Phase-Field Method

Phase-field model [2010Wan, 2002Chen] is widely used to simulate microstructural evolution of compositional/structural domains and kinetics of interfaces. By applying Khachaturyan’s microscopic elasticity theory [2013Kha], phase-field model can precisely predict precipitate morphologies and effects of point/line/planar/bulk defects. Phase-field model can also predict microstructure evolution in existence of external fields such as elastic field, electric field, and magnetic field. A general expression of phase field model is

(1)

In the first part of the integration, energy terms such as chemical energy and self-elastic energy are considered in , where is some field such as order parameter, and is usually composition field. Interfacial energy and chemical gradient energy are calculated in and . When applying long-range external field such as elastic field and magnetic field, counts the long-range interactions. Time evolution of microstructure is controlled by the total energy F.