Simplified energy analysis on the equilibrium shape of coherent γ′ precipitates in γ matrix with a superspherical shape approximation

The shape transitions of coherent γ′ precipitates from spherical to cuboidal observed in Ni-base alloys with γ matrix are discussed with simplified energy consideration. Possible shapes of the γ′ precipitates are approximated with superspheres that are described by x12/a2p/2+x22/a2p/2+x32/a2p/2⩽1 with appropriate values of p p⩾2, where the xi axes are parallel with 100 of the γ′ precipitates. The supersphere becomes a sphere when p=2 and a cuboid when p→∞. The elastic strain energy and interface energy due to the misfit γ′ precipitates are evaluated approximately. The equilibrium shape of the γ′ precipitates is obtained as the shape that causes the minimum of sum total of the elastic strain energy and interface energy. It is shown that the present analysis reasonably explains the previous experimental results on the shape change of the γ′ precipitates in the Ni–Ni3Al alloy.