Cutting Element LiF–LiVO<Subscript>3</Subscript>–LiKMoO<Subscript>4</Subscript>–KBr of the Quinary Reciprocal System Li,K||F,Br, VO<Subscript>3</Subscript>, MoO<Subscript>4</Subscript>

The cutting element LiF–LiVO₃–LiKMoO₄–KBr of the quinary reciprocal system Li, K||F, Br, VO₃, MoO₄ was studied by differential thermal analysis. The composition and melting point of the alloy corresponding to a quaternary eutectic were determined (7.0 mol % LiF, 32.0 mol % LiVO3, 47.7 mol % Li2MoO4 + K2MoO4, 12.3 mol % KBr, 410°С).     

Secant Tetrahedron LiF–KBr–KVO<Subscript>3</Subscript>–LiKMoO<Subscript>4</Subscript> of the Five-Component Reciprocal System Li,K‖F,Br,VO<Subscript>3</Subscript>,MoO<Subscript>4</Subscript>

The secant tetrahedron LiF–KBr–KVO₃–LiKMoO₄ of the five-component reciprocal system Li,K‖F,Br,VO₃,MoO₄ was studied by differential thermal analysis (DTA). The composition corresponding to the quaternary eutectic (mol %) was determined to be the following: LiF, 6.0; KBr, 11.4; KVO₃, 57.0; Li₂MoO₄ + K₂MoO₄, 25.6; the melting temperature: 358°С.     

Study of the stable tetrahedron LiVO<Subscript>3</Subscript>–Li<Subscript>2</Subscript>MoO<Subscript>4</Subscript>–KBr–LiKMoO<Subscript>4</Subscript> of the quaternary reciprocal system Li,KǁBr,VO<Subscript>3</Subscript>,MoO<Subscript>4</Subscript>

Phase equilibria in the stable tetrahedron LiVO₃–Li₂MoO₄–KBr–LiKMoO₄ of the quaternary reciprocal system Li,K∥Br,VO₃,MoO₄ were studied by differential thermal analysis. The composition (mol %) and melting point of the alloy corresponding to a quaternary eutectic were determined: (24.2% LiVO₃, 10.4% Li₂MoO₄, 13.5% KBr, 51.9% LiKMoO₄, 407°С).     

Tree of phases of the quinary reciprocal system Li,K || F,Br, MoO<Subscript>4</Subscript>, WO<Subscript>4</Subscript> and study of the stable tetrahedron LiF–KBr–Li<Subscript>2</Subscript>MoO<Subscript>4</Subscript>–Li<Subscript>2</Subscript>WO<Subscript>4</Subscript>

The quinary reciprocal system Li, K || F, Br, MoO₄, WO₄ was partitioned into simplexes using graph theory by writing an adjacency matrix and solving a logical expression. A tree of phases of the system was constructed. The tree of phases has a linear structure and consists of four stable partitioning tetrahedra, two stable pentatopes, and three stable hexatopes. In the quinary reciprocal system Li, K || F, Br, MoO₄, WO₄, crystallizing phases were predicted. The stable tetrahedron LiF–KBr–Li₂MoO₄–Li₂WO₄ of the quinary reciprocal system Li, K || F, Br, MoO₄, WO₄ was studied by differential thermal analysis and X-ray powder diffraction. There are no invariant equilibrium points in the tetrahedron. Continuous series of solid solutions Li₂Mo_xW_1–xO₄ do not decompose.     

Phase equilibria in the stable tetrahedron LiF–KF–KBr–Li<Subscript>2</Subscript>CrO<Subscript>4</Subscript> of the quaternary reciprocal system Li,K||F,Br,CrO<Subscript>4</Subscript>

Phase equilibria in the stable tetrahedron LiF–KF–KBr–Li₂CrO₄ of the quaternary reciprocal system Li,K||F,Br,CrO₄ were studied by differential thermal analysis. The characteristics of a quaternary eutectic were found.     

Ternary Systems LiBr–LiVO<Subscript>3</Subscript>–Li<Subscript>2</Subscript>CrO<Subscript>4</Subscript> and KBr–KVO<Subscript>3</Subscript>–K<Subscript>2</Subscript>CrO<Subscript>4</Subscript>

The binary system KVO₃–K₂CrO₄ and two ternary systems, LiBr–LiVO₃–Li₂CrO₄ and KBr–KVO₃–K₂CrO₄, were studied. In the ternary systems, the compositions and melting points of eutectic alloys were determined by differential thermal analysis: (49.0 mol % LiBr, 5.0 mol % LiVO₃, 46.0 mol % Li₂CrO₄, 400°C) and (17.0 mol % KBr, 78.0 mol % KVO₃, 5.0 mol % K₂CrO₄, 458°C), respectively.     

Phase Equilibria of Three-Component Reciprocal System Na,K║I,MoO<Subscript>4</Subscript>

The three-component reciprocal system Na,K║I,MoO₄ has been studied by differential thermal analysis (DTA). The compositions and melting temperatures have been determined, and the enthalpies of melting of eutectic mixtures measured. Phase equilibria in the system are described, and phase fields are demarcated.     

Phase equilibria in the stable tetrahedron LiF–LiBr–Li<Subscript>2</Subscript>CrO<Subscript>4</Subscript>–KBr of the quaternary reciprocal system Li,KǁF,Br,CrO<Subscript>4</Subscript>

Phase equilibria in the stable tetrahedron LiF–LiBr–Li₂CrO₄–KBr of the quaternary reciprocal system Li,K∥F,Br,CrO₄ were studied by differential thermal analysis. The composition (equiv %) and melting point of a quaternary eutectic were found as (2% LiF, 60% LiBr, 3% Li₂CrO₄, 35% KBr, 315°C).     

Stable tetrahedron LiF–KI–K<Subscript>2</Subscript>CrO<Subscript>4</Subscript>–Li<Subscript>2</Subscript>CrO<Subscript>4</Subscript> of the quaternary reciprocal system Li,K||F,I, CrO<Subscript>4</Subscript>

The stable tetrahedron LiF–KI–K₂CrO₄–Li₂CrO₄ of the quaternary reciprocal system Li, K||F, I, CrO₄ was experimentally studied by differential thermal analysis. The compositions and melting points of mixtures of components at two eutectic points were determined. Based on experimental data, a T–x–y–z model of the phase complex was constructed, which allows one to solve problems of building polythermal and isothermal sections. A method for constructing the diagram of material balance of equilibrium phases for a given composition was developed. The diagram enables one to find the ratio between the amounts of the liquid and solid phases at constant temperature and also monitor the change in the composition of the phases within a chosen temperature range.     

Quaternary reciprocal system Li,K‖F,Br,NO<Subscript>3</Subscript>

The quaternary reciprocal system Li,K‖F,Br,NO₃ was described and studied for the first time. The system was partitioned into simplexes by writing an adjacency matrix and solving a logical expression. The partition was confirmed by the results of differential scanning calorimetry of two partitioning triangles (LiF-KBr-KNO₃ and LiF-KBr-LiNO₃) and three stable triangles (LiBr-LiF-KBr-LiNO₃, LiNO₃-LiF-KNO₃-KBr, and KF-LiF-KNO₃-KBr). The compositions (mol %) and melting points of quaternary eutectics of the system Li,K‖F,Br,NO₃ were determined: E ₁ ^□ (4.0% LiF, 48.0% LiNO₃, 17.28% KBr, 30.7% LiBr, T _melt = 186°C), E ₂ ^□ (7.35% LiF, 47.53% KNO₃, 2.0% KBr, 43.12% LiNO₃, T _melt = 102°C), and E ₃ ^□ (2.0% LiF, 84.28% KNO₃, 0.98% KBr, 12.74% KF, T _melt = 280°C).     

Phase equilibria in the Na,K||SO<Subscript>4</Subscript>,CO<Subscript>3</Subscript>,HCO<Subscript>3</Subscript>-H<Subscript>2</Subscript>O system at 25°C

Phase equilibria in the system Na,K|SO₄,CO₃,HCO₃-H₂O at 25°C are studied by the translation method. Thirty two double-saturation fields, 36 triple-saturation monovariant curves, and 13 quadruple-saturation points are distinguished in the system. The first closed phase diagram (phase complex) of the title system is designed.     

Ternary Reciprocal System K,Pb∥Cl,WO<Subscript>4</Subscript>

The phase diagram of the ternary reciprocal system K, Pb∥Cl, WO₄ was studied for the first time by the calculation–experimental method and differential thermal and X-ray powder diffraction analyses. Chemical interactions between components were described, metathesis and complexation reactions were revealed, and the coordinates of binary and ternary eutectics were found (mol %): e₄(410°C, 48% KCl, 52% PbCl₂), e₅(424°C, 23% KCl, 77% PbCl₂), P(490°C, 63.5% KCl, 36.5% PbCl₂), e₆(487°C, 91% PbCl₂, 9% PbWO₄), e₇(428°C, 30.5% KCl, 60.5% PbCl₂, 9% PbWO₄) (eutectic in the stable section D₂–PbWO₄), e₈(650°C, 80% KCl, 20% PbWO₄), e₉(650°C, 70% KCl, 15% K₂WO₄, 15% PbWO₄) (binary eutectic in the stable section D₁–KCl), E₁(620°C, 59% KCl, 34% K₂WO₄, 7% PbWO₄), E₂(640°C, 75% KCl, 5% K₂WO₄, 20% PbWO₄), E3(400°C, 46% KCl, 6% PbWO₄, 48% PbCl₂), E₄(410°C, 21% KCl, 9% PbWO₄, 70% PbCl₂), and P_о(468°C, 56% KCl, 10% PbWO₄, 34% PbCl₂).     

Phase formation in the system Li<Subscript>2</Subscript>MoO<Subscript>4</Subscript>–MgMoO<Subscript>4</Subscript>–Sc<Subscript>2</Subscript>(MoO<Subscript>4</Subscript>)<Subscript>3</Subscript>

Phase formation in the system Li₂MoO₄–MgMoO₄–Sc₂(MoO₄)₃ was studied by X-ray powder diffraction analysis and differential thermal analysis. Ternary molybdate LiMgSc(MoO₄)₃ was synthesized, which crystallizes in the triclinic system (space group P\(\bar 1\)). In the Li₂Mg₂(MoO₄)₃–Li₃Sc(MoO₄)₃ section, a continuous solid solution in the rhombic system was found to form (space group Pnma).     

Four-component reciprocal system Na,K∥F,CO<Subscript>3</Subscript>, WO<Subscript>4</Subscript>

The four-component reciprocal system Na,K∥F, CO₃, WO₄ has been studied using differential thermal analysis in combination with projective and differential geometry. The a priori prediction of the crystallization path (CP) shows six quaternary invariant points; of them, three are eutectics and the others are peritectics. The dominant exchange and complexing reactions have been recognized. The following four-component systems have been studied: (NaF)₂-(KF)₂-K₂CO₃-K₃FWO₄ (1), (NaF)₂-K₂CO₃-K₂WO₄-K₃FWO₄ (2), (NaF)₂-Na₂CO₃-Na₂WO₄-K₂WO₄ (3),, and (NaF)₂-Na₂CO₃-K₂CO₃-K₂WO₄ (4); the coordinates of all quaternary invariant points have been determined.     

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.     

Phase Equilibria in the K,Cа∥SO<Subscript>4</Subscript>,CO<Subscript>3</Subscript>,HCO<Subscript>3</Subscript>–H<Subscript>2</Subscript>O System at 25°С

Phase equilibria in the system K,Cа∥SO₄,CO₃,HCO₃–H₂O have been studied at 25°С. This system at 25°С involves 7 invariant points, 21 monovariant curves, and 22 divariant fields. The data gained served to plot the first phase diagram (phase complex) of the studied system at 25°С.     

Solubility in the Na,Са||SO<Subscript>4</Subscript>,СО<Subscript>3</Subscript>–H<Subscript>2</Subscript>O system at 25°С

Solubility at the invariant points of the Na,Са||SO₄,СО₃–H₂O system at 25°C was studied, and a solubility diagram at this temperature constructed.     

KF–KBr–K<Subscript>2</Subscript>SO<Subscript>4</Subscript> system

The KBr–D (K₃FSO₄) quasi-binary system and the KF–KBr–K₂SO₄ ternary system were studied by differential thermal analysis. The melting points and compositions of eutectic mixtures were determined. In-, mono-, and divariant equilibria were described.     

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.     

Stable triangle (LiF)<Subscript>2</Subscript>–(KI)<Subscript>2</Subscript>–Li<Subscript>2</Subscript>CrO<Subscript>4</Subscript> of the quaternary reciprocal system Li,K∥F,I,CrO<Subscript>4</Subscript>

The quaternary reciprocal system Li,K||F,I,CrO₄ was partitioned into stable simplexes using graph theory. The system consists of five stable tetrahedra separated by four stable triangles. The chemical interaction between components was described based on the material balance written with account for occurring chemical reactions. Phase equilibria in the quasi-ternary system (LiF)₂–(KI)₂–Li₂CrO₄ were studied for the first time; in this system, the temperature and composition of a ternary eutectic were determined. The limited solubility of two liquid phases manifests itself in the concentration region adjacent to the LiF–KI quasibinary system. A three-dimensional model of the phase complex of the system was constructed in temperature– concentration coordinates.