Isotope Effects in Close-Packed Metals and in Alkali Halides

Abstract

Abstract An expression was obtained earlier by the authors, on the basis of Vineyard's rate theory, for the sharing of the kinetic energy of a diffusing isotope at the saddlepoint with other host atoms. The theory is expressed in terms of the (imaginary) frequency of the localised vibration in which the diffusing atom at the saddlepoint is coupled to its neighbours.Numerical results are presented for the case of a Cu isotope diffusing by the vacancy mechanism in a pure Cu lattice. The pair potential determined by Englert, Tompe and Bullough, which fits the phonon spectra and the stacking fault energy, has been employed in the calculation.The effects of coupling between the diffusing atom and its immediate neighbours are very small with this potential. The main coupling is found to be to the eight third-nearest neighbours. Treating the vibrations of these nine atoms, a sharing of kinetic energy is found, which is in quantitative agreement with the experimentally observed isotope effect, assuming a vacancy mechanism for self­ diffusion. This situation for Cu is in marked contrast to Na, where it was shown in earlier work that the present theory could not explain the observed mass effect, assuming a vacancy mechanism for diffusion.The diffusion of Cs in the CsCl lattice is also discussed using the same theory. Following our earlier work on NaCl, the localized normal mode considered is that in which the Cs isotope at the saddlepoint is at the centre of a square with four Cl near-neighbour ions at the vertices. A formula for the sharing of kinetic energy is derived, and it is pointed out that, as for NaCl, the force con­ stants can be obtained from the classical approach of Mott and Littleton. An argument is proposed which suggests that, as with NaCl, the sharing of kinetic energy will be small. No experimental data appear as yet to be avaialable for the CsCl structure