Phase rule for critical coexistence manifolds

Abstract

In high-dimensional phase diagrams there appear variations of singular manifolds other than coexistence and critical manifolds, e.g. the critical endpoint. The general singular manifold can be taken as a manifold on which p phases coexist and each phase of the order O j , whereas O j = 1 for an ordinary phase. In an n-dimensional phase diagram, the dimension of the singular manifold d has been shown to satisfy d ⩾ n + p + 1–2 Σ p j = 1 O j . This is the general phase rule including those of coexistence points and critical points as special cases.