Isotope Effect in Diffusion

A derivation of the classical jump rate $\Gamma$ for tracer diffusion aimed at a clear expression for the mass dependence of the frequency factor $\overline{\nu }$ is presented. The derivation is effected without using the usual collective normal coordinates which usually combine the masses in a complicated way. $\overline{\nu }$ depends explicitly on the mass of the surrounding host atoms (as well as on the tracer-atom mass) if these atoms must move to new equilibrium positions after the jump. $\overline{\nu }$ then has much the same form as suggested for a many-atom jump process. The contribution of the surrounding atoms is reduced (increased) for light (heavy) tracer atoms.