The influence of elastic stress on the thermodynamic (equilibrium and kinetic) behavior of single phase and multiphase, multicomponent crystalline solids is examined. The proposed research includes theoretical analyses and experimental approaches to the problem. There are two thrusts in the proposal: (1) the development of a general paradigm for the treatment of phase equilibria, including equilibrium phase conditions, phase coexistence and phase diagram construction in homogeneously stressed and heterogeneously stressed systems; (2) the effect of stress on material response to imposed gradients in such thermodynamic potentials as the temperature, chemical activity, electric field and deformation (stress or strain). %%% Although most crystalline materials are subjected to various potential gradients in practice, little is known on how elastic stress affects material behavior in such circumstances. Elastic stresses can arise from internal sources such as composition gradients and coherency strains between phases or from external sources such as applied load.