Effect of anharmonicity on diffusion jump rates (original) (raw)

Rate theory is modified to take explicit account of anharmonicity. In general, the "watershed" saddle surface is curved rather than. planar. Certain almost tangential trajectories then cut the saddle surface two or more times without intervening randomization. We calculate explicit saddle surfaces for model fcc crystals using potential-energy functions derived from Morse and Lennard-Jones pair potentials. The theory is developed to determine how the fraction of dynamical return jumps which occur in thermal equilibrium depends on the shape of the saddle surface. For models of Ag, Al, Ar, and Cu we determine that an upper limit of only about 5% of return jumps take place, even at temperatures near the melting temperatures, and still less occur at lower temperatures. The validity of the rate-theory approach is therefore established. The shape of the saddle surface also determines the isotope effect in diffusion. The anharmonic contribution to the isotope effect factor a. does not exceed 2% of the harmonic part for any of the four substances, and the values calculated from the model results appear reasonable when compared with experimentally detern:ined values for metals. The results presented here prepare the way for explicit Monte Carlo calculations of the jump frequency and of its precise dependence on state variables in model crystals.