Correlation factor for diffusion in cubic crystals with solute–vacancy interactions of arbitrary range

Abstract

Using a double Laplace and Fourier transform of the transport equation for the vacancy, we obtain the exact values of the return probabilities of the vacancy in the close vicinity of the tracer atom in the presence of a solute-vacancy interaction of arbitrary range. The study of model cases shows that taking into account the interaction up to the third neighbour shell is mandatory to obtain the solute diffusivity in BCC and FCC structures with a good precision. A thorough ab initio evaluation of all the migration barriers is rarely available in the literature; it is shown that the approximations often used to overcome this lack of data must be chosen with care in order to avoid puzzling conclusions. An examination of dilute systems studied in the recent literature is presented.

Keywords:

• cubic crystals
• correlation factor
• solute–vacancy interaction
• integral methods