Nuclear magnetic relaxation in disordered solids: a Monte Carlo study of metal-hydrogen systems

Abstract

The dipolar nuclear magnetic relaxation rate associated with the hopping diffusion of atoms in a disordered solid is calculated by Monte Carlo methods. The model is intended to simulate the diffusion of hydrogen atoms trapped at interstitial positions in the matrix of metal atoms in amorphous alloys. 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. Calculated at constant 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 found to be broadened and shifted in frequency, particularly when the occupancy of the traps is high. The long-range diffusion constant is also calculated and used to evaluate the effect of atom-vacancy correlations. It is found that the shifts in the relaxation peak cannot be accounted for solely by these correlation effects and it is suggested that multiple hopping of the more rapidly diffusing spins is a contributory factor. The shifts have a profound effect on the temperature dependence of the relaxation rate when the distribution of jump rates is also dependent on temperature. The adjustments to the peak in the relaxation caused by the distribution are small when the temperature dependence is taken into account, showing that experiments involving only the temperature variation of the relaxation are unlikely to be a sensitive method for detecting the presence of a jump-rate distribution. This aspect of the results of the computer model is illustrated by comparison with experimental data.