High spatial resolution studies of phase transitions within organic aperiodic crystals

Abstract

The understanding of the symmetry breakings within crystals that are aperiodic by construction is actually very limited. Quasicrystals and incommensurate composite crystals may potentially allow such studies. We focus on the phase transitions of the aperiodic n-nonadecane/urea which recovers a translational symmetry within a four-dimensional space at room temperature. High-resolution neutron and synchrotron studies are reported as a function of the temperature on this organic crystal which presents an exceptional mosaicity. They reveal the richness of such approach, showing the appearance of very long wavelength supplementary intermodulations. This work generalizes the Landau theory to incommensurate composite crystals.

Phase transitions within crystals that are aperiodic by construction

“…As already discussed in the literature [40][41][42][43][44][49][50][51][52][53], this supplementary modulation doubles the unit cell within five-dimensional superspace. Two cases are encountered: a C-centered superspace group C222 1 (00γ )(10δ) and the lower symmetry P2 1 2 1 2 1 (00γ )(00δ).…”

“…This is the case for n = 15, 19 and 24, which present ferroelastic phase transitions leading to the rank-five C-centered superspace group C222 1 (00γ )(10δ). Such phase transitions may result from the softening either of a phonon branch or of the branch associated with the sliding mode, a specific excitation of the internal space of the superspace [42]. Further dynamical studies of pretransitional phenomena in which collective excitations in these materials are measured are required before definitive conclusions concerning the origin of these transitions can be made.…”

“…More surprising is the third set, which presents an increase in the dimension of the crystallographic superspace from 4 to 5 (n = 15, 16, 18, 19, 21, 24). As developed above, these phase transitions are described by group/subgroup relations with the appearance of a supplementary modulation Ae iφ along the aperiodic channel direction within the four-dimensional superspace [39][40][41][42][43]. In this five-dimensional crystal, there is a supplementary reciprocal unit cell vector along the direction of the aperiodic modulation, c m * , and the basis is…”

“…The value of the supplementary modulation misfit parameter δ is found to be the same in both phases and is independent of temperature. The most heavily studied compound that exhibits this sequence of phases is n-nonadecane/urea [41,42,44,45].…”

“…The present paper is based on high-resolution diffraction studies, many of them already discussed in the literature [13,[38][39][40][41][42][43][44][45][46]. The guest molecules concerned are the linear molecules of n-heptane (n = 7), n-octane/urea (n = 8), nnonane/urea (n = 9), n-decane/urea (n = 10), n-dodecane (n = 12), n-hexadecane (n = 16), n-octadecane (n = 18), nnonadecane (n = 19) and n-tetracosane (n = 24).…”