IV. CONCLUSIONS Within the context of classical nucleation theory, kinetic roughening is understood as occurring when the supersaturation is so high that the size of the critical cluster becomes smaller than one molecule[1]. At low supersaturations, growth is dominated by the hetero- geneous nucleation of steps that then grow smoothly to cover the crystal surface while at high supersaturation, above the transition, homogeneous nucleation also occurs leading to rapid growth of a rough surface. In this paper, the possibility of a similar transition for finite-sized critical clusters has been investigated. Two models for the growth of crystal surfaces which show a transition from a slow to a fast growth regime were presented. In the mean field model, adsorption onto the surface with subsequent surface diffusion and aggregation competes with direct formation of clusters to give two different growth regimes for the formation of islands of new crystal. At low bulk concentrations, the adsorption and aggregation mechanism are dominant whereas at high bulk concentrations, the formation of critical clusters by the formation of subcritical aggregates with direct incorporation of material from solution dominates. The difference in growth rates is greatest when the crit- ical cluster is small (being a factor of 2 for a critical size of 2). These results elaborate on previous theoretical work that indicated the importance of direct incorporation of material from the bulk[31]. A one-dimensional Kinetic Monte Carlo model based on the well-known SOS model showed both different growth regimes and roughening. The main difference from the usual SOS model is the definition of a critical cluster size to simulate nucleation as it actually oc- curs on a two-dimensional surface. This model showed a clear cross-over between a smooth, step-growth dominated regime at low supersaturation and a rough, nucleation-dominated regime at high supersaturation thus exhibiting the observed features of the kinetic rough- ening transition. The growth velocities both below and above the transition are roughly linear functions of the hit rate (Fig. 4), or in physical terms, the concentration, just as in the mean-field model (see, e.g., Eqs.(5, 6)). The main conclusion from this work is that the kinetic roughening-like transitions do not necessarily require the vanishing of the critical cluster size. Instead, “kinetic” effects suffice to give qualitatively different growth regimes and roughening of the surface. In future work, it is intended to further elaborate the simple mean field model presented here to give a 13