Diffusion and relaxation kinetics in stochastic models for crystal growth

The combined influence of relaxation and diffusion processes on the dynamic behavior of stochastic models for crystal growth is systematically investigated. The models are the kinetic Ising model, the discrete Gaussian model, and the SOS–Kossel model. The relaxation kinetics are introduced by single-site transition probabilities to account for adsorption and evaporation. The diffusion kinetics are introduced by two-site transition probabilities to account for nearest-neighbor exchange. The kinetic equations are studied by Monte Carlo simulation, quasichemical(pair) approximation (QCA), and high temperature expansion. The diffusion is found to generally enhance the growth rate of the crystal. In the range of validity of the QCA, i.e., outside the nucleation regime, the results are in very good quantitative agreement with previous Monte Carlo simulations. In the limit of infinite diffusion speed the growth rate approaches the Wilson–Frenkel rate. The local roughness or surface energy is reduced if surface diffusion occurs. The relative influence of diffusion on the response of the system to a chemical potential difference between the two phases depends significantly upon the particular type of transition probability. For the homogeneous Glauber–Ising chain no influence of the diffusion upon the dynamic behavior could be detected.