Energy analysis with a superspherical shape approximation on the spherical to cubical shape transitions of coherent precipitates in cubic materials

Energy consideration is made to discuss the spherical to cubical shape transitions of coherent precipitates in cubic materials. A superspherical shape approximation is adopted to describe intermediate shapes of the precipitates between a sphere and a cube. The elastic strain energy due to the misfit precipitates is evaluated by solving three-dimensional inclusion problems of cubic materials for superspherical inclusions with uniform eigenstrains. One of the advantages of the present analysis is that the shape transitions of the precipitates from spherical to cubical can be discussed with simple analysis using a parameter describing the cubic character of precipitates. The present theoretical results well explain the previous experimental results on the shape transitions of precipitates for Ni–Ni3Al and Cu–Co–Cr alloys.