A Note on the Hole Theory of Diffusion

Abstract

The activation energy $Q_x$ for diffusion in a dilute metallic solution cannot be less than the activation energy $Q_0$ for self-diffusion, if the solute atoms can move only through the medium of "holes" which diffuse to them from the solvent lattice, displace them, and leave in another direction. Since the experiments show that generally $Q_x<Q_0$ an alternative mechanism is required. Solute atoms which are not so firmly bound in the lattice as are solvent atoms will tend to trap holes to form solute-hole molecules. These molecules can move as units through the dense solvent lattice by cycles of inversion and re-orientation. This mechanism yields for the diffusion constant the value $D=A^{*} \exp [-\frac{\mathrm{}(W+S)\mathrm{}}{\mathrm{RT}}],$ where $W$ is the energy required to form a hole adjacent to a solute atom, and $S$ is the activation energy for re-orientation or inversion of a solute-hole molecule. $Q_x(\equiv W+S)$ may be much smaller than either $Q_0$ or the binding energy of the solvent. $A^{*}$ should be significantly less than the corresponding $A$ for self-diffusion. Both these predictions are in accord with the data. The same considerations should apply also to diffusion in liquids.