A NEW METHOD FOR THE DERIVATION OF THE CLOSED NETS IN THE PHASE DIAGRAM SPACE OF MULTISYSTEMS. I. THE ABSENT PHASE SUBSTITUTION METHOD

Abstract

A new convenient combinatorial method is developed here to derive the invariant points in multisystem closed nets - the absent phase substitution (APS) method. It substantially simplifies the derivation of the closed nets in multisystems with many components and phases. For the multisystems whose total phase number (N PS ) ≤ twice the number of the absent phases (m ) in an invariant assemblage, the method can yield regular closed nets with or without globally absent phases; for other multisystems, the method can yield the regular closed nets with globally absent phases. As examples, the APS method was used to predict: (1) the regular closed nets of unary to quinary n + 4-phase multisystems, unary 6-phase multisystem and ternary 8-phase multisystem; (2) the basic properties of the regular closed nets of the quaternary and quinary multisystems with n + 4 and n + 5 phases. Two multisystems were chosen to demonstrate how to select a realistic closed net from the numerous possible closed nets of a complex multisystem, and how to derive a realistic partially closed-net, closed-net-diagram and the related realistic straight-line-net-diagram. Comparisons of our APS method for the derivation of complicated closed nets with other methods indicate that this method is much simpler and more efficient.