Resonance Offset Effects in Multiple-Pulse NMR Experiments

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Abstract
The behavior of multiple‐pulse NMR line narrowing experiments in solids as a function of the frequency offset from resonance is examined experimentally and theoretically. Resolution in the four‐pulse, six‐pulse, and phase‐alternated tetrahedral angle experiments was found to increase on going off resonance. These results are explained using coherent averaging theory. The effective Hamiltonian which determines the width of the spectral line off resonance must be averaged over the motion caused by both the rf pulse Hamiltonian and the resonance offset Hamiltonian. It is assumed that the period of the motion caused by one of these two cyclic Hamiltonians is much shorter than the other so that the averages can be carried out sequentially rather than simultaneously. Two relaxation rates are evident in the four‐pulse experiment on solids, corresponding to relaxation parallel and perpendicular to one of the body diagonals, e.g., the (111) direction, in the coordinate frame appropriate to that experiment. For solids containing a single magnetic nuclear species the two rates appear to be equal on resonance, but off resonance relaxation along the (111) direction is slower than relaxation perpendicular to it. This behavior is explained qualitatively by the fact that average Hamiltonians which do not in general commute with (I x + I y + I z ) do commute with this operator when they are further averaged over the motion caused by an offset from resonance. The effective heteronuclear dipole–dipole interaction Hamiltonian commutes with (I x + I y + I z ) both on and off resonance, which accounts for the difference in the two relaxation rates independent of resonance offset observed in solids containing more than one magnetic nuclear species.