A discrete lattice plane analysis of the energy of coherent {0001}h.c.p. • {111}f.c.c., 〈1120〉h.c.p.• 〈110〉f.c.c. interfaces

Abstract

A discrete lattice plane, regular solution, broken bond model, previously used to calculate the interfacial energy of f.c.c.:f.c.c. and b.c.c.:b.c.c. interphase boundaries, is extended to the situation in which there is a change in crystal structure across the interphase boundary, specifically to an interface between an f.c.c. and h.c.p. crystal. The particular interface studied, {0001}_h.c.p. • {111}_f.c.c., 〈11$\text{2}$0〉_h.c.p.• 〈1$\text{1}$0〉_f.c.c. was made fully coherent by choosing the appropriate lattice parameter ratio. Both f.c.c. and h.c.p. phases are taken to be regular solutions. Minimization of the grand potential yields a set of non-linear equations in the equilibrium composition of the planes in the interface region whose solute concentration differs from that of the bulk composition in either phase. These values of the compositions are then used to compute the interfacial free energy of the boundary. The variations in the concentration profile and interfacial free energy with temperature and regular solution constants were investigated. The concentration profile was found to be diffuse and also asymmetric. The diffuseness does not vary in any simple manner with temperature. The interfacial energy decreases with increasing temperature in the various situations considered.