Diffraction gratings of isotropic negative-phase velocity materials

Diffraction of electromagnetic plane waves by the gratings made by periodically corrugating the exposed planar boundaries of homogeneous, isotropic, linear dielectric-magnetic half-spaces is examined. The phase velocity vector in the diffracting material can be either co-parallel or anti-parallel to the time-averaged Poynting vector, thereby allowing for the material to be classified as of either the positive- or the negative-phase velocity (PPV or NPV) type. Three methods used for analyzing dielectric gratings — the Rayleigh-hypothesis method, a perturbative approach, and the C formalism — are extended here to encompass NPV gratings by a careful consideration of field representation inside the refracting half-space. Corrugations of both symmetric as well as asymmetric shapes are studied, as also the diversity of grating response to the linear polarization states of the incident plane wave. The replacement of PPV grating by its NPV analog affects only nonspecular diffraction efficiencies when the corrugations are shallow, and the effect on specular diffraction efficiencies intensifies as the corrugations deepen. Whether the type of the refracting material is NPV or PPV is shown to affect surface wave propagation as well as resonant excitation of surface waves.     

Low-energy electron diffraction on the planes non parallel with the surface

Some problems of the interpretation of the geometry of low-energy electron diffraction patterns obtained on metal samples with a general crystallographic orientation near that of some densely occupied atomic plane are discussed. It appears that for the interpretation of these diffraction patterns the commonly used classical model of the diffraction on the surface plane cannot be used. The new geometrical model — model of the diffraction on densely occupied planes non parallel with the surface — in constructed. Using this model the calculation of the diffraciton patterns is made for a surface with an orientation close to the densely occupied (100) plane. The calculated diffraction patterns are compared with those obtained on monocrystalline niobium with known surface orientation near that of the (100) plane. Experimental results confirm the mentioned model to be rightful. This diffraction model can be used for determination of the polycrystalline grain orientation by means of the selected area low-energy electron diffraction. The experiments were made in the emission electron microscope adapted for low-energy electron diffraction.     

Mapping charge-mosaic surfaces in electrolyte solutions using surface charge microscopy

A significant limitation of electrokinetic measurements is that only an average value of the zeta potential/streaming potential is measured—regardless of whether the surface charge distribution is homogeneous or otherwise. However, in real-world situations, nearly all solids (and liquids) of technological significance exhibit surface heterogeneities. To detect heterogeneities in surface charge, analytical tools which provide accurate and spatially resolved information about material surface potential—particularly at microscopic and sub-microscopic resolutions—are needed.A novel AFM-based technique for mapping surface charge domains on heterogeneous surfaces, which we call Surface Charge Microscopy (SCM), was recently introduced by our research team. It relies on recording colloidal force curves over multiple locations on the substrate surface using small probes. The surface charge characteristics of the heterogeneous substrate are determined from the recorded colloidal force curves, allowing for the surface charge variation to be mapped. In this communication, we briefly review the SCM technique. Examples of results of measurements of the surface interaction forces that were recorded between a silicon nitride AFM cantilever and a multi-phase volcanic rock and heterogeneous surface of bitumen are also given.     

Structure and reactivity of the hydrated hematite (0 0 0 1) surface

The structure of the hydroxylated hematite (0 0 0 1) surface was investigated using crystal truncation rod diffraction and density functional theory. The combined experimental and theoretical results suggest that the surface is dominated by two hydroxyl moieties—hydroxyls that are singly coordinated and doubly coordinated with Fe. The results are consistent with the formation of distinct domains of these surface species; one corresponding to the hydroxylation of the surface Fe-cation predicted to be most stable under UHV conditions, and the second a complete removal of this surface Fe species leaving the hydroxylated oxygen layer. Furthermore, our results indicate that the hydroxylated hematite surface structures are significantly more stable than their dehydroxylated counterparts at high water partial pressures, and this transition in stability occurs at water pressures orders of magnitude below the same transition for α-alumina. These results explain the observed differences in reactivity of hematite and alumina (0 0 0 1) surfaces with respect to water and binding of aqueous metal cations.     

The (1 × 1) structure of Si(111): Strong correlations in surface state bands?

It is shown that a model in which surface states in the semiconductor gap are described by the Hubbard model yields an interpretation of photoemission from the (1 × 1) structure of Si(111) which is compatible with the relaxed upper layer structure extracted from analyses of low energy electron diffraction intensities. The model predicts a low temperature antiferromagnetic ground state for the two-dimensional surface state electron fluid. This state should be observable experimentally.     

Measuring statistical heterogeneity: The Pietra index

There are various ways of quantifying the statistical heterogeneity of a given probability law: Statistics uses variance — which measures the law’s dispersion around its mean; Physics and Information Theory use entropy — which measures the law’s randomness; Economics uses the Gini index — which measures the law’s egalitarianism. In this research we explore an alternative to the Gini index-the Pietra index-which is a counterpart of the Kolmogorov-Smirnov statistic. The Pietra index is shown to be a natural and elemental measure of statistical heterogeneity, which is especially useful in the case of asymmetric and skewed probability laws, and in the case of asymptotically Paretian laws with finite mean and infinite variance. Moreover, the Pietra index is shown to have immediate and fundamental interpretations within the following applications: renewal processes and continuous time random walks; infinite-server queueing systems and shot noise processes; financial derivatives. The interpretation of the Pietra index within the context of financial derivatives implies that derivative markets, in effect, use the Pietra index as their benchmark measure of statistical heterogeneity.     

LEED studies of adsorption on vicinal copper surfaces

As a means for studying the role of atomic steps in adsorption phenomena LEED has been used to investigate the properties of vicinal copper surfaces. Single crystalline surfaces were cut at angles up to 20° from the (100) pole along [001] and [011̄] zones. The diffraction patterns obtained for the clean surfaces and after adsorption of oxygen, nitrogen ions, carbon and sulphur are described. The emphasis of the paper is on the method of interpretation of the geometry of the patterns, which may be done by straightforward kinematic analyses. In the case of nitrogen it is found that if the steps are widely separated the structure of the layer adsorbed on the terrace is the same as that on the low index surface. When the step spacing is small, and comparable with the crystalline parameter of the adsorbed layer, modifications occur which give rise to different superlattices which extend over several terraces. Adsorption of sulphur on 〈11〉 steps can produce a change in the periodicity of the adsorbed layer parallel to the step direction. The study of diffraction patterns for vicinal surfaces with different step spacings may provide an interesting technique for verifying the interpretation of patterns for low index surfaces.     

Influence of surface disorder on RHEED patterns from GaAs(001)−2 × 4 surfaces

Reflection high-energy electron diffraction measurements have been carried out for a nearly perfect and a disordered GaAs(001)−2 × 4 surface in the [ 10] azimuth. The surfaces were prepared in-situ by molecular beam epitaxy and the measurements were made at a substrate temperature of 560 °C under different flux conditions, giving the different degrees of surface ordering. Diffracted intensity distributions along various reciprocal surface lattice rods were measured for different angles of incidence using a primary beam energy of 15 keV. Drastic differences with surface order were found for both the (quasi) elastically diffracted beams (rocking curves) and the diffuse beams. The rocking curves can be interpreted largely by Bragg reflection from the bulk crystal and a number of causes for the intensity changes are given. In the case of the disordered surface the intensity distributions along the reciprocal lattice rods are dominated by broad diffuse peaks which occur at the intersection of reciprocal rods and Kikuchi lines. It is shown that while a kinematical model is unable to explain the experimental observations, a previously published model provides a very satisfactory interpretation.     

Melting curve of silicon to 15 GPa determined by two-dimensional angle-dispersive diffraction using a Kawai-type apparatus with X-ray transparent sintered diamond anvils

The melting curve of silicon has been determined up to 15 GPa using a miniaturized Kawai-type apparatus with second-stage cubic anvils made of X-ray transparent sintered diamond. Our results are in good agreement with the melting curve determined by electrical resistivity measurements [V.V. Brazhkin, A.G. Lyapin, S.V. Popova, R.N. Voloshin, Nonequilibrium phase transitions and amorphization in Si, Si/GaAs, Ge, and Ge/GaSb at the decompression of high-pressure phases, Phys. Rev. B 51 (1995) 7549] up to the phase I (diamond structure)—phase II (β-tin structure)—liquid triple point. The triple point of phase XI (orthorhombic, Imma)—phase V (simple hexagonal)—liquid has been constrained to be at 14.4(4) GPa and 1010(5) K. These results demonstrate that the combination of X-ray transparent anvils and monochromatic diffraction with area detectors offers a reliable technique to detect melting at high pressures in the multianvil press.     

Structural evolution of nanocrystalline/amorphous Fe/Ni75B25 multilayers: temperature dependence of electrical resistivity

X-ray specular-reflectivity measurements have been carried out on nanocrystalline/amorphous Fe/Ni₇₅B₂₅ multilayer films which were sputter-deposited on Si substrates, to investigate the evolution of interface roughness and the correlation between structure and transport properties. A significant interface roughness correlation with increasing Fe/NiB layer repetition was observed. The investigated films indicated a temperature dependent high electrical resistivity—10⁴ μΩ-cm at 10 K and 10³ μΩ-cm at 300 K—with a semiconductor-metal transition like behavior. Selected area electron diffraction revealed the presence of crystalline bcc Fe phase and NiB in amorphous state. The structural and transport properties of the multilayers are discussed.     

Diffraction of a two-shock configuration by a convex cylindrical surface

The subject of this work is numerical investigation into the diffraction of a shock-wave configuration by a convex cylindrical surface. The diffraction is a stage of interaction of a shock wave with a two-dimensional body. It is preceded by the stage of shock wave reflection from the front surface of the body, the back surface of which has a convex cylindrical shape. The two-or three-shock configuration formed on the front surface diffracts by the back cylindrical surface. The emphasis is on studying the diffraction of the two-shock wave configuration with the diffraction angle varying continuously. The object under study a wedge with an inclined front surface and convex cylindrical back surface. The results of numerical investigation are obtained by integrating the Euler equations. Flow features associated with the simultaneous diffraction of the incident and reflected shock waves are revealed. The evolution of the gasdynamic system (stagnation wave + TU layer) arising inside the diffraction area is studied. Breakaway and vorticity initiation are considered. It is shown that the positions of the line of separation and TU layer change in the course of diffraction. They merge together at the stage of steady flow. Comparison is made between the flow formed upon diffraction of the two-shock configuration by the cylindrical surface and the flow generated upon diffraction by horizontal and vertical surfaces.     

Diffraction model of multiple-ray propagation above a rough surface at low grazing angles

On the basis of diffraction by wedge-like crests we present a theoretical interpretation of the peculiarities of millimeter and centimeter radiowave fields above a rough surface, in particular, a sea surface, that are experimentally observed when the elevation of one of the corresponding points is comparable with surface roughness heights.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 5, pp. 547–558, May, 1996.     

Crystal-chemistry from XPS analysis of carbide-derived Mn+1AXn (n=1) nano-laminate compounds

The M_n+1AX_n layered carbide/nitride-derived phases, where M is an early transition metal, A is an A-group element and X is N or C, have an unusual combination of mechanical, electrical and thermal properties. The surface and crystal-chemistries of several recently synthesized n=1 members have been investigated by X-ray photoelectron spectroscopy. The results show that the constituent species are characterized by low binding energies, sometimes exceptionally so. The C 1s energies are in the lower end of the range for carbides, at 281.1-282.0 eV. The M-species—Ti, V, Nb and Hf—have binding energies at or below those corresponding to the elemental metallic state. The binding energies of the A-species in apparent planar coordination—In, Ge, As and Al—are quite exceptional, being 0.5-2 eV below those corresponding to the elemental state. Those results suggest that screening of the A-group species is derived from out-of-plane interactions, while the XPS signatures of the species associated with the MX blocks are reminiscent of those obtained from the relevant carbide phases.     

Phosphorus and hydrogen atoms on the (0 0 1) surface of silicon: A comparative scanning tunnelling microscopy study of surface species with a single dangling bond

We present a comparative scanning tunnelling microscopy (STM) study of two features on the Si(0 0 1) surface with a single dangling bond. One feature is the Si-P heterodimer—a single surface phosphorus atom substituted for one Si atom of a Si-Si dimer. The other feature is the Si-Si-H hemihydride—a single hydrogen atom adsorbed to one Si atom of a Si-Si dimer. Previous STM studies of both surface species have reported a nearly identical appearance in STM which has hampered an experimental distinction between them to date. Using voltage-dependent STM we are able to distinguish and identify both heterodimer and hemihydride on the Si(0 0 1) surface. This work is particularly relevant for the fabrication of atomic-scale Si:P devices by STM lithography on the hydrogen terminated Si(0 0 1):H surface, where it is important to monitor the distribution of single P dopants in the surface. Based on the experimental identification, we study the lateral P diffusion out of nanoscale reservoirs prepared by STM lithography.     

A non-dimensional approach to diffraction phenomena in the Fresnel approximation

The paper presents a theoretical and numerical study of the diffraction problem approached in the Fresnel approximation. The problem was formulated by a non-dimensional approach, which implies the definition of two non-dimensional quantities: F and ζ. In particular the parameter F is the well-known Fresnel number, whose value was usually used to classify diffraction regime. In analyzing the numerical approach some limitations imposed by the discretization arise; in particular these limitations constrain the level of sampling to be used for the diffracting field by requiring more and more elements when the diffraction conditions become more severe — i.e. increasing the dimension of the diffracting aperture and/or decreasing the distance of the plane where the diffracted field is observed.     

Spacetime topology change and black hole information

Topology change—the creation of a disconnected baby universe—due to black hole collapse may resolve the information loss paradox. Evolution from an early time Cauchy surface to a final surface which includes a slice of the disconnected region can be unitary and consistent with conventional quantum mechanics. We discuss the issue of cluster decomposition, showing that any violations thereof are likely to be unobservably small. Topology change is similar to the black hole remnant scenario and only requires assumptions about the behavior of quantum gravity in Planckian regimes. It does not require non-locality or any modification of low-energy physics.     

Photoemission studies of the interactions of CdTe and Te with Si(100)

The interactions between CdTe, and in particular Te, and the (100) surface of Si have been probed using photoemission and low energy electron diffraction with a view to investigating the mechanisms responsible for (100) and (111) growth orientations for CdTe on Si(100). The interfacial reactions have been studied both on room temperature deposition followed by annealing and on depositions at typical epitaxial growth temperatures. In both cases the same precursor stage of an ordered submonolayer of Te on the Si(100) surface has been identified. Line shape analysis of the Si 2p core level has suggested a structural model in which Te adatoms make up an incomplete monolayer bound in bridge sites. This model is in excellent agreement both with the (1 × 1) LEED pattern and recent SEXAFS studies of this surface. The implications of the cubic symmetry of this surface in terms of the subsequent growth orientation of CdTe are discussed. Termination of the surface by Te was also seen to induce band bending suggestive of Fermi level pinning at around midgap, in contrast to the passivating behaviour of other group VI elements on this surface. The Si 2p core level line shape analysis on termination by Te has also provided evidence to support the “covalent dimer” interpretation of the clean dimerised Si(100) surface.     

The measurement of fluorescence decay curves with the single-photon counting method and the evaluation of rate parameters

The single-photon counting technique which is used in the measurement of fluorescence decays of weak intensity is treated in some detail. The so-called dead-time correction — already stated by Bollinger and Thomas — is derived using the laws of the photoeffect. This derivation is based on very few assumptions, and so shows that the method provides a very direct intensity measurement. The correction can be avoided if photomultipliers with a high-gain first dynode are used. Disturbing effects such as statistical fluctuations of the light intensity, noise and the wavelength dependence of the photocathode quantum yield are investigated and corrections to be applied to the measured curves are given. The measurable intensity range is over wide limits independent of the absolute fluorescence intensity, but depends on the noise of the photomultipliers used. In the second part the interpretation of the measured intensity curves is discussed. A simple, direct evaluation of rate parameters is in most cases not possible. A set of possible evaluation methods (catalog of curves, regression, characteristic values of measured curves, momentum method, analog simulation) is described. No method shows decisive advantages. The optimal procedure in evaluating rate parameters is the simultaneous use of several of the methods in order to reduce systematic errors.     

Photoactive materials prepared by homogeneous hydrolysis with thioacetamide: Part 2—TiO2/ZnO nanocomposites

Photocatalytic active titanium dioxide (TiO₂)/zinc oxide (ZnO) composite was prepared by homogeneous hydrolysis of a mixture of titanium oxo-sulphate and zinc sulphate in aqueous solutions with thioacetamide and subsequent annealing at the temperature of 600 °C. The prepared samples were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM) and high-resolution transmission microscopy (HRTEM). Nitrogen adsorption-desorption was used for surface area (Brunauer-Emmett-Teller—BET) and porosity determination. The photoactivity of the prepared TiO₂/ZnO samples was assessed by the photocatalytic decomposition of Orange II dye in an aqueous slurry under irradiation of 254 and 365 nm wavelengths. Under the same conditions, the photocatalytic activity of a commercially available photocatalyst (Degussa P25), the pure anatase TiO₂ nanoparticles and cubic ZnO were examined.