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International audience; Aperiodic crystals possess long-range order without translational symmetry. They constitute a state of matter that has forced a profound paradigm shift in solid-state physics. A common feature of aperiodic crystals is that they recover periodicity in higher dimensional spaces, the so-called crystallographic superspaces. Much work has been dedicated to the structural order within these superspaces and also to their specific dynamics. This paper focuses on the phase transitions within crystallographic superspaces. Aperiodic crystals are divided into three families: incommensurately modulated crystals, composite crystals, and quasicrystals. Incommensurately modulated crystals have been studied heavily and appear now to be relatively well understood, since they possess a periodic high-symmetry phase. The other two members of the family are aperiodic by construction. In this paper, we present a comprehensive and systematic study of a prototype composite host-guest family of n-alkane/urea inclusion compounds [$n−$ C$_n$H$_{2n+2}$/CO(NH$_2$)$_2$]. For these materials, which exhibit a rich sequence of phases, the phase transitions are described in terms of group/subgroup symmetry breaking within crystallographic superspaces. Such phase transitions may decrease, increase, or maintain the dimension of the crystallographic superspace. These results highlight the multiplicity of specific structural solutions thataperiodicity offers.

Cooperative molecular switching at the solid state is exemplified by spin crossover phenomenon in crystals of transition metal complexes. Time-resolved studies with temporal resolutions that separate molecular level dynamics from macroscopic changes, afford clear distinction between the time scales of the different degrees of freedom involved. In this work we use 100 ps X-ray diffraction to follow simultaneously the molecular spin state and the structure of the lattice during the photoinduced low spin to high spin transition in microcrystals of [FeIII(3-MeO-SalEen)2]PF6. We show the existence of a delay between the crystalline volume increase driven by the propagation of collective volumic strain waves, and the cooperative macroscopic switching of molecular state. Such behaviour is different from the expectation that phase transformation only requires atomic displacements in the unit cell, that can occur simultaneously with propagation of a volumic strain. Model simulations and discussions of the physical picture explain the phenomenon with thermally activated kinetics governed by local energy barriers separating the molecular states.

International audience; Photo-induced structural dynamics in molecular materials often involve two main components; local molecular distortions induced by the self-trapping of electronic excited state and incoherent lattice dynamics due to energy dissipation. The latter component frequently hinders clear manifestation at macroscopic scale of local self-trapped entities and their coupling to the lattice. The studied photoactive MnFe Prussian blue analogue exhibits no thermal expansion, which allows observing long-range lattice dynamics induced by the structural trapping of photo-induced charge-transfer (CT) states. The self-trapping of the photo-induced (MnFeII)-Fe-III -> (MnFeIII)-Fe-II is responsible for the emergence of various physical properties. At equilibrium, the lattice volume expansion and the ferroelastic Jahn-Teller distortion associated with the charge-transfer-based phase transition, evolve in a coupled way. Here, we use time resolved X-ray diffraction to investigate the anisotropic out-of-equilibrium lattice dynamics triggered by the self-trapping of photo-induced (MnFeII)-Fe-III -> (MnFeIII)-Fe-II CT. The observed dynamics evidence a decoupling of both types of lattice deformations in the time domain, with an impulsive lattice response driven by the local Jahn-Teller reorganization and a displacive volume expansion controlled by the long-lived photo-induced CT small-polarons, due to the population of antibonding orbitals centered on Mn-N bonds in the (a,b) lattice plane.

International audience; 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.

International audience

The complex relaxation from the photoinduced high-spin phase (PIHS) to the low-spin phase of the bimetallic two-dimensional coordination spin-crossover polymer [Fe[(Hg(SCN)3)2](4,4′-bipy)2]nis reported. During the thermal relaxation, commensurate and incommensurate spin-state concentration waves (SSCWs) form. However, contrary to the steps forming at thermal equilibrium, associated with long-range SSCW order, the SSCWs forming during the relaxation from the PIHS phase correspond to short-range order, revealed by diffuse X-ray scattering. This is interpreted as resulting from the competition between the two types of SSCW order and another structural symmetry breaking, due to ligand ordering, occurring at low temperature and precluding long-range SSCW order.

The discovery in materials of long range order without lattice periodicity has generated a very broad field of research with the introduction of totally new concepts. The common feature of this new state of matter is the translational symmetry recovered by adding supplementary dimensions to the physical space, defining a crystallographic superspace. Along these supplementary directions, specific low excitations, so-called phasons, are predicted and observed. These quasi-periodic crystals may present phase transitions as function of external parameters, which have then to be described as symmetry breakings within these crystallographic superspaces. Three different families of quasi-periodic crystals are usually considered: incommensurate modulated crystals, aperiodic composites and quasicrystals. Their crystallography and dynamics are discussed.

This paper reports on symmetry breaking in the aperiodic inclusion compound $n\text{-octadecane/urea}$ and its isotopomer $n\text{-octadecane/urea-}{d}_{4}$. The high-symmetry phase is described by a hexagonal rank-4 superspace group. Pretransitional phenomena in this crystallographic superspace reveal competing short-range-ordering phenomena within the high-symmetry phase. Very high-resolution diffraction data show that critical scattering appears at inequivalent points within the four-dimensional Brillouin zone, although the first phase transition at ${{T}_{c}}_{1}$ near 158 K implies the condensation at only one of those points. The resulting superspace group remains of dimension 4. Two other phase transitions are reported at ${{T}_{c}}_{2}\phantom{\rule{4pt}{0ex}}=152.8(4)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and ${{T}_{c}}_{3}=109(4)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ in $n\text{-octadecane/urea-}{d}_{4}$. The two low-symmetry phases that arise are described by rank-5 superspace groups.

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 inn-nonadecane–urea, revealing a fifth higher-dimensional phase at low temperature.

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= c h/c g (c host/c guest), 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.

International audience; Inorganic nanotubes represent an emerging class of nanobuilding blocks. Among them, imogolites are alumino-silicate or alumino-germanate nanotubes with well controlled diameter and helicity. As such, they constitute a model platform for the study of molecular interactions and confinement at the nanoscale, complementing the one constituted by carbon nanotubes. We focus here on double-walled alumino-germanate nanotubes, discovered very recently [1]. They are formed of two concentric tubes (figure inset), with respective internal diameters of 1.6 and 3.1nm and up to 1 micron in length [2]. We report the first experimental study, using wide angle x-ray scattering, performed on films of oriented nanotubes (figure). Structural changes of the nanotubes and behavior of the confined water under heating are investigated in-situ. The study of oriented samples gives new information that is not available with powder diffraction. Above all, the contribution to the scattering signal of internal and external tubes can be separated as well as the translational/rotational correlations. The use of wide image plate detectors allows one to access large area of the reciprocal space in a single image. Simulations of the two-dimensionnal scattering diagrams will be presented. A key question, the correlation between internal and external tube, which is of great interest for understanding friction properties at the nanoscale, will be discussed.

International audience; n-Heptane/urea is an aperiodic inclusion compound in which the ratio of host and guest repeats along the channel axis is very close to unity and is found to have a constant value (0.981) from 280 K to 90 K. Below 280 K, two phase transitions are observed. The first (T(c1) = 145 K) is a ferroelastic phase transition that generates superstructure reflections for the host while leaving the guest with 1D order. The second (T(c2) = 130 K) is a "phase ordering" transition to a four-dimensional structure (P2(1)11(0βγ)) with pronounced host-guest intermodulation and a temperature dependent phase shift between guests in adjacent channels.

International audience; Aperiodic composite crystals belong to a new state of matter that possesses long-range order without translational symmetry. We report measurements of low-lying phonon branches in a n-alkane/urea compound that provide a new insight to the urea sub-lattice and the commensurate basal plane dynamics. Focusing on the thoroughly studied n-nonadecane/urea compound makes a comparison with other inelastic scattering results possible, allowing the observation of a new aperiodic elastic signature. Using three techniques, slight but reproducible difference in sound velocities is observed between the transverse mode propagating along the aperiodic direction and polarized in the commensurate basal plane, and the one polarized along the aperiodic direction propagating in the basal plane.