Self-diffusion studies in solids using nuclear magnetic resonance techniques

Abstract

N.m.r. measurements of spin–lattice relaxation time, T₁, and spin–spin relaxation time, T₂, give valuable information on diffusive motion in a wide variety of solids when self-diffusion provides the dominant relaxation mechanism. These measurements however have a limited useful range. As the mean time, τ, between jumps increases, the effects of paramagnetic impurities can dominate T₁ and T₂ reaches a constant rigid lattice value. These limitations can be overcome by measuring the spin–lattice relaxation time in the presence of an r.f.field, T_1ρ, or the spin–lattice relaxation time in the dipolar field, T_1D. Recent theoretical developments often allow τ to be evaluated with reasonable accuracy and if the jump distance is known then the self-diffusion coefficient, D, can be calculated. Paramagneticimpurity effects can also cause anomalous results in the solid in the fast diffusion range. The technique and its limitations will be illustrated by recent work on ¹⁹F^– diffusion studies in fluorite lattices. Measurements of these relaxation times provide information at the microscopic level on the atomic motion and thus can indicate the dominant diffusion mechanism.

Diffusion coefficients can be measured by macroscopic methods and in particular by using the pulsed field gradient n.m.r. spin echo technique in which pulsed magnetic field gradients are applied to the sample during a T₂ measurement sequence. Since it is a direct measurement of D this technique also serves to complement the information from relaxation studies and can provide a useful check on existing theoretical interpretation.

Comparisons with the results of other experimental methods such as radio-tracer or ionic conductivity for ionic solids are similarly informative. F^– diffusion in barium fluoride and lead fluoride together with new results for strontium fluoride are discussed. N.m.r. measurements are seen to be particularly useful in the regions of fast ion diffusion above the high temperature phase transitions.