The response to the Jeener-Broekaert three-pulse sequence of spin systems having inhomogeneous lineshapes dominated by distributions of second-rank spin interactions

Abstract

A theoretical analysis is given of the response to a 90 _x-τ -45 _y -T-45 _y r.f. pulse sequence of nuclear spin systems whose spectra are dominated by inhomogeneous distributions of second rank interactions. In particular, the cases of (i) a spin-1 system subjected to a distribution of quadrupole interactions and (ii) strongly dipolar-coupled spin-1/2 pairs are considered. A full analysis is presented for the spin-1 system whilst the case of the dipolar-coupled spin-1/2 pairs is considered by analogy. It is shown that, in contrast to the situation where a uniform spin temperature may be established following the 90 _x-τ -45 _y pulse pair, the signal in phase with and following the third pulse, for the cases considered here, takes the form of spin echoes centred at t = τ and t = (T ± τ) rather than a single signal having the shape of the derivative of the FID and starting at t = 0. It is pointed out that, whenever the single crystal spectrum of a spin system consists of highly resolved lines arising from second rank interactions, it is unlikely that a uniform spin temperature can ever be established following the 90 _x-τ -45 _y pulse pair in a polycrystalline sample. In addition it is noted that there is a complete analogy of the response to the 90 _x-τ -45 _y -T-45 _y sequence of systems with inhomogeneous distributions of second rank interactions with that to the 90-τ-90-T-90 sequence (the Hahn stimulated echo sequence) of systems with a distribution of first rank interactions (e.g. B ₀ inhomogeneity). Experimental measurements on the deuterons in solid d ₆-dimethylsulphoxide and on the protons in a powder sample of gypsum are presented which confirm the predictions of the theoretical analysis.