Search

International audience; Replacing noble metal catalysts with inexpensive, environmentally harmless, active, selective and stable substitutes, is a great challenge for the chemical industry. In this paper, the noble metal-free Al5Co2(210) complex intermetallic surface is experimentally identified as active and selective for the semi-hydrogenation of butadiene. The catalyst surface structure and chemical composition are determined by experimental techniques-surface X-ray diffraction (SXRD), scanning tunneling microscopy (STM)-combined with ab initio calculations. Theoretical investigations of the adsorption properties under reaction conditions demonstrate that the surface Co atomic density drastically impacts the thermodynamic feasibility of the hydrogenation reaction, and they provide information on the reaction mechanism. This work offers insights for the rational design of Al-based catalysts for hydrocarbon hydrogenation reactions.

International audience; In order to obtain high-quality single grains of the Al-Cu-Ru icosahedral quasicrystal (iQC), suitable for a structure analysis, the crystal growth conditions with the self-flux method have been studied. The melts of the master alloys with the compositions of Al57.0+xCu39.5-xRu3.5 (x = 0, 2.5, 5, 7.5, 10) and Al62.0Cu34.0+y Ru4.0-y (y = 0, 0.5, 1.5) were held at 1150°C for 2 h, then cooled down to 800, 900, or 1000°C at a rate of −2 K/h, and subsequently retained for various durations, up to 750 h. Single grain iQCs having several millimetre-sizes, which were evaluated their quality by powder X-ray diffraction (XRD), were grown throughout this study. The peak of (664004) reflection in powder XRD of the iQCs grown at 1000°C has approximately 50% narrower width than that grown at 800°C. The inhomogeneity of the compositions intra- as well as inter-grains grown at 800°C was observed. High-quality single grains with homogeneous composition could be achieved with a long-time annealing at 900°C or regardless of the annealing time at 1000°C. By changing the Al/Cu ratio of the master alloys, the composition could also be controlled for the iQCs grown at 1000°C. Single-crystal XRD experiment with synchrotron radiation on Al66.6Cu16.4Ru17.0 iQC, grown at 1000°C, resulted in the collection of 2680 independent Bragg reflections that confirms the high-quality of the sample. The phase retrieval of the diffraction data resulted successfully in obtaining the structure solution, which reveals some characteristic features of this face-centred iQC structure.

Atomic structures of ternary icosahedral (i) Yb–Cd–Mg quasicrystals (QCs) with five different Mg contents up to 46.4 at.% and a corresponding 1/1 approximant (AP), which has a composition of Yb13.3Cd70.3Mg16.5, have been analysed by single-crystal X-ray diffraction. The structures of the iQCs were found to be isostructural to the parent i-YbCd5.7, which consists of a so-called Tsai-type rhombic triacontahedron (RTH) cluster and double Friauf polyhedron, and that of the 1/1 AP was found to be isostructural to YbCd6, which is described by a body-centred packing of the same type of RTH cluster. In the iQCs, it was found that there are three types of Cd/Mg occupation, namely, Cd preferential site, Mg preferential site and Cd/Mg mixed site, and the occupation probabilities of Mg atoms at the Mg preferential site show a saturation behaviour around the Mg content of 20 at.%. This selective Mg occupation is identified as a cause of the non-linear increase in the icosahedral lattice constant with increasing Mg content. The 1/1 AP has a similar selective Mg occupation to that of the iQCs in terms of the shell structures of the Tsai-type RTH cluster. In both iQCs and the 1/1 AP, the Mg preferential sites have a smaller number of Yb atoms among their coordination numbers. Moreover, short-range order (s.r.o.) diffuse scattering was observed on the diffraction patterns of the iQCs at the positions corresponding to a face-centred-type (F-type) icosahedral superlattice. The F-type s.r.o. was found to result from the Mg substitution.

International audience

This chapter discusses tilings as mathematical models for quasicrystals. In a first approximation quasicrystals may be described as being space filling with copies of two or more types of tiles. This description gives a connection with the mathematical notion of tilings, which have been well studied. A brief introduction of tilings is presented in this chapter along with the method of substitution to create aperiodic tilings. The symmetry of the tilings is also treated in this chapter, as are model sets and random tilings. Quasiperiodic crystals often have approximants, that is, periodic structures that are close to the aperiodic ones. The relations between quasiperiodic crystals and approximants also is described in this chapter.

This chapter discusses the X-ray and neutron diffraction methods used to study the atomic structures of aperiodic crystals, addressing indexing diffraction patterns, superspace, ab initio methods, the structure factor of incommensurate structures; and diffuse scattering. The structure solution methods based on the dual space refinements are described, as they are very often applied for the resolution of aperiodic crystal structures. Modulation functions which are used for the refinement of modulated structures and composite structures are presented and illustrated with examples of structure models covering a large spectrum of structures from organic to inorganic compounds, including metals, alloys, and minerals. For a better understanding of the concept of quasicrystalline structures, one-dimensional structure examples are presented first. Further examples of quasicrystals, including decagonal quasicrystals and icosahedral quasicrystals, are analysed in terms of increasing shells of a selected number of polyhedra. The notion of the approximant is compared with classical forms of structures.

The law of rational indices to describe crystal faces was one of the most fundamental law of crystallography and is strongly linked to the three-dimensional periodicity of solids. This chapter describes how this fundamental law has to be revised and generalized in order to include the structures of aperiodic crystals. The generalization consists in using for each face a number of integers, with the number corresponding to the rank of the structure, that is, the number of integer indices necessary to characterize each of the diffracted intensities generated by the aperiodic system. A series of examples including incommensurate multiferroics, icosahedral crystals, and decagonal quaiscrystals illustrates this topic. Aperiodicity is also encountered in surfaces where the same generalization can be applied. The chapter discusses aperiodic crystal morphology, including icosahedral quasicrystal morphology, decagonal quasicrystal morphology, and aperiodic crystal surfaces; magnetic quasiperiodic systems; aperiodic photonic crystals; mesoscopic quasicrystals, and the mineral calaverite.

Physical properties of aperiodic crystals present some theoretical challenges due to the lack of three-dimensional periodicity. For the description of the structure there is a periodic representation in higher-dimensional space. For physical properties, however, this scheme cannot be used because the mapping between interatomic forces and the high-dimensional representation is not straightforward. In this chapter methods are described to deal with these problems. First, the hydrodynamic theory of aperiodic crystals and then the phonons and phasons theory are developed and illustrated with some examples. The properties of electrons in aperiodic crystals are also presented. Finally, the experimental findings of phonon and phason modes for modulated and quasicrystals are presented. The chapter also discusses diffuse scattering, the Debye–Waller factor, and electrical conductivity.

First a general description of the concept of crystalline structures is presented with some historical background information. The classical approach of periodic structures is presented along with the important topic of symmetry and its role characterizing physical properties. The limitations of the classical model are then introduced in view of the new experimental observations discovered since the 1970s. New forms of crystalline structures including incommensurately modulated and composite structures are presented along with quasicrystalline structures (quasicrystals). The necessity to extend the theory of space group symmetry is then discussed and the concept of superspace symmetry is introduced in order to describe these new forms of matters.

This chapter first introduces the mathematical concept of aperiodic and quasiperiodic functions, which will form the theoretical basis of the superspace description of the new recently discovered forms of matter. They are divided in three groups, namely modulated phases, composites, and quasicrystals. It is shown how the atomic structures and their symmetry can be characterized and described by the new concept. The classification of superspace groups is introduced along with some examples. For quasicrystals, the notion of approximants is also introduced for a better understanding of their structures. Finally, alternatives for the descriptions of the new materials are presented along with scaling symmetries. Magnetic systems and time-reversal symmetry are also introduced.

The hexagonal ZrNiAl-type (space group: P-62m) and the tetragonal Mo2FeB2-type (space group: P4/mbm) structures, which are frequently formed in the same Yb-based alloys and exhibit physical properties related to valence-fluctuation, can be regarded as approximants of a hypothetical dodecagonal quasicrystal. Using Pd-Sn-Yb system as an example, a model of quasicrystal structure has been constructed, of which 5-dimensional crystal (space group: P12/mmm, aDD=5.66 {\AA} and c=3.72 {\AA}) consists of four types of acceptance regions located at the following crystallographic sites; Yb [00000], Pd[1/3 0 1/3 0 1/2], Pd[1/3 1/3 1/3 1/3 0] and Sn[1/2 00 1/2 1/2]. In the 3-dimensional space, the quasicrystal is composed of three types of columns, of which c-projections correspond to a square, an equilateral triangle and a 3-fold hexagon. They are fragments of two known crystals, the hexagonal {\alpha}-YbPdSn and the tetragonal Yb2Pd2Sn structures. The model of the hypothetical quasicrystal may be applicable as a platform to treat in a unified manner the heavy fermion properties in the two types of Yb-based crystals., Comment: 19 pages, 6 figures

The detailed atomic structure of the binary icosahedral ScZn7.33 quasicrystal has been investigated by means of high-resolution synchrotron single-crystal X-ray diffraction and absolute scale measurements of diffuse scattering., The detailed atomic structure of the binary icosahedral (i) ScZn7.33 quasicrystal has been investigated by means of high-resolution synchrotron single-crystal X-ray diffraction and absolute scale measurements of diffuse scattering. The average atomic structure has been solved using the measured Bragg intensity data based on a six-dimensional model that is isostructural to the i-YbCd5.7 one. The structure is described with a quasiperiodic packing of large Tsai-type rhombic triacontahedron clusters and double Friauf polyhedra (DFP), both resulting from a close-packing of a large (Sc) and a small (Zn) atom. The difference in chemical composition between i-ScZn7.33 and i-YbCd5.7 was found to lie in the icosahedron shell and the DFP where in i-ScZn7.33 chemical disorder occurs on the large atom sites, which induces a significant distortion to the structure units. The intensity in reciprocal space displays a substantial amount of diffuse scattering with anisotropic distribution, located around the strong Bragg peaks, that can be fully interpreted as resulting from phason fluctuations, with a ratio of the phason elastic constants K 2/K 1 = −0.53, i.e. close to a threefold instability limit. This induces a relatively large perpendicular (or phason) Debye–Waller factor, which explains the vanishing of ‘high-Q perp’ reflections.

Despite their crystalline nature, thermoelectric clathrates exhibit a strongly reduced lattice thermal conductivity. While the reason for this unexpected behavior is known to lie in the peculiarities of the complex crystal structure and the interplay of the underlying guest-host framework, their respective roles are still not fully disentangled and understood. Our ab initio study of the most simple type-I clathrate phase, the binary compound ${\mathrm{Ba}}_{8}{\mathrm{Si}}_{46}$ and its derivatives ${\mathrm{Ba}}_{8\ensuremath{-}x}{\mathrm{Si}}_{46}$ seeks to identify these mechanisms and provides insight into their origin. Indeed, the strongly decreased lattice thermal conductivity in thermoelectric clathrates is a consequence of a reduction of the acoustic phonon bandwidth, a lowering of the acoustic phonon group velocities, and the amplification of three-phonon-scattering processes. While the complexity of the crystal structure is demonstrated not to be the leading factor, the reasons are manifold. A modified Si-Si interaction causes a first decrease of the sound velocity, whereas the presence of flat Ba modes results in an additional lowering. These modes correspond to confined Bloch states that are localized on the Ba atoms and significantly increase the scattering phase space and, together with an increased anharmonicity of the interatomic interactions, strongly affect the phonon lifetimes.

Ted Janssen’s contributions to the field of aperiodic crystals are reviewed., This article reviews some of Ted Janssen’s (1936–2017) major contributions to the field of aperiodic crystals. Aperiodic crystals are long-range ordered structures without 3D lattice translations and encompass incommensurately modulated phases, incommensurate composites and quasicrystals. Together with Pim de Wolff and Aloysio Janner, Ted Janssen invented the very elegant theory of superspace crystallography that, by adding a supplementary dimension to the usual 3D space, allows for a deeper understanding of the atomic structure of aperiodic crystals. He also made important contributions to the understanding of the stability and dynamics of aperiodic crystals, exploring their fascinating physical properties. He constantly interacted and collaborated with experimentalists, always ready to share and explain his detailed understanding of aperiodic crystals.

The (lattice) dynamics of quasicrystals differs in many aspects from that of lattice periodic systems. This they have in common with other aperiodic crystals. The dynamics of quasicrystals is discussed here in the context of these general aperiodic crystals, but the special features of quasicrystals are stressed. The lattice dynamics is now fairly well understood. Especially for aperiodic crystals, there are excitations related to the possibility to describe the systems in superspace. These ‘phasons’ are discussed in particular.

We present the refinement results of atomic structures of binary icosahedral (i) ScZn7.3, GdCd7.9, DyCd7.5 and TmCd7.3 quasicrystals (QCs) [1, 2] and the study of phason modes. Bragg peak intensities data collection has been carried out on the CRISTAL beamline at the synchrotron SOLEIL, using an incoming X-ray energies equal to 25.5 keV (Sc-Zn) and 24.2 keV (R-Cd), and a CCD camera located at 8 cm from the samples. For all iQC samples a high redundancy (average 50) has been obtained resulting in 4057 (Sc-Zn) and 4871 ~ 5130 (R-Cd) unique reflections having intensity larger than 3 sigma and internal R factors around 8 %. The atomic structures of the iQCs were solved using the measured Bragg intensity data based on a six-dimensional model that is isostructural to the i-YbCd5.7 one [3] and the refinement program named qcdiff by A. Yamamoto, resulting in R factors equal to 10.9 % (Sc-Zn) and 8.9 ~ 10.9 % (R-Cd). The resulting structures are described with a quasiperiodic packing of large Tsai-type rhombic triacontahedron clusters (RTH) and double Friauf polyhedra (DFP), both resulting from a close-packing of large (Sc, R) and small (Zn, Cd) atoms. The significant difference in alloy composition between i-ScZn7.3, i-RCd~7.9 and the ideal model of i-YbCd5.7 was found to lay mainly on the DFP where one of the two large atom site (Sc, R) is replaced by a small atom (Zn, Cd) resulting in a significant distortion of the DFP. Residual disorder with relative occupancies of Sc(R)/Zn(Cd)=80/20 was also found on the icosahedral site. This illustrates that a detailed understanding of the atomic structure can now be achieved in QCs. The stabilization mechanism for these binary iQCs and the microscopic origins to explain the phason fluctuations will be discussed in this presentation. (1) Canfield, P. C., Caudle, M. L., Ho, C. S., Kreyssig, A., Nandi, S., Kim, M. G., Lin, X., Kracher, A., Dennis, K. W., McCallum, R. W. & Goldman, A. I. (2010) Phys. Rev. B, Solution growth of a binary icosahedral quasicrystal of Sc12Zn88, 81, 020201. (2) Goldman, A. I., Kong, T., Kreyssig, A., Jesche, A., Ramazanoglu, M., Dennis, K. W., et al. (2013). Nature Materials, A family of binary magnetic icosahedral quasicrystals based on rare earths and cadmium, 12(8), 714–718. (3) Takakura, H., Gómez, C. P., Yamamoto, A., de Boissieu, M., & Tsai, A. P. (2006). Nature Materials, Atomic structure of the binary icosahedral Yb–Cd quasicrystal, 6(1), 58–63.

The discovery of quasicrystals not only has changed our view on long-range order, but was a breakthrough for solid state physics and chemistry, since the Bloch theorem can no longer be applied. We review some of the results obtained for icosahedral quasicrystals for lattice dynamics and phonons, as well as for phason modes, which are diffusive excitations characteristic of the quasicrystalline state.

Quasicrystals are long-range-ordered materials that lack translational invariance, so the study of their physical properties remains a challenging problem. Here, we have carried out inelastic-X-ray- and neutron-scattering experiments on single-grain samples of the Zn-Mg-Sc icosahedral quasicrystal and of the Zn-Sc periodic cubic 1/1 approximant, with the aim of studying the respective influence of the local order and of the long-range order (periodic or quasiperiodic) on lattice dynamics. Besides the overall similarities and the existence of a pseudo-gap in the transverse dispersion relation, marked differences are observed, the pseudo-gap being larger and better defined in the approximant than in the quasicrystal. This can be qualitatively explained using the concept of a pseudo-Brillouin-zone in the quasicrystal. These results are compared with simulations on atomic models and using oscillating pair potentials, and the simulations reproduce in detail the experimental results. This paves the way for a detailed understanding of the physics of quasicrystals.

Icosahedral quasicrystals (i-QCs) are long-range ordered solids that show non-crystallographic symmetries such as five-fold rotations. Their detailed atomic structures are still far from completely understood, because most stable i-QCs form as ternary alloys suffering from chemical disorder. Here, we present the first detailed structure solution of i-YbCd(5.7), one of the very few stable binary i-QCs, by means of X-ray structure determination. Three building units with unique atomic decorations arrange quasiperiodically and fill the space. These also serve as building units in the periodic approximant crystals. The structure is not only chemically feasible, but also provides a seamless structural understanding of the i-YbCd(5.7) phase and its series of related i-QCs and approximant crystals, revealing hierarchic features that are of considerable physical interest.

International audience

Dimensions ‏ : ‎ 16.51 x 5.08 x 22.23 cm; International audience

An X-ray standing waves experiment was performed at the ID32 beam line of the ESRF on an Al–Pd–Mn quasicrystal with the X-ray beam at normal incidence. The X-ray photoemission core levels for each element were recorded to probe the surface. The drain current, i.e. the electron current from ground needed to neutralize the irradiated sample and to compensate the photoemitted electrons was also recorded as a bulk probe that integrates over all atoms of the sample. Within the two-beam approximation applied to quasicrystals, a simple analysis of this effect is proposed. This provides a direct-space illustration of the diffraction process in a quasiperiodic structure.

We have measured the electron energy losses on different Al–Pd–Mn quasicrystal surface states established by low energy electron diffraction, X-ray photoelectron spectroscopy and Auger electron spectroscopy. On the well characterized and ordered Al–Pd–Mn quasicrystalline surfaces, the energy loss signal with an energy of incident electrons at 2 keV shows a strong peak at 16 eV and a satellite at about 33 eV. As the electron primary energy is decreased to 260 eV, an energy loss at 10.5 eV is clearly observed. A short ion bombardment (1 μA at 500 eV during 1 min) erases this loss at 10.5 eV which can be recovered by annealing at 800 K. All these observations are simply attributed to the existence of a bulk plasmon at about 16 eV and a surface plasmon at 10.5 eV. The ratio between these two energies is 1.52. This is quite close to the expected 2 from the classical plasmon model. On the crystalline partially annealed surface, a bulk plasmon is observed at about 16.5 eV. Oxygen-contaminated surface presents a bulk plasmon shifted towards higher energy of about 20 eV.

Fivefold surfaces of Al–Pd–Mn quasicrystal have been prepared under ultra-high vacuum (UHV) by sputtering and annealing above 700 K and characterized by electron diffraction, Auger spectroscopy and X-ray photoemission spectroscopy (LEED, AES, XPS). X-ray reflectivity at grazing incidence reveals that an in situ temperature annealing at 900 K is necessary to irreversibly produce the signature of a flat and bulk terminated surface. Air-AFM investigations of surfaces prepared below or in the vicinity of this transformation temperature show a large scale structure in the micrometer range with high steps and parallel terraces. Terrace morphology is dominated by clusters with a typical size of about 10 nm. Nanometer steps can coexist with this cluster structure. With UHV-STM, terrace roughness based on cluster assembly is found to extend down to the nanometer scale.

International audience; The Zn6Sc 1/1 cubic approximant to a quasicrystal has been studied in-situ at high pressures by single-crystal X-ray diffraction. This phase can be described as a bcc packing of Tsai-type icosahedral clusters whose center is occupied by a disordered Zn-4 tetrahedron. At ambient pressure the Zn6Sc undergoes a structural phase transition at 159 K to a monoclinic superstructure in which the Zn-4 tetrahedra are orientationally ordered along the [101] direction of the high-temperature bcc phase. In the pressure range up to 35 GPa, two new superstructures have been observed. The second phase corresponds to a four-fold pseudo cubic superstructure, i.e. a very large unit cell with a lattice parameter of about 5.5 nm. The resulting pressure-temperature phase diagram is different from that of Cd6Yb, which was reported by Watanuki et al. (2006).

International audience; It has generally been accepted that the orientational ordering of the Cd4 tetrahedron within the Cd6 R quasicrystal approximants is kinetically inhibited for R = Ho, Er, Tm and Lu by steric constraints. Our high-resolution X-ray scattering measurements of the Cd6Ho quasicrystal approximant, however, reveal an abrupt (first-order) transition to a monoclinic structure below T S = 178 K for samples that have 'aged' at room temperature for approximately one year, reopening this question. Using X-ray resonant magnetic scattering at the Ho L 3-edge we have elucidated the nature of the antiferromagnetic ordering below T N = 8.5 K in Cd6Ho. The magnetic Bragg peaks are found at the charge forbidden H + K + L = 2n + 1 positions, referenced to the high-temperature body-centred cubic structure. In general terms, this corresponds to antiferromagnetic arrangements of the Ho moments on adjacent clusters in the unit cell as previously found for Cd6Tb.