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.     

Determination of low-melting alloys in the ternary reciprocal system Na,K‖Br,WO<Subscript>4</Subscript>

The ternary reciprocal system Na,K‖Br,WO₄ was studied by differential thermal analysis. The compositions and melting points of the alloys corresponding to invariant equilibrium points were determined, and the enthalpies of melting of eutectic mixtures were measured. Phase equilibria in systems were described, and the fields of crystallizing phases were delineated.     

Phase complex of the Li,K,Ba‖F,Br quaternary reciprocal system

The partition of the Li,K,Ba??F,Br quaternary reciprocal system into simplexes was performed and confirmed by X-ray powder diffraction. Internal partitioning elements, LiF-2KBr · BaBr₂ and KBr-LiF · BaF₂, were identified; the tree of phases forms two cycles. Simplexes involving phase separation were determined. The stable partitioning triangles LiF-KBr-BaBr₂ and LiF-KBr-BaF₂ · BaBr₂ were experimentally studied by differential thermal and X-ray powder diffraction analyses. The T-x diagrams of explored sections and the liquidi of the systems were constructed. Phase separation regions within the systems under investigations were delimited. The characteristics of alloys corresponding to invariant compositions were determined.     

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).     

Li, K‖Br, VO3 ternary mutual system

Phase equilibria in the Li, K‖Br, VO₃ ternary mutual system were studied by differential thermal analysis. The composition square of the ternary mutual system is divided into two phase triangles, LiVO₃-KBr-KVO₃ and LiBr-LiVO₃-KBr. The ternary eutectics E ₁ at 331°C and E ₂ at 330°C have the compositions 40.0 mol % LiVO₃, 6.0 mol % KBr, 54.0 mol % KVO₃ and 58.0 mol % LiBr, 3.2 mol % LiVO₃, 38.8 mol % KBr, respectively. The fields of phases crystallizing in the system were delimited.     

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.     

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).     

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 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.     

Crystal structure of [Pb<Subscript>3</Subscript>(OH)<Subscript>4</Subscript>Co(NO<Subscript>2</Subscript>)<Subscript>3</Subscript>](NO<Subscript>3</Subscript>)(NO<Subscript>2</Subscript>)·2H<Subscript>2</Subscript>O

The structure of [Pb₃(OH)₄Co(NO₂)₃](NO₃)(NO₂)·2H₂O is determined by single crystal X-ray diffraction. The crystallographic characteristics are as follows: a = 8.9414(4) Å, b = 14.5330(5) Å, c = 24.9383(9) Å, V = 3240.6(2) ų, space group Pbca, Z = 8. The Co(III) atoms have a slightly distorted octahedral coordination formed by three nitrogen atoms belonging to nitro groups (Co–N_av is 1.91 Å) and three oxygen atoms belonging to hydroxyl groups (Co–O_av is 1.93 Å). The hydroxyl groups act as μ₃-bridges between the metal atoms. The geometric characteristics are analyzed and the packing motif is determined.     

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

The cutting tetrahedron LiVO₃–KBr–KVO₃–LiKMoO₄ 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 (11.3 mol % LiVO₃, 18.0 mol % KBr, 57.0 mol % KVO₃, 13.7 mol % Li₂MoO₄ + K₂MoO₄, 318°С).     

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.     

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

Phase equilibria in the Na,K‖CO₃,HCO₃,F-H₂O system at 25°C are studied by the translation method. Twenty nine double-saturation divariant fields, 31 triple-saturation monovariant curves, and 11 quadruple-saturation points for equilibrium solid phases are distinguished in the system. The first looped phase diagram (phase complex) of the title system is designed.     

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.     

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).     

Separation of rare earth elements in the tributyl phosphate–Ln(NO<Subscript>3</Subscript>)<Subscript>3</Subscript>–Ca(NO<Subscript>3</Subscript>)<Subscript>2</Subscript> system in the counter current process

The 40-step extraction process to separate rare earth elements (RЕEs) according to the praseodymium–cerium line with the use of mixer–settler extractors in a 100% TBP–Ln(NO₃)₃–Ca(NO₃)₂ system is implemented. A lanthanum–cerium concentrate containing less than 0.03 wt % of the remaining REEs is obtained. The flow diagram of the separation process of a rare earth (RE) concentrate isolated from phosphogypsum is considered.     

Simulating equilibrium processes in the Ga(NO<Subscript>3</Subscript>)<Subscript>3</Subscript>–H<Subscript>2</Subscript>O–NaOH system

Equilibrium processes in the Ga(NO₃)₃–H₂O–NaOH system are simulated with allowance for the formation of precipitates of various compositions using experimental data from potentiometric titration and theoretical studies. The values of the instability constants are calculated along with the stoichiometric compositions of the resulting compounds. It is found that pH ranges of 1.0 to 4.3 and 12.0 to 14.0 are best for the deposition of gallium chalcogenide films.     

Study of the Pr(NO<Subscript>3</Subscript>)<Subscript>3</Subscript>-H<Subscript>8</Subscript>L-H<Subscript>2</Subscript>O system by Tananaev’s method

Conditions for the formation of praseodymium ethylenediaminetetramethylphosphonates were studied by Tananaev’s method.     

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.