Non-Arrhenius diffusional behavior and high-field nuclear spin relaxation in crystals

In terms of Eisenstadt and Redfield's encounter model, the dipolar pair correlation functions associated with two point-defect mechanisms of self-diffusion in cubic crystals assumed to rearrange the nuclear spins simultaneously, are calculated. As a special case, the correlation functions for a single correlated self-diffusion mechanism presented earlier are obtained. Also, assuming random nearest-neighbor jumps of the atoms arranged in a crystal lattice, the random-walk correlation functions of Torrey, Eisenstadt and Redfield, Sholl, and the present author are included in the limit of uncorrelated self-diffusion. Starting from the Fourier-transform relations between the nuclear spin relaxation rates and the dipolar pair correlation functions, the high-field relaxation properties due to two point-defect mechanisms are analyzed in the temperature region where the related Arrhenius plot shows a curvature. For the simultaneous self-diffusion via mono- and divacancies in fcc and bcc single crystals, it is found that the orientation dependences of the high-field relaxation rates are not much affected by a change of the dominant diffusion mechanism. However, the effect of different activation energies and attempt frequencies assumed to characterize the two mechanisms results in asymmetric shapes of the $T_1$ and $T_{1\rho }$ minimum as a function of temperature. It is illustrated how these phenomena allow one to determine both self-diffusion mechanisms involved if the related $T_1$ and (or) $T_{1\rho }$ minimum may be studied experimentally in the temperature region where the dominant self-diffusion mechanism changes, i.e., where the corresponding Arrhenius plot exhibits a curvature.