SINGULAR POINT ANALYSIS - CONSTRUCTION OF SCHREINEMAKERS PROJECTIONS FOR SYSTEMS WITH A BINARY-SOLUTION

Variation in the composition of a solution phase in a univariant equilibrium can lead to a condition such that the reaction coefficient of one phase in the equilibrium vanishes. This condition is known as a singular point, and at such points the univariant equilibrium becomes degenerate with a singular univariant equilibrium. In general, in a (c + 2)-phase system that contains a single binary solution any two univariant equilibria will share a common singular equilibrium. The number of ways two univariant equilibria can be related by a singular equilibrium is constrained by Schreinemakers principles. These constraints are summarized by seven rules that limit the number of ways in which singular points can be arranged about an invariant point in a Schreinemakers projection. The resulting projection is a singular-point net, and for each singular-point net the direction of compositional variation in the solution phase is uniquely determined along every univariant curve. This has the interesting consequence that if the direction of compositional variation along one univariant curve around an invariant point is known, then the directions of compositional variation along the remaining curves can be determined solely from topologic constraints. The same constraints can be applied to systems containing simple mineral solutions or melts in order to predict compositional variations.