Effect of elastic interaction on nucleation: I. Calculation of the strain energy of nucleus formation in an elastically anisotropic crystal of arbitrary microstructure

We analyze the anisotropic elastic interaction of a nucleating particle with an arbitrary pre-existing coherent microstructure. Under the assumption that the length scale of the microstructure is considerably larger than the size of the nucleus, their elastic interaction energy can be expressed as a linear function of the nucleus’s volume, and combined directly with the chemical nucleation driving force in the classical nucleation theory. Using cubic → cubic and cubic → tetragonal transformations as examples, we evaluate the elastic energy associated with the formation of a nucleus in a pre-existing microstructure. It is found that, similar to other stress-generating crystalline defects, coherent precipitates could have a significant effect on the spatial location of nuclei, resulting in correlated nucleation where the existing particles dictate where the new particles appear. This effect seems to be generic for nucleation in coherent solids and it could be responsible for the formation of self-organized morphological patterns during coherent transformations.