On the diffuse interface theory of nucleation

Abstract

A quantitative model of nucleation would be essential for many problems in materials science. The experiments are usually interpreted in terms of a simple and flexible phenomenological model; the classical nucleation theory (CNT) which assumes an interface thickness negligible compared to the size of the nucleus. Under such conditions, the rate of nucleus formation can be expressed using bulk thermodynamic properties and interface free energy [gamma][sub [infinity]], leading to an easily applicable formalism. Computer simulations and first principles calculations imply, however, that the liquid/fluid and solid/fluid interfaces are diffuse, which is hardly negligible when compared to the size of nuclei containing typically 30 to a 100 molecules as predicted by the CNT. Expressing the excess free energy of nuclei in terms of the distance [delta] of the enthalpy and entropy surfaces, a simple diffuse interface theory (DIT) has recently been proposed. Evaluating [delta] from the bulk interface free energy and thermodynamic quantities, a reasonable agreement with experiments on condensation of some non-polar vapors has been obtained. In this work the authors present a rigorous derivation of the DIT. It is to be shown that the expression for the Gibbs free energy of nuclei contains an implicit assumption justifiable for condensedmore » matter-condensed matter transformations, however, further verification is needed in case of vapor condensation. Therefore, an extensive comparison with experiments has been performed which demonstrates the importance of interface diffuseness. Except for liquids with ordered surfaces, the DIT is in a substantially better agreement with experiments than the CNT.« less