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 (NPS) ≤ 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. © 2004 Blackwell Publishing Ltd.