On the correlation between self-diffusion and the low-frequency LA ⅔⟨111⟩ phonon mode in b.c.c. metals

Abstract

A new approach is proposed for understanding the strongly diverging self-diffusion behaviour in b.c.c. metals by relating the atomic mobility to the characteristic low-frequency LA 2/3⟨111⟩ phonon mode. The frequency v _2/3 of this mode is controlled by restoring forces, which oppose in particular the atomic displacements for a diffusion jump in the ⟨111⟩ direction, influencing in this way the migration enthalpy H ^M. A simple semi-empirical expression is derived which relates H ^M to the square of v _2/3. On the basis of experimental results an excellent correlation between the activation energy for self-diffusion and the LA 2/3⟨111⟩ phonon frequency is found. It is concluded that the extremely different mobilities in b.c.c. metals result from corresponding alterations in H ^M. Changes in H ^M originate from systematic variation in the d electron charge density distribution, which is responsible for the strength of the ⟨111⟩ directional bond-bending forces in b.c.c. transition metals. This model of phonon-assisted diffusion processes yields a uniform explanation of self-diffusion in b.c.c. metals. Furthermore a correlation is found between the diverging results of the energy factor ΔK in the isotope effect and the square of v _2/3. Finally it is suggested that the large differences in positron trapping at vacancies in b.c.c. transition metals can be related to a corresponding soft-mode-induced delocalization of the vacancy defect.