Monte Carlo simulation study on the dissolution of a train of infinitely straight steps and of an infinitely straight crystal edge

Abstract

The dissolution of a train of infinitely straight steps and of an infinitely straight crystal edge was studied over a wide range of undersaturations by Monte Carlo simulation using the solid-on-solid (SOS) Kossel model for the SC(100) solid/fluid interface. The simulation was carried out below the roughening temperature to ensure that step movement is involved. Surface diffusion was not included in order to minimise computing time. Both the movement of the infinite steps and of the steps produced from layer opening by means of nucleation were apparent in the case of step trains at high undersaturations. For this reason, dissolution involving only pure step movement was also studied with nucleation excluded. A linear dependence of rate on undersaturation in terms of concentration ( C/ C eq) was found for dissolution involving solely step train movement and for the dissolving crystal edge. In the dissolution of the step train, the rate was also found to be proportional to the step density. This rate equation is in agreement with theoretical predictions with combined volume and surface diffusion. The involvement of nucleation at large undersaturations in the step train movement case resulted in enhancement of the rate, and deviation of the linearity of the rate equation. However, the extent of nucleation and hence its influence on the dissolution rate were found to decrease with increasing step density. Nucleation was not apparent in the dissolution of the infinite edge at all undersaturations. At the steady state, both the separation between steps in the step trans fluctuate slightly. In the case of high step density, steps were found to infrequently catch up with preceding ones which results in bunching. Similarly, instead of producing steps with equidistant spacing as assumed in a previous theoretical studies, the dissolution of the crystal edge resulted in a persistent bunching of steps with the exception of the region near the boundary of which the leading step and with its image and annihilated. Such roughness attributable to the dissolving edge, however, is not consistent with the kinetic roughening proposed earlier because nucleation was not involved in the dissolution. The mean density of kinks along the steps on the entire surface and for leading steps were almost constant at all undersaturations. Both measurements of kink density, though unequal when the step densities gets larger, indicated agreement with the assumption of constant density of kinks made by Burton, Cabrera and Frank (BCF) and not the proportion to ( C/ C eq) 1 2 , as suggested recently by Nielsen.