A theory was presented which assumed the applicability of the Engel-Brewer valences for elements (unity for body-centered cubic structures, 2 for hexagonal close-packed structures, 3 for face-centered cubic structures). It considered the effects of balancing the solute and solvent Fermi energy levels, and differences in zero-point energy between solvent and solute atoms, in order to calculate an effective relative valence for solute impurities. The calculated results agreed very well with experimental data for most solutes. The theory could describe solute impurity diffusion in α-Fe, γ-Fe, Al, and Ni, and in noble metals. A low activation energy for impurity diffusion of the alkali metals (ground state valence of unity) in Al (ground state valence of 3) was explained by the theory. It was shown that diffusion of electronegative solute impurities (Cr, Mn, Fe, Co) in Al was not anomalous when the relative valence was calculated as in the present theory. The diffusion of electronegative solute impurities in noble metals, which had been difficult to explain in the past, was also accurately described by the present theory. The latter introduced a simple method for estimating the effective electron densities of solute impurities, and showed that the Lazarus-LeClaire theory adequately described solute impurity diffusion in the solvent metals.

V.Burachynsky, J.R.Cahoon: Metallurgical and Materials Transactions A, 1997, 28[3], 563-82