Solid–liquid equilibrium for non-hydrostatic stress Original Research Article

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 pF. We show that the equilibrium melting temperature TN for the non-hydrostatically stressed solid in contact with a melt at pressure pF is below the equilibrium melting temperature TH of the hydrostatically stressed solid at pF. Furthermore, for small strain and linear isotropic elasticity, the deviation, TH−TN, is shown to be quadratic in the differences between the principal values of the stress tensor and −pF. 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, TH−TN 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.