Dynamics of Phase Separation of Crystal Surfaces

Abstract

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.

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

References in corpus (2)

• Logarithmically slow domain growth in nonrandomly frustrated systems: Ising models with competing interactions
• Phase Ordering Dynamics in the Continuum q-state Clock Model

Cited by in corpus (18)

• Measuring the surface stress polar dependence
• Stationary solutions of driven fourth- and sixth-order Cahn-Hilliard type equations
• A diffuse-interface approach for solid-state dewetting with anisotropic surface energies
• Nonlinear wavelength selection in surface faceting under electromigration
• Dewetting of an ultrathin solid film on a lattice-matched or amorphous substrate
• Contrasts between coarsening and relaxational dynamics of surfaces
• Coarsening scenarios in unstable crystal growth
• Morphologies and kinetics of a dewetting ultrathin solid film
• Phase Separation of Crystal Surfaces: A Lattice Gas Approach
• Effect of driving on coarsening dynamics in phase-separating systems
• Nucleation of crystal surfaces with corner energy regularization
• Comparative study of a solid film dewetting in an attractive substrate potentials with the exponential and the algebraic decay
• Dendritic growth at very low undercoolings
• Coarsening dynamics at unstable crystal surfaces
• Interplay of Quantum Size Effect, Anisotropy and Surface Stress Shapes the Instability of Thin Metal Films
• Electromigration-driven Evolution of the Surface Morphology and Composition for a Bi-Component Solid Film
• A Mean-Field Theory for Coarsening Faceted Surfaces
• Regularity of gradient vector fields giving rise to finite Caccioppoli partitions