Relative Orientation of Quadrupole Tensors from Two-Dimensional Multiple-Quantum MAS NMR

Abstract High-resolution NMR spectra of half-integer spin quadrupolar nuclei (I = 3/2, 5/2, 7/2, etc.) in powdered solids can be recorded using a variety of techniques (DOR, DAS, MQMAS, STMAS) developed in recent years. These methods resolve inequivalent nuclei in the crystallographic unit cell and can be analysed to yield the quadrupole coupling constant, CQ, and asymmetry, η, of each crystallographic site. However, they provide no information, such as internuclear distances or relative orientations, that can be used to relate one quadrupole tensor to another. Here, we show that using a modified version of the two-dimensional multiple-quantum magic-angle spinning (MQMAS) technique to cross-correlate second-order broadened NMR lineshapes allows the relative orientation of quadrupole, and hence electric field gradient, tensors to be determined. The new method is demonstrated on sodium molybdate dihydrate (Na2MoO4.2H2O) and the angles between the principal axes of the two 23Na quadrupole tensors in the unit cell (α', β', γ')is estimated to be (90°, 24° 15°).

(a) 23Na triple-quantum MAS NMR spectrum of Na2MoO4.2H2O. (b) Corresponding correlation spectrum with mixing time, τm = 200 ms. (c) Expansions of low-field cross peak in (b) and corresponding simulation with α = 90°, β = 24°, γ= 15°.