CALCULATED EVALUATION OF THE DEGREE OF SUBSOLIDUS STRUCTURE COMPLEXITY OF THE PHYSICO-CHEMICAL THREE-COMPONENT SYSTEMS

The study of state diagrams of multicomponent physicochemical systems is the most science-intensive task of materials science. Without knowledge about the structure of the state diagrams of such systems, it is impossible for technologists to predict the phase composition of materials during their production and use of products from them; the systematic analysis of the results of experimental studies to optimize the properties of the materials being developed becomes much more complicated. In refractory technology, the defining stage of production is solid-phase sintering, which makes the information on the subsolidus structure of state diagrams of physicochemical systems represented by a set of components in accordance with the planned phase composition of materials particularly important. Three-component systems, the simple components of which are refractory oxides, constitute the physicochemical basis of most mass-produced refractories and their subsolidus structure is quite clearly displayed in the concentration triangle of the system by a set of triangles, the vertices of which are the points of the composition of the compounds. The study is devoted to the establishment of an analytical relationship between the number of double and triple compounds and the number of all possible segments of connecting lines between the points of the composition of the connections, as well as the points of intersection of the compounds between themselves. During the research, the general principles of systems analysis, logical methods and terminology of physicochemical analysis of multicomponent systems, as well as information on elementary mathematics from the sections on numerical series, the basics of combinatorics and algebra were used. The corresponding analytical expressions make it possible to calculate the quantitative classification characteristics in the taxonomy of multicomponent systems by the degree of complexity of the structure of their subsolidus regions, in particular, when comparing the complexity of studies of three-component oxide systems and their typification. The formulas obtained were tested for calculations using examples of specific oxide systems. The research results allow one to obtain important quantitative characteristics for assessing the degree of complexity of the subsolidus structure of three-component systems.