Frustrated pretransitional phenomena in aperiodic composites

Abstract

This Letter reports on symmetry breaking in the aperiodic inclusion compound noctadecane/urea and its isotopomer n-octadecane/urea-d 4 . The high-symmetry phase is described by a hexagonal rank four superspace group. Pretransitional phenomena in this crystallographic superspace reveal competing short-range ordering phenomena within the high-symmetry phase. Very high-resolution diffraction data shows that critical scattering appears at inequivalent points within the four-dimensional Brillouin zone, although the first phase transition at T c1 near 158 K implies the condensation at only one of those points. The resulting superspace group remains of dimension four. Two other phase transitions are reported at T c2 = 152.8(4) K and T c3 = 109(4) K in n-octadecane/urea-d 4 . The two lowsymmetry phases that arise are described by rank five superspace groups.

High spatial resolution studies of phase transitions within organic aperiodic crystals

“…In addition, since satellite Bragg peaks appear along the incommensurate directions out of the (a * , b * ) plane at h + k odd, we have to assume a doubling of the unit cell within the crystallographic superspace. This C-centered C222 1 (00γ )(10δ) five-dimensional superspace group for phase II has been extensively described in previous articles [36,38]. The present study reports in n-nonadecane/urea a wavelength for the new incommensurate intermodulation along the aperiodic direction (0.23 μm) that is much longer than the one previously reported doing neutron-scattering studies [31,33] due to the very high-momentum resolution of the x-ray backscattering spectrometer.…”

“…Their model considers again the critical point M within the reciprocal (a * , b * ) plane [44]. We have shown here that this is not correct: in phase II, the critical wave vector is outside the (a * , b * ), in the point (1/2, 1/2, 0, 0, 1/2) of the five-dimensional Brillouin zone [33,36,38]. It corresponds to a completely different symmetry within a Landau description of the phase transition.…”

“…Four indices are needed to describe four different types of structure Bragg peaks (h k l m): a convenient but simplistic labeling is that (h k 0 0), (h k l 0), (h k 0 m), and (h k l m), with l and m different from zero, are the common, host, guest, and satellite Bragg peaks, respectively. Within this family of aperiodic intergrowth nanotubular structures, the organic guest/host n-alkane/urea compounds constitute a prototype family [7,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. In almost all of the n-alkane/urea inclusion compounds, a four-dimensional hexagonal superspace group P6 1 22(00γ ) is reported in the literature at room temperature.…”

Comment on Couzi et al . (2018): a phenomenological model for structural transitions in incommensurate alkane/urea inclusion compounds

“…The first-phase transition at T c1 is associated with the symmetry breaking from the hexagonal high-temperature phase to a second phase (phase II); a second transition to a different space group (phase III) occurs at a lower temperature T c2 . These results have been discussed extensively in the literature [3,4,[6][7][8][9] and were obtained using excellent spatial resolution and temperature calibration, including measurements using cold neutron scattering on triple axis spectrometers [3,4], and on a synchrotron X-ray diffractometer [7]. For n-nonadecane-h 40 / urea-h 4 , T c1 = (158.8 ± 0.1) K and T c2 = (147.0 ± 0.1) K, according to adiabatic measurements [10].…”

Phase transitions within crystals that are aperiodic by construction

“…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).…”