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

The shape transitions of coherent gamma' precipitates from spherical to cuboidal observed in Ni-base alloys with gamma matrix are discussed with simplified energy consideration. Possible shapes of the gamma' precipitates are approximated with superspheres that are described by (x(1)(2)/a(2))(p/2)+(x(2)(2)/a(2))(p/2)+(x(3)(2)/a(2))(p/2) less than or equal to 1 with appropriate values of p (p greater than or equal to 2), where the x(i) axes are parallel with <100> of the gamma' precipitates. The supersphere becomes a sphere when p = 2 and a cuboid when p --> infinity. The elastic strain energy and interface energy due to the misfit gamma' precipitates are evaluated approximately. The equilibrium shape of the gamma' 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 gamma' precipitates in the Ni-Ni3Al alloy. (C) 2002 Elsevier Science Ltd. All rights reserved.