Strain-induced shape changes of cubic precipitates in a cubic matrix with positive anisotropy

This paper considers the evolution of equilibrium shape during the coarsening of a system of cubic precipitates in a cubic matrix with positive anisotropy Δ = C11 - C12 - 2C44 > 0). The system is assumed to have homogeneous elastic constants and isotropic surface tension. The low-energy shapes include the sphere, and the octahedron, tetrahedron and plate with {111} faces. Minimization of the sum of the elastic and surface energies shows that the sphere is preferred at arbitrarily small sizes, but ordinarily transforms into a tetrahedron, and finally in a plate as size increases. When Δ > 0.79C11 the octahedron is preferred for a small range of sizes between sphere and tetrahedron. Analytic expressions are given from the equilibrium shape transitions. The results are compared to experimental observations of shape changes during coarsening in (mg, Y)-ZrO2. The experimentally observed absence of octahedral shaped precipitates and the size at which tetrahedral shaped precipitates become stable in this system are consistent with the theoretical predictions