  Coherency misfit stresses and their related anisotropies are known to
influence the equilibrium shapes of precipitates. Additionally, mechanical
properties of the alloys are also dependent on the shapes of the precipitates.
Therefore, in order to investigate the mechanical response of a material which
undergoes precipitation during heat treatment, it is important to derive the
range of precipitate shapes that evolve. In this regard, several studies have
been conducted in the past using sharp interface approaches where the influence
of elastic energy anisotropy on the precipitate shapes has been investigated.
In this paper, we propose a diffuse interface approach which allows us to
minimize grid-anisotropy related issues applicable in sharp-interface methods.
In this context, we introduce a novel phase-field method where we minimize the
functional consisting of the elastic and surface energy contributions while
preserving the precipitate volume. Using this method we reproduce the
shape-bifurcation diagrams for the cases of pure dilatational misfit that have
been studied previously using sharp interface methods and then extend them to
include interfacial energy anisotropy with different anisotropy strengths which
has not been a part of previous sharp-interface models. While we restrict
ourselves to cubic anisotropies in both elastic and interfacial energies in
this study, the model is generic enough to handle any combination of
anisotropies in both the bulk and interfacial terms. Further, we have examined
the influence of asymmetry in dilatational misfit strains along with
interfacial energy anisotropy on precipitate morphologies.
