Representation of high-dimensional solid-liquid phase diagrams of ionic systems

A generic framework is presented for representation of the solid-liquid phase behavior of multicomponent ionic systems with and without compound formation. Isothermal isobaric phase behavior is represented in form of digraphs. The invariant points in the composition space are identified as vertices of the digraph. These vertices are connected by edges identified from the adjacency matrix, which is constructed by using a set of generic rules based on Gibbs phase mle. These edges form the boundaries of high-dimensional saturation varieties which are identified from the saturation variety matrix. For graphical representation, the number of independent coordinates is calculated and a suitable set of coordinates is developed. Projections are used to view high-dimensional phase diagrams in their entirety and to simplify the analysis of the phase behavior. Potential applications of this framework include facilitation of experimental development and computer-aided design of crystallization-based separation processes.