Solid-Liquid Equilibrium for Non-Hydrostatic Stress
R F. Sekerka, John W. Cahn
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(superscriptF). We show that the equilibrium melting temperature T(subscriptN) for the non-hydrostatically stressed solid in contact with a melt at pressure p (superscript F) is below the equilibrium melting temperture T(subscript H) of the hydrostatically stressed solid at p (superscript F). Furthermore, for small strain and linear isotropic elasticity, the deviation, T(subscript H) - T(subscript N), is shown to be quadratic in the differences between the principal values of the stress tensor and -p(superscript 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(subscript H) - T(subscript N) is equal to 1K or less.