Relative Orientation of Quadrupole Tensors from High-Resolution NMR of Powdered Solids

Techniques such as dynamic-angle spinning (DAS), double rotation (DOR), multiple-quantum MAS (MQMAS), and satellite-transition MAS (STMAS) may be used to obtain high-resolution NMR spectra of half-integer quadrupolar nuclei in powdered solids. These methods enable resolution of crystallographically inequivalent nuclei and also yield the quadrupolar coupling constant C Q, quadrupolar asymmetry η, and isotropic chemical shift δ CS of each crystallographic site. However, no information is obtained that relates one quadrupole tensor to another, such as internuclear distances or relative orientations. Here, we discuss a recently developed modification of the MQMAS NMR experiment that utilizes two-dimensional correlation of second-order (rank l = 4) broadened MAS line shapes to obtain the relative orientation of quadrupole tensors. This new method involves the insertion of a “mixing time”, τ m, into the MQMAS experiment such that magnetization transfer between two distinct nuclei within a crystallite during this period will result in a two-dimensional “cross-peak” correlating the two line shapes. The shapes of these cross-peaks are characteristic of the three Euler angles, α‘, β‘, and γ‘, that describe the relative orientation of the two quadrupole tensors. In this work we use the example of 23 Na ( I = 3 / 2 ) NMR of borax (Na 2 B 4 O 7 ·10H 2 O) to discuss in more detail the nature of the magnetization transfer. We also derive an analytical expression for the rank l = 4 orientational dependence of the second-order quadrupolar interaction in terms of the relative orientation of two quadrupole tensors and simulate the effect upon the shape of the cross-peak when the angles α‘, β‘, and γ‘ are changed. Finally, the use of this novel technique is demonstrated in a 23 Na NMR study of sodium metasilicate pentahydrate (Na 2 SiO 3 ·5H 2 O) and in a comparative 23 Na NMR study of sodium tungstate dihydrate (Na 2 WO 4 ·2H 2 O) and sodium molybdate dihydrate (Na 2 MoO 4 ·2H 2 O).