PHASE-DIAGRAM TOPOLOGY AND THE INTRINSIC STABILITY RULE

An analysis of the ways in which n + 3 invariant points may be interconnected in phase diagrams reveals a fundamental relationship between the chemography of any system of n + 3 phases and the relative stabilities of those invariant points. The intrinsic stability rule as formulated here states that only those straight line nets (potential solutions) are possible for which the composition space defined by the missing phases at the stable invariant points overlaps the space defined by the missing phases at the metastable invariant points. In the absence of such overlap, the missing phases in each space are intrinsically stable (or metastable), because there are no chemical reactions among the phases in the one space that can affect the stabilities of phases in the other space. In the special case proven by Zharikov (1961) where only one of n + 3 invariant points is metastable, we show that this invariant point must be chemographically interior; that is, the phase that is missing at this invariant point is inside the space defined by the remaining phases. Application of the intrinsic stability rule results in 14 and 22 straight line nets for unary 4-phase and binary 5-phase systems, respectively. Each of the 16 nondegenerate chemographies in ternary systems with 6 phases yields exactly 32 straight line nets, although the number of combinatorial possibilities is far greater. These results are in accordance with the number given by the Mohr and Stout (1980) formulation of (n + 2)(n + 3) + 2. The intrinsic stability rule allows the identity and correct numbers of straight line nets for any system of n + 3 phases to be determined simply by visual inspection of the chemography alone or from an appropriate set of mass balance equations. These procedures are useful for evaluating whether the topology of a proposed phase diagram is a valid one and for analyzing more complex systems with greater numbers of phases