The hole theory of diffusion

We show that in a dilute substitutional solid solution of one metal in another the diffusion of the solute atoms is determined by the compound activation energy A + ABA where A is the energy necessary for the formation of a hole next to a dissolved atom and ABA the energy of activation for the hole to make one jump round that atom, provided ABA - BB >> kT , where BB is the energy of activation for the hole to diffuse away from the dissolved atom. This mechanism provides an explanation of the cases where diffusion of a foreign metal atom in a lattice has a lower activation energy than self-diffusion in the same lattice, gold in lead being a conspicuous example. However, the assumption of next-neighbour interactions made in the description in this paper does not correspond to the facts of metallic structure. The statistical argument is not invalidated by this, but the calculation of the actual energies involved becomes a very difficult problem in quantum mechanics which has not yet been solved.