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Introducing the new Section Editor of Acta Crystallographica Section B.
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High-Entropy Alloys (HEAs) are a new family of crystalline random alloys with four or more elements in a simple unit cell, at the forefront of materials research for their exceptional mechanical properties. Their strong chemical disorder leads to mass and force-constant fluctuations which are expected to strongly reduce phonon lifetime, responsible for thermal transport, similarly to glasses. Still, the long range order would associate HEAs to crystals with a complex disordered unit cell. These two families of materials, however, exhibit very different phonon dynamics, still leading to similar thermal properties. The question arises on the positioning of HEAs in this context. Here we present an exhaustive experimental investigation of the lattice dynamics in a HEA, Fe20Co20Cr20Mn20Ni20, using inelastic neutron and X-ray scattering. We demonstrate that HEAs present unique phonon dynamics at the frontier between fully disordered and ordered materials, characterized by long-propagating acoustic phonons in the whole Brillouin zone.
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Dodecagonal oxide quasicrystals are well established as examples of long-range aperiodic order in two dimensions. However, despite investigations by scanning tunneling microscopy (STM), low-energy electron diffraction (LEED), low-energy electron microscopy (LEEM), photoemission spectroscopy as well as density functional theory (DFT), their structure is still controversial. Furthermore, the principles that guide the formation of quasicrystals (QCs) in oxides are elusive since the principles that are known to drive metallic QCs are expected to fail for oxides. Here we demonstrate the solution of the oxide QC structure by synchrotron-radiation based surface x-ray diffraction (SXRD) refinement of its largest-known approximant. The oxide QC formation is forced by large alkaline earth metal atoms and the reduction of their mutual electrostatic repulsion. It drives the n = 6 structure of the 2D Ti2O3 honeycomb arrangement via Stone-Wales transformations into an ordered structure with empty n = 4, singly occupied n = 7 and doubly occupied n = 10 rings, as supported by DFT.
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A Special Issue on the topic of Electron Crystallography, now available in the August 2019 issue of Acta Crystallographica, Section B, contains contributions which we hope will interest readers of IUCrJ.
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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.
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Engineering lattice thermal conductivity requires to control the heat carried by atomic vibration waves, the phonons. The key parameter for quantifying it is the phonon lifetime, limiting the travelling distance, whose determination is however at the limits of instrumental capabilities. Here, we show the achievement of a direct quantitative measurement of phonon lifetimes in a single crystal of the clathrate Ba7.81Ge40.67Au5.33, renowned for its puzzling 'glass-like' thermal conductivity. Surprisingly, thermal transport is dominated by acoustic phonons with long lifetimes, travelling over distances of 10 to 100 nm as their wave-vector goes from 0.3 to 0.1 Å-1. Considering only low-energy acoustic phonons, and their observed lifetime, leads to a calculated thermal conductivity very close to the experimental one. Our results challenge the current picture of thermal transport in clathrates, underlining the inability of state-of-the-art simulations to reproduce the experimental data, thus representing a crucial experimental input for theoretical developments.Phonon lifetime is a fundamental parameter of thermal transport however its determination is challenging. Using inelastic neutron scattering and the neutron resonant spin-echo technique, Lory et al. determine the acoustic phonon lifetime in a single crystal of clathrate Ba7.81Ge40.67Au5.33.
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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.
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Using in situ x-ray scattering and synchrotron radiation, we have experimentally elucidated the mechanism of the cubic to monoclinic phase transition in the Zn6Sc 1/1 approximant to an icosahedral quasicrystal. The high-temperature cubic phase is described as a bcc packing of a large Tsai-type icosahedral cluster whose center is occupied by an orientationally disordered Zn4 tetrahedron. A clear monoclinic distortion has been found to take place within 2 K around Tc = 157 K, in excellent agreement with the observed anomalies in the electrical resistivity and heat capacity. Also, a rapid variation of the super-structure reflection intensity is observed. The low-temperature monoclinic phase, as determined by single-crystal x-ray diffraction at 40 K, has been confirmed to consist of ordered Zn4 tetrahedra, oriented in an anti-parallel way along the [[Formula: see text]] direction. Above Tc, a diffuse scattering signal is observed at the position of the super-structure reflections, which evidences that a short-range ordering of the Zn4 tetrahedra takes place. In a way similar to a second-order phase transition, the correlation length describing this short-range ordering increases rapidly when the temperature diminishes and almost diverges when the temperature is close to Tc, going from 200 Å at 220 K to reach the very large value of 1200 Å at 161 K. Finally, using single-crystal x-ray diffraction, the atomic structure of the low-temperature monoclinic super-structure (space group C2/c) could be solved. The ordering of the Zn4 tetrahedra is accompanied by a strong distortion of the surrounding shells.
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Periodic approximants to quasicrystals offer a unique opportunity to better understand the structure, physical properties and stabilizing mechanisms of their quasicrystal counterparts. We present a detailed study of the order-disorder phase transition occurring at about 160 K in the Zn(6)Sc cubic approximant to the icosahedral quasicrystal i-MgZnSc. This transition goes along with an anti-parallel ordering of the tetrahedra located at the centres of large atomic clusters, which are packed on a bcc lattice. Single crystal x-ray diffuse scattering shows that the tetrahedra display pre-transitional short range ordering above T(c) (Yamada et al 2012 in preparation). Using quasielastic neutron scattering (QENS) we clearly evidence this short range order to be dynamical in nature above T(c). The QENS data are consistent with a model of tetrahedra 'jumping' between almost equivalent positions, which is supported by molecular dynamics simulations. This demonstrates a unique dynamical flexibility of the Zn(6)Sc structure even at room temperature.
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We review some of the results obtained for the study of phason, phonon and atomic dynamics in quasicrystals. In the framework of the hydrodynamic theory long-wavelength phason modes are characteristic of quasicrystal and are diffusive modes. Quenched-in phason mode gives rise to a characteristic diffuse scattering, observed in all the 'stable' icosahedral quasicrystals studied so far. In the AlPdMn icosahedral phase, above T = 500 °C, equilibrium phason modes are shown to be diffusive modes in agreement with the hydrodynamic theory. The lattice dynamics has been studied by inelastic neutron or X-ray scattering. Well defined acoustic modes are only observed for wavevectors smaller than 0.3 Å(-1). Above this value, the mode rapidly broadens as a result of mixing with higher energy modes. We show that the results can be interpreted using the concept of pseudo-Brillouin zone boundary and can qualitatively explain the differences observed in the response function of the ZnSc 1/1 approximant and its quasicrystalline counterpart. The observations are qualitatively and quantitatively reproduced using oscillating pair potentials, which open the route for a detailed analysis of the lattice dynamics at the atomic scale. An exceptional dynamical flexibility is also evidenced in the 1/1 approximant. A brief discussion on the implication of those results on the stabilizing mechanisms of quasicrystals is given at the end of the paper.
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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.
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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.
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We study the structure of very thin liquid crystal films frustrated by antagonistic anchorings in the smectic phase. In a cylindrical geometry, the structure is dominated by the defects for film thicknesses smaller than 150 nm and the detailed topology of the defects' cores can be revealed by x-ray diffraction. They appear to be split in half tube-shaped rotating grain boundaries (RGB). We determine the RGB spatial extension and evaluate its energy per unit length. Both are significantly larger than the ones usually proposed in the literature.
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Through the combination of three different, complementary techniques (optical microscopy, x-ray diffraction and atomic force microscopy), we reveal the deformations inside thin smectic films frustrated between two interfaces imposing antagonistic anchorings. We study the model system, 4-n-octyl-4'-cyanobiphenyl (8CB) between MoS2 and air, which is characterized by the competition between homeotropic anchoring at air and planar unidirectional anchoring on the substrate, with thicknesses varying around 0.3 microm. Optical microscopy and x-ray diffraction demonstrate the continuous topology of smectic layers between the interfaces, which are stacked into periodic flattened hemicylinders. These latter are one-dimensional (1D) focal conic domains which form an optical grating in the smectic film, of a period ranging from 1 to 2.5 microm. The interpretation of our results through an energetic model, associated with the atomic force microscopy (AFM) measurements, shows the presence below a critical thickness of a new type of curvature wall between neighboring hemicylinders.
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We have studied the anchoring directions imposed on 4-n-octyl-4(')-cyanobiphenyl (8CB) smectic-A and nematic phases by a single crystal of molybdenum disulfide (MoS2). Combining optical microscopy and x-ray diffraction under grazing incidence we have demonstrated the occurrence of a bistable planar anchoring. A previous study of the two-dimensional (2D) network of adsorbed 8CB molecules under the liquid crystal film allows a direct connection to be made between the interface structure and the anchoring directions, demonstrating that bistability is induced by the presence of two dipolar groups in the skeleton of the 2D network. It is demonstrated that the Landau-de Gennes theory cannot account for the observed anchoring in the nematic phase. The Landau-de Gennes free energy has to be associated with a coupling with both the surface order and the MoS2 substrate to explain the experimental observations. The hypothesis of a nematic layer under the liquid crystal bulk is postulated in the smectic phase.
