A theory for solute impurity diffusion, which considers Engel-Brewer valences, balancing the Fermi energy levels of solvent and solute, and differences in zero point energy

A theory that assumes the Engel-Brewer valence of elements (one for bcc structures, two for cph structures, and three for fee structures) and considers the effects of balancing the solute and solvent Fermi energy levels and differences in zero point energy between solvent and solute atoms to calculate an ''effective'' relative valence for solute impurities is presented. The calculated values of relative valence and the experimental values of the differences in diffusional activation energy between solute and solvent atoms, Delta Q, are compared to the values of Delta H-2 + Delta E calculated from the Lazarus-LeClaire theory for several solute impurities in ten solvent metals. The calculated results agree very well with the experimental values for the large majority of solutes. The theory presented adequately describes solute impurity diffusion in both alpha-Fe and gamma-Fe, Al, Ni, and the noble metals. In particular, the low activation energies for impurity diffusion of the alkali metals (ground state valence of one) in Al (ground state valence of three) are accounted for by the theory. It is shown that the diffusion of the electronegative solute impurities (Cr, Mn, Fe, and Co) in Al is not anomalous when the relative valence is calculated by the proposed theory. The diffusion of electronegative solute impurities in the noble metals, which has been problematic in the past, is also well described by the proposed theory. The proposed theory introduces a simple method of estimating the effective electron densities of solute impurities and illustrates that the Lazarus-LeClaire theory adequately describes solute impurity diffusion in the ten solvent metals studied. It is expected that more accurate calculations of effective electron density for solute impurities would result in even better agreement between experimental and calculated results.