Effect of immobile impurities on two-dimensional nucleation

We study the dependence of the critical size of the nucleus on the density of impurity by carrying out a Monte Carlo simulation. We assume that the impurities are fixed on a crystal surface, and neglect restoration of bonds between an impurity atom and an adsorbed atom. We initially prepare one cluster in the system and investigate the change of the cluster size. When the cluster size is the critical value, the frequency of increasing the cluster size is equal to that of decreasing the size. With increasing the impurity density, the critical nucleus becomes large. When the impurity density is sufficiently high, regardless of the initial cluster size, the cluster vanishes after a long time interval, namely, the critical cluster size is diverged.