NMR line shape analysis in the incommensurate phase of bis(4‐chlorophenyl)sulfone

Abstract

High quality single BCPS crystals were used to study the influence of a structurally incommensurate (IC) modulation on the line shape in 35 Cl NMR spectra where the phase transition from the normal into the IC phase at ca. 150 K is clearly reflected in the appearance of an asymmetric frequency distribution with edge singularities. The line shape calculations are performed in a temperature range where the validity of the plane wave limit may be assumed. In nice agreement with an X-ray analysis of the rotational symmetry modes in the IC phase by Zuniga et al., the evaluation of the 35 Cl NMR frequency distributions is based on the IC modulation of the Euler angles which describe the orientation of 35 Cl NMR quadrupole coupling tensor in the crystal frame.

Phason and amplitudon dynamics in the incommensurate phase of bis(4-chlorophenyl)sulphone

“…For BCPS such a complete description of the N-IC phase transition was achieved in an x-ray-diffraction study. 11 The simulation of the experimental NMR spectra shows, similarly as reported for measurements at lower Larmor frequencies, 23 that the line shape in the IC phase can be nicely reproduced by mainly using the modulation of the angle ␣. Hence, the effective contribution to the IC modulation wave mainly consists of rotations of the molecules around the axes R 3 [mainly influenced by first-order contribution in the harmonic expansion of Eq.…”

“…In extension of the previous work 23 we perform here a quantitative 35 Cl NMR line-shape analysis in the IC phase only for the spectra measured at the highest available dc magnetic field B 0 . Since the quadrupole frequency (ca.…”

“…This assumption is supported by a detailed x-ray study 11 of the active symmetry modes in the IC phase and is discussed in our previous paper. 23 The analysis of the IC line shape is compared with the experimental line shape in the temperature range [T i , T i −10 K] where the validity of the plane-wave limit can be assumed. To describe the IC modulation, a Fourier series expansion of the QCT in terms of the harmonics of the IC modulation is used as introduced by Perez-Mato, Walisch, and Petersson.…”

“…To find the modulated QCT components V kl in the IC phase, we start from the principal values and the orientation of the 35 Cl QCT in the principal-axis frame (PAF, abbreviated as X , Y , Z) in the normal phase which are well known from our previous work. 23 The calculations of the 35 Cl NMR frequency distributions in the IC phase have been performed under the assumption that only the orientations of the principal axes of the QCT are modulated. Suitable Euler angles ␣ , ␤ , ␥ were introduced in order to characterize the orientation of the QCT in the crystal axis frame CAF.…”

“…The extension of the 35 Cl NMR studies is based on previous NMR line-shape measurements at lower fields where also a calculation of the 35 Cl NMR line shape was performed. 23 Experimental details are reported in Sec. II.…”