Céline Mariette

Neutron Laue and X‐ray diffraction study of a new crystallographic superspace phase in n‐nonadecane–urea

Aperiodic composite crystals present long-range order without translational symmetry. These materials may be described as the intersection in three dimensions of a crystal which is periodic in a higher-dimensional space. In such materials, symmetry breaking must be described as structural changes within these crystallographic superspaces. The increase in the number of superspace groups with the increase in the dimension of the superspace allows many more structural solutions. This is illustrated in n-nonadecane-urea, revealing a fifth higher-dimensional phase at low temperature.

The creation of modulated monoclinic aperiodic composites in n-alkane/urea compounds

Abstract n-Dodecane/urea is a member of the prototype series of n-alkane/urea inclusion compounds. At room temperature, it presents a quasi-one dimensional liquid-like state for the confined guest molecules within the rigid, hexagonal framework of the urea host. At lower temperatures, we report the existence of two other phases. Below Tc=248 K there appears a phase with rank four superspace group P61 22(00γ), the one typically observed at room temperature in n-alkane/urea compounds with longer guest molecules. A misfit parameter, defined by the ratio γ=ch/cg (chost/cguest), is found to be 0.632±0.005. Below Tc1=123 K, a monoclinic modulated phase is created with a constant shift along c of the guest molecules in adjacent channels. The maximal monoclinic space group for this structure is P121 1(α0γ). Analogies and differences with n-heptane/urea, which also presents a monoclinic, modulated low-temperature phase, are discussed.

Diffuse scattering and phase transitions in aperiodic inclusion compounds

Small molecules, such as urea, thiourea, perhydrotriphenylene can be co-crystallised with long-chain hydrocarbon molecules to form inclusion compounds. The guest chains are confined to narrow, approximately cylindrical, channels created by the host smallmolecule lattice. The stoichiometry and the conformations of the chains included inside the channels are function of internal interactions such as intra-chain interaction, but also of overall co-operative properties of the resulting three dimensionally ordered single crystal. These intergrowth compounds may form incommensurate composite crystals. A prototype example of such uniaxial intergrowth aperiodic crystals is n-alkane (CnH2n+2)/urea (CO(NH2)2). In these supra-molecular systems, urea molecules are connected by H-bonds and form helical ribbons, which repeat every six urea molecules to form a series of linear, hexagonal tunnels that can accommodate linear alkanes. Because the channels (~0.53 nm) are larger than the hydrocarbon chains, guests are held loosely and can undergo substantial motions. A significant amount of diffuse scattering of the first and second kinds can be depicted in scattering experiments, static or dynamic. These materials undergo a large variety of continuous or weakly first order structural phase transitions when changing the alkane molecule length and giving place to large pre-transitional effects. The talk will give an overview of the diffuse scattering in these compounds and will focus on connection with aperiodicity.

Phase Transitions in Aperiodic Composite Crystals

Aperiodic alkane/urea inclusion compounds (UIC) are prototype composites which exhibit complex sequences of phases that can clearly be described in the (3+d) dimension crystallographic superspace. By simply changing the length of the guest alkane molecules (C n H2n+2) which pile up in the channels of the host urea honeycomb-like framework, it is, for instance, possible to have phase-ordering phase transition from 3 to (3+1) dimension in the case of n-heptane/urea (n=7), or as in the case of n-hexadecane/urea (n=16) or n-nonadecane/urea (n=19), a generalization to higher dimensions of the phase transitions found in modulated structures. Such results are successfully obtained with the help of high resolution diffraction methods.

Symmetry breakings in aperiodic composite crystals

Aperiodic crystals have the property to possess long range order without translational symmetry. These crystals are described within the formalism of superspace crystallography [1-4]. Aperiodicity in composite materials may appear rather naturally due to the possible misfit of host and guest parameters along their crystallographic directions. A huge simplification exists in one dimensional (1D) composite aperiodic crystals since the colinearity of the incommensurate vectors is always maintained allowing a definite assignment of all the diffraction Bragg peaks. Urea inclusion compounds (UIC) constitute such a family of molecular composite structures, where long-chain guest molecules are embedded in parallel channels of the host urea sublattice and among them, most of the nalkane UIC are incommensurate [5]. In this contribution, we will focus on symmetry breakings which take place in such crystallographic superspace groups, considering this prototype family. Studies performed by X-ray diffraction using synchrotron sources reveal multiple structural solutions implying or not changes of the dimension of the superspace. Most fascinating ones concern phase transitions which increase the dimension of the crystallographic superspace [6-8]. We will present the characterization of the order parameter and of the critical pretransitionnal phenomena associated to these phase transitions of group/subgroup types. Anomalously large correlation lengths are reported along the incommensurate direction [9]. This symmetry breaking which double only the internal dimension of the crystallographic superspace could be interpreted as resulting of the softening of a phason branch. The specific excitations of aperiodic crystals such as phasons can be directly observed and analyzed by coherent neutron and inelastic Xray scattering. Such measurements performed on nnonadecane/urea revealed the coupling of the phason and the acoustic modes polarized along the incommensurate direction [10]. Recent studies done in the reciprocal space close to internal vectors of the superspace evidenced a low frequency damped excitation that we tentatively interpret as the sliding mode of this composite.