PHASE-DIAGRAM TOPOLOGY AND THE INTRINSIC STABILITY RULE

An analysis of the ways in which n + 3 invariant points may be interco nnected in phase diagrams reveals a fundamental relationship between t he chemography of any system of n + 3 phases and the relative stabilit ies of those invariant points. The intrinsic stability rule as formula ted here states that only those straight line nets (potential solution s) are possible for which the composition space defined by the missing phases at the stable invariant points overlaps the space defined by t he missing phases at the metastable invariant points. In the absence o f such overlap, the missing phases in each space are intrinsically sta ble (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 o nly one of n + 3 invariant points is metastable, we show that this inv ariant point must be chemographically interior; that is, the phase tha t is missing at this invariant point is inside the space defined by th e remaining phases. Application of the intrinsic stability rule result s 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, al though 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 rul e allows the identity and correct numbers of straight line nets for an y system of n + 3 phases to be determined simply by visual inspection of the chemography alone or from an appropriate set of mass balance eq uations. These procedures are useful for evaluating whether the topolo gy of a proposed phase diagram is a valid one and for analyzing more c omplex systems with greater numbers of phases.