Small Angle Range Research Articles

Small-angle X-ray scattering (SAXS) studies of the structure of mesoporous silicas

Abstract Mesoporous ordered silica nanostructures show strong interaction with X-ray radiation in the range of small-angles. Small-angle X-ray scattering (SAXS) measurements based on the elastically scattered X-rays are important in analysis of condensed matter. In the case of mesoporous silica materials SAXS technique provides information on the distribution of electron density in the mesoporous material, in particular describing their structure and size of the unit cell as well as type of ordered structure and finally their parameters. The characterization of nanopowder materials, nanocomposites and porous materials by Small-Angle X-ray Scattering seems to be valuable and useful. In presented work, the SAXS investigation of structures from the group of mesoporous ordered silicates was performed. This work has an objective to prepare functional materials modified by noble metal ions and nanoparticles and using the small-angle X-ray scattering to illustrate their properties. We report the new procedure for describing mesoporous materials belonging to SBA-15 and MCM-41 family modified by platinum, palladium and silver nanoparticles, based on detailed analysis of characteristic peaks in the small-angle range of X-ray scattering. This procedure allows to obtained the most useful parameters for mesoporous materials characterization and their successfully compare with experimental measurements reducing the time and material consumption with good precision for particles and pores with a size below 10 nm.

Ultrahigh-definition dynamic 3D holographic display by active control of volume speckle fields

Holographic displays generate realistic 3D images that can be viewed without the need for any visual aids. They operate by generating carefully tailored light fields that replicate how humans see an actual environment. However, the realization of high-performance, dynamic 3D holographic displays has been hindered by the capabilities of present wavefront modulator technology. In particular, spatial light modulators have a small diffraction angle range and limited pixel number limiting the viewing angle and image size of a holographic 3D display. Here, we present an alternative method to generate dynamic 3D images by controlling volume speckle fields significantly enhancing image definition. We use this approach to demonstrate a dynamic display of micrometre-sized optical foci in a volume of 8 mm × 8 mm × 20 mm. Control of speckle fields yields high-definition 3D holographic images.

A unified approach for beam-to-beam contact

Existing beam contact formulations can be categorized in point-to-point contact models that consider a discrete contact force at the closest point of the beams, and line-to-line contact models that assume distributed contact forces. In this work, it will be shown that line contact formulations applied to slender beams provide accurate and robust mechanical models in the range of small contact angles, whereas the computational efficiency considerably decreases with increasing contact angles. On the other hand, point contact formulations serve as sufficiently accurate and very efficient models in the regime of large contact angles, while they are not applicable for small contact angles as a consequence of non-unique closest point projections. In order to combine the advantages of these basic formulations, a novel all-angle beam contact (ABC) formulation is developed that applies a point contact formulation in the range of large contact angles and a recently developed line contact formulation in the range of small contact angles, the two being smoothly connected by means of a variationally consistent model transition. Based on a stringent analysis, two different transition laws are investigated, optimal algorithmic parameters are suggested and conservation of linear momentum, angular momentum and total energy is shown. All configuration-dependent quantities within the point-, the line- and the transition-contact regime are consistently linearized, thus allowing for their application within implicit time integration schemes. Furthermore, a step size control of the nonlinear solution scheme is proposed that allows for displacement increments per time step that exceed the order of magnitude of the beam cross-section radius. For many standard beam-to-beam contact algorithms, this is the typical limitation concerning possible time step sizes, especially when considering high beam slenderness ratios. Finally, an efficient two-stage contact search based on dynamically adapted search segments is proposed. This algorithm yields in a tight set of potential contact pairs and enables a subdivision into potential point and potential line contact pairs, which is essential in order to fully exploit the efficiency potential of the proposed contact formulation. A series of numerical test cases is analyzed in order to verify the accuracy and consistency of the proposed contact model transition regarding contact force distributions and conservation properties, but also for quantifying the efficiency gains as compared to standard beam contact formulations.

Non-specular reflection of walking droplets

Since their discovery by Yves Couder and Emmanuel Fort, droplets walking on a vibrating liquid bath have attracted considerable attention because they unexpectedly exhibit certain features reminiscent of quantum particles. While the behaviour of walking droplets in unbounded geometries has to a large extent been rationalized theoretically, no such rationale exists for their behaviour in the presence of boundaries, as arises in a number of key quantum analogue systems. We here present the results of a combined experimental and theoretical study of the interaction of walking droplets with a submerged planar barrier. Droplets exhibit non-specular reflection, with a small range of reflection angles that is only weakly dependent on the system parameters, including the angle of incidence. The observed behaviour is captured by simulations based on a theoretical model that treats the boundaries as regions of reduced wave speed, and rationalized in terms of momentum considerations.

Effect of Meniscus Curvature on Apparent Thermal Slip

We analytically consider the effect of meniscus curvature on heat transfer to laminar flow across structured surfaces. The surfaces considered are composed of ridges. Curvature of the menisci, which separates liquid in the Cassie state and gas trapped in cavities between the ridges, results from the pressure difference between the liquid and the gas. A boundary perturbation approach is used to develop expressions that account for the change in the temperature field in the limit of small curvature of a meniscus. The meniscus is considered adiabatic and a constant heat flux boundary condition is prescribed at the tips of the ridges in a semi-infinite and periodic domain. A solution for a constant temperature ridge is also presented using existing results from a mathematically equivalent hydrodynamic problem. We provide approximate expressions for the apparent thermal slip length as function of solid fraction over a range of small meniscus protrusion angles. Numerical results show good agreement with the perturbation results for protrusion angles up to ± 20 deg.

A Linear Quadratic Regulator-Based Optimal Direct Thrust Force Control of Linear Permanent-Magnet Synchronous Motor

Linear permanent-magnet machines are often characterized by low inductance and short pole-pitch which leads to a small operational range of load angles. The resultant control performance using conventional direct thrust force control (DTFC) techniques is poor with high force ripple. This research improves this aspect of DTFC. A novel multiple-input multiple-output (MIMO) state-space model, independent of the mover’s speed, having stator flux and thrust force as states, is formulated for the linear permanent-magnet synchronous motor (PMSM). An optimal linear state feedback control scheme is then designed using the optimal linear quadratic regulator technique. Integral action is added to the designed control scheme by state augmentation to minimize the steady-state error and reduce the force ripple. Experimental results clearly prove that the proposed optimal control scheme results in a faster transient response of speed and force with improved steady-state regulation of force and flux when compared to the state of the art.

Flux pinning in Ba[formula omitted]KxFe2As2 superconductor with splayed columnar defects

It has been theoretically proposed that the enhancement of the critical current density (Jc) through dispersing the angle of columnar defects should be greater than that of parallel columnar defects. Yet, the complication caused by decrease in pinning owing to vortex-field misalignment upon tilting of columnar defect makes it a crucial task to determine the optimal splay angle in order to fully take advantage of enhanced pinning among splayed systems. Using Ba0.6K0.4Fe2As2 as a target material, we probe the effects of various splay angles on Jc and determine that the ‘optimal-angle’ lies within the small angle range (0--10∘).

Experimental Test of Reflectivity Formulas for Turbid Colloids: Beyond the Fresnel Reflection Amplitudes.

We compare light reflectivity measurements as a function of the angle of incidence for an interface between an optical glass and a turbid suspension of small particles, with theoretical predictions for the coherent reflectance calculated with different available theoretical models. The comparisons are made only in a small range of angles of incidence around the critical angle of the interface between the glass and the matrix of the colloidal suspensions. The experimental setup and its calibration procedure are discussed. We considered two Fresnel-based approximations and another two based on a multiple-scattering approach, and we present results for monodisperse latex colloidal suspensions of polymeric spherical particles in water with particle diameters of 120 and 520 nm, polydisperse titanium dioxide (rutile) particles suspensions in water with a most probable diameter of 404 nm, and suspensions of copper particles in water with diameters of 500 nm. The comparisons between experiment and theory are made without fitting any parameters.

Large Low-Frequency Oscillations Initiated by Flow Control on a Poststall Airfoil

A large-amplitude low-frequency oscillation has been reported in the literature for some airfoils in a small range of angles of attack before stall. In the current study, the same low-frequency oscillations are shown to be triggered by two methods of active flow control at poststall angles. Active control is applied in the form of external acoustic excitation or a row of discrete jets that are operated in a pulsed or steady mode. Conditionally averaged particle image velocimetry and time-resolved surface pressure measurements are used to evaluate the spatial and temporal characteristics of the oscillation. By systematically increasing forcing amplitude, each flow control technique is shown to first excite low-frequency oscillation up to a maximum lift increase, after which subsequent increases in forcing amplitude attenuate and ultimately eliminate low-frequency oscillation altogether. At maximum oscillation amplitude, the behavior is highly periodic in the case of acoustic forcing and intermittent in the case of pulsed or steady jets. The dynamics associated with the oscillation are shown to include the shedding of a large vortex structure, with noted similarity to the dynamic stall vortex seen on pitching or plunging airfoils.

Numerical solution of a nonlinear least squares problem in digital breast tomosynthesis

In digital tomosynthesis imaging, multiple projections of an object are obtained along a small range of different incident angles in order to reconstruct a pseudo-3D representation (i.e., a set of 2D slices) of the object. In this paper we describe some mathematical models for polyenergetic digital breast tomosynthesis image reconstruction that explicitly takes into account various materials composing the object and the polyenergetic nature of the x-ray beam. A polyenergetic model helps to reduce beam hardening artifacts, but the disadvantage is that it requires solving a large-scale nonlinear ill-posed inverse problem. We formulate the image reconstruction process (i.e., the method to solve the ill-posed inverse problem) in a nonlinear least squares framework, and use a Levenberg-Marquardt scheme to solve it. Some implementation details are discussed, and numerical experiments are provided to illustrate the performance of the methods.

Plasmonic random laser on the fiber facet.

A random laser on the optical fiber facet is constructed by dipping an optical fiber end face into the solution of polydimethylsiloxane doped with rhodamine 6G organic dye and silver nanowires. The PDMS film doped with rhodamine 6G acts as the active waveguide layer, and the silver nanowires provide a three-dimensional plasmonic feedback. The plasmon resonance of silver nanowires significantly improves the pump efficiency of the random laser. The most output energy of random laser concentrates in a small angle range along the axis of the optical fiber. This fabrication technique provides a simple and efficient way for the fabrication of random lasers on the optical fiber facet with low cost.

Comet C/2012 S1 (ISON) coma composition at ~4 au from HST observations

We analyze the first color and polarization images of Comet ISON (C/2012 S1) taken during two measurement campaigns of the Hubble Space Telescope (HST) on UTC 2013 April 10 and May 8, when the phase angles of Comet ISON were α≈13.7° and 12.2°, respectively. We model the particles in the coma using highly irregular agglomerated debris particles. Even though the observations were made over a small range of phase angle, the data still place significant constraints on the material properties of the cometary coma. The different photo-polarimetric responses are indicative of spatial chemical heterogeneity of coma in Comet ISON. For instance, at small projected distances to the nucleus (<500km), our modeling suggests the cometary particles are composed predominantly of small, highly absorbing particles, such as amorphous carbon and/or organics material heavily irradiated with UV radiation; whereas, at longer projected distances (>1000km), the refractive index of the particles is consistent with organic matter slightly processed with UV radiation, tholins, Mg−Fe silicates, and/or Mg-rich silicates contaminated with ~10% (by volume) amorphous carbon. The modeling suggests low relative abundances of particles with low material absorption in the visible, i.e., Im(m)≤0.02. Such particles were detected unambiguously in other comets in the vicinity of nucleus through very strong negative polarization near backscattering (P≈−6%) and very low positive polarization (P≈3–5%) at side scattering. These materials were previously attributed to Mg-rich silicates forming a refractory surface layer on the surface of cometary nuclei (Zubko et al., 2012). The absence of such particles in Comet ISON could imply an absence of such a layer on its nucleus.

Negative refraction in molybdenum disulfide.

Recently, negative refractions have been demonstrated in uniaxial crystals with no necessary of negative permittivity and permeability. However, the small anisotropy parameterγin the uniaxial crystals limits the negative refraction occurrence only in a small range of the incident light angle, retarding its practical applications. In this paper, we report negative refraction induced by a pronounced anisotropic behavior in the bulk MoS(2). Using the first-principles, the dielectric function and refractive index calculations confirm a uniaxial trait of MoS(2) with a calculated anisotropy parameterγlarger than 2.5 in the entire range of visible wavelength. The critical incident angle to trigger a negative refraction in the bulk MoS(2) is calculated up to 90°. The finite-difference time-domain simulations prove that the incident light with a density of 59.5% can be negatively refracted in a MoS(2) slab with a thickness of 0.1 µm. Our results open up a new pathway for MoS(2)-like materials to a novel field of optical integration.

Quasimonoenergetic electron beam and brilliant gamma-ray radiation generated from near critical density plasma due to relativistic resonant phase locking

We show that a high current quasi-monoenergetic electron beam and a peaked brilliant gamma-ray beam can be generated by irradiating an ultra-intense laser pulse on uniform near critical density plasma, with a laser spot radius RL∼(λ/π)2a/n, here λ is the laser wave length, a denotes the normalized laser intensity, and n denotes the normalized plasma density. Due to a relativistic resonant phase locking mechanism, high energy oscillating electrons are trapped to ride on the laser electric field, and an unprecedented ultra-fast ultra-brilliant gamma-ray pulse is emitted from the electrons. Both the high energy electrons and gamma-ray photons are emitted in a small polar angle range. It is similar to a conventional wiggler synchrotron, except that the curvature radius of electron orbits in the laboratory coordinate frame measures in microns rather than in meters.

UV contrasts and microphysical properties of the upper clouds of Venus from the UV and NIR VMC/VEx images

The nature of UV contrasts observed on the upper cloud deck of Venus is still not known. To constrain better the properties of particles that may cause the UV contrasts, the phase dependences of brightness of the venusian clouds measured by the ultraviolet and near-infrared channels of the Venus Express Venus Monitoring Camera (VMC) in the UV dark and bright regions are jointly analyzed. The range of small phase angles, where the glory phenomenon is observed, is of key importance, since the properties of cloud particles can be reliably estimated from the shape and position of glory. However, from more than 2500 orbits of the mission, only in ten orbits the images were taken simultaneously in UV and near-IR channels at small phase angles. Their analysis have yielded the following results. In the UV dark and bright clouds of the equatorial region near the local noon, the derived radii of cloud particles turned out to be the same and rather large, 1.3–1.6μm. No unambiguous connection between the UV contrasts and the brightness in the near-IR channel was found. In some cases, the regions that appear contrasting in UV show no difference in the near-IR brightness. This means that the properties of 1-μm mode particles are the same in these regions and only the contribution of small submicron particles differs, because the near-IR channel is weakly sensitive to the presence of particles smaller than ≈0.3μm in radius. The difference in the composition of 10% of the number of submicron particles (if sulfur and sulfuric acid compositions are considered as probable for the submicron mode) is enough to produce the observed UV contrasts. In the other cases, the UV contrasts are accompanied by the differences in near-IR brightness. This suggests that the cloud particles of the 1-μm mode contribute to these contrasts as well. However, the modeling showed that exactly the variations in the composition of submicron particles in the clouds produce a key effect on the UV contrasts observed. Moreover, a portion of submicron particles with a high refractive index, when incorporated into the sulfuric acid aerosols during the condensation process, may provide the higher refractive index (relative to that of sulfuric acid) of the 1-μm mode derived from modeling. The glory phenomenon was also observed at latitudes 30–60°S, in the transition region from the mottled clouds in dark tropics to streaky cloud morphology at higher latitudes. This allowed the sizes of cloud particles near the frequently seen UV-bright bands to be estimated. It was found that the radii of particles in the upper cloud layer decrease from 1.05–1.2 to 0.8–0.9μm with increasing latitude from ∼35°S to ∼62°S. Our present modeling also clearly showed that the high brightness in the UV-bright band is caused by an additional amount of non-absorbing (in UV) particles with Reff≈0.9μm at the cloud top and/or by the decrease of a portion of absorbing particles inside the clouds below this layer. No variations of the effect with the local solar time for the interval from 10 to 13h available in the data were detected.

Polarization properties of optical metasurfaces of different symmetries

Optical metasurfaces have become a new paradigm for creating flat optical devices. While being typically an order of magnitude thinner than the wavelength of light, metasurfaces allow control of the phase of propagating light waves across the full $2\ensuremath{\pi}$ range and therefore enable the realization of optical elements such as lenses, waveplates, and beam converters. Currently one of the limiting factors of functional metasurfaces is their small range of operational angles. Here we demonstrate both theoretically and experimentally that the angular range can be broadened by increasing the rotational symmetry of metasurfaces. We develop an analytical model based on the discrete dipole approximation that quantitatively describes the response of metasurfaces under oblique excitation. It shows that the effective optical symmetry is doubled for structures with odd rotational symmetry, increasing the angular range correspondingly. We apply and experimentally verify our model for metasurfaces consisting of identical meta-atoms, arranged into square lattices, hexagonal lattices, and on the vertices of a Penrose tiling. The results demonstrate the increasing angular performance with increasing rotational symmetry.

Computer simulation of the single crystal surface modification and analysis at grazing low-energy ion bombardment

The specific peculiarities of 0.5-10 keV Ne+, Ar+, Kr+, Be+ and Se+ ions scattering, sputtering and implantation processes at grazing ion bombardment of GaAs (001), Si(001), SiC(001) and Cu(100) surfaces and their possible application for the surface modification and analysis have been studied by computer simulation. Sputtering yields in the primary knock-on recoil atoms reghne versus the initial energy of incident ions (E0 = 0.5-5 keV) and angle of incidence (ψ = 0-30°) counted from a target surface have been calculated. The colliding particles mass ratio influence on the energy losses of scattering particles, sputtering yields and near-surface depth distributions of implanted particles is established, ft was shown that in the case of grazing ion bombardment the layer-by-layer sputtering is possible and its optimum are observed within the small angle range of the glancing angles near the threshold sputtering angle. Comparative studies of layer-by-layer sputtering for Si(001) and SiC(001) surfaces versus the initial energy of incident ions as well as an effective sputtering and sputtering threshold are discussed.

Focal lengths of Venus Monitoring Camera from limb locations

The Venus Monitoring Camera (VMC) carried by European Space Agency’s Venus Express orbiter (Svedhem et al., 2007) consists of four optical units, each with a separate filter casting an image on a single CCD (Markiewicz et al., 2007a, 2007b). The desire to capture as much of the planet in a single frame during the spacecraft’s 24h, 0.84 eccentricity orbit led to optics with 18° field of view. Analysis of Venus images obtained by the VMC indicated that the computed limb radius and altitude of haze layers were somewhat inconsistent with prior knowledge and expectations. Possible causes include errors in the knowledge of image geometry, misalignment of the optic axis from the pointing direction, and optical distortion. These were explored and eliminated, leaving only deviations from the ground and pre-solar damage estimate of the focal length lengths as the most likely reason. We use the location of planet’s limb to estimate the focal length of each camera using images of the planet when the orbiter was more than 20,000km from planet center. The method relies on the limb radius to be constant at least over a small range of solar zenith angles. We were able to achieve better estimates for the focal lengths for all four cameras and also estimate small offsets to the boresight alignment.An outcome of this analysis is the finding that the slant unit optical depth varies more rapidly with solar zenith angle in the afternoon as compared to morning, with lowest values at local noon. A variation of this level is also observed with latitude. Both are indicative of the presence of overlying haze above the clouds, and the morning afternoon asymmetry suggests different photochemical processes in destruction and production of the haze.

A method of measuring the incidence angle of intense electron beam

In recent years, a great many of effect data obtained from the high current pulsed electron beam play an important role in the studying of X-ray thermal-mechanical effects. Energy deposition profile is the criterion to measure the equivalence of thermal-mechanical effects between high-current electron beam and X-rays. To adjust the energy deposition profiles to improve the equivalence of the simulations of X-ray and thermal-mechanical effect, the intense electron beam energy deposition profile measurement should be studied. Two-dimensional distribution measurement which is an important part of the energy deposition profile is to obtain a two-dimension (r, θ) incidence angle distribution. A new method of measuring the incidence angle based on small Faraday cup array covered with aluminum films, called modified multi-layer stacking, is presented in this paper. With the help of the filtered Faraday cups, the transmission fraction of the electron beam confined at a specific position and time is stored. Two-dimension incidence angle distribution on the anode target that changes over the working time is obtained with these transmission fractions by computer calculation. The result indicates that the two-dimension incidence angle distribution has a close relationship with the pinch of the beam. The electrons tend to move vertically to the equipotential line when the diode is under Child-Langmuir flow, then they hit the target in a small angle range (E×B drift, the trajectory of the electrons becomes a slanted helix with pitch changing. The incidence angle then increases to about 60° from small angle.

A small-angle x-ray scattering system with a vertical layout.

A small-angle x-ray scattering (SAXS) system with a vertical layout (V-SAXS) has been designed and constructed for in situ detection on nanostructures, which is well suitable for in situ study on self-assembly of nanoparticles at liquid interface and polymer processing. A steel-tower frame on a reinforced basement is built as the supporting skeleton for scattering beam path and detector platform, ensuring the system a high working stability and a high operating accuracy. A micro-focus x-ray source combining parabolic three-dimensional multi-layer mirror and scatteringless collimation system provides a highly parallel beam, which allows us to detect the very small angle range. With a sample-to-detector distance of 7 m, the largest measurable length scale is 420 nm in real space. With a large sample zone, it is possible to install different experimental setups such as film stretching machine, which makes the system perfect to follow the microstructures evolution of materials during processing. The capability of the V-SAXS on in situ study is tested with a drying experiment of a free latex droplet, which confirms our initial design.