Solid–liquid equilibrium for non-hydrostatic stress

Abstract We examine Gibbs’ conditions for equilibrium of a non-hydrostatically stressed single component solid in equilibrium across one of its faces with a pure liquid at pressure p F . We show that the equilibrium melting temperature T N for the non-hydrostatically stressed solid in contact with a melt at pressure p F is below the equilibrium melting temperature T H of the hydrostatically stressed solid at p F . Furthermore, for small strain and linear isotropic elasticity, the deviation, T H − T N , is shown to be quadratic in the differences between the principal values of the stress tensor and − p F . The result depends on both the bulk modulus and the shear modulus of the solid. Even for stresses as large as a typical yield stress, T H − T N is equal to 1 K or less. Nevertheless, the liquid in equilibrium with this non-hydrostatically stressed solid is always unstable with respect to the formation of hydrostatic solid.