Thermodynamics of Microcrystallites and Its Relation to Nucleation Theory

Abstract

We develop a generalized Einstein model for calculating the thermodynamic properties of small crystalline clusters of atoms. The validity of the model is established through the molecular dynamics calculations by Dickey and Paskin and the numerical normal mode analysis by Burton for certain cluster packings. The rapid computational procedure and low computer storage requirements for our model calculations enable us to easily compute thermodynamic quantities for cluster configurations and sizes beyond those previously studied. Polyhedron cluster packings and “approximately spherical” cluster packings are used to generate clusters of various configurations. The Einstein theory is used to study the Helmholtz free energy, vibrational energy, and entropy for the various cluster configurations and for cluster sizes up to ∼ 1000 atoms. The model calculations are compared with the predictions based on the capillarity approximation used in nucleation theory. The simplicity of the method enables one to calculate the thermodynamic quantities for other types of systems.