Toward a better description of the nucleation rate of crystals and crystalline monolayers

The ability of the classical nucleation theory (CNT) and atomistic nucleation theory (ANT) to predict the stationary nucleation rate $J$ of single-component crystals and crystalline monolayers is verified with the aid of numerical and computer simulation data obtained in the scope of the Kossel crystal model. It is found that in both cases CNT significantly overestimates $J$ because it does not account for the work needed to attach an atom to the periphery of the two-dimensional nucleus or to form such a nucleus on the surface of the three-dimensional one. In contrast, ANT is successful in providing a good quantitative description of $J$⁠, especially for high enough effective binding energy between nearest-neighbor atoms in the crystal and in capturing the existence of extended, nearly linear portions in the dependence of $lnJ$ on the supersaturation $s$ when the values of both $s$ and the binding energy are sufficiently great. However, the ANT prediction about broken linear $lnJ$ versus $s$ dependence is not confirmed by the numerical and simulation results presented. General formulas for the nucleation work, the nucleus size, and the nucleation rate are proposed which are applicable to nucleation of single-component crystals and crystalline monolayers in vapors, solutions, or melts and which correct the respective CNT formulas. The proposed $J(s)$ formula provides a good description of the numerical and simulation data and can justifiably be used up to the supersaturation at which the nucleus becomes monomer. When experimental data for the $J(s)$ dependence are available and the nucleus specific edge and surface energies are unknown parameters, the proposed $J(s)$ formula can be employed for estimation of these energies even if the nucleus is constituted of a few atoms only.