SMOOTHING OF PERTURBED VICINAL SURFACES

The decay rate of a periodic profile in an arbitrary direction on a vi cinal surface is calculated on the basis of the following assumptions: (i) isotropic step energy and step interaction energy, the latter bei ng proportional to the square of the step density, (ii) small slopes o f the perturbation compared to the vicinal angle alpha, and (iii) surf ace migration limited kinetics. These assumptions are also generalized for two special perturbation directions (parallel and normal to the u nperturbed steps) to include anisotropy of step energies, a general la w of step-step interaction, and slopes not restricted to being small. In the latter case, numerical calculation yields profiles that are blu nter at the top and bottom than sinusoids and decay rates that increas e (at a declining rate) with amplitude A. Following Cahn and Taylor (A cta Metall. Mater. 42 (1994) 1045), a treatment of profile decay is al so given that incorporates attachment-detachment kinetics together wit h surface migration kinetics, providing a formal comparison of the two processes. A corresponding treatment, presented for an isolated step, gives a unified description of the fluctuation spectrum and shows tha t the rang of wave numbers q for which surface migration kinetics (q(4 )) holds for a vicinal surface is substantially greater than for the c orresponding isolated step.