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) is similar to t(n) of the typical pattern size is attained with exponent n almost-equal-to 0.23 and n almost-equal-to 0.13, for the two ordering mechanisms dominated by evaporation and condensation and by surface diffusion, respectively.