Mode Coupling at around M-Point in PZT

The question of the microscopic origin of the M-superstructure and additional satellite peaks in the Zr-rich lead zirconate-titanate is discussed for nearly 50 years. Clear contradiction between the selection rules of the critical scattering and the superstructure was found preventing unambiguous attributing of the observed superstructure either to the rotation of the oxygen octahedra or to the antiparallel displacements of the lead cations. Detailed analysis of the satellite pattern explained it as the result of the incommensurate phase transition rather than antiphase domains. Critical dynamics is the key point for the formulated problems. Recently, the oxygen tilt soft mode in the PbZr0.976Ti0.024O3 (PZT2.4) was found. But this does not resolve the extinction rules contradiction. The results of the inelastic X-ray scattering study of the phonon spectra of PZT2.4 around M-point are reported. Strong coupling between the lead and oxygen modes resulting in mode anticrossing and creation of the wide flat part in the lowest phonon dispersion curves is identified. This flat part corresponds to the mixture of the displacements of the lead and oxygen ions and can be an explanation of the extinction rules contradiction. Moreover, a flat dispersion surface is a typical prerequisite for the incommensurate phase transition.

Incommensurate phase in Λ-cobalt (III) sepulchrate trinitrate governed by highly competitive N–H···O and C–H···O hydrogen bond networks

Phase transitions in molecular crystals are often determined by intermolecular interactions. The cage complex of [Co(C12H30N8)]3+·3NO3– is reported to undergo a disorder–order phase transition at Tc1 ≈ 133 K upon cooling. Temperature-dependent neutron and synchrotron diffraction experiments revealed satellite reflections in addition to main reflections in the diffraction patterns below Tc1. The modulation wave vector varies as function of temperature and locks in at Tc3 ≈ 98 K. Here, we demonstrate that the crystal symmetry lowers from hexagonal to monoclinic in the incommensurately modulated phases in Tc1 ˂ T ˂ Tc3. Distinctive levels of competitions: trade-off between longer N–H···O and shorter C–H···O hydrogen bonds; steric constraints to dense C-H···O bonds give rise to pronounced modulation of the basic structure. Severely frustrated crystal packing in the incommensurate phase is precursor to optimal balance of intermolecular interactions in the lock-in phase.