A generalized thermodynamic treatment of phase equilibria in coherent multilayers

We present a generalized way of treating phase equilibria in coherent planar multilayers. A correct recognition of elastic stress and strain components as thermodynamic potentials or densities is crucial for the use of the criteria for intrinsic stability as well as for the applicability of the conventional method of common tangent construction and the Gibbs phase rule. It is shown that a method analogous to the conventional common tangent construction exists in thermodynamic density subspaces for which some of density variables are held constant. In a thermodynamic density subspace with m_s density variables fixed, a common tangent construction can be made between the extremized free energies for systems of (m_s+1)-phase coexistence in order to satisfy the thermodynamic equilibrium conditions of systems with more than m_s+1 coexisting phases. This method is applied to a coherent binary system configured as plane-parallel plates to demonstrate that equilibrium states with more than two coexisting phases cannot be thermodynamically stable in the binary multilayer system under certain mechanical loading conditions.