The Czjzek distribution in solid-state NMR: Scaling properties of central and satellite transitions

Abstract

In the Czjzek model of disorder in a solid, the electric field gradient tensor elements are drawn from a Gaussian distribution. The resulting NMR spectral lineshape for the central transition of quadrupolar nuclei such as 27Al has been shown to be a good fit to experimental results in glasses. Here we study by experiment and exact simulation the effect of the Czjzek distribution on the satellite transitions, for both the original and so-called extended Czjzek models. We find that the satellite lineshapes are an important check on the applicability of the Czjzek model, and furthermore, as the field strength is reduced, the satellites skew the apparent location of the central transition. Therefore, at lower fields, an overall apparent shift of the central transition itself cannot be confidently assigned to an isotropic chemical shift, but rather is a combination of any underlying shift and the Czjzek distribution. We apply these ideas to experimental spectra of 27Al, 71Ga, and 139La, to show both the Gaussian nature of the satellite transitions and the apparent skewing of the chemical shift at low fields.