Electric Field Gradient Quadrupolar Nuclei

The electric field gradient is simply the change in electric field with direction due to the local distribution of nuclear and electronic charges at a particular point in space in which the nucleus in question is located. For example, a sodium ion in a sodium chloride crystal would see an electric field and an electric field gradient associated with the presence of all neighboring Na+ and Cl- ions. In this special case, the electric field gradient is zero because the crystal symmetry is cubic. If this nucleus is magnetic, but has spherical nuclear charge symmetry (spin 1, e.g., 13C), then it is unaffected by a field gradient. If the nuclear charge symmetry is not spherical (spin greater than 1, e.g., 27Al with spin 2), it can orient in an electric field gradient, which is to say that its nuclear energy levels that determine the NMR spectrum are sensitive to the field gradient. The spectrum associated with the central, 1 -1 transition of 27Al in an electric field gradient that has axial symmetry for a sample of a powdered solid is shown in Fig. 3f, Section IV. Thus, the NMR spectrum of a quadrupolar nucleus associated with the presence of a nonzero electric field gradient is a measure of both local nuclear, and electron-cloud geometries. The ellipsoid characterizing the spatial symmetry of the electric field gradient is in general completely asymmetric (i.e., Exx = Eyy = Ezz). While in general the isotropic value of the electric field gradient ellipsoid is not zero, to a first approximation it may be taken to be so. This fact will be important in considering the effects of motion on the NMR of quadrupolar nuclei.

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