The terms superhard and ultra-incompressible are commonly used to describe a material's hardness and compressibility approaching the properties of diamond, the hardest and most incompressible single-phase material known so far. Superhard and ultra-incompressible materials are of great interest for applications as well as for basic research. The materials are widely used in various industrial applications, e.g., such as cutting tools or wear-resistant coatings. Basic research focuses on the understanding of structure-property relationships, which yields hints for the design of new superhard and ultra-incompressible materials. Attempts to synthesize or theoretically predict new superhard and ultraincompressible materials are the subject of intensive current research activities. Experimentally accessible and predicted single-phase materials can be classified into three groups: [1] i) crystalline and disordered carbon modifications, ii) compounds formed by the light elements B, C, N, O, and Si, and iii) compounds of transition metals (TMs) with light elements B, C, N, or O. As another more recently developed group of superhard materials, the nanocomposites as multiphase materials have to be mentioned. Most of the materials of classes (i) and (ii) have to be synthesized under extreme conditions. Although these processes are difficult and expensive, materials of these classes have become the most used hard materials for applications (like c-BN and synthetic diamond). The third class of compounds, especially TM carbides and borides, can be synthesized in a comparably facile way at ambient pressure in an arc furnace. Two design parameters are of importance for the selection of superhard or ultra-incompressible TM compounds, [2] i.e., a high electron concentration (EC, electrons per atomic volume) of the TM and the presence of directional covalent bonding. High ECs can be found among the heavy TMs, whereas carbon and boron form short covalent bonds. Among the TMs, 5d metals of groups 6-9, i.e., W, Re, Os, and Ir are the most promising candidates as they show the highest ECs, small atomic volume, and high bulk modulus. Very recently, the properties of several TM borides with high hardness and bulk modulus were studied experimentally and theoretically. [3][4][5][6][7] ReB 2 and OsB 2 were found to be superhard and ultra-incompressible, while OsB was predicted to be ultra-incompressible.In this study, we will focus on boron-rich compounds of the systems Ru-B, Os-B, and W-B. These systems have been investigated for several decades, [7][8][9][10][11]

High-entropy alloys (HEAs) are multicomponent mixtures of elements in similar concentrations, where the high entropy of mixing can stabilize disordered solid-solution phases with simple structures like a body-centered cubic or a face-centered cubic, in competition with ordered crystalline intermetallic phases. We have synthesized an HEA with the composition Ta34Nb33Hf8Zr14Ti11 (in at. %), which possesses an average body-centered cubic structure of lattice parameter a=3.36  Å. The measurements of the electrical resistivity, the magnetization and magnetic susceptibility, and the specific heat revealed that the Ta34Nb33Hf8Zr14Ti11 HEA is a type II superconductor with a transition temperature Tc≈7.3  K, an upper critical field μ0H_c2≈8.2  T, a lower critical field μ0Hc1≈32  mT, and an energy gap in the electronic density of states (DOS) at the Fermi level of 2Δ≈2.2  meV. The investigated HEA is close to a BCS-type phonon-mediated superconductor in the weak electron-phonon coupling limit, classifying it as a "dirty" superconductor. We show that the lattice degrees of freedom obey Vegard's rule of mixtures, indicating completely random mixing of the elements on the HEA lattice, whereas the electronic degrees of freedom do not obey this rule even approximately so that the electronic properties of a HEA are not a "cocktail" of properties of the constituent elements. The formation of a superconducting gap contributes to the electronic stabilization of the HEA state at low temperatures, where the entropic stabilization is ineffective, but the electronic energy gain due to the superconducting transition is too small for the global stabilization of the disordered state, which remains metastable.

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. Micelles are the simplest type of self-assembly structure found in nature. They are formed by the association of amphiphilic molecules in solution. Micelles are ubiquitous colloids being used in washing detergents, for the solubilization of pharmaceuticals as well as for the preparation of advanced materials (1). Above concentrations of about 10%, there is an order-disorder transition, where micelles self-assemble into liquid crystalline structures. In the case of spherical micelles, the most common structure types are of cubic symmetry with space groups Fm3m (fcc) or Im3m (body-centered cubic).We were investigating the liquid crystalline phase behavior of polymeric micelles in this concentration range in greater detail. For this investigation we used block copolymer micelles that have a well-defined micellar core containing the hydrophobic polymer blocks, surrounded by a relatively large shell consisting of the hydrophilic polymer blocks. As block copolymers we used polyðisoprene-b-ethylene oxideÞ, PI n -PEO m , with different degrees of polymerization n and m of the respective polymer blocks. By shear orientation using plate-plate or Searle-type rheometers, large monodomain samples of centimeter dimension can be prepared that allows one to determine the liquid crystalline structure by using small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) (2). ResultsWhen investigating the phase behavior of PI 30 -PEO 120 micelles near the order-disorder transition with synchrotron SAXS and SANS, we discovered phases with diffraction patterns of 12-(Q12) and 18-fold (Q18) diffraction symmetry (Fig. 1). With increasing concentration we find at a temperature of 20°C a sequence of phases Disordered j13%jQ12j18%j Cubic (fcc). In the concentration range between 13 and 18%...

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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.