Phase field modelling of interfacial anisotropy driven faceting of precipitates

We use extended Cahn-Hilliard (ECH) equations to study faceted precipitate morphologies; specifically, we obtain four sided precipitates (in 2-D) and dodecahedron (in 3-D) in a system with cubic anisotropy, and, six-sided precipitates (in 2-D, in the basal plane), hexagonal dipyramids and hexagonal prisms (in 3-D) in systems with hexagonal anisotropy. Our listing of these ECH equations is fairly comprehensive and complete (upto sixth rank tensor terms of the Taylor expansion of the free energy). We also show how the parameters that enter the model are to be obtained if either the interfacial energy anisotropy or the equilibrium morphology of the precipitate is known.