Phase equilibrium and thermodynamic properties of silver-saturated compounds BiSI and Bi<Subscript>19</Subscript>S<Subscript>27</Subscript>I<Subscript>3</Subscript> of the AgI–Bi–Bi<Subscript>2</Subscript>S<Subscript>3</Subscript>–BiSI system

The phase composition of alloys in the Ag–Bi–S–I system (in the region AgI–Bi–Bi2S3–BiSI) for Т ≤ 550 K was studied by physicochemical analysis methods. Equations of overall potential-forming reactions involving the BiSI and Bi₁₉S₂₇I₃ phases were composed. The reactions were performed in the C|Ag|glass Ag₃GeS₃I|D|C electrochemical cells (C are inert (graphite) electrodes; Ag, D are the cell electrodes; D are the four-phase alloys of the system; and glass Ag₃GeS₃I is a membrane with pure Ag⁺ ion conductivity). The linear dependences of EMF of the cells in the range 485–525 K were used for calculating the standard thermodynamic properties of saturated solid solutions of the compounds BiSI and Bi₁₉S₂₇I₃ in the AgI–Bi–Bi₂S₃–BiSI system.     

Phase equilibria in the ZnGeAs<Subscript>2</Subscript>–MnAs system

The ZnGeAs₂–MnAs system is a eutectic-type system as determined by X-ray powder diffraction, DTA, and microstructure observation, with the eutectic coordinates: 61 mol % ZnGeAs₂ mol %, 39 mol % MnAs, and T_m = 816°C. The eutectic is a lamellar eutectic as shown by microstructure examination. A characteristic feature of the system is a small mutual solubility of the components. Precision analysis of diffraction patterns enabled us to refine unit cell parameters for cubic and tetragonal ZnGeAs₂ phases. MnAs in alloys is shown to consist of a hexagonal phase and a orthorhombic phase. ZnGeAs₂ and MnAs alloys are ferromagnets (T_C ~ 320 K). Their magnetization increases in response to increasing MnAs content.     

Phase equilibria in the PbBi<Subscript>2</Subscript>S<Subscript>4</Subscript>–PbSnS<Subscript>2</Subscript> system

The PbBi₂S₄–PbSnS₂ system was studied by physicochemical analysis methods, and its state diagram was constructed. The system is partially quasi-binary; regions of solid solutions based on PbSnS₂ are determined. At a ratio between the initial components of 1: 1, congruently melting compound Pb₂SnBi₂S₆ forms. The unit cells parameters of Pb₂SnBi₂S₆ crystallizing in the orthorhombic system are: a = 15.60 Å, b = 7.80 Å, c = 4.26 Å; space group Pbmm.     

Review of the thermodynamic and transport properties of EuBr<Subscript>2</Subscript>–RbBr binary system

Differential Scanning Calorimetry was used to study phase equilibrium in EuBr₂–RbBr binary system. It was established that this system includes two eutectics and three stoichiometric compounds. First of them, Rb₂EuBr₄, decomposes peritectically at 778 K. Second one, RbEuBr₃, undergoes the solid–solid phase transition at 732 K and melts incongruently at 852 K. Third compound, RbEu₂Br₅, melts congruently at 888 K. The composition and temperature values of eutectics were determined as x(EuBr₂) = 0.316; T _eut = 776 K and x(EuBr₂) = 0.797; T _eut = 859 K. Mixing enthalpy was measured by direct calorimetry on the whole composition range. The minimum of the mixing enthalpy occurs around the composition x(EuBr₂) ≈ 0.4. The electrical conductivity of liquid mixtures was also investigated over the whole composition range and measured down to temperatures below solidification. The specific conductance (liquid phase) plotted against the mole fraction of EuBr₂ shows a broad minimum at x(EuBr₂) ~ 0.6. The activation energy for conductivity changes with temperature. Results obtained are discussed in terms of possible complex formation.     

Phase equilibria in the MgS–In<Subscript>2</Subscript>S<Subscript>3</Subscript> system

Phase equilibria in the MgS–In₂S₃ system were studied. This system is of the dystectic type with a limited region of a solid solution based on β-In₂S₃. In the MgS–In₂S₃ system, a compound of the composition MgIn₂S₄ forms, which forms congruently at 1180 K and crystallizes in the cubic system (space group Fd3m) with the unit cell parameter a = 1.0689 nm. Eutectics have the compositions 47 and 62 mol % In₂S₃ and the melting points 1150 and 1120 K, respectively. The MgS solubility in β-In₂S₃ at 1070 K reaches 9 mol % MgS.     

Formation of solid solutions of multiferroics in the Bi<Subscript>2</Subscript>O<Subscript>3</Subscript>–Nd<Subscript>2</Subscript>O<Subscript>3</Subscript>–Fe<Subscript>2</Subscript>O<Subscript>3</Subscript> system

The sequence of phases appearance during the formation of Bi_1–xNd_xFeO₃ solid solutions in powder oxides mixtures of bismuth, neodymium, and iron has been determined. It has been shown that the closeness of the reaction mixture composition to that of the individual compound (BiFeO₃ or NdFeO₃) is essential for the realization of the series of phase transformations yielding solid solutions of multiferroics Bi_1–xNd_xFeO₃ as the final product, due to the prevalence of various interphase contacts in the starting reaction zone.     

Phase equilibria in the CdAs<Subscript>2</Subscript>–Cd<Subscript>3</Subscript>As<Subscript>2</Subscript>–MnAs ternary system

We determined, using a set of physicochemical methods, including X-ray powder diffraction (XRD), differential thermal analysis, and microstructure studies, that the CdAs₂–Cd₃As₂–MnAs ternary system is bounded by three eutectic-type quasi-binary sections: Cd₃As₂–MnAs, CdAs₂–MnAs, and Cd₃As₂–CdAs₂. For Cd₃As₂–MnAs and CdAs₂–MnAs sections, the eutectic coordinates are, respectively, 75 mol % Cd₃As₂ + 25 mol % MnAs, T _m.eut = 604°C; and 92 mol % CdAs₂ + 8 mol % MnAs, T _m.eut = 608°C. These are rod eutectics. Manganese solubilities in Cd₃As₂ and CdAs₂ phases are insignificant and, according to XRD and SEM, they do not exceed 1 at %. The binary eutectics of the quasi-binary sections form ternary eutectic Cd₃As₂ + CdAs₂ + MnAs, whose average composition as probed by SEM is 34.5 at % Cd, 63 at % Cd and 2.5 at % As and T _m.eut = 600°C. Cadmium and manganese arsenide alloys are ferromagnets with the Curie point at ~320 K. The magnetic and electric properties are due to ferromagnetic MnAs microinclusions.     

Phase equilibria in the NaCl–KI–K<Subscript>2</Subscript>CrO<Subscript>4</Subscript> stable triangle of the Na,K‖Cl,I,CrO<Subscript>4</Subscript> system

The NaCl–KI–K₂CrO₄ stable triangle was studied by differential thermal analysis. The melting temperature, melt composition, and specific melting enthalpy corresponding to the ternary eutectic were determined in the system. The compositions of crystallizing phases in the eutectic were confirmed by X-ray diffraction.     

Phase equilibria in the cutting elements LiF–KCl–Li<Subscript>2</Subscript>WO<Subscript>4</Subscript> and LiF–KCl–LiKWO<Subscript>4</Subscript> of the quaternary reciprocal system Li,K‖F,Cl, WO<Subscript>4</Subscript>

The quaternary reciprocal system comprising fluorides, chlorides, and tungstates of lithium and potassium was partitioned into simplexes using graph theory, and a phase tree of the system was constructed. In the cutting triangles LiF–KCl–Li₂WO₄ and LiF–KCl–LiKWO₄ by differential thermal analysis, the melting points and compositions of ternary eutectics were determined, and the crystallization fields of phases are delineated. For each element of the state diagram, phase reactions were described. The compositions of crystallizing phases in the cutting triangles LiF–KCl–Li₂WO₄ and LiF–KCl–LiKWO₄ were confirmed by X-ray powder diffraction analysis.     

Ionic mobility and electrophysical properties of solid solutions in PbF<Subscript>2</Subscript>–SbF<Subscript>3</Subscript> and PbF<Subscript>2</Subscript>–SnF<Subscript>2</Subscript>–SbF<Subscript>3</Subscript> systems

Ionic mobility and electrical conductivity of solid solutions with fluorite structure, obtained with solid-state approach in PbF₂–SbF₃ and PbF₂–SnF₂–SbF₃ systems, are studied by 19F NMR and electrochemical impedance spectroscopy methods. The 19F NMR spectra parameters, types of ion motions in the fluoride sublattice, and the ionic conductivity magnitude are shown to be determined by the temperature and fluoride concentration in the solid solutions. The solid solution specific conductivity in the PbF₂–SbF₃ and PbF₂–SnF₂–SbF₃ systems at 420–450 K is as high as ~10^–2 S/cm, which allows accounting the solid solutions as a base for preparation of functional materials.     

Phase equilibria in the Cu<Subscript>2</Subscript>S–Cu<Subscript>3</Subscript>AsS<Subscript>4</Subscript>–S system

Phase equilibria in the Cu₂S–Cu₃AsS₄–S system were studied by differential thermal analysis and X-ray powder diffraction. Important plots characterizing this system were constructed, namely, the T–x diagrams of the lateral quasi-binary systems Cu₂S–Cu₃AsS₄ and Cu₃AsS₄–S, some internal sections, the isothermal section of the phase diagram at 300 K, and the projection of the liquidus surface. The fields of primary crystallization of phases and the types and coordinates of in- and monovariant equilibria were found. A wide region of separation of liquid phases was detected in the system.     

Theoretical analysis of the system Li,K, Ca,Ba||F,WO<Subscript>4</Subscript>: Physicochemical properties of the system LiF–K<Subscript>2</Subscript>WO<Subscript>4</Subscript>–BaF<Subscript>2</Subscript>–CaF<Subscript>2</Subscript>–BaWO<Subscript>4</Subscript>

The differentiation of the quaternary reciprocal system Li, K, Ca, Ba||F, WO₄ was performed based on the graph theory using special software. Stable and metastable complexes of the system were found using a matrix of reciprocal pairs of salts. For the first time, by a set of physicochemical analysis methods (differential thermal, visual polythermal, and X-ray powder diffraction analyses), based on the method of thermal analysis of successive projections of the composition polytope, the quaternary system LiF–K₂WO₄–CaF₂–BaF₂–BaWO₄, which is a stable complex of the quaternary reciprocal system Li, K, Ca, Ba||F, WO₄, was studied and the coordinates of invariant points were determined.     

Thermodynamic study of solid solutions in the SnTe–AgSbTe<Subscript>2</Subscript> system by means of EMF with solid electrolyte Ag<Subscript>4</Subscript>RbI<Subscript>5</Subscript>

The results from studying the SnTe–AgSbTe₂ system by means of EMF with the solid electrolyte Ag₄RbI₅ in the temperature range of 300–430 K are presented. The formation of a wide (≥80 mol % of AgSbTe₂) region of solid solutions based on SnTe is confirmed. Partial thermodynamic functions ΔG?, ΔH?, and ΔS? of silver in alloys are calculated from the equations for the EMF temperature dependences. Based on the literature data regarding solid-phase equilibria in the Ag₂Te–SnTe–Sb₂Te₃–Te system, potential-determining reactions are identified that allow us to calculate the standard thermodynamic formation functions and standard entropies of solid solutions (2SnTe) _x (AgSbTe₂)_1?x (х = 0.2, 0.4, 0.6, 0.8, and 0.9).     

Synthesis and properties of γ-Ga<Subscript>2</Subscript>O<Subscript>3</Subscript>–Al<Subscript>2</Subscript>O<Subscript>3</Subscript> solid solutions

The textural and structural properties of mixed oxides Ga₂O₃–Al₂O₃, obtained via impregnating γ-Al₂O₃ with a solution of Ga(NO₃)₃ and subsequent heat treatment, are studied. According to the results from X-ray powder diffraction, gallium ions are incorporated into the structure of aluminum oxide to form a solid solution of spinel-type γ-Ga₂O₃–Al₂O₃ up to a Ga₂O₃ content of 50 wt % of the total weight of the sample, accompanied by a reduction in the specific surface area, volume, and average pore diameter. It is concluded that when the Ga₂O₃ content exceeds 50 wt %, the β-Ga₂O₃ phase is observed along with γ-Ga₂O₃–Al₂O₃ solid solution. ⁷¹Ga and ²⁷Al NMR spectroscopy shows that gallium replaces aluminum atoms from the tetrahedral position to the octahedral coordination in the structure of γ-Ga₂O₃–Al₂O₃.     

The Sections GeSnSb<Subscript>4</Subscript>Te<Subscript>8</Subscript>–GeTe and GeSnSb<Subscript>4</Subscript>Te<Subscript>8</Subscript>–SnTe of the Quasi-Ternary System GeTe–Sb<Subscript>2</Subscript>Te<Subscript>3</Subscript>–SnTe

By differential thermal, X-ray powder diffraction, and microstructural analyses and microhardness and density measurements, phase equilibria in the sections GeSnSb₄Te₈–GeTe and GeSnSb₄Te₈–SnTe were studied and their state diagrams were constructed. It was determined that these sections are quasi-binary sections of the eutectic type of the GeTe–Sb₂Te₃–SnTe system. The coordinates of the eutectic points in the sections GeSnSb₄Te₈–GeTe and GeSnSb₄Te₈–SnTe are (40 mol % GeTe, 700 K) and (30 mol % SnTe, 750 K), respectively. Regions of solid solutions based on the initial components in the sections were identified. Alloys in the regions of solid solutions are p-type semiconductors.     

Liquid-phase synthesis and physicochemical properties of xerogels,nanopowders and thin films of the CeO<Subscript>2</Subscript>–Y<Subscript>2</Subscript>O<Subscript>3</Subscript> system

Low-agglomerated xerogels, ultrafine oxide powders with particle sizes of 12–20 nm, and uniform thin films with particle sizes of 8–14 nm are prepared in the CeO₂–Y₂O₃ system using liquid-phase low-temperature methods, namely via coprecipitation of hydroxides and cocrystallization of salts, sol—gel technology. A comparative characterization of the prepared xerogels and nanopowders is performed using a set of physicochemical analytical methods. A dependence of phase composition, microstructure, and particle size on synthetic parameters is elucidated.     

Phase equilibria in the Nb<Subscript>2</Subscript>O<Subscript>5</Subscript>–CdO system and the thermal stability of Cd<Subscript>2</Subscript>Nb<Subscript>2</Subscript>O<Subscript>7</Subscript> and CdNb<Subscript>2</Subscript>O<Subscript>6</Subscript>

Phase equilibria were studied in the Nb₂O₅–CdO system in the Nb₂O₅-rich region including CdNb₂O₆ and Cd₂Nb₂O₇. It was determined that CdNb₂O₆ and Cd₂Nb₂O₇ in air are stable to 1150 and 1120°C, respectively, and that, above these temperatures, there is solid-phase decomposition of niobates with CdO release in the gas phase. Along with the cadmium oxide evaporation, the Cd₂Nb₂O₇ decomposition is accompanied by the formation of cadmium metaniobate CdNb₂O₆ and the CdNb₂O₆ decomposition results in the formation of niobium oxide Nb₂O₅. No thermal events were observed in the differential thermal analysis curve for a 1: 1 CdNb₂O₆–Cd₂Nb₂O₇ mixture heated to 1100°C in air, which suggests that there are neither phase transformations in cadmium niobates, nor a eutectic within this temperature and concentration ranges. A study of the morphology of compacted samples of niobates determined specific conditions for producing dense composite ceramics, a mixture of niobates, that is suitable for using as a dielectric material.     

Phase equilibria in the BaS–Ga<Subscript>2</Subscript>S<Subscript>3</Subscript> system

In the BaS–Ga₂S₃ system, the following compounds form: congruently melting compound BaGa₄S₇ (rhombic system, space group Pmn2₁, a = 1.477 nm, b = 0.624 nm, c = 0.593 nm, and T_melt = 1490 K) and incongruently melting compounds BaGa₂S₄ (cubic system, space group Pa3, a = 1.2661 nm, and Tmelt = 1370 K), Ba₂Ga₂S₅ (monoclinic system, space group C2/c, a = 1.529, b = 1.479, c = 0.858 nm, ß = 106.04°, and T_melt = 1150 K), Ba₃Ga₂S₆ (monoclinic system, space group C2/c, a = 0.909 nm, b = 1.448 nm, c = 0.903 nm, ß = 91.81°, and T_melt = 1190 K), Ba₄Ga₂S₇ (monoclinic system, space group P2₁/m, a = 1.177 nm, b = 0.716 nm, c = 0.903 nm, ß = 108.32°, and T_melt = 1230 K), and Ba₅Ga₂S₈ (rhombic system, space group Cmca, a = 2.249 nm, b = 1.215 nm, c = 1.189 nm, and T_melt = 1480 K). The compositions of eutectics are 38 and 72 mol % Ga₂S₃, and their melting points are 1120 and 1160 K, respectively. The BaS solubility in γ-Ga₂S₃ at 1070 K reaches 3 mol %.     

Phase equilibria in the Cu<Subscript>2</Subscript>S–La<Subscript>2</Subscript>S<Subscript>3</Subscript>–EuS system

Phase equilibria in the isothermal (970 K) and polythermal LaCuS₂–EuS, Cu₂S–EuLaCuS₃, LaCuS₂–EuLa₂S₄, and EuLaCuS₃–EuLa₂S₄ sections of the Cu₂S–La₂S₃–EuS system have been studied. EuLaCuS₃ (annealing at 1170 K) is of orthorhombic system, space group Pnma, a = 8.1366(1) Å, b = 4.0586(1) Å, c = 15.9822(2) Å, is isostructural to Ba₂MnS₃, and incongruently melts by the reaction EuLaCuS_3cryst (0.50 EuS; 0.50 LaCuS₂) ? 0.22 EuS SS (0.89 EuS; 0.11 LaCuS₂) + 0.78 liq (0.39 EuS; 0.61 LaCuS₂); ΔН = 52 J/g. The Cu₂S–La₂S3–EuS system has been found to contain five major subordinate triangles. At 970 K, tie-lines lie between EuLaCuS₃ and the Cu₂S, EuS, LaCuS₂, and EuLa₂S₄ phases and between the LaCuS₂ phase and the γ-La₂S₃–EuLa2S4 solid solution. Eutectics are formed between LaCuS₂ and EuLaCuS₃ at 26.0 mol % of EuS and T = 1373 K and between EuLaCuS3 and EuLa₂S₄ at 29.0 mol % of EuLa₂S₄ and T = 1533 K.     

Phase diagram of the NaF–CaF<Subscript>2</Subscript> system and the electrical conductivity of a CaF<Subscript>2</Subscript>-based solid solution

The phase diagram of the NaF–CaF₂ system was studied by thermal analysis and X-ray powder diffraction analysis with the determination of the chemical composition. The system was found to be of the eutectic type. A narrow range of the existence of solid solution Ca_1–xNa_xF_2–x was established. The NaF solubility reaches a maximal value of x = 0.035 at 1200 ± 50°C (the temperature at which there is a diffuse phase transition in fluorite). At 920 ± 25°C, the NaF solubility reaches a minimum (<0.4 mol %) and increases again to 2.2 ± 0.2 mol % at a eutectic temperature (818°C). The ionic conductivity increases by three orders of magnitude after adding NaF to CaF₂.