Nonlinear interaction of macrosteps on vicinal surfaces at crystal growth from vapor

•Kinematic waves form on the vicinal NaCl(1 0 0) surfaces at growth from vapor.•The KdV-Burgers equation for the growth model is derived by the averaging method.•Vicinal NaCl(1 0 0) profile is described by monotone shock waves without oscillation.•Shock wave amplitude and velocity decrease with decreasing average density of steps. The profile dynamics of a macroscopic curved vicinal surface of a crystal, during its growth from the vapor phase, has been investigated. The averaging method on large intervals of spatial coordinate change, which nevertheless remained infinitely small, was used. The expressions for average values of adatom concentration and velocity of elementary steps were obtained. With a phenomenological account of the boundary curvature, the nonlinear Korteweg-de Vries-Burgers equation describing the concentration of adatoms on a macroscopically curved vicinal surface of a crystal was obtained. A monotone shock wave without oscillation was considered and its parameters were determined. The obtained theoretical results have been confirmed by experimental data for some alkali-halide crystals.