Dynamics of Phase Separation of Crystal Surfaces

Details Dynamics of Phase Separation of Crystal Surfaces Dynamics of Phase Separation of Crystal Surfaces

1993-03-09

arxiv.org/abs/cond-mat/9303018v1

Physics

Condensed Matter

26 pages in Tex, 7 figures (not included), NSF-ITP-93-28

Scientific paper

10.1103/PhysRevB.48.5808

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. Our analysis emphasizes the importance of crystalline anisotropy and the interaction between phase boundaries in controlling the long time dynamics. 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 $L(t)\sim t^n$ of the typical pattern size is attained with exponent $n\approx 0.23$ and $n\approx 0.13$, for the two ordering mechanisms dominated by evaporation-condensation and by surface-diffusion respectively.

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