Step Motion on Crystal Surfaces

It is postulated that steps on crystal surfaces capture atoms diffusing on the surface with certain probabilities and, in addition, that the capture probability depends on the direction from which adsorbed atoms approach the step. A general solution for the time-dependent step distribution is obtained in terms of these probabilities and an arbitrary initial distribution of an infinite sequence of parallel steps. It is shown that coalescence of steps or stabilization of step spacings can occur as a consequence of assuming that capture probabilities are directionally dependent. Some of the implications of the theoretical model are related to the growth of real crystal surfaces.