Coherent Precipitation — Phase Field Method

Abstract

Phase transformation is still the most efficient and effective way to produce various microstructures at mesoscales, and to control their evolution over time. In crystalline solids, phase transformations are usually accompanied by coherency strain generated by lattice misfit between coexisting phases. The coherency strain accommodation alters both thermodynamics and kinetics of the phase transformations and, in particular, produces various self-organized, quasi-periodical array of precipitates such as the tweed [1], twin [2], chessboard structures [3], and fascinating morphological patterns such as the stars, fans and windmill patters [4], to name a few (Fig. 1). These microstructures have puzzled materials researchers for decades. Incorporation of the strain energy in models of phase transformations not only allows for developing a fundamental understanding of the formation of these microstructures, but also provides the opportunity to engineer new microstructures of salient features for novel applications. Therefore, it is desirable to have a model that is able to predict the formation and time-evolution of coherent microstructural patterns.