Computer simulation of hydrogen diffusion and nuclear magnetic relaxation on a disordered lattice

Abstract

The dipolar nuclear magnetic relaxation rate associated with the hopping diffusion of interstitial hydrogen atoms in a disordered alloy is calculated by Monte Carlo methods. The principal features of the model system are that the atoms hop on a spatially disordered array of traps and the trapping energy varies from trap to trap so that the diffusion of the hydrogen is characterized by a distribution of jump rates. The effective jump rate from a trap is assumed to have an Arrhenius dependence on temperature causing the distribution of jump rates to depend on temperature. Unlike earlier work, the method fully explores the way in which this dependence affects the mean jump rate as well as providing the means to calculate the relaxation as a function of both Larmor frequency and temperature. The mean jump rate is found to deviate from the Arrhenius form in a manner that depends on the concentration of the hydrogen nuclear spins. At a given temperature the characteristic peak in the relaxation rate, which occurs in ordered solids when the product of the average jump rate and the Larmor frequency is approximately unity, is broadened, becomes asymmetric and is shifted in frequency by the presence of the jump rate distribution. The broadening is found to be less apparent when the relaxation rate is calculated as a function of temperature but the asymmetry remains.