Walter Steurer

Classical vibrational modes in phononic lattices: theory and experiment

Abstract We present a review, through selected illustrative examples, of the physics of classical vibrational modes in phononic lattices, which elaborates on the theory, the formalism, the methods, and mainly on the numerical and experimental results related to phononic crystals. Most of the topics addressed here, are written in a self-consistent way and they can be read as independent individual parts.

Photonic and phononic quasicrystals

This review focuses on the peculiarities of quasiperiodic order for the properties of photonic and phononic (sonic) heterostructures. The most beneficial feature of quasiperiodicity is that it can combine perfectly ordered structures with purely point-diffractive spectra of arbitrarily high rotational symmetry. Both are prerequisites for the construction of isotropic band gap composites, in particular from materials with low index contrast, which are required for numerous applications. Another interesting property of quasiperiodic structures is their scaling symmetry, which may be exploited to create spectral gaps in the sub-wavelength regime. This review covers structure/property relationships of heterostructures based on one-dimensional (1D) substitutional sequences such as the Fibonacci, Thue–Morse, period-doubling, Rudin–Shapiro and Cantor sequence as well as on 1D modulated structures, further on 2D tilings with 8-, 10-, 12- and 14-fold symmetry as well as on the pinwheel tiling, the Sierpinski gasket and on curvilinear tilings and, finally, on the 3D icosahedral Penrose tiling.

The structure of decagonal Al70Ni15Co15

The quasiperiodic structure of decagonal Al 70 Ni 15 Co 15 was determined on the basis of X-ray single-crystal intensity data using the n-dimensional embeding method. Centrosymmetric five-dimensional space group P10 5 /mmc, three-dimensional reciprocal and direct quasilattice parameters: a i * =0.2636 (1) A -1 , i=1,..., 4, a 5 * =0.24506 (3)A -1 , a i =3.794 (1)A, i=1,..., 4, a 5 =4.0807 (3) A

Colloidal quasicrystals with 12-fold and 18-fold diffraction symmetry

Micelles are the simplest example of self-assembly found in nature. As many other colloids, they can self-assemble in aqueous solution to form ordered periodic structures. These structures so far all exhibited classical crystallographic symmetries. Here we report that micelles in solution can self-assemble into quasicrystalline phases. We observe phases with 12-fold and 18-fold diffraction symmetry. Colloidal water-based quasicrystals are physically and chemically very simple systems. Macroscopic monodomain samples of centimeter dimension can be easily prepared. Phase transitions between the fcc phase and the two quasicrystalline phases can be easily followed in situ by time-resolved diffraction experiments. The discovery of quasicrystalline colloidal solutions advances the theoretical understanding of quasicrystals considerably, as for these systems the stability of quasicrystalline states has been theoretically predicted for the concentration and temperature range, where they are experimentally observed. Also for the use of quasicrystals in advanced materials this discovery is of particular importance, as it opens the route to quasicrystalline photonic band gap materials via established water-based colloidal self-assembly techniques.

The Samson phase, β-Mg2Al3, revisited

Co-Authors: Michael Feuerbacher, Carsten Thomas, Julien P. A. Makongo, Stefan Hoffmann, Wilder Carrillo-Cabrera, Raul Cardoso, Yuri Grin, Guido Kreiner, Jean-Marc Joubert, Thomas Schenk, Joseph Gastaldi, Henri Nguyen-Thi, Nathalie Mangelinck-Noël, Bernard Billia, Patricia Donnadieu, Aleksandra Czyrska-Filemonowicz, Anna Zielinska-Lipiec, Beata Dubiel, Thomas Weber, Philippe Schaub, Günter Krauss, Volker Gramlich, Jeppe Christensen, Sven Lidin, Daniel Fredrickson, Marek Mihalkovic, Wieslawa Sikora, Janusz Malinowski, Stefan Brühne, Thomas Proffen, Wolf Assmus, Marc de Boissieu, Francoise Bley, Jean-Luis Chemin, Jürgen Schreuer Abstract. The Al−Mg phase diagram has been reinvestigated in the vicinity of the stability range of the Samson phase, β-Mg2Al3 (cF1168). For the composition Mg 38.5 Al 61.5, this cubic phase, space group Fd-3m (no 227), a = 28.242(1) Å, V = 22526(2) Å3, undergoes at 214 °C a first-order phase transition to rhombohedral β′-Mg2Al3(hR293), a = 19.968(1) Å, c = 48.9114(8) Å, V = 16889(2) Å3, (i.e. 22519 Å3 for the equivalent cubic unit cell) space group R3m (no 160), a subgroup of index four of Fd-3m. The structure of the β-phase has been redetermined at ambient temperature as well as in situ at 400 °C. It essentially agrees with Samsons model, even in most of the many partially occupied and split positions. The structure of β′-Mg2Al3is closely related to that of the β-phase. Its atomic sites can be derived from those of the β-phase by group-theoretical considerations. The main difference between the two structures is that all atomic sites are fully occupied in case of the β′-phase. The reciprocal space, Bragg as well as diffuse scattering, has been explored as function of temperature and the β- to β′-phase transition was studied in detail. The microstructures of both phases have been analyzed by electron microscopy and X-ray topography showing them highly defective. Finally, the thermal expansion coefficients and elastic parameters have been determined. Their values are somewhere in between those of Al and Mg.

Diffuse scattering data acquisition techniques

Abstract Techniques are presented for acquiring and reducing X-ray diffuse scattering data from disordered crystalline materials. These methods are part of a comprehensive approach to study disorder in novel quasicrystalline phases as a function of temperature, but can be applied without further adaptation to periodic crystalline systems. By fully exploiting the possibilities of modern two-dimensional X-ray detector systems - using imaging plates or charge coupled devices (CCD) - large volumes of reciprocal space can be measured in a quantitative and rapid way. For this purpose, the classical rotation method for collecting integrated Bragg intensities is extended for acquiring quasi-continuous diffuse diffraction data. A new high-temperature furnace and helium beam path, designed for the diffraction geometry of the rotation method, are integral parts of the diffraction system. New methods are presented for handling the reduction of diffuse diffraction data from area detectors. One of the key techniques is...

Structure solution of the basic decagonal Al–Co–Ni phase by the atomic surfaces modelling method

The atomic surfaces modelling technique has been used to solve the structure of the basic Ni-rich Al-Co-Ni decagonal phase. Formula Al70.6Co6.7Ni22.7, space group P10, five-dimensional unit-cell parameters: d1 = d4 = 4.752 (3) A, d2 = d3 = 3.360 (2) A, d5 = 8.1710 (2) A; alpha12 = alpha34 = 69.295 degrees, alpha13 = alpha24 = 45 degrees, alpha14 = 41.410 degrees, alpha23 = alphai5 = 90 degrees (i = 1-4), V = 291.2 (7) A5; D(x) = 3.887 Mg x m(-3). Refinement based on /F/; 2767 unique reflections (/F/ > 0), 749 parameters, R = 0.17, wR = 0.06. Describing the structure of quasicrystals embedded in n-dimensional superspace in principle takes advantage of n-dimensional periodicity to select the minimal set of degrees of freedom for the structure. The method of modelling of the atomic surfaces yielded the first fully detailed structure solution of this phase. Comparison with numerous former, less accurate models confirms several features already derived, but adds a new essential insight of the structure and its complexity. The atoms fill the space forming recurrent structure motifs, which we will (generically) refer to as clusters. However, no unique cluster exists, although differences are small. Each cluster shows a high degree of structural disorder. This gives rise to a large configurational entropy, as much as expected in a phase which is stable at high temperature. On the other side, the cluster spatial arrangement is perfectly quasiperiodic. These considerations, corroborated by analysis of the structural relationship with neighbouring periodic phases, strongly suggest the existence of a non-local, long-range interaction term in the total energy which may be essential to the stability.

The periodic average structure of particular quasicrystals

The non-crystallographic symmetry of d-dimensional (dD) quasiperiodic structures is incompatible with lattice periodicity in dD physical space. However, dD quasiperiodic structures can be described as irrational sections of nD (n > d) periodic hypercrystal structures. By appropriate oblique projection of particular hypercrystal structures onto physical space, discrete periodic average structures can be obtained. The boundaries of the projected atomic surfaces give the maximum distance of each atom in a quasiperiodic structure from the vertices of the reference lattice of its average structure. These maximum distances turn out to be smaller than even the shortest atomic bond lengths. The metrics of the average structure of a 3D Ammann tiling, for instance, with edge lengths of the unit tiles equal to the bond lengths in elemental aluminium, correspond almost exactly to the metrics of face-centred-cubic aluminium. This is remarkable since most stable quasicrystals contain aluminium as the main constitutent. The study of the average structure of quasicrystals can be a valuable aid to the elucidation of the geometry of quasicrystal-to-crystal transformations. It can also contribute to the derivation of the physically most relevant Brillouin (Jones) zone.

Discussion on clusters, phasons and quasicrystal stabilisation

This paper summarises a two-hour discussion at the Ninth International Conference on Quasicrystals, including nearly 20 written comments sent afterwards, concerning (i) the meaning [if any] of clusters in quasicrystals; (ii) phason elasticity, and (iii) thermodynamic stabilisation of quasicrystals.

Single-phase high-entropy alloys – an overview

Abstract The term “high-entropy alloys (HEAs)” first appeared about 10 years ago defining alloys composed of n=5–13 principal elements with concentrations of approximately 100/n at.% each. Since then many equiatomic (or near equiatomic) single- and multi-phase multicomponent alloys were developed, which are reported for a combination of tunable properties: high hardness, strength and ductility, oxidation and wear resistance, magnetism, etc. In our paper, we focus on probably single-phase HEAs (solid solutions) out of all HEAs studied so far, discuss ways of their prediction, mechanical properties. In contrast to classical multielement/multiphase alloys, only single-phase multielement alloys (solid solutions) represent the basic concept underlying HEAs as mixing-entropy stabilized homogenous materials. The literature overview is complemented by own studies demonstrating that the alloys CrFeCoNi, CrFeCoNiAl0.3 and PdFeCoNi homogenized at 1300 and 1100°C, respectively, for 1 week are not single-phase HEAs, but a coherent mixture of two solid solutions.