Study of Non-Equilibrium Surface Diffusion from an Initial Step-Concentration Profile with a New Probability-Based Continuum Method

Abstract

We have studied the non-equilibrium diffusion coefficient in an adsorbate system which is initially in a state of step-concentration profile to understand the role of adsorbate-adsorbate interactions. We use a new kinetic algorithm based on the probability p(t,x) to find a particle at site x in time t. This probability is a measure of the local concentration. The main advantage of this method over standard Monte Carlo methods is the parallel update of the local concentration over the whole lattice (instead of the sequential updates as in conventional Monte Carlo methods; which is particularly important when the system is in the ordered phase). We have calculated the tracer diffusion coefficient, the diffusion coefficient based on the Boltzmann Matano method, and the diffusion coefficient based on the spreading of the width of the profile (which it is easier to measure experimentally). The system is studied both for the case of repulsive nearest-neighbor and competing (nearest-neighbor and next-nearest-neighbor) interactions. We have also analysed the non-equilibrium growth laws describing the evolution of the domains of the ordered phase for T < T _c . We confirm that the c(2 × 2) phase grows with the characteristic power law in time t ^1/2 (similar to the growth law observed during the evolution of the ordered phase out of a uniform initial random configuration).