Angle Of Total External Reflection Research Articles

Probing the Electrode-Liquid Interface Using Operando total-Reflection X-Ray Absorption Spectroscopy

Traditional operando methods to study electrochemical (EC) processes, although successful, are based on EC measurements, lacking in direct sensitivity of chemical and structural changes. A fundamental understanding of the underlying mechanism occurring during an EC reaction could allow to improve performances and properties of applied material systems. EC processes are localized at the electrode-electrolyte interfacial regions, but several surface sensitive experimental techniques are often limited to ex situ conditions, owing to the need of a Ultra High Vacuum (UHV) environment, e.g., Scanning Tunneling Microscopy (STM), X-ray Photoelectron Spectroscopy (XPS), Low Energy Electron Diffraction (LEED), etc.1 On the contrary, synchrotron-based hard x-rays provide an intense and highly energetic source that can penetrate the electrolyte without undergoing significant attenuation. Furthermore, the x-ray beam can be focused on a flat metal surface adopting a grazing incidence geometry, increasing surface sensitivity up to a few nanometers in subcritical condition. The latter case is achieved when the incident angle is set below the critical angle for total external reflection (TER), characterized by the occurrence of an evanescent wave confined at the surface. As a result, x-ray photon-in photon-out techniques can be used to probe the electrode-liquid interface in working conditions.2,3 In this contribution, we performed operando Grazing Incidence X-ray Absorption Spectroscopy (GI-XAS) in total external reflection (TER) mode4 (Fig. 1) at P64 (DESY, Hamburg), using our EC setup designed for multimodal studies with hard x-ray scattering and spectroscopy techniques3. XAS can provide unique information about the local chemical and structural environment of absorbing atoms during electrochemical polarization. The electro-oxidation of polycrystalline gold, relevant for the understanding of electrolysis, and the surface passive film development and breakdown of Ni-Cr-Mo corrosion resistant alloys, have been investigated. Despite the presence of the electrolyte and the PEEK walls of the EC cell, 1-3 nm thick surface oxides film can be detected in TER mode using energies down to 8 keV. Advantages and challenges of this method will be discussed showing experimental results. Figure 1 Left: Schematic of our EC cell showing sample geometry for GI-XAS in TER mode, the incidence angle q is always lower than the critical angle. Right: GI-XAS in TER mode from a Ni 59 alloy sample at the Ni k-edge at increasing EC polarization in 1M NaCl and pH 12. Maurice, V. Progress in corrosion science at atomic and nanometric scales. Progress in Materials Science 40 (2018).Timoshenko, J. & Roldan Cuenya, B. In Situ / Operando Electrocatalyst Characterization by X-ray Absorption Spectroscopy. Chem. Rev. 121, 882–961 (2021).Långberg, M. Redefining passivity breakdown of super duplex stainless steel by electrochemical operando synchrotron near surface X-ray analyses. npj Materials Degradation, 3(1): p. 22. (2019).D. Gajdek. Structural Changes in Monolayer Cobalt Oxides under Ambient Pressure CO and O 2 Studied by In Situ Grazing-Incidence X-ray Absorption Fine Structure Spectroscopy, J. Phys. Chem. C, vol. 126, n. 7, pagg. 3411–3418 (2022) Figure 1

SHIFTS OF THE KIESSIG OSCILLATIONS AND FARADAY ROTATION FOR X-RAY REFLECTIVITY FROM A MAGNETIZED FILM

Appearance of the refraction effects and Faraday rotation of the plane of polarization of linearly polarized X rays has been analyzed for transmission and reflection at grazing incidence angles for a resonant film with allowance for the X-ray magnetic or Mössbauer scattering. It is shown that, when the magnetization is oriented along the radiation beam direction, magnetic additives to the susceptibility do not affect the phase shifts between the waves reflected from the surface and the substrate; however, they induce “orthogonal polarization” in the reflected beam, which corresponds to rotation of the plane of polarization. Rotation of the plane of polarization is maximum for the critical angle of total external reflection; it is characterized by an oscillating dependence on the grazing angle, which can be used in future to vary the polarization state of X-ray beams.

Multislice forward modeling of coherent surface scattering imaging on surface and interfacial structures.

To study nanostructures on substrates, surface-sensitive reflection-geometry scattering techniques such as grazing incident small angle X-ray scattering are commonly used to yield an averaged statistical structural information of the surface sample. Grazing incidence geometry can probe the absolute three-dimensional structural morphology of the sample if a highly coherent beam is used. Coherent surface scattering imaging (CSSI) is a powerful yet non-invasive technique similar to coherent X-ray diffractive imaging (CDI) but performed at small angles and grazing-incidence reflection geometry. A challenge with CSSI is that conventional CDI reconstruction techniques cannot be directly applied to CSSI because the Fourier-transform-based forward models cannot reproduce the dynamical scattering phenomenon near the critical angle of total external reflection of the substrate-supported samples. To overcome this challenge, we have developed a multislice forward model which can successfully simulate the dynamical or multi-beam scattering generated from surface structures and the underlying substrate. The forward model is also demonstrated to be able to reconstruct an elongated 3D pattern from a single shot scattering image in the CSSI geometry through fast-performing CUDA-assisted PyTorch optimization with automatic differentiation.

Evolution of the magnetic hyperfine field profiles in an ion-irradiated Fe60Al40 film measured by nuclear resonant reflectivity.

Nuclear resonant reflectivity (NRR) from an Fe60Al40 film was measured using synchrotron radiation at several grazing angles near the critical angle of total external reflection. Using laterally resolved measurements after irradiation with 20 keV Ne+ ions of gradually varying fluence of 0-3.0 × 1014 ions cm-2, the progressive creation of the ferromagnetic A2 phase with increasing ion fluence was confirmed. The observed depth selectivity of the method has been explained by application of the standing wave approach. From the time spectra of the nuclear resonant scattering in several reflection directions the depth profiles for different hyperfine fields were extracted. The results show that the highest magnetic hyperfine fields (∼18-23 T) are initially created in the central part of the film and partially at the bottom interface with the SiO2 substrate. The evolution of the ferromagnetic onset, commencing at a fixed depth within the film and propagating towards the interfaces, has been directly observed. At higher fluence (3.0 × 1014 ions cm-2) the depth distribution of the ferromagnetic fractions became more homogeneous across the film depth, in accordance with previous results.

X-ray reflectivity investigation of multilayer macroporous silicon structures

In this work, the X-ray reflectivity was used to study the porosity of multilayer macroporous silicon samples obtained under various conditions. The porosity calculation is based on a change in the position of the critical angle of total external reflection resulting from a decrease in the density of the porous silicon layer. Our findings show that the absence of photoluminescence in the samples is due to a porosity of about 30 % in the surface layer. The morphological features were characterized by scanning electron and atomic force microscopy.

A refraction correction for buried interfaces applied to in situ grazing-incidence X-ray diffraction studies on Pd electrodes.

In situ characterization of electrochemical systems can provide deep insights into the structure of electrodes under applied potential. Grazing-incidence X-ray diffraction (GIXRD) is a particularly valuable tool owing to its ability to characterize the near-surface structure of electrodes through a layer of electrolyte, which is of paramount importance in surface-mediated processes such as catalysis and adsorption. Corrections for the refraction that occurs as an X-ray passes through an interface have been derived for a vacuum-material interface. In this work, a more general form of the refraction correction was developed which can be applied to buried interfaces, including liquid-solid interfaces. The correction is largest at incidence angles near the critical angle for the interface and decreases at angles larger and smaller than the critical angle. Effective optical constants are also introduced which can be used to calculate the critical angle for total external reflection at the interface. This correction is applied to GIXRD measurements of an aqueous electrolyte-Pd interface, demonstrating that the correction allows for the comparison of GIXRD measurements at multiple incidence angles. This work improves quantitative analysis of d-spacing values from GIXRD measurements of liquid-solid systems, facilitating the connection between electrochemical behavior and structure under in situ conditions.

The Kinetics of Growth of a Nanosized Germanium Film Deposited on the Si(001) Surface by Magnetron Sputtering

Abstract—The kinetics of growth of a nanosized germanium film deposited by magnetron sputtering on the Si(001) surface is studied using a developed experimental X-ray reflectometry technique distinguished by the joint recording of specularly reflected and diffusely scattered radiation. By using this technique, it is possible to perform in situ both the analysis of the morphology of the growing film and the control of its thickness with an accuracy to 1 nm. Dependences of the intensity of specular reflection, diffuse scattering, rate of growth, and mean square roughness and density of the film on the deposition time are obtained. According to the results of the measurement of specularly reflected radiation, the film roughness increases with time according to a power law. However, at a thickness of the film of 4 nm, a clearly defined maximum of diffuse scattering is observed, the angular position of which corresponds to the critical angle of total external reflection of germanium of 0.31°. This pattern of distribution of scattered radiation is explained by the manifestation of the Yoneda effect that consists in the anomalous X-ray scattering, the maximum of which corresponds to the critical angle θC of total external reflection from the film. It is established experimentally that, at the initial stage of growth, the film is formed by the Volmer–Weber mechanism. It is found using in situ X-ray reflectometry that the formation of a continuous layer of a germanium film occurs at its thickness of 7 nm; the subsequent growth of the film proceeds according to the power law σf ~ tβ, where β = 0.23.

Grazing Incidence X-Ray Diffraction Study of Tantalum Thin Films

The features of the analysis of thin films by small-angle X-ray reflectometry and grazing incidence X-ray diffractometry are considered by the example of tantalum films. In particular, it is shown that a substantial shift of the diffraction peak at small angles of incidence is associated with the refraction of X-rays near the angle of total external reflection. The results of the measurements are in good agreement with calculations. These factors should be considered in grazing incidence X-ray diffractometry to obtain a correct description of the distribution of the properties of thin films over their depth. It is demonstrated that the approach proposed in this paper can be used to determine the material constants (δ, β) and the thickness of tantalum films.

Development of multilayer mirrors for space-based astronomical X-ray optics

X-ray reflectivity of single layer coated X-ray mirror is confined to small grazing angles (< 1°) grazing incidence X-ray telescopes usually are bulky and have large focal lengths in trade of effective area which is expensive for a space based telescope. Critical angle for total external reflection of a mirror varies inversely with the energy of the incident photon. This practically limits the possibility of making an X-ray telescope sensitive to higher energy X-rays $$( < 10 \,{\text{keV}}$$ ). Use of multilayer mirrors makes it possible to operate the instrument at higher angles and also significantly improves the high energy sensitivity (80 keV). Fabricated $$W /B_{4} C$$ multilayer mirror provides a peak reflectivity of 19% at first Bragg peak (2.3°) when tested with 8.047 keV X-rays. Multi-wavelength reflectivity analysis of $$W /B_{4} C$$ multilayer mirror from 9 to 16 keV is presented with a discussion on applications of multilayer mirrors in high energy astronomy.

X-Ray reduction imaging of inclined reflective masks at critical angles

We have proposed and simulated optical schemes for producing reduced images by X-ray lasers or harmonic generators at a wavelength of . The mask in this case is placed at a small angle to the optical axis, corresponding to the angle of total external reflection of the material. We have determined the optimal position of the detector (resist) and the corresponding spatial resolution. The results can be used to solve problems in nanotechnology and nanostructuring of surfaces.

Asymmetric skew X-ray diffraction at fixed incidence angle: application to semiconductor nano-objects

A procedure for obtaining three-dimensionally resolved reciprocal-space maps in a skew X-ray diffraction geometry is described. The geometry allows tuning of the information depth in the range from tens of micrometres for symmetric skew diffraction down to tens of nanometres for strongly asymmetric skew geometries, where the angle of incidence is below the critical angle of total external reflection. The diffraction data are processed using a rotation matrix formalism. The whole three-dimensional reciprocal-space map can be measured by performing a single azimuthal rotation of the sample and using a two-dimensional detector, while keeping the angle of incidence and the X-ray information depth fixed (FIXD method). Having a high surface sensitivity under grazing-incidence conditions, the FIXD method can be applied to a large variety of Bragg reflections, particularly polar ones, which provide information on strain and chemical composition separately. In contrast with conventional grazing-incidence diffraction, the FIXD approach reveals, in addition to the lateral (in-plane) components, the vertical (out-of-plane) component of the strain field, and therefore allows the separation of the scattering contributions of strained epitaxial nanostructures by their vertical misfit. The potential of FIXD is demonstrated by resolving the diffraction signal from a single layer of InGaN quantum dots grown on a GaN buffer layer. The FIXD approach is suited to the study of free-standing and covered near-surface nano-objects, as well as vertically extended multilayer structures.

Multiple scattering in grazing-incidence X-raydiffraction: impact on lattice-constant determinationin thin films.

Dynamical scattering effects are observed in grazing-incidence X-ray diffraction experiments using an organic thin film of 2,2':6',2''-ternaphthalene grown on oxidized silicon as substrate. Here, a splitting of all Bragg peaks in the out-of-plane direction (z-direction) has been observed, the magnitude of which depends both on the incidence angle of the primary beam and the out-of-plane angle of the scattered beam. The incident angle was varied between 0.09° and 0.25° for synchrotron radiation of 10.5 keV. This study reveals comparable intensities of the split peaks with a maximum for incidence angles close to the critical angle of total external reflection of the substrate. This observation is rationalized by two different scattering pathways resulting in diffraction peaks at different positions at the detector. In order to minimize the splitting, the data suggest either using incident angles well below the critical angle of total reflection or angles well above, which sufficiently attenuates the contributions from the second scattering path. This study highlights that the refraction of X-rays in (organic) thin films has to be corrected accordingly to allow for the determination of peak positions with sufficient accuracy. Based thereon, a reliable determination of the lattice constants becomes feasible, which is required for crystallographic structure solutions from thin films.

Extinction depth in a smooth X-ray waveguide

An approximate solution to the dispersion equation for the dynamics of an X-ray beam trapped in a plane waveguide with smooth walls is used to study the dependence of extinction depth on the optical density of wall material and X-ray energy. For angles of incidence of the X-ray beam that are no greater than the Fresnel angle, the extinction depth in nonabsorbing medium depends only on difference N e1–N e1 of electron densities in the wall material and waveguide layer as (πr 0(N e1–N e2))–1/2, where r 0 ~ 2.81794 × 10–13 cm is the classical electron radius. The results are in good agreement with the penetration depth of X-ray radiation into surface that is obtained using the Fresnel formulas in the approximation of plane waves at grazing angles that range from zero to one half of the critical angle of total external reflection.

Grazing diffraction of X-ray radiation in a planar single-crystal waveguide

The propagation of an X-ray beam through a plane-parallel waveguide is studied with allowance for Bragg grazing diffraction on the crystalline structure of the plates. Expressions for the waveguide modes are obtained and nondecaying waveguide modes are shown to exist at angles that are larger than the critical one (the angle of total external reflection), which permits one to increase the capture angle of radiation incident on the waveguide. The calculated intensity at the waveguide output is compared with the intensity of waveguide modes in the absence of grazing diffraction in the waveguide material.

Structural analysis of amorphous-nanocrystalline silicon thin films by grazing incidence X-ray diffraction

The amorphous-nanocrystalline silicon thin films doped with about 10% of hydrogen (a-nc-Si), 50–100nm thick, were deposited by plasma enhanced chemical vapor deposition (PECVD) on glass covered with amorphous Si:H, using mixture of silane and hydrogen as working gas. The power of discharge was either constant or it was decreased during deposition, starting with higher values than average and ending with lower values than average. By high resolution transmission electron microscopy (HRTEM) it was found that the average size of crystals in samples deposited in that way were similar, about 8–9nm, whereas crystal size distributions were generally broad and varied for different samples.The structure of a-nc-Si was further examined by grazing incidence X-ray diffraction (GIXRD) at the MCX beam line at synchrotron Elettra in Italy using 8keV X-ray beam. The scattered intensity was obtained at the critical angle for total external reflection and at several larger angles, in order to probe samples at different depth below the sample surface. At the critical angle, the beam penetration is estimated at about 10nm. The average values of crystal size obtained by Rietveld refinement of diffraction patterns were similar to those obtained by HRTEM. The GIXRD measurements at different incidence angles showed that average size of crystals and strain were more homogeneous across the depth for samples deposited with decreasing power. The crystal to amorphous fraction for all samples was between 15% and 20%.Measurement of optical properties of deposited a-nc-Si:H samples showed that films have high absorption coefficient in visible part of spectrum, similar to amorphous Si. Optical gap was larger than in amorphous Si and larger for samples with larger fraction of smaller crystals (with sizes up to 5nm), which is consistent with the quantum size effects associated with quantum dots.

Debye–Scherrer rings from block copolymer films with powder-like order

The powder-like orientation of lamellar domains in thin films of the diblock copolymer polystyrene-block-poly(methyl methacrylate) is investigated using grazing-incidence small-angle X-ray scattering (GISAXS) and grazing-incidence small-angle neutron scattering (GISANS). Conventional monochromatic GISANS and GISAXS measurements are compared with neutron time-of-flight GISANS. For angles of incidence and exit larger than the critical angle of total external reflection of the polymer, Debye–Scherrer rings are observed. The position of the Debye–Scherrer rings is described quantitatively based on a reduced version of the distorted-wave Born approximation. A strong distortion of the ring shape is caused by refraction and reflections from the film interfaces. Close to the critical angle, the ring shape collapses into a banana shape.

X-ray diffracted intensity for double-reflection channel-cut Ge monochromators at extremely asymmetric diffraction conditions

The width and integrated intensity of the 220 X-ray double-diffraction profile and the shift of the Bragg condition due to refraction have been measured in a channel-cut Ge crystal in an angular range near the critical angle of total external reflection. The Bragg angle and incidence condition were varied by changing the X-ray energy. In agreement with the extended dynamical theory of X-ray diffraction, the integrated intensity of the double diffraction remained almost constant, even for the grazing-incidence condition very close to the critical angle for total external reflection. A broadening of the diffraction profile not predicted by the extended theory of X-ray diffraction was observed when the Bragg condition was at angles of incidence lower than 0.6°. Plane wave topographs revealed a contrast that could be explained by a slight residual crystal surface undulation of 0.3° due to etching to remove the cutting damage and the increasing effect of refraction at glancing angles close to the critical angle. These findings confirm that highly asymmetric channel-cut Ge crystals can also work as efficient monochromators or image magnifiers at glancing angles close to the critical angle, the main limitation being the crystal surface preparation.

Resonant soft x-ray reflectivity of Me/B_4C multilayers near the boron K edge

Energy dependence of the optical constants of boron carbide in the short period Ru/B(4)C and Mo/B(4)C multilayers (MLs) are evaluated from complete reflectivity scans across the boron K edge using the energy-resolved photon-in-photon-out method. Differences between the refractive indices of the B(4)Cmaterial inside and close to the surface are obtained from the peak profile of the first order ML Bragg peak and the reflection profile near the critical angle of total external reflection close to the surface. Where a Mo/B(4)C ML with narrow barrier layers appears as a homogeneous ML at all energies, a Ru/B(4)C ML exhibits another chemical nature of boron at the surface compared to the bulk. From evaluation of the critical angle of total external reflection in the energy range between 184 and 186eV, we found an enriched concentration of metallic boron inside the Ru-rich layer at the surface, which is not visible in other energy ranges.

Structures of regenerated cellulose films revealed by grazing incidence small-angle x-ray scattering

The characteristic in-plane length scales of ultrathin films of regenerated cellulose are measured using noncontact atomic force microscopy (NC-AFM) and grazing incidence small-angle x-ray scattering (GISAXS) in ambient atmosphere and under various humidity conditions. The aim is to elucidate the structural basis for the excellent compatibility of cellulose supports to planar lipid membranes. Films are deposited on silicon wafers by Langmuir-Blodgett (LB) transfer and spin coating. NC-AFM height profiles and the resulting calculated power spectral density functions indicate that both kinds of cellulose films have almost identical root-mean-square roughness values (0.7-0.8 nm) and very similar characteristic length scales (32 nm), respectively. GISAXS measurements, both above and below the critical angle of total external reflection, show that the dominant length scales in the bulk and near the surface of the films are comparable ( approximately 50 nm). The origin of these length scales can be attributed to the bundle of rodlike molecules of cellulose that result during the regeneration process (i.e., as a consequence of the cleavage of the silyl side chains of trimethylsilylcellulose). Exposure of the cellulose samples to various humidities shows that above a relative humidity of 97% a significant swelling of the films occurs, which is consistent with our previous findings. The swelling of films with more than 30 LB monolayers of cellulose induces a remarkable out-of-plane rearrangement of the cellulose bundles, due to a reduced influence of the solid substrate compared to thinner films with only eight to ten LB monolayers.

Blazed high-efficiency x-ray diffraction via transmission through arrays of nanometer-scale mirrors

Diffraction gratings are ubiquitous wavelength dispersive elements for photons as well as for subatomic particles, atoms, and large molecules. They serve as enabling devices for spectroscopy, microscopy, and interferometry in numerous applications across the physical sciences. Transmission gratings are required in applications that demand high alignment and figure error tolerances, low weight and size, or a straight-through zero-order beam. However, photons or particles are often strongly absorbed upon transmission, e.g., in the increasingly important extreme ultraviolet (EUV) and soft x-ray band, leading to low diffraction efficiency. We demonstrate the performance of a critical-angle transmission (CAT) grating in the EUV and soft x-ray band that for the first time combines the advantages of transmission gratings with the superior broadband efficiency of blazed reflection gratings via reflection from nanofabricated periodic arrays of atomically smooth nanometer-thin silicon mirrors at angles below the critical angle for total external reflection. The efficiency of the CAT grating design is not limited to photons, but also opens the door to new, sensitive, and compact experiments and applications in atom and neutron optics, as well as for the efficient diffraction of electrons, ions, or molecules.