Orientation dependence of motion-induced nuclear spin relaxation in single crystals

Abstract

Starting from Eisenstadt and Redfield's encounter model, the dipolar pair correlation functions governing the NMR relaxation behavior in crystals may be calculated for some arbitrary (correlated or uncorrelated) self-diffusion mechanism. In several temperature and field ranges, these correlation functions allow prediction of the variation of the relaxation times ${T}_{1}$, ${T}_{2}$, and ${T}_{1\ensuremath{\rho}}$ as a function of the crystallographic orientation of the Zeeman field ${\stackrel{\ensuremath{\rightarrow}}{H}}_{0}$ and of temperature for a given self-diffusion mechanism. In the theoretical part of the present article, the encounter model is applied to a monovacancy and an interstitialcy mechanism of self-diffusion of the anions in a fluorite lattice. The theoretical predictions for the anisotropies and the actual values of ${T}_{1}$, ${T}_{2}$, and ${T}_{1\ensuremath{\rho}}$ in the different regions are compared with those for a random-walk mechanism of self-diffusion in a single-crystalline simple cubic lattice. In single crystals of barium fluoride, the orientation dependence of ${T}_{1}$, ${T}_{2}$, and ${T}_{1\ensuremath{\rho}}$ has been investigated in several temperature and field regions. To affect the dominant diffusion mechanism, the experiments included also ${\mathrm{La}}^{3+}$- and ${\mathrm{K}}^{+}$-doped samples of barium fluoride. The comparison of the anisotropy measurements with our theoretical calculations rules out random-walk diffusion as a mechanism causing the relative jumps of the fluorine ions. Although the differences in the anisotropy of ${T}_{1}$, ${T}_{2}$, and ${T}_{1\ensuremath{\rho}}$ predicted for vacancy and interstitialcy diffusion in fluorites were found to require too high an experimental precision for the unambiguous identification of the dominant diffusion mechanism, this theoretical and experimental investigation has confirmed all of the basic predictions of the encounter-model theory and its application to fluorites.