Subnanometric-scale motion of the modulation wave in incommensurate solids studied by two-dimensional exchange-difference NMR

Abstract

The two-dimensional (2D) exchange-difference NMR technique is suitable for the observation of slow molecular motions in solid systems with single inhomogeneously broadened NMR spectra. The difference signal originates from those nuclei only, which undergo motion during the mixing period, whereas the signal from the effectively static nuclei is eliminated from the spectrum. In an inhomogeneously broadened 2D exchange difference spectrum the continuous diagonal peaks appear negative whereas the continuous cross peaks show positive intensity. These two kinds of peaks appear resolved in the difference technique, whereas they remain unresolved in the standard 2D exchange NMR experiment, which shows positive intensity only. From the analysis of the cross peaks it is possible to determine the maximum traveling distance and the frequency range of the random thermally induced modulation wave motion in INC systems. The motion in space is traced by the changes of nuclear resonance frequencies which is possible in view of the existing frequency-space relation in solids with modulated structure. Slow motion of the incommensurate modulation wave has been studied in substitutionally disordered (${\mathrm{Rb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{K}}_{\mathrm{x}}$${)}_{2}$${\mathrm{ZnCl}}_{4}$ mixtures by the $^{87}\mathrm{Rb}$ 2D exchange-difference NMR. The maximum traveling distances of the modulation wave in the thermally induced motion have been determined for the ${\mathrm{K}}^{+}$ impurity concentrations x=0.0, 0.02, and 0.06. The motion has been observed on the subnanometric scale and the traveling distances were found small compared to the wavelength of the modulation wave. The increase of the ${\mathrm{K}}^{+}$ concentration results in a decrease of the maximum traveling distance, reflecting the increased pinning of the modulation wave by impurities.