Search for internal diagonals in polyhedration of reciprocal systems by the algorithm for topological correction of lists of simplexes of different dimensions

The algorithm for topological correction of lists of simplexes of different dimensions was used for analyzing the published methods for determining internal diagonals in polyhedration of reciprocal systems. By this algorithm, errors were found in the polyhedration of the quaternary systems Ca,Na,K‖F,MoO₄, K,Na,Li‖Cl,NO₃, Ba,Na,K‖F,MoO₄, Na,K‖Cl,NO₃,NO₂, and Li,K,Ba‖F,WO₄ and the quinary system Li,K,Ca,Ba‖F,WO₄, which were used for illustrating the application of the methods. Advantages of the algorithms were demonstrated in cases of competition of internal secants.     

Thermochemical Transformations in the Twelve-Salt Six-Component Reciprocal System Na,K,Ca,Ba∥F,SO4,WO4

Thermochemical characterization of the twelve-salt system Na,K,Ca,Ba∥F,SO₄,WO₄ (a 4∥3 system) and the four nine-salt five-component reciprocal subsystems is presented. A comparison of thermochemical relationships is carried out for these nine-salt systems, and the internal structural thermochemical transformations of exchange-reaction stages between all these systems are considered. The effect of a reaction stage on the final product yield is considered for sample chemical reactions. The thermochemical structure of basal tetrahedra of the singular star in the twelve-salt system is studied, and relationships are derived between various models of the system (salt-node indices in the matrix, reaction stages, geometrical figures) and chemical processes that occur in the system. These relationships can be used in experimental design.     

Thermochemical interpretation of phase diagrams for multinary reciprocal salt systems

For the first time the thermochemical evaluation of simplexes of the singular star for a type B five-component reciprocal nine-salt system has been carried out using the Na,K,Ba‖F,MoO₄,WO₄ system by the way of example, and a correlation has been found between the stages of exchange reactions and the morphology of the crystallization surfaces and volumes of salts in a simplex. This correlation can be used to design systems with desired properties. The largest crystallization volumes belong to salts that are formed by the exchange reactions of the highest stages for the given system.     

Differentiation of the Na,K,Ca,Ba‖F,WO4 multicomponent system and phase equilibria in its stable secant complex NaF-K2WO4-CaF2-BaF2

The Na,K,Ca,Ba‖F,WO₄ quinary mutual system was differentiated based on graph theory with consideration of identified internal secant elements using a program complex. For the first time, by a combination of physicochemical analysis methods (differential thermal, visual polythermal, X-ray diffraction and projection-thermal-analytical), the NaF-K₂WO₄-CaF₂-BaF₂ quaternary system was studied, which is a stable secant complex of the quinary mutual system. The coordinates of invariant points were determined.     

Phase equilibria in the quaternary systems Li‖F,Cl,Br,CrO4 and Li‖F,Cl,Br,WO4

Phase equilibria in the quaternary systems Li‖F,Cl,Br,CrO₄ and Li‖F,Cl,Br,WO₄ were studied by differential thermal analysis. In these systems, the stability of continuous series of solid solutions based on lithium chloride and bromide is preserved. The number and compositions of crystallizing phases in the systems Li‖F,Cl,Br,CrO₄ and Li‖F,Cl,Br,WO₄ were confirmed by X-ray powder diffraction analysis.     

Structural features of the singular star of type ABCC six-component 12-salt reciprocal systems in melts

This is the first consideration of utility of the geometrical model that represents the type BACC ⇆ ABCC six-component 12-salt reciprocal system Li,Na,K‖Cl,Br,NO₃,SO₄ as a singular star. The cells (hexatopes) of this model are considered in thermodynamic and chemical terms. Chemical appraisal is given to the cycles of the equilibrium (singular) star. Its utility is demonstrated for approaching practical problems. Criteria of the status of salts in salt mixtures are developed for predicting the heat contents of salt mixtures. A fundamentally new methodological approach is proposed to an experimental investigation of a hexatope is via parts of lower dimension systems involved in the hexatope and transition from one part to another by adding individual salts.     

Five-component reciprocal systems Na,K∥Cl,CO<Subscript>3</Subscript>,MoO<Subscript>4</Subscript>,WO<Subscript>4</Subscript> and Na,K∥F,CO<Subscript>3</Subscript>,MoO<Subscript>4</Subscript>,WO<Subscript>4</Subscript>

Five-component reciprocal systems Na,K∥Cl,CO₃,MoO₄,WO₄ and Na,K∥F,CO₃,MO₄,WO₄ have been studied by differential thermal analysis (DTA) and X-ray powder diffraction (XPD). The systems have been triangulated to phase simplexes. The main reciprocal and complex-formation reactions have been revealed. The stability of [Na,K]₂CO₃, Na₂[Mo,W]O₄, and K₂[Mo,W]O₄ binary solid solutions and the nonexistence of quintuple invariant points in the title systems have been verified.     

Chemical interaction in the quaternary mutual systems Li,K‖F,Cl,MoO4 and Li,K‖F(Cl),VO3,MoO4

The Li,K‖Cl,VO₃,MoO₄ system was partitioned into simplexes using graph theory, and the tree of phases for this system was constructed. The equations of the main reactions describing the chemical interaction in the quaternary mutual systems Li,K‖F,Cl,VO₃(MoO₄) and Li,K‖F(Cl),VO₃,MoO₄ were derived using the conversion patterns of partitioning elements. Based on the reaction equations and the data on the boundary elements, the prediction of phases crystallizing in the studied systems was made and confirmed by X-ray powder diffraction analysis.     

Interaction of salts in ionic melts of the ternary reciprocal systems Na,K‖BO2,MoO4 and Na,K‖BO2,WO4

The phase diagrams of the ternary reciprocal systems Na,K‖BO₂,MoO₄ and Na,K‖BO₂,WO₄ were studied for the first time by a calculation-experimental method and differential thermal analysis. The coordinates were determined for binary eutectics of the diagonal stable sections NaBO₂-K₂MoO₄(K₂WO₄) and the ternary invariant points e(55 mol % NaBO₂, 45 mol % K₂MoO₄, 740°C), e(55 mol % NaBO₂, 45 mol % K₂WO₄, 730°C), E(4.5 mol % NaBO₂, 78 mol % Na₂MoO₄, 17.5 mol % K₂MoO₄, 652°C), E(4.5 mol % NaBO₂, 78 mol % Na₂WO₄, 17.5 mol % K₂WO₄, 643°C), P₂(5 mol % NaBO₂, 56 mol % Na₂MoO₄, 39 mol % K₂MoO₄, 673°C), P₂(5 mol % NaBO₂, 56 mol % Na₂WO₄, 39 mol % K₂WO₄, 671°C). Binary solid solutions based on sodium and potassium metaborates were shown to be stable. Analytical models of phase equilibrium states of the ternary reciprocal systems Na,K‖BO₂,MoO₄(WO₄) were obtained, which enable one to calculate melting (crystallization) points and construct isotherms at any given composition. The specific heats of melting of samples of invariant compositions were found by quantitative differential thermal analysis.     

Topology of the Li‖F,Cl,CO<Subscript>3</Subscript>,MoO<Subscript>4</Subscript> four-component system

A computation-and-experiment technique and differential thermal analysis were used to study the Li‖F,CO₃,MoO₄ three-component system and Li‖F,Cl,CO₃,MoO₄ four-component system for the first time and to restudy the Li‖Cl,CO₃,MoO₄ and Li‖F,Cl,MoO₄ three-component systems.     

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.     

Solubilities in the Na,Ca‖SO4,F-H2O system at 0°C

Solubilities at invariant points of the Na,Ca‖SO₄,F-H₂O system at 0°C was studied, and a phase diagram of this system at 0°C was constructed.     

Phase equilibria in the Na,K,Mg,Ca‖SO4,Cl-H2O system at 50°C in the astrakhanite crystallization region

Phase equilibria of the Na,K,Mg,Ca‖SO₄,Cl-H₂O system at 50°C in the astrakhanite (Na₂SO₄ · MgSO₄ · 4H₂O) crystallization region were studied using the translation method. Astrakhanite was found to be involved, as an equilibrium phase of the title system, in 35 divariant fields, 39 monovariant curves, and 22 invariant points. The data gained were used to construct a fragment of a schematic equilibrium phase diagram of the title system in the astrakhanite crystallization region.     

Cobalt tungstate synthesis in melts of the (K2WO4-KCl)eut-CoSO4 (K,Co‖Cl,SO4,WO4) system

A rational process is developed for preparing cobalt tungstate. Cobalt tungstate samples are synthesized and identified in melts of the(K₂WO₄-KCl)_eut-CoSO₄ (K,Co‖Cl,SO₄,WO₄) system.     

Phase equilibria in the Na,K,Mg,Ca‖SO4,Cl-H2O system at 50°C in the halite crystallization field

Phase equilibria of the Na,K,Mg,Ca‖SO₄,Cl-H₂O system at 50°C in the halite (NaCl) crystallization field were studied using the translation method. Halite, which is an equilibrium phase of the title system at 50°C, was found to be involved in 25 invariant points, 59 monovariant curves, and 43 divariant fields. A fragment of the equilibrium phase diagram of the title system in the halite crystallization field was constructed.     

Phase equilibria in the Na,Ca‖SO4,CO3,F-H2O at 0°C

Phase equilibria in the Na,Ca‖SO₄,CO₃,F-H₂O system at 0°C were studied using the translation method. Seven invariant points, 18 monovariant curves, and 17 divariant fields were found to exist. A looped phase diagram (phase complex) of the title system was constructed.     

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.     

Certification of reference materials for the quality control of major element determinations in groundwater Part 2: Certification

The quality control of groundwater monitoring requires the availability of representative CRMs. This paper describes the preparation of two artificial groundwater reference materials, CRM 616 (high carbonate content) and CRM 617 (low carbonate content), the homogeneity and stability studies and the analytical work performed for the certification of a range of major elements (Ca, Cl, Fe, K, Mg, Mn, Na, NO₃, PO₄ and SO₄).     

Methodology for determining hidden partitioning elements in mutual multicomponent systems and physicochemical interactions in the LiF-K2WO4-CaF2-BaF2 system

A methodology for determining hidden partitioning elements while differentiating complexing multicomponent systems was developed using exchange reactions in ternary mutual systems and tested on ten quaternary mutual systems. For the first time, using a combination of such physicochemical analysis methods as differential thermal, X-ray powder diffraction, and projection-thermographic analyses, the LiF-K₂WO₄-CaF₂-BaF₂ quaternary system was studied, which involves the hidden partitioning element K₂WO₄-LiBaF₃ and is a stable partitioning complex of the Li,K,Ca,Ba∥F,WO₄ quinary mutual system. The coordinates of nonvariant points of the quaternary system were found.     

Partitioning of the quinary reciprocal system Li,K‖F,Cl,Br,MoO4 into simplexes and the investigation of its partitioning and stable elements

The quinary reciprocal system Li,K‖F,Cl,Br,MoO₄ was partitioned into simplexes using graph theory. A tree of phases of the system was constructed, and stable elements were identified. The chemical interaction in the system Li,K‖F,Cl,Br,MoO₄ was described by the ion balance method. The stable tetrahedra LiF-KCl-KBr-K₂MoO₄, LiF-KCl-KBr-LiKMoO₄, and LiF-Li₂MoO₄-KCl-KBr and the united stable pentatope LiF-KF-KCl-KBr-K₂MoO₄ were studied by differential thermal analysis, and phase states in the studied simplexes were determined. The compositions of crystallizing phases in the bulk of the studied tetrahedra and pentatope were confirmed by X-ray powder diffraction analysis.