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Science 4 January 2008:
Vol. 319. no. 5859, pp. 69 - 71
DOI: 10.1126/science.1146745
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Reports

Hidden Degrees of Freedom in Aperiodic Materials

Bertrand Toudic,1,2* Pilar Garcia,1,2 Christophe Odin,1,2 Philippe Rabiller,1,2 Claude Ecolivet,1,2 Eric Collet,1,2 Philippe Bourges,3 Garry J. McIntyre,4 Mark D. Hollingsworth,5 Tomasz Breczewski6

Numerous crystalline materials, including those of bioorganic origin, comprise incommensurate sublattices whose mutual arrangement is described in a superspace framework exceeding three dimensions. We report direct observation by neutron diffraction of superspace symmetry breaking in a solid-solid phase transition of an incommensurate host-guest system: the channel inclusion compound of nonadecane/urea. Strikingly, this phase transition generates a unit cell doubling that concerns only the modulation of one substructure by the other—an internal variable available only in superspace. This unanticipated pathway for degrees of freedom to rearrange leads to a second phase transition, which again is controlled by the higher dimensionality of superspace. These results reveal nature's capacity to explore the increased number of phases allowed in aperiodic crystals.

1 Université de Rennes 1, Institut de Physique de Rennes (IPR), 35042 Rennes Cedex, France.
2 CNRS, UMR 6251, IPR, 263 Avenue du Général Leclerc, 35042 Rennes Cedex, France.
3 Laboratoire Léon Brillouin, CEA-CNRS, CE-Saclay, 91191 Gifsur-Yvette, France.
4 Institut Laue-Langevin, 38042 Grenoble Cedex 9, France.
5 Department of Chemistry, Kansas State University, Manhattan, KS 66506, USA.
6 Facultad de Ciencias, Universidad del Pais Vasco, Apdo 644, Bilbao, Spain.

* To whom correspondence should be addressed. E-mail: bertrand.toudic{at}univ-rennes1.fr

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