Phase equilibrium in non-fluids and non-fluid mixtures

A criterion of phase equilibrium for mixtures of materials with arbitrary symmetry (e.g. between solid and fluid or two solid mixture phases) is deduced using a rational thermodynamics approach. This criterion, known also as Maxwell relation, is expressed via the difference of chemical potential tensors (Eshelby tensors) on the singular surface dividing the bulk phases.The thermomechanical balance equations, the entropy inequality and the Maxwell relation for phase equilibrium are given first for the case of pure (one-constituent) materials of arbitrary symmetry and then for the case of mixtures (including chemically reacting ones) of arbitrary symmetry.In the special case of fluids it is shown that the chemical potential tensors reduce to the classical scalar chemical potentials and the Maxwell relations to the classical thermodynamic criterion for the phase equilibrium.