Thermodynamics and Kinetics of Surface Area Changes of Faceted Particles

Abstract

An equation is derived that describes the influence of particle size and shape on the free energies of particles of anisotropic specific surface free energies. When the specific surface free energy is isotropic, the general equation reduces directly to the Gibbs–Thomson equation for the chemical potential of spherical drops and predicts the accepted driving force for neck growth between two spherical particles. The general equation is also used to obtain equations for the chemical potentials of particles of non‐equilibrium shapes and to derive alternate rate equations for different possible rate‐controlling steps of mass transport when faceted {100} ridge/channel arrays etched into a {100} single‐crystal surface decrease in depth to reduce the surface free energy. Edge free energies are suggested to sometimes play important roles in determining the sequence of shape changes that occur when particles of non‐equilibrium shapes are annealed.