Coherent phase diagrams

Phase equilibria in coherent solids differ significantly from equilibria in fluids or incoherent solids. Gibbs' phase rule usually does not apply, the field lines on a phase diagram do not coincide with the equilibrium phase compositions, phase compositions in a two-phase field depend on the bulk alloy composition and, for a given set of imposed thermodynamic variables, several equilibrium states may exist. These conditions place significant constraints on the use of coherent phase diagrams. This paper discusses some aspects of phase equilibria that are unique to coherent systems and how phase information may be conveyed when phase stability diagrams are used in lieu of coherent phase diagrams. The utility of phase stability diagrams lies in their ability to display graphically the equilibrium states of a two-phase coherent system as a function of alloy composition (in much the same way that Gibbs energy vs composition curves show equilibrium states for a fluid system).