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A metallic solid (Al-14-at. pct.-Mn) with long-range orientational order, but with icosahedral point group symmetry, which is inconsistent with lattice translations, has been observed. Its diffraction spots are as sharp as those of crystals but cannot be indexed to any Bravais lattice. The solid is metastable and forms from the melt by a first-order transition.

Content uploaded by D. Gratias

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All content in this area was uploaded by D. Gratias on Apr 15, 2014

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... A high degree of long-range quasiperiodic and orientational order is the main feature of a quasicrystal (QC). Metastable quasicrystalline phases were first identified in rapidly solidified Al-Mn alloys by Shechtman et al. [1] in 1984. Since the discovery of QCs revolutionized crystallography, Shechtman was awarded the 2011 Nobel Prize in chemistry [2]. ...

An ultrafine-grained Al71Ni14.5Co14.5/CNT poly-quasicrystal (QC/CNT) composite was synthesized using spark plasma sintering of powder components developed through electroless Ni-P/CNT plating of Co particles and mechanical alloying. The performance of the synthesized samples was studied using various testing methods, such as room temperature/hot compression, wear, and corrosion tests. The results were compared to the properties of alloy samples fabricated from raw and coated powders (without CNTs). The wear rate and friction coefficient of the quasicrystalline samples improved significantly due to the contribution of the CNTs. The wear rate of the CNT-containing specimens was 0.992 × 10−4 mm3/N/m, which is 47.1% lower than that of the QC sample. The positive impact of the CNTs on the corrosion potential and current density was further validated by the potentiodynamic polarization tests in a saline solution. However, these improvements in surface properties came at the cost of a 21.5% reduction in compressive strength, although the compressive strength still remained above 1.1 GPa at 600 °C. The results highlight an interesting trade-off between surface properties and mechanical strength, pointing toward the development of materials suitable for extreme conditions.

... Note that the term photon is used, even though these PCL do not originate from the quantum nature of light, but from discrete symmetries of the classical field. Our approach is based on superspace representation concept (a representation standardly used in the context of quasicrystals [37]; see Sec. 5 of the Supplemental Material (SM) [38]) and the recent multiscale dynamical symmetries concept [15]. Then, we employ this methodology to derive two more PCLs that were not previously known: reflection parity (RP) and space-time parity (STP). ...

Conservation laws are some of the most generic and useful concepts in physics. In nonlinear optical parametric processes, conservation of photonic energy, momenta and parity often lead to selection rules, restricting the allowed polarization and frequencies of the emitted radiation. Here we present a scheme to derive conservation laws in optical parametric processes in which many photons are annihilated and a single photon is emitted. We first rederive with it the known nonlinear optical conservation laws, and then utilize it to predict and explore conservations of reflection parity and space-time parity. Conservation of arises from a generalized reflection symmetry of the polarization in a superspace, analogous to the superspace employed in the study of quasicrystals. Conservation of similarly arises from space-time reversal symmetry in superspace. We explore these conservation laws numerically in the context of high-harmonic generation and outline experimental setups where they can be tested.
Published by the American Physical Society 2024

Die Riemannsche Vermutung zählt zu den tiefgründigsten offenen Fragen der Mathematik und bietet potenziell revolutionäre Einsichten in die Struktur der Zahlen und die Verteilung der Primzahlen. Seit Bernhard Riemanns Formulierung im Jahr 1859 suchen Mathematiker weltweit nach einem Beweis, der möglicherweise weitreichende Konsequenzen für die Zahlentheorie hätte. Die Vermutung besagt, dass die Nullstellen der Riemannschen Zeta-Funktion entlang einer kritischen Linie symmetrisch verteilt sind. Doch angesichts der unendlichen Struktur dieser Funktion stoßen traditionelle Beweisansätze an ihre Grenzen, da sie die unendliche Anzahl an Nullstellen nicht vollständig erfassen können.
In dieser Arbeit wird daher ein neuer Ansatz vorgestellt, der auf einer Kombination visueller und geometrischer Vergleichstechniken sowie der Spektraltheorie basiert. Letztere ermöglicht die Analyse von Operatoren und deren Eigenwerten und eröffnet so neue Perspektiven auf die Struktur der Zeta-Funktion. Durch den Einsatz moderner Computertechnologie werden Muster und Gesetzmäßigkeiten in der Verteilung der Nullstellen sichtbar gemacht, die sich rein numerisch schwer erfassen lassen. Ein Paradigmenwechsel wird angestrebt, der die klassischen Methoden ergänzt und erweitert: „Nicht mit herkömmlichen Mitteln kann eine Vermutung dieser Größenordnung bewiesen werden – sondern nur durch neue Sichtweisen und Ansätze, die uns helfen, die unendliche Struktur zu erfassen.“
Es ist jedoch wichtig, diese Herangehensweise als eine von vielen möglichen Perspektiven zu verstehen. Die mathematische Forschung erkennt eine Vielzahl unterschiedlicher Methoden an, um die Riemannsche Vermutung zu analysieren und zu verstehen. Während die hier vorgestellte Kombination von geometrischen und spektraltheoretischen Techniken eine innovative Sichtweise bietet, bleiben klassische und alternative Zugänge unerlässlich. Ein vollständiges Verständnis dieser Hypothese wird voraussichtlich erst durch die synergetische Bereicherung verschiedener methodischer Ansätze und wissenschaftlicher Disziplinen erreicht.

Bond-orientational order in molecular-dynamics simulations of supercooled liquids and in models of metallic glasses is studied. Quadratic and third-order invariants formed from bond spherical harmonics allow quantitative measures of cluster symmetries in these systems. A state with short-range translational order, but extended correlations in the orientations of particle clusters, starts to develop about 10% below the equilibrium melting temperature in a supercooled Lennard-Jones liquid. The order is predominantly icosahedral, although there is also a cubic component which we attribute to the periodic boundary conditions. Results are obtained for liquids cooled in an icosahedral pair potential as well. Only a modest amount of orientational order appears in a relaxed Finney dense-random-packing model. In contrast, we find essentially perfect icosahedral bond correlations in alternative "amorphon" cluster models of glass structure.

Complex alloy structures, particularly those of transition metals, are ; considered as determined by the geometricnl requirements for sphere packing. A ; characteristic of the class of structures discussed is that tetrahedral groupings ; of atoms occur everywhere in the structure--alternatively stated, coordination ; polyhedra have only triangular faces. The topological and geometrical properties ; of such polyhedra are examined and rules and theorems regarding them are deduced. ; Justification is given for the prominence of four such polyhedra (for ; coordination numbers of 12, 14, 15, and 16) in actual structures. General ; principles regarding the combination of these polyhedra into full structures are ; deduced and necessary definitions are given for terms that facilitate the ; detailed discussion of this class of structures. (auth);

Three-dimensional bond orientational order is studied via computer simulations of 864 particles interacting through a Lennard-Jones pair potential. Long-range orientational fluctuations appear upon supercooling about ten percent below the equilibrium melting temperature. The fluctuations suggest a broken icosahedral symmetry with extended correlations in the orientations of local icosahedral packing units.

An analysis of orientational order in dense, three-dimensional liquids is presented. The alignment of neighboring regions of local orientational order with both icosahedral and cubic symmetry is studied with the use of mean-field theory. The theory predicts a first-order transition to a phase which possesses long-range orientational order but no translational order. This is the phase which appears to have been seen in recent computer simulations of a supercooled liquid.

A defect description of liquids and metallic glasses is developed. In two dimensions, surfaces of constant negative curvature contain an irreducible density of point disclinations in a hexatic order parameter. Analogous defect lines in an icosahedral order parameter appear in three-dimensional flat space. Frustration in tetrahedral particle packings forces disclination lines into the medium in a way reminiscent of Abrikosov flux lines in a type-II superconductor and of uniformly frustrated spin-glasses. The defect density is determined by an isotropic curvature mismatch, and the resulting singular lines run in all directions. The Frank-Kasper phases of transition-metal alloys are ordered networks of these lines, which, when disordered, provide an appealing model for structure in metallic glasses.

The stability of the shape of a moving planar liquid‐solid interface during the unidirectional freezing of a dilute binary alloy is theoretically investigated by calculating the time dependence of the amplitude of a sinusoidal perturbation of infinitesimal amplitude introduced into the planar shape. The calculation is accomplished by using gradients of the steady‐state thermal and diffusion fields satisfying the perturbed boundary conditions (capillarity included) to determine the velocity of each element of interface, a procedure justified in some detail. Instability occurs if any Fourier component of an arbitrary perturbation grows; stability occurs if all components decay. A stability criterion expressed in terms of growth parameters and system characteristics is thereby deduced and is compared with the currently used stability criterion of constitutional supercooling; some very marked differences are discussed.

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