NMR SOLID ECHOES IN SYSTEMS OF DIPOLAR-COUPLED INEQUIVALENT SPINS-1 OR DIPOLAR-COUPLED INEQUIVALENT PAIRS OF SPINS-1/2

Proton solid-echo transverse relaxation functions for many thermotropic and lyotropic mesophases, mapped by measurement of the echo amplitude Syx(t' = τ) as a function of t using a Py(90°)-τ-Px(90o)-t' sequence, yield gauss-ian behaviour of the form exp [-1/2|M2Eτ2] for decays up to 20-30 per cent of the value at τ = 0. ME2, the second moment for the dipolar interactions between the spin-1/2 pairs, is related to the van Vleck second moment M2vv through a factor f. Whilst experiments suggested a value of 0-70-0-72 for f= M2E\ M2vv, simple models that ignored the non-equivalence of the dipolar-coupled spin-pairs had predicted f = 0-65. In this paper we derive an exact analytic expression for the spin response of a model of two dipolar-coupled inequivalent spins-1 to the pulse sequence Py(90o)-τ-Pα(β)-t', and show that the present model, with the quenching of the spin-flip terms of the dipolar hamiltonian, resolves the aforementioned discrepancy. We also reconcile the differences between the experimental and the earlier predicted values of/for deuteron N.M.R. spin echoes in perdeuterated solids. © 1990 Taylor & Francis Ltd.