The Effects of Mobile Vacancies and Impurities on the Kinetics of Ordering at Surfaces

Abstract

The kinetics of the ordering processes in two-dimensional lattice models with annealed vacancies (inert impurities) and non-conserved order parameter is studied as a function of vacancy concentration by means of Monte Carlo temperature-quenching simulations. The models are Ising antiferromagnets with couplings leading to two-fold degenerate as well as four-fold degenerate (2 × 1)-ordering. The growth for the pure systems is found to be described by a power law with the classical growth exponent, n — 1/2. For the dilute systems there is a distinct crossover at late times to a much slower growth behavior similar to that found in systems with quenched randomness. These results apply to both types of ordering suggesting that the effects on ordering kinetics of vacancy diffusion and annealed randomness do not depend on the symmetry of the order parameter. The results of the model study are relevant for the interpretation of experiments on ordering in impure overlayers on solid surfaces. The finding of a crossover from an algebraic growth law for the pure system to a much slower growth mode in the dilute system is in accordance with recent high-resolution LEED experiments on the oxygen ordering on W(112)-surfaces doped with nitrogen.