On the classification of phase transitions involving changes in composition

We show that phase transitions involving the decomposition of a homogeneous phase into two phases with different compositions cannot be described adequately within the context of the Ehrenfest classification scheme. The Gibbs free energy and its first derivatives with respect to temperature, pressure, and alloy composition are continuous at the transition temperature (in the absence of coherency stress effects) while the second derivatives are usually discontinuous implying, within the context of the Ehrenfest scheme, that these phase transitions are second-order. We suggest that order parameters, defined as the difference between the equilibrium phase compositions and the bulk alloy composition, can be used more effectively to classify phase transitions involving compositional changes; the order of the transition being determined by the discontinuities in the order parameters. In this way we are able to identify three different types of phase transitions in simple solid binary alloys.