Phase Equilibria in the Quasi-Ternary System Cu₂Se-In₂Se₃-CuI and the Crystal Structure of the A^IB^III₂X^VI₃Y^VII Compounds, Where A^I-Cu, Ag; B^III-Ga; X^VI-Cl, Br, I; Y^VII-S, Se, Te

Abstract

The quasi-ternary system Cu₂Se-In₂Se₃-CuI has been investigated by x-ray diffraction and differential thermal analysis. The isothermal section at 770 K and the liquidus surface projection of the system have been built. For the first time, the primary crystallization regions, and the coordinates of the invariant and monovariant equilibria have been determined. In the system, the regions of the solid solutions based on the binary, ternary, and quaternary compounds have been investigated. The formation of the CuIn₂Se₃I quaternary compound, which melts congruently at 1213 K and has a homogeneity region of 15 and 9 mol.% CuI within the composition triangle has been established. For the first time, the crystal structures of CuGa₂Te₃I and AgGa₂Te₃Br compounds have been studied using a powder method. They crystallize in the tetragonal symmetry, Space Group I-4, a = 5.9147(4) Å, c = 11.952(2) Å for CuGa₂Te₃I; a = 6.2977(3) Å, c = 11.9473(7) Å for AgGa₂Te₃Br compound, respectively. The connection of their structures with the structures of the defective diamond-like semiconductors has been discussed.

1 Introduction

The multiphase compositions used in semiconductor devices require the study of phase equilibria in multicomponent systems. Therefore, the Cu₂Se-In₂Se₃-CuI system of the mixed 2-anion chalcogen halide type has been chosen for this study. The quasi-ternary system is formed by binary halides and chalcogenides, which already have vast practical application, in particular A^IY^VII, where the number of cations is equal to the number of anions (A^I-Cu, Ag; Y^VII-Cl, Br, I), cation excess compound A^I₂X^VI, where A^I-Cu, Ag; X^VI-S, Se, Te, and cation-defective B^III₂X^VI₃ compounds, where B^III-Ga, In. Since the compounds formed in this system belong to diamond-like semiconductors of the A^IB^IIIX^VI₂ and A^IY^VII types, it will be interesting to investigate the interaction between chalcogenides and halides. The construction of the quasi-binary phase diagrams and liquidus surface projection of the quasi-ternary system allows for determining the regions of the primary crystallization of the compounds and the coordinates of the invariant and monovariant equilibria. Previously, we partially investigated the system Cu₂Se-In₂Se₃-CuI and established a character of the CuIn₂Se₃I quaternary compound formation in the In₂Se₃-CuI system.^[1] In this work, we present additional results obtained for 3 vertical sections (Cu₃InSe₃-″Cu₃SeI″; ″Cu₃SeI″-CuIn₂Se₃I; CuIn₃Se₅-CuIn₂Se₃I), results for the isothermal section at 770 K and the liquidus surface projection of the quasi-ternary system Cu₂Se-In₂Se₃-CuI. The authors of Ref 2, 3 studied quaternary compounds A^IB^III₂X^VI₃Y^VII, where A^I-Cu, Ag; B^III-In; X^VI-S, Se, Te; Y^VII-Cl, Br, I. Phases with structures of the defective zincblende, spinel, and defective NaCl, respectively, were obtained. For example, it was established that the CuIn₂Se₃I compound crystallizes in the cubic symmetry, Space Group (SG) F-43 m, a = 5.781(1) Å.^[2] In our work, we decided to investigate the crystal structures of the other quaternary compounds of such type, where B^III-Ga. Some of them were investigated by us previously, like CuGa₂S₃I,^[4] CuGa₂Se₃I,^[4] AgGa₂S₃Cl,^[5] AgGa₂Se₃Cl,^[6] AgGa₂Se₃Br,^[6] AgGa₂Te₃Cl,^[7] AgGa₂Te₃I.^[8] In this work, CuGa₂Te₃I and AgGa₂Te₃Br compounds were synthesized to investigate their crystal structures for a better understanding of the nature of the quaternary compounds. Their crystal structures and connection with known defective semiconductors were discussed.

2 Method of Synthesis

Simple substances of high purity (Cu-99.99, In-99.99, Se-99.997 wt.%) were used to synthesize all alloys of the investigated systems. Cuprous iodide was obtained by the interaction of CuSO₄·5H₂O with NaI taken in stoichiometric amounts in the presence of SO₂. During the interaction of the solutions, a brown precipitate was formed, which, after passing SO₂, turned into a white precipitate of cuprous iodide. The precipitate was filtered on a Buchner funnel and washed with water to remove SO₄²⁻ ions. It was washed with ethanol and diethyl ether to prevent the product from oxidizing. The ampoules with prepared weights were evacuated to a residual pressure of 1.33·10⁻² Pa and sealed using a gas-oxygen burner. Before the synthesis, pumped and sealed ampoules were placed in metal tubes. The synthesis was carried out in the automatic furnaces ″Thermodent″ with a furnace temperature regulation system of ± 5 K. Samples were synthesized as follows: heating to 670 K at a rate of 10 K/h, annealing for 48 h; heating to a maximum temperature of 1070 K, holding for 48 h; cooling to a temperature of 770 K at a rate of 20 K/h and homogenizing annealing was carried out for 300 h to establish the equilibrium state of the synthesized alloys.^[1] They were investigated by x-ray diffraction (XRD) method on DRON 4-13 diffractometer (CuKα radiation) and differential thermal analysis (DTA) (″Thermodent″ H307/1 furnace with a PDA-1 XY-recorder, Pt/Pt-Rh thermocouple). To study the crystal structure of CuGa₂Te₃I and AgGa₂Te₃Br, high purity Cu-99.99, Ag-99.99, Ga-99.999 and Te-99.99 wt.% were used. AgBr was obtained by reacting the AgNO₃ water solution with the KBr solution.

3 Results and Discussion

3.1 The Isothermal Section of the Quasi-Ternary System Cu₂Se-In₂Se₃-CuI at 770 K (497 °C)

The isothermal section of the quasi-ternary system Cu₂Se-In₂Se₃-CuI at 770 K (497 °C) was constructed based on the results of x-ray diffraction analysis (Fig. 1). According to the obtained data, the CuI compound crystallizes in cubic symmetry, SG $Fm\overline{3}m$, a = 6.1512(3) Å, which agrees well with Ref 9 (Fig. 2). In the system In₂Se₃-CuI, the existence of the quaternary compound CuIn₂Se₃I, which crystallizes in cubic symmetry, is confirmed, SG $F\overline{4}3m$, a = 5.8012(1) Å, which is in good agreement with Ref 2. Cu₂Se is indexed as monoclinic symmetry, SG C2/c, a = 7.1379 Å, b = 12.3823 Å, c = 27.3904 Å, β = 94.308°.^[10] In₂Se₃ is indexed as hexagonal symmetry, SG P6₃/mmc, with unit cell periods a = 4.0242(5) Å, c = 19.251(2) Å, which agrees well with Ref 11. The preliminary results of the x-ray phase analysis of the Cu₂Se-In₂Se₃ system were described in our previous work.^[12,13,14] The following ternary compounds were established: CuInSe₂, SG $I\overline{4}2d$, a = 5.7855(2) Å, c = 11.551(3) Å; CuIn₃Se₅, SG $P\overline{4}2c$, a = 5.7602(1) Å, c = 11.515(3) Å; CuIn₇Se₁₁, SG P3m1, a = 4.0263(2) Å, c = 16.2992(7) Å; and layered CuIn₅Se₈ and CuIn₁₁Se₁₇ compounds with unknown structures. The largest single-phase regions in Cu₂Se-In₂Se₃-CuI are based on CuInSe₂ and CuIn₂Se₃I compounds. It is known that CuIn₂Se₃I is a cation defect compound, with a ratio of cations to anions of 3:4. In our opinion, this affects the largest extent of the solid solution based on CuIn₂Se₃I towards defective compounds CuIn₃Se₅, CuIn₅Se₈, CuIn₇Se₁₁, CuIn₁₁Se₁₇, but not to the CuInSe₂ or CuI side, which have the same number of cations and anions. Solubility based on all other binary and ternary compounds is negligible. Between the single-phase regions there are regions of 2-phase equilibria, which divide the system into corresponding 3-phase fields.

Fig. 1

Isothermal section of the quasi-ternary system Cu₂Se-In₂Se₃-CuI at 770 K

Fig. 2

The diffractograms of the samples of the system In₂Se₃-CuI in the region of 50-100 mol.% CuI

3.2 The Liquidus Surface Projection of the Cu₂Se-In₂Se₃-CuI Quasi-Ternary System

The liquidus surface projection (Fig. 3) was built based on the results of the DTA analyses of more than 150 samples (Fig. 4). It consists of fields of primary crystallization of α-solid solution based on HTM-Cu₂Se (e₂-U₁-U₂-p₁-u (e₂-U₁-e₃-Cu₃InSe₃-e₂), ζ-solid solution based on HTM-CuInSe₂ (e₃-U₁-U₂-E₁-m₁-E₂-U₃-e₁-U₄-p₄-CuInSe₂-e₃), ε-solid solution based on LTM-CuInSe₂ (m₁-E₂-p₂-E₁-m₁), η-solid solution based on HTM-CuI (p₁-U₂-E₁-p₂-E₂-U₃-p₃-CuI-p₁), δ-solid solution based on 1-HTM-In₂Se₃ (e₄-E₃-e₅-In₂Se₃-e₄), θ-solid solution based on CuIn₂Se₃I (e₅-E₃-U₅-U₄-e₁-U₃-p₃-CuIn₂Se₃I-e₅), compounds CuIn₅Se₈ (p₄-U₄-U₅-p₅-p₄), CuIn₁₁Se₁₇ (p₅-U₅-E₃-e₄-p₅). These areas are separated by 19 monovariant curves and 19 nonvariant points. The systems CuInSe₂-CuI and CuInSe₂-CuIn₂Se₃I are quasi-binary (Fig. 5, 6, 7, 8)^[1] and divide the investigated quasi-ternary system into 3 subsystems Cu₂Se-CuInSe₂-CuI, CuInSe₂-CuIn₂Se₃I-CuI and CuInSe₂-CuIn₂Se₃I-In₂Se₃. To simplify the reading of the following text the formulas of the compounds and their polymorphic modifications on which the solid solutions are based will be indicated in parentheses. Three nonvariant transition reactions take place in the first subsystem (Fig. 9). The first one, L_U1 + Cu₃InSe₃ ↔ ζ(HTM-CuInSe₂) + α(HTM-Cu₂Se), takes place at 1185 K (912 °C). Curves of monovariant processes: L_e2-U1 ↔ Cu₃InSe₃ + α(HTM-Cu₂Se), L_e3-U1 ↔ ζ(HTM-CuInSe₂) + Cu₃InSe₃ converge to the point U₁. The second nonvariant transition reaction L_U2 + α(HTM-Cu₂Se) ↔ η(HTM-CuI) + ζ(HTM-CuInSe₂) occurs at 1010 K (737 °C). Curves of monovariant processes converge to the point U₂: L_U1-U2 ↔ α(HTM-Cu₂Se) + ζ(HTM-CuInSe₂), L_p1-U2 ↔ η(HTM-CuI) + α(HTM-Cu₂Se). Point E₁ lies on the plane of the nonvariant eutectic process L_E1 ↔ ε(LTM-CuInSe₂) + η(HTM-CuI) + ζ(HTM-CuInSe₂), which takes place at 978 K (705 °C). Curves of monovariant processes converge to this nonvariant point: L_U2-E1 ↔ η(HTM-CuI) + ζ(HTM-CuInSe₂), L_m1-E1 ↔ ζ(HTM-CuInSe₂) + ε(LTM-CuInSe₂) and L_p2-E1 ↔ η(HTM-CuI) + ε(LTM-CuInSe₂). As the temperature decreases, another nonvariant eutectoid process ζ(HTM-CuInSe₂) ↔ ε(LTM-CuInSe₂) + η(HTM-CuI) + α(HTM-Cu₂Se) occurs in the subsolidus region at 890 K (617 °C). Below it, the alloys contain crystals of 3 phases: ε(LTM-CuInSe₂), η(HTM-CuI), α(HTM-Cu₂Se), which agrees with Fig. 1.

Fig. 3

The liquidus surface projection of the quasi-ternary system Cu₂Se-In₂Se₃-CuI

Fig. 4

Phase compositions of the synthesized samples of the quasi-ternary system Cu₂Se-In₂Se₃-CuI

Fig. 5

Phase diagram of CuInSe₂-CuI system: 1−L, 2−L + ζ, 3−L + ε, 4−L + η, 5−ζ, 6−ζ + ε, 7−ε, 8-η − ε, 9-η, with ζ and ε-solid solutions based on HTM-CuInSe₂ and LTM-CuInSe₂, accordingly, η-solid solution based on HTM-CuI^[1]

Fig. 6

Some diffractograms of the samples of the CuInSe₂-CuI system.

Fig. 7

Phase diagram of CuInSe₂-CuIn₂Se₃I system: 1−L, 2−L + ζ, 3−L + θ, 4−ζ, 5−ζ + θ, 6−θ, 7−ζ + ε, 8−ε, 9−ε + θ, with ζ-solid solution based on HTM-CuInSe₂, ε-solid solution based on LTM-CuInSe₂, θ-solid solution based on CuIn₂Se₃I^[1]

Fig. 8

Some diffractograms of the samples of the CuInSe₂-CuIn₂Se₃I system

Fig. 9

Scheil reaction scheme of the quasi-ternary system Cu₂Se-In₂Se₃-CuI

In the subsystem CuInSe₂-CuIn₂Se₃I-CuI the nonvariant process L_U3 + θ(CuIn₂Se₃I) ↔ η(HTM-CuI) + ζ(HTM-CuInSe₂) takes place at 1000 K (727 °C). Further, crystallization is completed by the nonvariant eutectic process L_E2 ↔ η(HTM-CuI) + ε(LTM-CuInSe₂) + ζ(HTM-CuInSe₂) at 975 K (702 °C), and in the subsolidus region at 900 К (627 °C) the eutectoid process ζ(HTM-CuInSe₂) ↔ η(HTM-CuI) + ε(LTM-CuInSe₂) + θ(CuIn₂Se₃I) takes place, and the alloys contain the corresponding 3 phases (Fig. 1). In the subsystem CuInSe₂-CuIn₂Se₃I-In₂Se₃ the following nonvariant processes take place: L_U4 + ζ(HTM-CuInSe₂) ↔ θ(CuIn₂Se₃I) + CuIn₅Se₈ at 1123 K (850 °C); L_U5 + CuIn₅Se₈ ↔ θ(CuIn₂Se₃I) + CuIn₁₁Se₁₇ at 1073 K (800 °C), then crystallization completes through the nonvariant eutectic process L_E3 ↔ θ(CuIn₂Se₃I) + CuIn₁₁Se₁₇ + δ(1-HTM-In₂Se₃) at 1055 K (782 °C).

Part of the compounds in the system Cu₂Se-In₂Se₃ are formed by solid-phase reactions, namely CuIn₃Se₅ and CuIn₇Se₁₁. Therefore, there are no regions of the primary crystallization on the liquidus surface projection with them. The Scheil reaction scheme representing the sequence of all invariant reactions is shown on Fig. 9.

3.3 The Vertical Section Cu₃InSe₃-″Cu₃SeI″

The vertical section Cu₃InSe₃-″Cu₃SeI″ was built based on the DTA and x-ray phase analysis results. It passes through 2 surfaces of the primary crystallization of the compound Cu₃InSe₃ and α-solid solution, respectively (Fig. 10). The 3-phase space of secondary crystallization of the binary eutectic L ↔ α + Cu₃InSe₃ descends to the plane of the nonvariant process L_U1 + Cu₃InSe₃ ↔ α + ζ, which is shown with a horizontal line at 1185 K (912 °C). There are 3-phase spaces of solid phase decomposition Cu₃InSe₃ ↔ α + ζ and monovariant eutectic process L ↔ ζ + α below the line at 1185 K (912 °C). The 3-phase space of the eutectic process descends to the plane of the nonvariant process L_U2 + α ↔ η + ζ at 1010 K (737 °C), which results in the disappearance of the liquid. At 890 K (617 °C), this section intersects the plane of the eutectoid reaction: ζ(HTM-CuInSe₂) ↔ ε(LTM-CuInSe₂) + η(HTM-CuI) + α(HTM-Cu₂Se), below which the alloys are 3-phase ε + η + α in agreement with Fig. 1.

Fig. 10

The vertical section Cu₃InSe₃-″Cu₃SeI″: 1−L; 2−L + α; 3−L + Cu₃InSe₃; 4−L + α + Cu₃InSe₃; 5−Cu₃InSe₃; 6−Cu₃InSe₃ + α; 7−Cu₃InSe₃ + α + ζ; 8−α + ζ; 9−L + α + ζ; 10−L + α + η; 11−L + η + ζ; 12−α + ζ + ε; 13−α + ε; 14−α + η + ε; 15−η + α, with ζ-solid solution based on HTM-CuInSe₂, ε-solid solution based on LTM-CuInSe₂, α-solid solution based on Cu₂Se, η-solid solution based on CuI

3.4 The Vertical Section ″Cu₃SeI″-CuIn₂Se₃I

″Cu₃SeI″-CuIn₂Se₃I was built based on the DTA, x-ray phase analysis results and passes through 2 subsystems Cu₂Se-CuInSe₂-CuI and CuInSe₂-CuIn₂Se₃I-CuI (Fig. 11). The liquidus of the section is represented by the curves of the primary crystallization of α, ζ, θ-solid solutions. In the subsystem Cu₂Se-CuInSe₂-CuI, the section crosses the plane of the nonvariant reaction L_U2 + α ↔ η + ζ at 1010 K (737 °C), resulting in one region where the liquid disappears for some of the compositions (field 14, the 3-phase (α + η + ζ) region) while in the other region the crystals of α-solid solution disappear. Therefore, below the horizontal at 1010 K (737 °C) is field 12, where the monovariant eutectic process L ↔ η + ζ occurs. This field, together with the 3-phase field 10 (L + ε + η) of the monovariant eutectic process L ↔ ε + η, descends to the plane of nonvariant eutectic process L_E1 ↔ ε + η + ζ at 978 K (705 °C). At 890 K (617 °C), this section intersects the plane of the nonvariant eutectoid reaction ζ(HTM-CuInSe₂) ↔ ε(LTM-CuInSe₂) + η(HTM-CuI) + α(HTM-Cu₂Se). Below this plane, the alloys are 3-phase and contain crystals of ε, η, α -solid solutions (field 17), which agrees with the isothermal section in Fig. 1.

Fig. 11

The vertical section ″Cu₃SeI″-CuIn₂Se₃I: 1−L; 2−L + α; 3−L + ζ; 4−L + θ; 5−L + θ + ζ; 6−θ + ζ; 7−ζ + η + θ; 8−η + ε + ζ; 9−L + ζ + η; 10−L + ε + η; 11−L + ζ + α; 12−L + ζ + η; 13−ζ + η; 14−α + ζ + η; 15−L + α + η; 16−α + η; 17−α + ε + η; 18−ζ + ε + η; 19−η + ε; 20−η + ε + θ; 21−η + θ; 22−θ, with ζ-solid solution based on HTM-CuInSe₂, ε-solid solution based on LTM-CuInSe₂, θ-solid solution based on CuIn₂Se₃I, α-solid solution is based on Cu₂Se, η-solid solution based on CuI.

In the subsystem CuInSe₂-CuIn₂Se₃I-CuI at 1000 K (727 °C), the section intersects the plane of the nonvariant process L_U3 + θ ↔ η + ζ, which results in the disappearance of the liquid only in a part of the alloys of the section, that is why field 7 contains 3 phases: θ + η + ζ. In the other part of the section, the nonvariant transition reaction L_U3 + θ ↔ η + ζ results in the disappearance of the θ-solid solution. Therefore, below the horizontal at 1000 K (727 °C) is field 9, where the monovariant eutectic process L ↔ η + ζ takes place, which together with the 3-phase field L + ε + η of the monovariant eutectic process L ↔ ε + η descends to the plane of the nonvariant eutectic process L ↔ η + ε + ζ at 975 K (702 °C). The vertical section intersects the plane of the nonvariant eutectoid decomposition ζ(HTM-CuInSe₂) ↔ η(HTM-CuI) + ε(LTM-CuInSe₂) + θ(CuIn₂Se₃I) at 900 K (627 °C). Below this plane, the alloys are 3-phase and contain the crystals of η, ε, θ-solid solutions (field 20), which agrees with Fig. 1. The region between fields 7 and 8, is 2-phase η + ζ, since the process L_U3 + θ ↔ η + ζ at 1000 K (727 °C) for the composition of 30 mol.% ″Cu₃SeI″-70 mol.% CuIn₂Se₃I ends with the disappearance of the liquid and the crystals of θ-solid solution because this composition coincides with the connecting horizontal of the plane of the nonvariant process L_U3 + θ ↔ η + ζ.

3.5 The Vertical Section CuIn₃Se₅-CuIn₂Se₃I

The section was built based on the DTA results and x-ray phase analysis. The the regions with liquid (Fig. 12) are represented by the areas of primary crystallization of ζ-solid solution based on HTM-CuInSe₂ and θ-solid solution based on CuIn₂Se₃I. The section intersects the plane of the nonvariant process L_U4 + ζ ↔ θ + CuIn₅Se₈ at 1123 K (850 °C) where for compositions in this section the liquid disappears. In the subsolidus region, 2 planes of nonvariant processes ζ ↔ θ + CuIn₅Se₈ + Cu₂In₄Se₇ (1080 K) (807 °C), CuIn₅Se₈ + Cu₂In₄Se₇ ↔ ξ + θ (1030 K) (757 °C) intersect with the section, where ξ is solid solution based on CuIn₃Se₅. In alloys of this section, this results in the disappearance of CuIn₅Se₈ and Cu₂In₄Se₇ crystals, so below 1030 K (757 °C), crystals of ξ- and θ-solid solutions are present which agrees with Fig. 1. As the temperature decreases to 770 K (497 °C), the limit of ξ -solid solution decreases to 3 mol.% of the second component. The parameters of the unit cell increase a little from a = 5.7602(1) Å, c = 11.515(3) Å for CuIn₃Se₅ till a = 5.7657(2) Å, c = 11.525(4) Å for the composition of 95 mol.% CuIn₃Se₅-5 mol.% CuIn₂Se₃I. The region of θ-solid solution narrows to 17 mol.% CuIn₃Se₅ with a decrease in temperature to 770 K (497 °C). The parameter of the unit cell decreases from a = 5.8012(1) Å for CuIn₂Se₃I till a = 5.7722(3) Å for the composition of 20 mol.% CuIn₃Se₅-80 mol.% CuIn₂Se₃I.

Fig. 12

The vertical section CuIn₃Se₅-CuIn₂Se₃I: 1−L, 2−L + ζ, 3−L + ζ + θ, 4−L + θ, 5−ζ, 6−CuIn₅Se₈ + ζ, 7−L + CuIn₅Se₈ + ζ, 8−θ + CuIn₅Se₈ + ζ, 9−ζ + θ, 10−θ, 11−ζ + θ, 12−Cu₂In₄Se₇ + θ, 13−Cu₂In₄Se₇ + ζ + θ, 14−Cu₂In₄Se₇ + ζ, 15−Cu₂In₄Se₇ + CuIn₅Se₈ + ζ, 16−CuIn₅Se₈ + Cu₂In₄Se₇, 17−CuIn₅Se₈ + Cu₂In₄Se₇ + θ, 18−Cu₂In₄Se₇ + CuIn₅Se₈ + CuIn₃Se₅, 19−Cu₂In₄Se₇ + CuIn₃Se₅, 20−CuIn₃Se₅ (ξ), 21−CuIn₃Se₅ + θ, with ζ-solid solution based on HTM-CuInSe₂, θ-solid solution based on CuIn₂Se₃I

3.6 Crystal Structure of A^IB^III ₂X^VI ₃Y^VII Compounds, Where A^I-Cu, Ag; B^III-Ga; X^VI-Cl, Br, I; Y^VII-S, Se, Te

When the In₂Se₃-CuI system was investigated in Ref 1, the formation of the quaternary compound CuIn₂Se₃I, which belongs to a larger group of compounds with general formula A^IB^III₂X₃Y (A^I-Cu, Ag; B^III-Ga, In; X-S, Se, Te; Y-Cl, Br, I) was established. Replacing Cu⁺, In³⁺, Se²⁻ and I⁻ by Ag⁺, Ga³⁺, Te²⁻, and Br⁻ the quaternary compounds CuGa₂Te₃I, AgGa₂Te₃Br are obtained, for which the crystal structures were studied using the powder method. The measurement conditions and the calculation results are shown in Tables 1, 2, 3, 4, Fig. 13, 14. The coordinates and the isotropic thermal parameters of atoms in the structures of the CuGa₂Te₃I and AgGa₂Te₃Br are given in Tables 2 and 3. The interatomic distances and coordination numbers of the atoms are shown in Table 4. The Ga atoms occupy 2 Wyckoff positions 2a and 2c, have tetrahedral coordination and occupy these positions to 80% (Tables 2, 3; Fig. 15). 2 Wyckoff positions (2b, 2d) are occupied by the statistical mixtures M1 (Cu (Ag) + Ga) and M2 (Cu (Ag) + Ga), resulting in coordination polyhedron-tetrahedron [M1 4Te], [M2 4Te]. The statistical mixtures M1 and M2 are 50% Cu (Ag) and 20% Ga, and 30% of positions are not occupied.

Table 1 Results of crystal structure refinement of the CuGa₂Te₃I, AgGa₂Te₃Br compounds

Table 2 Refined coordinates of atoms and their isotropic thermal parameters in CuGa₂Te₃I

Table 3 Refined coordinates of atoms and their isotropic thermal parameters in AgGa₂Te₃Br

Table 4 Interatomic distances and coordination numbers, C.N. of atoms in the CuGa₂Te₃I, AgGa₂Te₃Br structures

Fig. 13

Experimental (dots), calculated (solid) and difference (bottom scale) diffractogram of the CuGa₂Te₃I compound

Fig. 14

Experimental (dots), calculated (solid) and difference (bottom scale) diffractogram of the AgGa₂Te₃Br compound.

Fig. 15

The structure of the unit cell and coordination polyhedra of statistical mixtures M1, M2 and Ga atoms in the structure of AgGa₂Te₃Br, where blue balls-Ga1, Ga2; grey balls-M1, M2; red balls-Anion

As previously mentioned, chalcohalides of the type A^IC^III₂X^VI₃Y^VII belong to cation-deficient compounds with a ratio of cations to anions of 3:4. The structure can be represented as a 3-layer packing of anions in which ¾ of the tetrahedral vacancies are occupied by C^III cations, for example, Ga or In. Statistical mixtures of M1 (Cu(Ag) + Ga) and M2 (Cu(Ag) + Ga), and ¼ of the voids remain vacant.^[15] According to Ref 16, other compounds have a cation:anion ratio of 3:4, for example, AgIn₅Se₈, AgZnPS₄, Cu₂HgI₄, and Hg₂SnSe₄. A similar ratio have CdGa₂Se₄ and β-Ag₂HgI₄, structural type CdAl₂S₄, both crystallize in the SG I-4. In the specified structures of the studied compounds A^IC^III₂X^VI₃Y^VII and CdGa₂Se₄, β-Ag₂HgI_4, a similar arrangement of cations is observed (Table 5), but in A^IC^III₂X^VI₃Y^VII the A^I atoms half occupy 2 positions 2b, 2d. The C^III cations are statistically in the same positions as A^I, filling them to 20%. The C^III positions, 2a and 2c, remain partially occupied at 80%. In the compounds CdGa₂Se₄ and β-Ag₂HgI₄, position 2a is occupied by a divalent cation, and position 2c and 2b-by other cations in the structure (Ga and Ag, respectively). The vacancy occupies the 2d position in these structures.

Table 5 Coordinates of atoms in the structures of ternary and quaternary compounds

The composition of the cation-deficient compounds with a ratio of cations to anions of 3:4 can be represented by the formula K_n-u□_uA_n, where K-cations, □-vacancies, A-anions, and u-the first letter of the word ″unoccupied″, which indicates the number of vacancies. For these compounds VEC > 4, in particular, AgIn₅Se₈, AgZnPS₄, Cu₂HgI₄, and Hg₂SnSe₄, VEC = 4.571.^{[17, 18]} The exact value is obtained for the quaternary chalcohalides A^IC^III₂X^VI₃Y^VII (1⋅1 + 2⋅3 + 3⋅6 + 1⋅7)/1 + 2 + 3 + 1 = 4.571. If we consider the vacancy as an atom with zero valence, then we get for the compounds A^IC^III₂□X^VI₃Y^VII 1⋅1 + 2⋅3 + 1⋅0 + 3⋅6 + 1⋅7)/1 + 2 + 1 + 3 + 1 = 4, which means that their structures are tetrahedral when the cations are surrounded by the 4 nearest anions located at the vertices of the tetrahedron.

4 Conclusions and Future Work

The quasi-ternary system Cu₂Se-In₂Se₃-CuI formed by binary halides and chalcogenides, which already have wide practical applications, has been investigated by x-ray and differential thermal methods. The isothermal section at 770 K (497 °C) and the liquidus surface projection of the system have been built. The regions of primary crystallization, types, and coordinates of the invariant and monovariant equilibria have been established for the first time. It allows us to know the areas of primary crystallization of the compounds, types and the coordinates of the invariant and monovariant equilibria. In the system, the regions of the solid solutions based on the binary, ternary, and quaternary compounds have been investigated. The formation of the CuIn₂Se₃I quaternary compound, which melts congruently at 1213 K (940 °C) and has a homogeneity region of 15 and 9 mol.% CuI in the composition triangle, has been established. For the first time, the crystal structures of CuGa₂ITe₃ and AgGa₂BrTe₃ compounds, which belong to the cation-deficient compounds A^IC^III₂X^VI₃Y^VII with a ratio of cations to anions of 3:4, have been studied using a powder method. They crystallize in the tetragonal symmetry, SG I-4, a = 5.9147(4) Å, c = 11.952(2) Å for CuGa₂ITe₃; a = 6.2977(3) Å, c = 11.9473(7) Å for AgGa₂BrTe₃ compound. The connection of their structures with the structures of the defect diamond-like semiconductors has been discussed, and a conclusion about their semiconducting properties has been made.

According to the results, future work will be on growing the single crystals of the quaternary compound CuIn₂Se₃I and solid solutions formed in the system to investigate their semiconducting properties.