NMR structural analysis of incommensurate modulated systems with multiple active symmetry modes: A case study of deuterated bis-(4-chlorophenyl)-sulfone

Abstract

We report single-crystal deuteron NMR measurements both in the normal (N) and the incommensurate (IC) phase of bis-(4-chlorophenyl)-sulfone (BCPS). From the quadrupole splitting data obtained in the N phase, the quadrupole coupling (QC) tensors of all deuterons in BCPS are derived. The central part of the paper is concerned with the analysis of the deuteron NMR frequency distributions observed in the IC phase as a function of the orientation of the applied magnetic field relative to the BCPS crystal. This analysis is carried out in terms of the amplitudes and phases of the rotational symmetry modes that contribute to the fundamental IC modulation wave in BCPS, i.e., directly in terms of the structural changes associated with the IC phase transition. Both a semiquantitative graphical, and a fully quantitative numerical approach are given. The former is used to identify particularly simple and therefore particularly informative crystal orientations. The latter uses as an input the deuteron QC tensors measured in the N phase. Quantitative and complete structural information about the rotational displacements that atoms experience in an N--IC phase transition is deduced from NMR spectra. Our results are in full agreement with corresponding data of an x-ray-diffraction study. We also report on measurements of the spin-lattice relaxation time ${T}_{1}$ across the deuteron NMR frequency distributions. The results are at variance with the established theory and this is traced back to the fact that multiple rotational modes are contributing to the IC modulation wave in BCPS.