Spinodal decomposition of a crystal surface

A phenomenological equation of motion for an unstable planar crystalline interface is derived and used to describe the early stages of hill and valley formation. We calculate the critical wave number for the growth of instabilities and the scattering structure function. Predictions for the temperature dependence of the width-to-length ratio and the front propagation velocity in Si are presented. The importance of an elastic interaction on the domain formation process is demonstrated and shown to explain existing experiments. Elastic interactions are also found to modify the decay rate of perturbations of stable surfaces at arbitrarily long wavelengths.