Calculation of N.M.R. spin echo responses in solids containing both resonant and non-resonant spin-1/2 nuclei

Abstract

Analytical expressions for the N.M.R. spin responses to a resonant P _y(90°)-τ-P _α(β)-t′-pulse sequence are obtained for model systems containing both resonant and non-resonant spin-1/2 nuclei: specifically the model systems IS ₂, I ₂ S and I ₂ S ₂ are considered where I is the resonant nucleus. A method is described for expressing the responses in terms of the general response of an I _N S _M spin assembly. Responses corresponding to isotropic orientational distributions for each model system are determined using numerical methods. Results for two of the sequences of practical interest, namely P _y(90°)-τ-P _{y, or x}(180°)-t′- and P _y(90°)-τ-P _x(90°)-′- sequences, are discussed more fully and the applicability of the model systems to experimental responses in solids is examined. For the former sequence it is shown that the magnitude of the homonuclear dipolar interactions largely determine the time scale of the loss of maximum spin echo amplitude, but for the latter sequence the predictions are in the main at variance with the limited experimental information available. The use of two pulse sequences to separately measure homonuclear and heteronuclear dipolar coupling is limited to the analysis of spin echo behaviour at short pulse spacings: longer time behaviour, contrary to previous suggestions, is more complex.