Nuclear SPin Relaxation in Periodically Perturbed Systems. III. The Relaxation in the Presence of Double Rotation

Abstract

The commonly applied high resolution NMR methods in solids (magic angle spinning (MAS) [1, 2] and pulse method proposed by Waugh, Huber, Haeberlen [3, 4]) do not give a possibility of elimination of second order anisotropy effects of dipole—dipole or quadupole interactions. These effects cause broadening of resonance lines. One can eliminate them by sample rotation about more than one axis. During the last few years new methods were developed, which eliminate the effects of second order anisotropy: namely double rotation (DOR) [5-7] and dynamic angle spinning (DAS) [8-11]. Spin relaxation processes in the presence of above-mentioned methods have not been studied yet. It is known that the spectral resolution is restricted by the rates of these processes. It is possible to describe these processes by spin—lattice and spin-spin relaxation times. The aim of this paper is to calculate effective spin relaxation times in the presence of double rotation. In the double rotation method a sample rotates simultaneously about two axes z1 , z2 at frequencies ω1, ω 2 and polar angles 81, 02, respectively, which fulfil a condition ΡL(cos θ1)ΡL(cos 02 ) = 0 for L = 2, 4, where PL(cos θ) are Legendre polynomials. These conditions have been satisfied by constuction of a donble rotor BETA (Berkeley-Tallin) [5, 7], which consists of the outer rotor and the inner rotor with a sample. The outer rotor rotates about a stable axis z 1 , which forms the magic angle 81 = 54.7° with the direction of the magnetic field B0. The