V. I. Lutsyk

Relation between the Mass-Centric Coordinates in Multicomponent Salt Systems

An algorithm which allows to define relations between concentration coordinates of subsystems formed in the initial system consisting of simple elements is proposed. The same algorithm gives a possibility to determine the conditions under which the point belongs to the given concentration simplex or complex.

Parametric and matrix algorithms for calculating heterogeneous states in systems with an incongruently melting binary compound

A matrix description of the crystallization process is proposed, according to which all transformations of a melt can be presented as a set of products of the matrices of phase compositions and the vectors comprised of the mass fractions of the phases. It was demonstrated that this approach is simpler, more illustrative, and more versatile in predicting the microstructure of heterogeneous materials compared to the traditional methods of solving the problems involving center-of-mass determination. An algorithm for calculating the characteristics of two-phase equilibria based on parametric equations of its boundaries in isobaric-isothermic sections is given.

Verification of the T–x–y diagram of the Ag–Au–Bi system using a 3D computer model

Using two variants (with and without decomposition of the compound Au2Bi) of a 3D computer model of the T–x–y diagram of the system Ag–Au–Bi, it was shown that the published polythermal sections (both experimental and calculated by the CALPHAD method) agree in the high-temperature range of the T–x–y diagram for phase regions with melt, whereas in the low-temperature range the decomposition of a solid solution based on the compound Au2Bi is not taken into account.

3D model of the T–x–y diagram of the Bi–In–Sn system for designing microstructure of alloys

The published experimental and calculated data (binary systems, x–y projection of the liquidus, table of invariant reactions with the liquid phase, and one isothermal and two polythermal sections) were used for constructing a spatial computer model of the T–x–y diagram of the Bi–In–Sn system that was supplemented with the regions of the decomposition of the compound BimInn and the polymorphic transformation of tin. It was determined that the T–x–y diagram comprises 173 surfaces and 74 phase regions. Using the model for analyzing the material balances of phases and their microstructural components at all the stages of crystallization was demonstrated.

Three-dimensional model of phase diagram of Au-Bi-Sb system for clarification of thermodynamic calculations

A three-dimensional (3D) computer model of a T–x–y-diagram for an Au-Bi-Sb system is developed. It is established that it consists of 60 surfaces and 24 phase areas. It is used to show that works devoted to experimental studies and thermodynamic calculations of this system miss two surfaces and two phase areas in the iso- and polythermic sections.

Determining the conditions for changes of the three-phase reaction type in a V‒Zr‒Cr system

A 3D computer model of the T–x–y diagram for a V–Zr–Cr system is constructed, in which the possibilities of both two- and three-polymorphic modifications of compound ZrCr2 participating in invariant reactions is considered. The temperature and concentration borders of eutectic–peritectic transitions in the three-phase regions on the corresponding surfaces of two-phase reactions are determined (upon degeneration of a three-phase reaction into a two-phase reaction in the presence of the third phase).

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.

Triangulation of salt systems with barium borate

A program has been developed that implies the following operations: vertices of an n-component system are presented in the form of a graph, the adjacency matrix and the adjacency list with zero adjacencymatrix elements are written, the elements of the adjacency list are multiplied taking into account the absorption rule, and inversion is performed. The local X(x1, …, xm) barycentric coordinate subsystems in the unified space of an n-component system Z(z1, …, zn) are related by the equation Z = KX, where the Z coordinates of subsystem vertices are located in the columns of the matrix K [m × n]. The membership of the composition G(g1, …, gn) in subsystem K is determined by the condition 0 < xi < 1 for the roots of the equation G = KX. When recognizing the simplices formed by internal vertices, polyhedration is performed twice: first without these points and then only with respect to the microcomplexes with internal points. Formulas that relate the number of obtained simplices to the adjacency matrix have been derived to verify the results of polyhedration.

T–x–y Diagram of the MgO–SiO2–Al2O3 System: Computer Model Assembly

A computer phase diagram model is constructed for the MgO–SiO2–Al2O3 system, giving its complete geometric description and containing 10 liquidus surfaces, a liquid–liquid phase separation surface, 75 ruled surfaces at the boundaries between two-phase and three-phase fields, 11 horizontal four-simplex at invariant temperatures, 21 two-phase fields, and 30 three-phase fields. The description of surfaces and three-phase fields is presented.

3D Computer Models of T – x – y Diagrams, Forming the Fe–Ni–Co–FeS–NiS–CoS Subsystem

Abstract3D computer models of Fe–Ni–Co, Fe–Ni–FeS–NiS, Fe–Co–FeS–CoS, Ni–Co–NiS–CoS T–x–y diagrams have been designed. The geometric structure (35 surfaces, two-phase surface of the reaction type change, 17 phase regions) of the Fe–Ni–FeS–NiS T–x–y diagram is investigated in detail. The liquidus hypersurfaces prediction of the Fe–Ni–Co–FeS–NiS–CoS subsystem is represented.