simultaneously. It is for this reason that this peritectic reaction in Cu₈GeSe₆-rich compositions ends by the formation of δ solid solutions, which immediately border the L + α + δ three-phase area (Fig. 8). In 15–85 mol % compositions, crystallization ends by invariant transition reaction L + δ ↔ α + γ₂ (U₃) to form the α + δ + γ₂ three-phase subsolidus area.

Section 0.4Cu₈GeSe₆–Cu₂SnSe₃ (Fig. 9) crosses the primary crystallization fields of the α phase (0–15 mol % Cu₂SnSe₃), δ phase (15–50 mol % Cu₂SnSe₃), and γ₂ phase (50–100 mol % Cu₂SnSe₃). The α phase primary crystallization is followed by peritectic monovariant reaction L + α ↔ δ, which gives rise to the L + α + δ three-phase area. This reaction ends at ∼1040 K by an excess of the liquid phase and the formation of the L + δ two-phase area. In this area, crystallization ends by reaction L + δ ↔ γ₂ (Table 4, U₂U₃), and the δ + γ₂ two-phase area appears in the subsolidus.

Fig. 9.

Polythermal section 0.4Cu₈GeSe₆–Cu₂SnSe₃.

In the 45–80 mol % Cu₂SnSe₃ range, transition reaction L + δ ↔ α + γ₂ (Table 3, U₃) ends with an excess of the δ phase to form the α + δ + γ₂ three-phase area. In Cu₂SnSe₃-rich areas, crystallization ends by L ↔ γ₂ and L ↔ α + 훾₂ equilibria (Table 4, U₃e₃).

Section GeSe₂–0.5Cu₂SnSe₃ (Fig. 10) has a liquidus of three branches that correspond to the primary crystallization of the β₁, γ₁, and γ₂ phases. Their intersection points correspond to the onset of a monovariant peritectic reaction (p₂K) and a eutectic reaction (e₁Е). The L + β₁ + γ₁ and L + γ₁ + γ₂ three-phase areas are formed as a result of these reactions. In the 80–95 mol % GeSe₂ area, crystallization ends by peritectic reaction р₂K and to form the β₁ + γ₁ two-phase area.

Fig. 10.

Polythermal section GeSe₂–0.5Cu₂SnSe₃.

The γ₂ phase primary crystallization field continues by the eutectic monovariant scheme L ↔ β₂ + γ₂ (е₄U₁) and ends in the 5–20 mol % GeSe₂ range to form the β₂ + γ₂ two-phase area. In the 20–25 mol % GeSe₂ narrow concentration range, crystallization ends by transition reaction U₁ (845 K) to form the β₂ + γ₁ + γ₂ three-phase area.

The 805-K horizontal (Е) corresponds to the invariant solidification of the β₁ + β₂ + γ₁ ternary eutectic.

Section 0.5Cu₂GeSe₃–SnSe₂ (Fig. 11) crosses the primary crystallization fields of the γ₁, γ₂, and β₂ phases. Below liquidus, there are monovariant equilibria (е₁Е, U₁Е, KU₁, and е₄U₁) and invariant equilibria (U₁ and Е). When the crystallization is over, a series of two- and three-phase mixtures are formed by these reactions.

Fig. 11.

Polythermal section 0.5Cu₂SnSe₃–SnSe₂.

Section Cu₂Se–Ge_0.5Sn_0.5Se₂ (Fig. 12) passes through the primary crystallization fields of the α, δ, γ₁, and γ₂ phases; in the subsolidus, it crosses four three-phase areas. Phase equilibria along this section can easily be recognized by comparing Fig. 11 with Figs. 4 and 6. The Т–х diagram of this section clearly features transition invariant equilibria U₁, U₂, U₃, and Е (horizontals at 845, 965, 950, and 805 K, respectively). The 398-K horizontal corresponds to the α ↔ LТ-Cu₂Se polymorphic transition.

Fig. 12.

Polythermal section Cu₂Se–Ge_0.5Sn_0.5Se₂.

CONCLUSIONS

We have elucidated the full pattern of phase equilibria in the Cu₂Se–GeSe₂–SnSe₂ quasi-ternary system, involving the solid-phase diagram at 750 K, the liquidus surface projection, and a series of polythermal sections of the phase diagram. Extensive solid solutions have been found to exist in the system along the Cu₂GeSe₃–Cu₂SnSe₃ quasi-binary section. Primary crystallization and homogeneity areas of phases have been determined, as well as the characters and types of invariant and monovariant equilibria in the title system. The prepared new phases of variable composition are of interest as environmentally safe candidate thermoelectric materials.