Equilibrium and diffusion in coherent multilayers

A thermodynamic treatment is presented of isothermal phase equilibria and diffusion in coherent planar multilayers. For two-component systems, coherent two-phase equilibrium compositions can often be generated using the familiar procedure in which a line is constructed doubly tangential to the coherent free energy functional(s). Only in special cases, however, are the phase equilibria so generated independent of the average composition (for unsupported multilayers) or the substrate effective composition (for multilayers coherently attached to a substrate). The common tangent construction is extended to ternary solution systems, and conditions for which the coherent ternary equilibria are independent of the average or substrate compositions defined.The formal thermodynamic aspects of diffusion in binary and ternary solids are reviewed, and the expected effects of coherency strain on the diffusional homogenization process outlined. The diffusion formalism can often be extended to account for coherency strains simply by substituting the coherent free energy density for its incoherent counterpart. In ternary and higher order systems, it is always possible to choose an initial condition that is free of strain; it is not in general possible to maintain this strain-free condition during the course of diffusional homogenization. The general effect of strain energy on ternary diffusion is to rotate the diffusion eigenvectors such that the strain is reduced. Some sample calculations are presented for the system CuAuAg.