Phase equilibria in the Tl2Te-SnTe-Bi2Te3 system

phase equilibria in the Tl₂Te-SnTe-Bi₂Te₃ system were studied by differential thermal analysis (DTA), X-ray powder diffraction, and microhardness measurements. Some polythermal sections and isothermal (at 600 and 800 K) sections of the phase diagram and a projection of the liquidus surface were constructed. It was shown that the system is characterized by the formation of solid solutions with the Tl₅Te₃ structure (δ) and solid solutions based on SnTe (γ₁), Tl₂Te (α), Bi₂Te₃ (β), and two TlBiTe₂ (γ₂ and γ′₂) phases. Their homogeneity regions were determined. The liquidus surface consists of the primary crystallization fields of the β-, γ₁-, γ′₂-, and δ phases and the compounds SnBi₂Te₄ and SnBi₄Te₇. The liquidus of the α phase is degenerate. The primary crystallization fields of phases were determined, and the types and coordinates of in- and monovariant equilibria were found.     

Phase equilibria in the Ag2Te-PbTe-Bi2Te3 system

Phase equilibria in the Ag₂Te-PbTe-Bi₂Te₃ quasi-ternary system were studied by differential thermal analysis, X-ray powder diffraction, and measurements of microhardness and emf of concentration circuits with an Ag₄RbI₅ solid electrolyte. Some polythermal sections and isothermal (600 and 800 K) sections of the phase diagram, and also a projection of the liquidus surface were constructed. The primary crystallization fields of phases were determined, and the types and coordinates of invariant and monovariant equilibria were found. The system is characterized by the formation of a wide continuous band of high-temperature solid solutions (γ phase) with a cubic structure along the PbTe-AgBiTe₂ section. With decreasing temperature (T ≤ 715 K), AgBiTe₂ and γ solid solutions, close in composition to this compound, experience solid-phase decomposition to form Bi₂Te₃, ternary tetradymite-like phases of the PbTe-Bi₂Te₃ boundary system, and the low-temperature phase of Ag₂Te.     

Phase equilibria and some properties of solid solutions in the Tl5Te3-Tl9BiTe6-Tl5Te2Cl system

Phase equilibria in the Tl₅Te₃-Tl₉BiTe6-Tl₅Te₂Cl system were studied by differential thermal analysis (DTA), X-ray powder diffraction, and measurements of microhardness and also emf of concentration circuits with reference to a thallium electrode. A number of polythermal sections, the isothermal sections of the phase diagram at 760 and 800 K, and projections of the liquidus and solidus surfaces were constructed. It was shown that the system is characterized by the formation of unlimited solid solutions with the Tl₅Te₃ structure. The concentration dependences of the crystal lattice parameters, microhardness, and emf in the solid solutions were described.     

Phase equilibria and some properties of solid solutions in the Tl5Te3-Tl9BiTe6-Tl5Te2Br system

Phase equilibria in the Tl₅Te₃-Tl₉BiTe₆-Tl₅Te₂Br system were studied by differential thermal analysis, X-ray powder diffraction, and measurements of microhardness and also emf relative to a thallium electrode. Polythermal and isothermal sections of the phase diagram at 760 and 800 K, and projections of the liquidus and solidus surfaces were constructed. The unit cell parameters, microhardness, and emf in the alloys were described as functions of concentration. The system is characterized by the formation of complete solid solutions with the Tl₅Te₃ structure.     

Phase equilibria in the Tl-TlBr-Te system and thermodynamic properties of the compound Tl5Te2Br

The Tl-TlBr-Te composition region of the Tl-Te-Br phase diagram has been explored by DTA, X-ray diffraction, microhardness measurements, and electromotive force (emf) measurements relative to a thallium electrode in concentrations cells. The phase diagrams along a number of joins, the isothermal section at 400 K of the phase diagram, and a projection of the liquidus surface have been constructed. Extensive phase-separation areas, including a three-liquid-phase field in the Tl-TlBr-Tl₂Te subsystem, have been revealed. The homogeneity ranges and primary crystallization fields of phases have been mapped, and the coordinates of nonvariant and univariant equilibria in the T-x-y diagram have been determined. The standard thermodynamic functions of formation of the Tl₅Te₂Br compound and its standard entropy have been derived from emf data.     

Projection of the liquidus surface of the Sb<Subscript>2</Subscript>Te<Subscript>3</Subscript>-Gd<Subscript>2</Subscript>Te<Subscript>3</Subscript>-Bi<Subscript>2</Subscript>Te<Subscript>3</Subscript> system

Phase equilibria in the Sb₂Te₃-Gd₂Te₃-Bi₂Te₃ ternary system have been studied using differential thermal analysis, namely, X-ray powder diffraction, microstructure examination, thermodynamic analysis, and microhardness and alloy density measurements. Phase diagrams of some polythermal joins and liquidus surface have been constructed. The regions of primary crystallization of phases and the coordinates of all invariant and univariant equilibria in the system under investigation have been established.     

Reciprocal system 3Tl2S + Bi2Se3 ↔ 3Tl2Se + Bi2S3

The reciprocal system 3Tl₂S + Bi₂Se₃ ? 3Tl₂Se + Bi₂S₃ has been investigated by DTA, X-ray powder diffraction analysis, and emf measurements. Some polythermal sections and the isothermal section at 500 K of the phase diagram and the projection of the liquidus surface of this system have been constructed, and the types and coordinates of the invariant and univariant equilibria have been determined. The existence of wide regions of quaternary solid solutions based on the binary compounds Tl₂S, Tl₂Se, Bi₂S₃, and Bi₂Se₃, and solid solutions between the temary compounds TlBiS₂ and TlBiSe₂ have been established.     

Interaction in the Tl2S-SnS-PbS quasi-ternary system

Phase equilibria in the Tl₂S-SnS-PbS quasi-ternary system were studied by differential thermal, X-ray powder diffraction, and microstructural analyses. The following schemes were constructed: the state diagrams of the partially quasi-binary sections Tl₄SnS₃-Tl₄PbS₃, PbS-Tl₄SnS₃, and PbS-Tl₂Sn₂S₃, the isothermal section at 520 K, and the projection of the liquidus surface to the concentration triangle of the Tl₂S-SnS-PbS system. The coordinates of invariant points and the boundaries of solid solutions were determined.     

Phase equilibria in the Tl-TlCl-Te system and thermodynamic properties of the compound Tl<Subscript>5</Subscript>Te<Subscript>2</Subscript>Cl

The Tl-Te-Cl system was studied in the Tl-TlCl-Te composition region by differential thermal analysis, X-ray powder diffraction, and emf and microhardness measurements. A series of polythermal sections, an isothermal section at 400 K, and a projection of the liquidus surface of the phase diagram were constructed. The ternary compound Tl₅Te₂Cl characterized by a wide homogeneity region and incongruent melting by a syntectic reaction at 708 K was shown to exist. This compound was found to crystallize in tetragonal lattice (space group I4/mcm) with the parameters a = 8.921 Å, c = 12.692 Å, Z = 4. Wide phase separation regions were also found in the system, including a three-phase separation region in the Tl-TlCl-Tl₂Te subsystem. Regions of primary crystallization of phases, and the types and coordinates of in- and monovariant equilibria in the T-x-y diagram were determined. From emf measurement data, the standard thermodynamic functions of formation and the standard entropy were calculated for the compound Tl₅Te₂Cl, as follows: ?ΔG ₂₉₈ ⁰ = 355.9 ± 1.1 kJ/mol, ?ΔH ₂₉₈ ⁰ = 377.1 ± 5.0 kJ/mol, and S ₂₉₈ ⁰ = 474.1 ± 6.8 J/(mol K).     

Interaction of components in the Cs2HgBr4-Cs2ZnBr4-CsBr ternary system

The interaction of components in the Cs₂HgBr₄-Cs₂ZnBr₄-CsBr ternary system was studied by differential thermal and X-ray powder diffraction analyses. The liquidus surface consists of the crystallization fields of three phases: CsBr, a solid solution of Cs₂HgBr₄ with Cs₂ZnBr₄ (??), and solid solution ?? based on Cs₃ZnBr₅. The ternary eutectic near Cs₂HgBr₄ has the coordinates ??83 mol % Cs₂HgBr₄, 2 mol % Cs₂ZnBr₄, and 15 mol % CsBr and the melting point ??415°C. The triangulating section Cs₂HgBr₄-Cs₃ZnBr₅ is characterized by the eutectic interaction with the eutectic that is degenerate near Cs₂HgBr₄, contains ??3 mol % Cs₃ZnBr₅, and melts at 420°C. This section divides the Cs₂HgBr₄-Cs₂ZnBr₄-CsBr ternary system into two ternary systems Cs₂HgBr₄-CsBr-Cs₃ZnBr₅ and Cs₂HgBr₄-Cs₃ZnBr₅-Cs₂ZnBr₄.     

Phase equilibria in the Tl-TlBr-S system

The polythermal sections TlBr-Tl₂S, TlBr-Tl₄S₃, TlBr-TlS, and Tl₆SBr₄-Tl; the isothermal section at 300 K of the phase diagram; and the projection of the liquidus surface of the Tl-S-Br system have been investigated in the composition region Tl-TlBr-S by DTA, X-ray powder diffraction analysis, and microhardness measurements. The primary crystallization regions, including that of the only ternary compound (Tl₆SBr₄), have been determined, and the types and coordinates of the invariant and univariant equilibria in the phase diagram are determined.     

Phase diagram of the Tl-TlI-S system and thermodynamic properties of the compound Tl<Subscript>6</Subscript>SI<Subscript>4</Subscript>

Phase equilibria in the Tl-TlI-S composition region of the Tl-S-I system were studied by differential thermal analysis, x-ray powder diffraction, and measurements of the microhardness and the emf of concentration circuits relative to a thallium electrode. A series of polythermal sections, an isothermal section at 300 K, and a projection of the liquidus surface were constructed. Primary crystallization regions of six phases, including the ternary compounds Tl₆SI₄ and Tl₃SI, were outlined, and the types and coordinates of non- and monovariant equilibria were determined. It was shown that the ternary compound Tl₆SI₄ forms tie lines with Tl, TlI, Tl₂S, Tl₄S₃, and TlS in the subsolidus region and that the homogeneity region of Tl₆SI₄ below 400 K does not exceed 1 mol %. From the emf measurement data, the standard thermodynamic functions of formation and standard entropy of the compound Tl₆SI₄ were calculated: G _f,298⁰ = −601.7 ± 2.5 kJ/mol, ΔH _f,298⁰= −595.1 ± 4.0 kJ/mol, and S ₂₉₈⁰ = 672 ± 10 J/(mol K).     

Phase equilibria in the La<Subscript>2</Subscript>S<Subscript>3</Subscript>-Bi<Subscript>2</Subscript>S<Subscript>3</Subscript>-La<Subscript>2</Subscript>O<Subscript>3</Subscript> ternary system

Phase equilibria in the La₂S₃-Bi₂S₃-La₂O₃ ternary system were studied by differential thermal, X-ray powder diffraction, and microstructure analyses. Phase diagrams of five vertical sections and a liquidus surface projection were plotted for the La₂S₃-Bi₂S₃-La₂O₃ system. The regions of primary crystallization of phases and coordinates of non- and monovariant equilibria were determined for the system.     

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.     

Ag2Se-Tl2Se-Bi2Se3 quasi-ternary system

The Ag₂Se-Tl₂Se-Bi₂Se₃ quasi-ternary system (system A) was studied using DTA, X-ray powder diffraction, microstructure examination, and microhardness measurements. TlBiSe₂-AgBiSe₂, AgTlSe-AgBiSe₂, AgTlSe-Bi₂Se₃, and Tl₂Se-AgBiSe₂ polytherms, isothermal sections at 500 and 800 K, and liquidus surface projection of system A were constructed. System A is congruently triangulated into the following subordinate triangles: Tl₂Se-AgTlSe-Tl₉BiSe₆ (I), AgTlSe-Tl₉BiSe₆-TlBiSe₂ (II), Ag₂Se-AgTlSe-TlBiSe₂ (III), Ag₂Se-AgBiSe₂-TlBiSe₂ (IV), and AgBiSe₂-TlBiSe₂-Bi₂Se₃ (V). Subsystems I, III, and V are ternary systems with three-phase eutectic equilibrium; system II has a three-phase eutectic, and system IV is characterized by several invariant and monovariant peritectic and eutectic equilibria. Primary crystallization and homogeneity fields were outlined, and the types and coordinates of invariant and monovariant equilibria in system A were determined. A characteristic feature of the title system is an extensive field of solid solutions between high-temperature cubic AgBiSe₂ and TlBiSe₂ phases; this field lies as a continuous belt along the AgBiSe₂-TlBiSe₂ quasibinary section and covers about one-fourth of the surface area of the triangular diagram of system A.     

Phase Diagram of the System Tl<Subscript>2</Subscript>Te–Tl<Subscript>5</Subscript>Te<Subscript>3</Subscript>–Tl<Subscript>9</Subscript>GdTe<Subscript>6</Subscript>

The ternary system Tl–Gd–Te within the composition range Tl₂Te–T_l5Te₃–T_l9GdTe₆ was studied by a set of physicochemical analysis methods. Some internal polythermal sections and the isothermal section at 300 K of the phase diagram were built, projections of the liquidus and solidus surfaces were constructed, and the graphs of the concentration dependences of the parameters and microhardness were plotted. It was shown that much (more than 90%) of the area of the concentration triangle is occupied by the homogeneity region of solid solutions with the Tl₅Te₃ structure (δ-phase). Solid solutions based on Tl₂Te (α-phase) form within a narrow region. The regions of the α- and δ-phases are separated by two-phase region α + δ.     

Phase Equilibria in the System Tl<Subscript>9</Subscript>SbSe<Subscript>6</Subscript>–TlSbSe<Subscript>2</Subscript>–Tl<Subscript>4</Subscript>SnSe<Subscript>4</Subscript>

For the first time, by differential thermal, X-ray powder diffraction, and microstructural analyses, phase equilibria in the ternary system Tl₉SbSe₆–TlSbSe₂–Tl₄SnSe₄ were investigated and the state diagram of the polythermal section Tl₄SnSe₄–Tl₃SbSe₃, the projection of the liquidus surface on the concentration triangle, and the isothermal section at 423 K were constructed. The types and coordinates of invariant processes, the lines of monovariant equilibria, and their temperature ranges were found. The formation mechanism and nature of solid solutions based on ternary compounds Tl₉SbSe₆ and TlSbSe₂ were studied in terms of crystal chemistry.     

Tl2S-Sb2S3-Bi2S3 quasi-ternary system

The Tl₂S-Sb₂S₃-Bi₂S₃ quasi-ternary system (system A) was studied using DTA, X- ray powder diffraction, microstructure examination, and microhardness measurements. TlSbS₂-Tl₄Bi₂S₅(TlBiS₂, Bi₂S₃), Sb₂S₃-TlBiS₂, Tl₃SbS₃-TlBiS₂(Bi₂S₃), and [TlSb_0.5Bi_0.5S₂]-Tl₂S isopleths; isothermal sections at 500 K; and liquidus surface projection of system A were constructed. Characteristic features of the title system are extensive fields of solid solutions extended along the TlSbS₂-TlBiS₂ quasi-binary section and a continuous solubility belt 1–2 mol % wide extended along the Sb₂S₃-Bi₂S₃ binary subsystem. Primary separation fields of phases and the types and coordinates of invariant and monovariant equilibria in system A were determined.     

Physicochemical Aspects of Development of Multicomponent Chalcogenide Phases Having the Tl<Subscript>5</Subscript>Te<Subscript>3</Subscript> Structure: A Review

The literature data on ternary structural analogues of the compound Tl₅Te₃ and multicomponent phases based on them are systematized. This class of inorganic substances is of considerable scientific and practical interest as promising functional materials having thermoelectric, optical, and magnetic properties, as well as topologically protected surface states and superconductivity. The focus of the survey is on phase equilibria in ternary and more complex systems where structural analogues of Tl₅Te₃ are formed. Crystalstructure features, thermodynamic and some physical properties of these compounds and phases of variable composition are considered.     

Study and 3D modeling of the phase diagram of the Ag–Ge–Se system

In view of the contradictoriness of the literature data, phase equilibria in the Ag–Ge–Se system were restudied by differential thermal analysis and X-ray powder diffraction analysis. A number of polythermal sections and an isothermal section at room temperature of the phase diagram were constructed, and so was the projection of the liquidus surface. The primary crystallization fields of phases and the types and coordinates of in- and monovariant equilibria were determined. It was shown that, in the system, a single ternary compound, Ag₈GeSe₆, forms, which undergoes congruent melting at 1175 K and a polymorphic transformation at 321 K. The formation of the compounds Ag₂GeSe₃ and Ag₈GeSe₅, which was previously reported in the literature, was not confirmed. Based on the phase diagrams of boundary binary systems and the results of the differential thermal analysis of a number of samples of the ternary system, equations were obtained for calculation and 3D modeling of the liquidus and phase-separation surfaces.