Kinetics of faceting of crystals in growth, etching, and equilibrium

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Abstract
The faceting of crystals in equilibrium with the gas phase and also during crystal growth and etching conditions is studied using the Monte Carlo method. The dynamics of the transformation of unstable crystallographic orientations into hill and valley structures and the spatial patterns that develop are examined as functions of surface temperature, crystallographic orientation, and strength of interatomic potential for two transport processes: adsorption-desorption and surface diffusion. The results are compared with the continuum theory for facet formation. Thermodynamically unstable orientations break into hill and valley structures, and faceting exhibits three time regimes: disordering, facet nucleation, and coarsening of small facets to large facets. Faceting is accelerated as temperature increases, but thermal roughening can occur at high temperatures. Surface diffusion is the dominant mechanism at short times and small facets but adsorption-desorption becomes important at long times and large facets. Growth and etching promote faceting for conditions close to equilibrium but induce kinetic roughening for conditions far from equilibrium. Simultaneous irreversible growth and etching conditions with fast surface diffusion result in enhanced faceting.