Phase-Field Models

The transport-limited growth of crystals can create complex morphologies due to the occurrence of morphological instabilities and subsequent evolution of the interfaces. The phase-field method has emerged as a compact and elegant mathematical tool for the modelling and numerical simulation of such phenomena. It is based on the evolution equations of out-of-equilibrium thermodynamics, which are derived from Ginzburg-Landau free energy functionals. Interfaces are represented implicitly by profiles of suitable order parameters. This chapter will first introduce some fundamentals underlying the construction of phase-field models, and then review several phase-field models for solidification as examples for the description of complex microstructure formation processes.