Moiré, Euler and self-similarity - the lattice parameters of twisted hexagonal crystals.

A real-space approach for the calculation of the moiré lattice parameters for superstructures formed by a set of rotated hexagonal 2D crystals such as graphene or transition-metal dichalcogenides is presented. Apparent moiré lattices continuously form for all rotation angles, and their lattice parameter to a good approximation follows a hyperbolical angle dependence. Moiré crystals, i.e. moiré lattices decorated with a basis, require more crucial assessment of the commensurabilities and lead to discrete solutions and a non-continuous angle dependence of the moiré-crystal lattice parameter. In particular, this lattice parameter critically depends on the rotation angle, and continuous variation of the angle can lead to apparently erratic changes of the lattice parameter. The solutions form a highly complex pattern, which reflects number-theoretical relations between formation parameters of the moiré crystal. The analysis also provides insight into the special case of a 30° rotation of the constituting lattices, for which a dodecagonal quasicrystalline structure forms.

Interface-driven formation of a two-dimensional dodecagonal fullerene quasicrystal.

Since their discovery, quasicrystals have attracted continuous research interest due to their unique structural and physical properties. Recently, it was demonstrated that dodecagonal quasicrystals could be used as bandgap materials in next-generation photonic devices. However, a full understanding of the formation mechanism of quasicrystals is necessary to control their physical properties. Here we report the formation of a two-dimensional dodecagonal fullerene quasicrystal on a Pt3Ti(111) surface, which can be described in terms of a square-triangle tiling. Employing density functional theory calculations, we identify the complex adsorption energy landscape of the Pt-terminated Pt3Ti surface that is responsible for the quasicrystal formation. We demonstrate the presence of quasicrystal-specific phason strain, which provides the degree of freedom required to accommodate the quasicrystalline structure on the periodic substrate. Our results reveal detailed insight into an interface-driven formation mechanism and open the way to the creation of tailored fullerene quasicrystals with specific physical properties.

Discovery of a superconducting high-entropy alloy.

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.

Stabilization mechanism of γ-Mg17Al12 and ß-Mg2Al3 complex metallic alloys.

Large-unit-cell complex metallic alloys (CMAs) frequently achieve stability by lowering the kinetic energy of the electron system through formation of a pseudogap in the electronic density of states (DOS) across the Fermi energy εF. By employing experimental techniques that are sensitive to the electronic DOS in the vicinity of εF, we have studied the stabilization mechanism of two binary CMA phases from the Al-Mg system: the γ-Mg17Al12 phase with 58 atoms in the unit cell and the ß-Mg2Al3 phase with 1178 atoms in the unit cell. Since the investigated alloys are free from transition metal elements, orbital hybridization effects must be small and we were able to test whether the alloys obey the Hume-Rothery stabilization mechanism, where a pseudogap in the DOS is produced by the Fermi surface-Brillouin zone interactions. The results have shown that the DOS of the γ-Mg17Al12 phase exhibits a pronounced pseudogap centered almost exactly at εF, which is compatible with the theoretical prediction that this phase is stabilized by the Hume-Rothery mechanism. The disordered cubic ß-Mg2Al3 phase is most likely entropically stabilized at high temperatures, whereas at lower temperatures stability is achieved by undergoing a structural phase transition to more ordered rhombohedral ß' phase at 214 ° C, where all atomic sites become fully occupied. No pseudogap in the vicinity of εF was detected for the ß' phase on the energy scale of a few 100 meV as determined by the 'thermal observation window' of the Fermi-Dirac function, so that the Hume-Rothery stabilization mechanism is not confirmed for this compound. However, the existence of a much broader shallow pseudogap due to several critical reciprocal lattice vectors [Formula: see text] that simultaneously satisfy the Hume-Rothery interference condition remains the most plausible stabilization mechanism of this phase. At Tc = 0.85 K, the ß' phase undergoes a superconducting transition, which slightly increases the cohesive energy and may contribute to relative stability of this phase against competing neighboring phases.

Al13Fe4 as a low-cost alternative for palladium in heterogeneous hydrogenation.

Replacing noble metals in heterogeneous catalysts by low-cost substitutes has driven scientific and industrial research for more than 100 years. Cheap and ubiquitous iron is especially desirable, because it does not bear potential health risks like, for example, nickel. To purify the ethylene feed for the production of polyethylene, the semi-hydrogenation of acetylene is applied (80 × 10(6) tons per annum; refs 1-3). The presence of small and separated transition-metal atom ensembles (so-called site-isolation), and the suppression of hydride formation are beneficial for the catalytic performance. Iron catalysts necessitate at least 50 bar and 100 °C for the hydrogenation of unsaturated C-C bonds, showing only limited selectivity towards semi-hydrogenation. Recent innovation in catalytic semi-hydrogenation is based on computational screening of substitutional alloys to identify promising metal combinations using scaling functions and the experimental realization of the site-isolation concept employing structurally well-ordered and in situ stable intermetallic compounds of Ga with Pd (refs 15-19). The stability enables a knowledge-based development by assigning the observed catalytic properties to the crystal and electronic structures of the intermetallic compounds. Following this approach, we identified the low-cost and environmentally benign intermetallic compound Al(13)Fe(4) as an active and selective semi-hydrogenation catalyst. This knowledge-based development might prove applicable to a wide range of heterogeneously catalysed reactions.

Mössbauer investigations of crystalline and quasicrystalline Al3(Mn, Fe) compounds.

(57)Fe Mössbauer and magnetic measurements are reported on Taylor phase compounds T-Al(3)(Mn,Fe), which can be seen as complex metallic alloys. The orthorhombic unit cell contains 156 atoms. These investigations are further extended to Al(71)Mn(19)Fe(10) crystallizing as a decagonal quasicrystal. Common to both structures are layers, which are oriented perpendicular to the b axis in the crystalline or to the periodic axis in the quasicrystalline compound, allowing the formation of characteristic building blocks. At low temperatures for all samples spin glass behavior is observed with freezing temperatures T(f) increasing with Fe content. Above T(f) the (57)Fe Mössbauer spectra were analyzed by a superposition of two subspectra with intensity ratio around 75:25, which can be allocated to Fe substituted on Mn sites surrounded either by Al and Mn or solely by Al with Mn only at the edge of the nearest neighbor shell. For both subspectra quadrupole splitting and center shift do not change significantly with Fe content and with structure. Below T(f) broad hyperfine field distributions with non-vanishing contributions at zero hyperfine field are present. Magnetic and electrostatic hyperfine interactions are governed by length scales which are determined by the very similar interatomic configurations forming the T-Al(3)Mn phase as well as the decagonal compound. The presence of long range atomic order is of less importance.

Geometric origin of magnetic frustration in the µ-Al4Mn giant-unit-cell complex intermetallic.

The structurally ordered µ-Al(4)Mn complex intermetallic phase with 563 atoms in the giant unit cell shows the typical broken-ergodicity phenomena of a magnetically frustrated spin system. The low-field zero-field-cooled and field-cooled magnetic susceptibilities show splitting below the spin freezing temperature T(f) = 2.7 K. The ac susceptibility exhibits a frequency-dependent cusp, associated with a frequency-dependent freezing temperature T(f)(ν). The decay of the thermoremnant magnetization is logarithmically slow in time and shows a dependence on the aging time t(w) and the cooling field H(fc) typical of an ultraslow out-of-equilibrium dynamics of a nonergodic spin system that approaches thermal equilibrium, but can never reach it on the experimentally accessible time scale. The above features classify the µ-Al(4)Mn complex intermettalic among spin glasses. The origin of frustration of magnetic interactions was found to be geometrical due to the distribution of a significant fraction of Mn spins on triangles with antiferromagnetic coupling. The µ-Al(4)Mn phase is a geometrically frustrated spin glass.

Plastic-deformation mechanism in complex solids.

In simple crystalline materials, plastic deformation mostly takes place by the movement of dislocations. Although the underlying mechanisms in these materials are well explored, in complex metallic alloys--crystalline solids containing up to thousands of atoms per unit cell--the defects and deformation mechanisms remain essentially unknown. Owing to the large lattice parameters of these materials, extended dislocation concepts are required. We investigated a typical complex metallic alloy with 156 atoms per unit cell using atomic-resolution aberration-corrected transmission electron microscopy. We found a highly complex deformation mechanism, based on the movement of a dislocation core mediating strain and separate escort defects. On deformation, the escort defects move along with the dislocation core and locally transform the material structure for the latter. This mechanism implies the coordinated movement of hundreds of atoms per elementary glide step, and nevertheless can be described by simple rearrangement of basic structural subunits.

Fermi surface-Brillouin-zone-induced pseudogap in γ-Mg17Al12 and a possible stabilization mechanism of ß-Al3Mg2.

The electronic structure of γ phase in the system Mg(17)Al(12) containing 58 atoms per unit cell with space group I43m has been calculated by using the WIEN2k-FLAPW program package. A pseudogap is found across the Fermi level. The FLAPW-Fourier spectra at the symmetry points N and Γ of the bcc Brillouin zone revealed that electronic states across the Fermi level at these symmetry points are dominated by |G|(2) = 26 and 24 states corresponding to centers of {510} + {431} and {422} zone planes, respectively. The 1253-wave nearly-free-electron (NFE) band calculations identified that a combination of the two Fermi surface-Brillouin-zone (FsBz) interactions associated with |G|(2) = 26 and 24 account well for the observed DOS pseudogap in γ-Mg(17)Al(12), most likely leading to the stabilization of this complex metallic compound. The ß-Al(3)Mg(2) containing 1178 atoms per cubic unit cell is suggested to be stabilized by satisfying the Hume-Rothery matching condition expressed in terms of e/uc, the number of electrons per unit cell, versus critical |G|(2). A critical |G|(2) is predicted to be 200 in ß-Al(3)Mg(2), which results in 84 Brillouin zone planes interacting almost simultaneously with a more or less spherical Fermi surface.

High-Temperature In Situ Straining Experiments in the High-Voltage Electron Microscope.

: Design rules are described here for high-temperature straining stages for transmission electron microscopy. Temperatures above 1000 degreesC can be attained by electron bombardment of the specimen grips. Thermal equilibrium can be reached in a short time by carrying off the heat by water cooling. Some applications of this stage are described. Ferroelastic deformation was observed at 1150 degreesC in t' and partially stabilized zirconia, which changes the microstructure for successive dislocation plasticity. In the oxide-dispersion-strengthened alloy INCOLOY MA 956, dislocations are impeded by oxide particles and move smoothly between the particles. At high temperatures, both the resting and traveling times control the average dislocation velocity. In MoSi2 single crystals of a soft orientation, dislocations with 1/2<111> Burgers vectors are created in localized sources and move on {110} planes in a viscous manner. The dislocations in Al-Pd-Mn single quasicrystals are oriented in preferred crystallographic directions and move in a viscous way as well. On the basis of in situ observations, conclusions are drawn for interpreting macroscopic deformation behavior at high temperatures.