The influence of molecular motions on the stabilities and shapes of solid particles

Abstract

A conjecture of Gibbs, that the relative weakness of bonds at crystal edges and corners would cause rounding which is not predicted by his thermodynamic expression for stable crystal shapes, is evaluated in two ways. First, the vacancy distribution necessary for dynamic equilibrium between adjacent crystal rows or layers of different bond energies is derived. Then it is shown that minimization of the total free energy of two parts of a crystal with respect to their total vacancy concentration leads to the same vacancy distribution. Generalization of these results shows that the stabilities of particles which have a fixed number of sites are greatest when vacancies are so distributed as to equalize molecular fluxes between every pair of regions of different bonding energies. Rounding will occur when the mole fractions of vacancies required at corners and edges to maintain the molecular flux balance approach unity.