Correlation Factors and Isotope Effect for Self‐Diffusion by Mono‐ and Divacancies in H.C.P. Crystals

Abstract

AbstractThe tensor components of the Bardeen‐Herring correlation factor for a divacancy mechanism of self‐diffusion in an h.c.p. crystal are calculated and compared with Mullen's results on the monovacancy mechanism. The relationship between the correlation factors and the isotope effect parameters is discussed, in the monovacancy case making use of the work of Batra. For monovacancy diffusion parallel to the c‐direction the correlation factor provides an upper limit for the isotope effect parameter, whereas for diffusion perpendicular to the c‐axis the isotope effect parameter can be slightly larger than the correlation factor. For the divacancy case it is demonstrated analytically that the correlation factor parallel to the c‐axis provides an upper limit for the isotope effect parameter in this direction. Numerical calculations show that the upper limit of the isotope effect parameter perpendicular to the c‐axis exceeds the correlation factor at most by a few per cent.