Nuclear magnetic resonance studies in solids containing dipolar coupled spin-half species.

Apperley, David Charles (1986). Nuclear magnetic resonance studies in solids containing dipolar coupled spin-half species. PhD thesis The Open University.



Closed analytical expressions for the NMR response to various pulse sequences for small, isolated heteronuclear spin systems containing dipolar coupled spin-half nuclei are derived and discussed. In particular, the responses of single crystal and polycrystalline assemblies of two, three and four spin systems to single, strong, resonant rf pulses and Py(90°)-T-P (8) pulse sequences are considered. The calculations are carried out using the density matrix formulism. The results of the moment expansion for the treatment of a general multi-spin system are included for comparison. The calculated response to one pulse (the FID) is compared to the experimentally observed FID for potassium hydrogen difluoride, caesium hydrogen difluoride and sodium fluoroethanoate. The calculated response to a two pulse sequence is compared to the experimentally observed response for KHF2. It is shown that the expressions for the responses to two pulse sequences can, in general, be decomposed into three components: an FID component, an echo component and a cross-term component. The effect that these components have on observed spin echoes is discussed for model systems. It is demonstrated that the separation of homonuclear and heteronuclear interactions using spin echo techniques is not as straightforward as has previously been suggested. The predictions of the operator formulism often used in spin echo studies are shown to be of limited value.

Finally, a general treatment of nuclear spin relaxation in heteronuclear spin systems is given. Two specific motional models are included: (i) a three spin, two site model and (ii) a four spin, two site model. A generalisation of the former model is also included. These models are used to interpret the spin-lattice relaxation behaviour of both polycrystalline KHF2 and CsHF2. The results of the study of the latter compound differ in several aspects from those previously reported.

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