Abstract General conditions are derived for thermochemical equilibrium among multiphase and multicomponent network solids that are stressed nonhydrostatically and nonuniformly, and are in contact with each other and with fluids. Different multiphase equilibrium conditions are obtained depending on whether or not vacancies are present and which of three types of phase contact, coherent or incoherent solid-solid or solid-fluid interfaces, govern the constraints on displacement and mass transfer at these contacts. When no vacancies are present, Gibbs' result for the solid-fluid case is obtained and generalized. When vacancies are present, nonuniform and nonhydrostatic equilibrium is possible, but strong restrictions are placed on solid-fluid (all fluids must have the same pressure) and incoherent boundaries. A local equilibrium condition may be valid in some cases when vacancies prevent global equilibrium. Equilibria at coherent boundaries are unaffected by the presence or absence of vacancies, because vacancies behave like any other conserved chemical species there. The additional constraints at coherent boundaries reduce the number of degrees of freedom for phase equilibria.
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