Hidden Degrees of Freedom in Aperiodic Materials

Toudic, Bertrand; Garcia, P.; Odin, Christophe; Rabiller, Philippe; Écolivet, C.; Collet, Éric; Bourgès, Philippe; McIntyre, Garry J.; Hollingsworth, Mark D.; Bréczewski, T.

doi:10.1126/science.1146745

Cited by 63 publications

(92 citation statements)

References 27 publications

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“…A large body of work has been dedicated to the phase transitions in this prototype family [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33], revealing recently a rich sequence of phases in high-dimensional crystallographic spaces [6,11,18,19,32,33]. Previously, we reported original behavior of the critical phenomena leading to a phase transition with an increase of the dimensionality of the crystallographic superspace from four to five [6,19].…”

Section: Fig 1 (Color Onlinementioning

confidence: 99%

Frustrated pretransitional phenomena in aperiodic composites

et al. 2016

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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.

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Section: Fig 1 (Color Onlinementioning

confidence: 99%

Frustrated pretransitional phenomena in aperiodic composites

et al. 2016

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“…Other recent examples of modulated organic structures comprise the channel inclusion compound of nonadecane/ urea, CH 3 (CH 2 ) 17 CH 3 /(NH 2 ) 2 CO, which was refined as an incommensurate host-guest system at low temperature (Toudic et al, 2008) with an alternating intermodulation between host and guest substructures from channel to channel, and the modulated structure of 1-phenyl-4-cyclohexylbenzene, C 14 H 20 (Evain et al, 2009), in which the cyclohexyl group is rotated with respect to the benzene ring. Sketch of the intramolecular torsion in biphenyl C 12 H 10 , re-drawn after Dzyabchenko & Scheraga (2004).…”

Section: Current Statusmentioning

confidence: 99%

A non-mathematical introduction to the superspace description of modulated structures

Wagner

Schönleber

2009

Acta Crystallogr Sect B

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The X-ray analysis of (6R,7aS)-6-(tert-butyl-dimethylsilanyloxy)-1-hydroxy-2-phenyl-5,6,7,7a-tetrahydropyrrolizin-3-one, C 19 H 27 NO 3 Si, revealed a diffraction pattern which is typical for modulated structures: strong Bragg peaks surrounded by weaker reflections which cannot be indexed with the same three reciprocal lattice vectors that are used to describe the strong peaks. For this class of crystal structures the concept of superspace has been developed which, however, for many crystallographers still constitutes a Gordian Knot. As a possible tool to cut this knot the crystal structure of the above-mentioned tetrahydropyrrolizinone derivative is presented as an illustrative example for handling and describing the modulated structure of a typical pharmaceutical (i.e. molecular) compound. Having established a working knowledge of the concepts and terminology of the superspace approach a concise and detailed description of the complete process of peak indexing, data processing, structure solution and structure interpretation is presented for the incommensurately modulated crystal structure of the above-mentioned compound. The superspace symmetry applied is P2 1 (0)0; the (incommensurate) q vector components at 100 K are = 0.1422 (2) and = 0.3839 (8).

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“…While studying the crystal structures of urea-hydrocarbon complexes, Smith reported in 1952 extra spots in the diffraction pattern with fractional "l" indices [37], indicating not a random but an ordered arrangement of the hydrocarbon molecules in the channels created by the urea molecules. Those structures are now known as urea inclusion compounds (host-guest structures) and have attracted until today quite some interest [38][39][40][41][42][43][44][45]. The urea molecules act as host and form a honeycomb structure which creates at room temperature parallel tunnels.…”

Section: Organic and Organometallic Compoundsmentioning

confidence: 99%

Organic molecular compounds with modulated crystal structures

Schoenleber¹

2011

Zeitschrift Für Kristallographie

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Abstract. Even though the higher-dimensional superspace approach is an established method to describe aperiodic crystal structures, it is not yet fully considered and applied by a larger community of scientists. In this contribution the structural description of incommensurately and commensurately modulated molecular compounds is discussed and it is shown, that the higher-dimensional superspace approach is an elegant way for an exact structural description and an exact crystal-chemical analysis of such structures. While discussing several modulated molecular compounds, the idea behind the higher-dimensional superspace approach is shown. On the examples treated in the discussion it is explained, how to understand and how to interprete modulated molecular compounds. Also a short introduction is given to the higher-dimensional superspace approach itself, to the basic principles and to the applied nomenclature.

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Hidden Degrees of Freedom in Aperiodic Materials

Cited by 63 publications

References 27 publications

Frustrated pretransitional phenomena in aperiodic composites

Frustrated pretransitional phenomena in aperiodic composites

A non-mathematical introduction to the superspace description of modulated structures

Organic molecular compounds with modulated crystal structures

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