Pair approximation for interface kinetics

A pair approximation method is described for the interface kinetics of a simple cubic (100) surface with no surface migration. Condensation and evaporation are considered explicitly in a system of master equations applied to a pair of sites; and the effect of the neighboring sites is treated with a set of parameters which are determined self-consistently. Runge Kutta numerical integration of the equations yields the time evolution of the surface. The results for a high entropy of transformation indicate a region of metastable states (zero growth rate) for small driving force, and the instantaneous growth rate is a periodic function of time for larger driving force. The period of the variations is the time required to grow a monolayer, and the amplitude is less than that obtained by Temkin using the mean field approximation. The variations appear as artifacts of most approcimation methods which treat a limited number of sites. The average growth rate is less than the limiting Wilson-Frenkel law for all growth conditions studied. This results since the surface becomes quite rough in the presence of a large condensation rate, and therefore its evaporation rate is greater than the evaporation rate of an equilibrium surface assumed in the Frenkel model. The metastable region is absent at low entropies of transformation and here the growth rate is nearly linear in the driving force. Agreement with Monte Carlo data is excellent for a low entropy of transformation and for all materials at high growth rates.