Topology of Isobaric–Isothermic Phase Diagrams for Five-Component Systems

Abstract

The simplest isobaric–isothermic phase diagram for a five-component system can be considered a four-dimensional simplex (pentatope) containing 5 vertices, 10 edges, 10 triangular faces, and 5 tetrahedral hyperfaces. Adding one compound formed from r components (2 ≤ r ≤ 5) to the system partitions the simplex into 2–5 filial pentatopes, in which the neighboring pentatopes have a common tetrahedral face. It is proposed that the topology of the system be described using two graphs. The vertices of the graph of a diagram are labeled with the symbols of components and compounds, while its edges indicate which of these phases are in thermodynamic equilibrium. The vertices of the pentatope adjacency graph symbolize pentatopes, and the edge connects two adjacent pentatopes with a common tetrahedral hyperface. Knowledge of the adjacency graph allows enumeration of all elements of the diagram and determination of their relative positions in 4D space. Topological properties characteristic of phase diagrams are considered.