Analytics

Abstract

AbstractThe chapter reviews the basic analytic solutions of phase-field models at the mesoscopic scale. First the phase-field equation is derived by the Clausius-Duhem relation applied to a simple phase-field functional. The concept of variational derivative, related to the gradient contribution in the phase-field functional, is introduced. The traveling wave solution, or solitonian wave solution, for the phase-field equation in 1-dimension is derived for two relevant potential functions. Finally, the relations between model parameters and physically defined material parameters are derived.