3 1P spectral spin diffusion in crystalline solids

Abstract

We give a derivation for the line shape function g(ω) involving the spin diffusion constant TSD, which had earlier been given by Suter and Ernst, and by Henrichs et al. using different methods. There are three approximations which lead to different ways to evaluate the zero quantum line shape function g(ω). The first used by Suter and Ernst, another by Henrich et al., and the third which we show leads to the same equations as the latter authors. The angular dependencies of TSD for 31P spectral spin diffusion in single crystals of dipotassium α-D-glucopyranose-1-phosphate dihydrate (GLP) and triphenylphosphine (TPP) were determined. We conclude that the 31P spin diffusion under the influence of extraneous protons is well described by a Gaussian zero quantum line shape [Eq. (20)] but not by a Lorentzian function. This distinguishes the present situation from the one treated by Suter and Ernst. It is also confirmed by theory and experiment that the equation for TSD given by Henrich et al. is satisfactory when the S1 and S2 spins involved in the flip–flop process are quite distant from each other.