EQUILIBRIUM AND DIFFUSION IN COHERENT MULTILAYERS

A thermodynamic treatment is presented of isothermal phase equilibria and diffusion in coherent planar multilayers. For two-component system s, coherent two-phase equilibrium compositions can often be generated using the familiar procedure in which a line is constructed doubly tan gential to the coherent free energy functional(s). Only in special cas es, however, are the phase equilibria so generated independent of the average composition (for unsupported multilayers) or the substrate eff ective composition (for multilayers coherently attached to a substrate ). The common tangent construction is extended to ternary solution sys tems, and conditions for which the coherent ternary equilibria are ind ependent of the average or substrate compositions defined. The formal thermodynamic aspects of diffusion in binary and ternary solids are re viewed, and the expected effects of coherency strain on the diffusiona l homogenization process outlined. The diffusion formalism can often b e extended to account for coherency strains simply by substituting the coherent Free energy density for its incoherent counterpart. Tn terna ry and higher order systems, it is always possible to choose an initia l condition that is free of strain; it is not in general possible to m aintain this strain-free condition during the course of diffusional ho mogenization. The general effect of strain energy on ternary diffusion is to rotate the diffusion eigenvectors such that the strain is reduc ed. Some sample calculations are presented for the system Cu-Au-Ag. Co pyright (C) 1996 Acta Metallurgica Inc.