Asymptotic Similarity of Time Correlation Functions and Shape of the 13C and 29Si NMR Spectra in Diamond and Silicon

Abstract

Based on the proposed theory, we have investigated the shape of the NMR absorption spectra for 13C and 29Si nuclei in diamond and silicon crystals attributable to the internuclear dipole–dipole interaction. In accordance with the available experimental data, we have considered both crystals with a 100% content of magnetoactive isotopes and crystals with a comparatively low dilution by nonmagnetic nuclei. The time correlation functions (the first of which is the Fourier transform of the NMR spectrum) arising in an infinite chain of coupled differential equations are shown to be mutually similar with a slight time delay. The proposed theory allows the spectrum to be calculated analytically. The results obtained agree satisfactorily with the experimental ones. It is noted that the mutual similarity of the time correlation functions is probably a corollary of the development of dynamical chaos in the system