Relaxation of Crystal Shapes Caused by Step Motion

Shape relaxation of a crystal faces and of vicinal faces is theoretically studied interms of step movement. When a flat vicinal surface is perturbed, the power of wave number dependence in the relaxation time τ is determined by the bottleneck process, step movement or diffusion, and the proportionality constant depends on the relative angle of the wave vector and the steps. If a small crystal is quenched through a roughening transition, a new equilibrium shape with a facet emerges when the step loops shrink or expand. If diffusion is fast, D s →∞, gradual flattening occurs with τ∝ R c 2 ( R c : radius of the 2D critical nucleus). If the step mobility is large, η s →∞ and the transport relies on slow diffusion, a small facet appears on the top of the crystal and the facet size expands as R f ∝ t 1/5 .