Predicting equilibrium shape of precipitates as function of coherency state

A general approach is proposed to predict the equilibrium shapes of precipitates in crystalline solids as function of size and coherency state. The model incorporates effects of interfacial defects such as misfit dislocations and structural ledges on transformation strain and on interfacial energy. Using α precipitation in α/β titanium alloys as an example, various possible equilibrium shapes of precipitates having different defect contents at interfaces are obtained by phase-field simulations. The simulation results agree with experimental observations in terms of both precipitate habit plane orientation and defect content at the interface. In combination with crystallographic theories of interfaces and experimental characterization of habit plane of finite precipitates, this approach has the ability to predict the coherency state (i.e. defect structures at interfaces) and equilibrium shape of finite precipitates.