Triangulation schemes of three-component systems

Abstract

According to Gibbs' phase rule, a section of the phase diagram of a threecomponent system at P,T = const is a partition of the concentration triangle into the regions of the existence of phases, two�, and three� phase complexes. To describe the topology of such a section, it is convenient to denote one�, two�, and threephase regions by points, lines, and triangles, respectively. If the system at given Р and Т contains no phases with unlimited solubility of two or three com� ponents, the topology of the section can be repre� sented as a partition of the concentration triangle into elementary triangles with the vertices corresponding to components or compounds. The scheme of triangu� lation of the concentration triangle uniquely repre� sents the structure of the network of lines of monova� riant equilibria in the melting diagram. Such schemes also describe the structure of the piecewise continuous solidus surface of the phase diagrams of ternary sys� tems. The triangulation schemes of the solidus surface should be constructed for analyzing possible variants of the structure of the liquidus surface of ternary sys� tems (1, 2). Let us denote the solid phases by α, β, and γ and the liquid by L. Each threephase region αβγ of the solidus surface corresponds to the invariant point of the liquidus surface that characterizes the equilib� rium Lαβγ between the liquid phase and the solid phases. The monovariant equilibrium lines Lαβ, Lαγ, and Lβγ issuing from this point correspond to the sides of the abc triangle. Therefore, the figure formed by monovariant equilibrium lines and the invariant points in the liquidus surface is dual to the triangulation scheme of the solidus surface. This fact was used for classifying the melting diagrams of ternary systems with solid phases of constant compositions (3). Note also that the topology of the phase diagram of a ternary system can be regarded as the topology of the partition of the Р-Т space into regions each of which is represented by a certain triangulation scheme. The union of such schemes with the identified correspond� ing region of the