Dynamics of phase separation of crystal surfaces

We investigate the dynamical evolution of a thermodynamically unstable crystal surface into a hill-and-valley structure. We demonstrate that, for quasi-one-dimensional ordering, the equation of motion maps exactly to the modified Cahn-Hilliard equation describing spinodal decomposition. Orderings in two dimensions follow the dynamics of continuum clock models. We establish that the hill-and-valley pattern coarsens logarithmically in time for quasi-one-dimensional orderings. For two-dimensional orderings, a power-law growth L(t){~}tⁿ of the typical pattern size is attained with exponent n{}0.23 and n{}0.13, for the two ordering mechanisms dominated by evaporation and condensation and by surface diffusion, respectively.