Real structure

Abstract: In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. The two algebras M_{2}(H) and M_{4}(C) are obtained, which are the exact constituents of the standard model. Using the two maps from M_{4} to S^{4} the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter, and area quantization of black holes.

Abstract: We have investigated the phases of the $\mathrm{Sn}∕\mathrm{Si}(111)\text{\ensuremath{-}}(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$ surface below $\frac{1}{3}$ ML coverage at room temperature by means of atomic force microscopy (AFM) and density functional theory based first-principles calculations. By tuning the Sn concentration at the surface we have been able to discriminate between Sn and Si adatoms, and to assure that the AFM topography for the different phases resembles the one reported using scanning tunneling microscopy. In the mosaic and the intermediate phases, a dependence of the topographic height of the Si adatoms on the number of surrounding Sn adatoms has been identified. In the pure phase, however, variations in the measured height difference between the Sn adatoms and the substitutional Si defects, which are intrinsic to the AFM observation, are reported. Reliable room-temperature force spectroscopic measurements using the atom-tracking technique and first-principles calculations provide an explanation for these striking induced height variations on the pure phase in terms of both the different strength of the short-range chemical interaction and tip-induced atomic relaxations. Our results suggest that the corrugation measured with true atomic resolution AFM operated at low interaction forces and close to the onset of significant short-range chemical interactions provides direct access to the real structure of heterogeneous semiconductor surfaces.

Abstract: Contrary to well-established recent theoretical results based on second-order Moller-Plesset perturbation theory, it is illustrated here that the distorted octahedron of ${D}_{4h}$ symmetry cannot be the ground state of the ``magic'' ${\mathrm{Si}}_{6}$ cluster, but a transition state, connecting two almost isoenergetic structures of lower symmetry, which can coexist. This conclusion, the consequences of which could be far reaching for other magic clusters, is based on higher-order perturbation theory, accurate coupled-cluster CCSD(T) calculations and density-functional theory at the hybrid B3LYP level. The discrepancy is due to the poor convergence of the perturbation expansion, related to the flatness of the energy hypersurface near the minimum. As a result, the structural and electronic properties of ${\mathrm{Si}}_{6}$ are still not well understood, although several suggestions are put forward here.

Abstract: Powder Diffraction Analysis.- Identification of X-ray Diffraction Patterns of Multicomponent Mixtures.- Quantitative Reference Intensity Analysis: Methodology and Means for Verification of Results.- Correction of Compositional Variability in the X-ray Diffraction Phase Analysis.- Dilution and Addition Methods in Quantitative X-ray Diffraction Phase Analysis.- Shape Memory Effect Analysis by X-ray Diffraction.- Formation of a Satellite Phase in the Neutron Irradiated Reactor Steel.- X-ray Phase Analysis of Cu and Pb Anodic Oxidation Products.- Phase Analysis of Rusts by X-ray Diffraction, IR-Spectroscopy and Thermal Analysis.- Dynamical X-ray Diffraction Study on the Phase Transformation in Rapidly Quenched Au71Sn29 Alloy.- Process Kinetics Studied by X-ray Diffraction.- X-ray Diffraction Analysis of 12 CaO. 7 Al2O3 Polymorphs.- X-ray Analysis of Mineral Substances of Blood Vessels.- Optical Diffraction of Computer Simulated Patterns of Transitions in Two Dimensional Regular Lattice.- Diffraction Analysis of Amorphous Materials, Glasses and Polymers.- Investigation of the Microscopic Mechanism of the High Strength of Amorphous Alloys.- Partial Structure Factors for Amorphous Fe75B25 Determined by Diffraction of Polarized Neutrons.- Neutron Diffraction Investigation of the Short-Range Atomic Order in Tellurite Glasses.- Supermolecular Structure of the "Ladder-Type" Styrene-Multimethacrylate Copolymers.- The Structure Evaluation of Polypropylene Fibres by Computational Resolution of WAXS.- Real Structure of Crystalline Materials.- Problems in Diffraction Analysis of Real Polycrystals.- Texture Investigation of Natural Rock-Salt by Neutron Diffraction.- Texture and Structure of Anisotropic FeSi Materials after Hot Rolling.- Real Structure of Gd3Co Single Crystals.- High Temperature Elastic Diffuse Neutron Scattering Study of the Defect Structure in TiN0.82.- X-ray Diffraction Studies of Interdiffusion in Solid Solutions of Semiconductors AIIIBV.- Polycrystal Thin Layers.- Kinematic Theory of X-ray and Neutron Scattering by Defects in Thin Films and Surface Layers.- Methodical Aspects of X-ray Diffraction Analysis of Surface Treated Materials.- Structure Investigation of Hard Coatings by Total Pattern Analysis.- The Determination of Lattice Parameters and Strains in Stressed Thin Films Using X-ray Diffraction: Extensions.- Use and Perspective of X-ray Diffraction in Science and Technology of Ceramic Coatings.- Application of X-ray Diffraction Techniques to Study Highly Dispersed Supported Metals.- Effective Depth of X-ray Penetration and its Orientation Dependence.- Structure of Laser Modified Surface Layers of AlZn Alloys.- Structure Characterization of Laser Treated WC-Co by Means of Position Sensitive Detectors.- Diffraction Studies of SnOX Thin Films Prepared by Vacuum Methods.- X-ray Diffractional Investigation of the Copper-Aluminium Interface Reaction.- X-ray Examination of (PbTe)1-x (GeTe)x Crystals.- Single Crystal Thin Layers.- Structural Studies of Garnet Films.- Location of Impurity Atoms in the Volume and Surface Layers of Silicon Crystals by X-ray Standing Wave in the Laue Geometry.- X-ray Standing Waves in the Study of Crystals and Surface Layers.- Development of Theoretical and Experimental Investigations of Thin Surface Structures by X-ray Methods.- Crystal Structure Determination.- New Trends in Determination of Crystal Structure.- Easy and Uneasy Superspace Groups for Incommensurate Crystals.- Structure Analysis of Modulated Molecular Crystals IV: Survey of our Recent Studies.- Controlled Growth of Polytypes and their Importance for Science and Technology.- Symmetry and Diffraction Patterns of Polytypes.- Structural Characteristics of Polytypes Delivered by Texture Diffraction Patterns.- The X-ray Method for Determining Crystalline Multilayer Polytype Structures in Metal Alloys.- The Analysis of Disorder Polytype Structures by Statistical Parameters.- Data Acquisition.- Bragg Reflection Analysis for Powdered Samples.- Rietveld Refinement of Y2O3 - Comparison of Two Profile Functions.- Three-Dimensional Multiple X-ray Diffraction.- Reduction of the Electronics of a ID Position Sensitive Detector.- A High Resolution Monochromator Module with X-ray Optics for Multipurpose Measurement of A3B5 Heterostructures.- List of Authors.- Abbreviations.