A simple theory of deuterium N.M.R. spin echoes in solids

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Abstract
Analytic expressions for the spin responses to Py (90°)-τ-Px (β) and Py (90°)-τ-Py (β) pulse sequences are obtained for a model of two dipolar coupled spins-1 each subject to local electric field gradients. Three distinct echoes with different time dependences are predicted. When ωQ > ωD, these echoes are not resolvable and only a single composite echo at t′ = τ will be observed. The amplitude of the Py (90°)-τ-Px (90°) echo as a function of τ corresponds to a time-domain spectrum reflecting the dipolar interaction and the orientational distribution. The applicability of the model to experimental deuterium spin responses in perdeuteriated molecular solids is examined. The β-dependences of the responses and the short time behaviour are accurately reproduced, though, as expected, there are discrepancies at long times. The failure of the time-expansion approach to predict the observed second order decay coefficient for the Py (90°)-τ-Px (90°) echo amplitude is explained; it is also shown that this coefficient will have the value 8/9M 2 vv for all materials of practical interest. The distortion of the shape of the echo compared with the FID signal is discussed briefly.