Concerning the Curvatures of Single Phase Surfaces in Ternary Phase Diagrams

The application of the common tangent principle to free energy - composition surfaces is considered. It is shown that the construction requires that single phase surfaces on either side of a two phase volume must always exhibit the same sign of curvature - contrary to that shown in many published phase diagrams. In general, these curvatures will be such that the surfaces are mutually concave towards the more stable phase. A number of examples are discussed.