Nuclear Spin Relaxation

Abstract

Nuclear spin relaxation rates due to magnetic dipole interactions and atomic diffusion in solids are calculated for some two- and three-dimensional systems and for some models of common diffusion mechanisms. NMR magnetic dipolar spectral density functions are obtained for some lattice diffusion models for two-dimensional lattice diffusion on a square lattice and compared with the results for the BPP and continuum diffusion models. Numerical results and analytic approximations are obtained for dipolar interactions between spins diffusing in a plane, and interactions between diffusing spins in a plane with fixed spins in a separate parallel plane. Results for the longitudinal spin relaxation rates in the laboratory and rotating frames are obtained for square lattices and show strong dependence on the direction of the applied magnetic field relative to the crystal axes. A simple matrix expression is derived for the atom jump probabilities due to an interstitial defect moving by an interstitialcy diffusion mechanism. This expression is used to obtain the tracer correlation factor and to calculate the atom jump probabilities numerically for various cubic and two-dimensional systems. An integral expression, involving atom jump probabilities, is obtained for the atomic displacement probabilities due to a single atom-defect encounter.