8. Precipitation kinetics for non-spherical precipitates

When precipitates form in a crystalline matrix, they are rarely spherical. Understandably, when two crystalline forms are in contact via an interface, the anisotropy of each of the two crystalline structures can generate an anisotropy in the shape of the precipitates. This may result from a combination of at least three factors:

• interface energy anisotropy, which favors certain interfaces over others that are more costly;

• growth rate anisotropy, which favors precipitate growth in certain directions, due, for example, to differences in interface mobility;

• elastic energy anisotropy, when interfaces are coherent.

By combining interface energy and elasticity calculations, we can predict the equilibrium shape of anisotropic precipitates. The...