Frequency factors and isotope effects in solid state rate processes

Abstract

The movement of defects in solids on the basis of classical absolute rate theory is reexamined with special attention to many-body aspects. The effective frequency in the Arrhenius expression governing these processes is shown to be, in harmonic approximation, the ratio of the product of the N normal frequencies of the entire crystal at the starting point of a transition to the product of the N−1 normal frequencies of the crystal when it is constrained in a saddle point configuration. The influence of the masses of the various atoms on the effective frequency is investigated. It is shown that an effective mass which depends on the direction of the path through the saddle point in configuration space determines this frequency. In the case of chemical diffusion by the vacancy mechanism the effective mass is approximately the same as the mass of the solute atom, and must always lie between the mass of the solute and the mass of the solvent. It is finally shown that the classical rate theory, even with many-body considerations, is unable to explain the recent observations of L azarus and O kkerse on the isotope effect in the diffusion of iron in silver.