The evolution of silicon surface roughness is studied under scanning ion beam etching for high precision manufacture applications. The experiment is carried out using an 800 eV Ar ion beam generated through metal mask and different etching depths from 240 nm to 1330 nm was carried out. The processed surface is characterized via atomic force microscope, grazing incidence X-ray reflectivity, and X-ray fluorescence spectroscopy, to study the surface morphology, optical contrast and composition changes. It is found that the processed surface is smoothed from 0.14 nm to 0.10 nm (Root mean square) in the initial stage of etching, while further etching (deeper than similar to 1 mu m) would cause growth of nanodots structure with increased roughness. Contaminants sputtered from the ion beam mask and sample holder are detected on the processed surface and the related agglomeration and micro-masking effects of the contaminants are considered as the main mechanism for surface roughening. The roughened surface can be smoothed from 0.41 nm down to 0.10 nm (Root mean square) using the same etching parameters with only similar to 10 nm etching depth after exposure to air. The results show that the surface smoothing or roughening mechanism of Si can be closely related to the surface composition and structure, which provide useful guidance for the manufacture of high precision and ultrasmooth optics.

Resonant inelastic X-ray scattering (RIXS) is a photon-in/photon-out spectroscopic technique which has become increasingly important for the condensed matter physics community. The development of the RIXS instrumentation in soft X-ray and hard X-ray range facilitated the research in 3d and 5d transition metal (TM)-based materials, respectively. However, the tender X-ray (2000–3000 eV) RIXS covering most of 4d TM-based materials severely falls behind due to the lack of high-performance energy dispersive optics. Here, we demonstrate the design and fabrication of a laterally graded multilayer grating (MLG) optics for the establishment of the tender RIXS at the I21 RIXS beamline in Diamond Light Source. The successful implementation of the MLG boosts the photon flux by more than an order of magnitude at the Sulfur K-edge (2475 eV) and the Ru L3-edge (2838 eV) in comparison to the solution of a single-layer coated grating (SLG). More importantly, MLG retains the high energy resolution of the SLG design (~10,000) and works continuously across the full range of 2000–3000 eV. It renders the I21 beamline as the very first RIXS facility in the world that covers both soft and tender X-rays (280–3000 eV) using a grating-based spectrometer for a wide range of science applications. Multilayer-grating-based spectrometer with high photon flux and moderate energy resolution for tender X-ray

What we believe to be a novel approach is proposed and theoretically justified to achieve the extremely high spectral purity and high diffraction efficiency of a wideband multilayer-coated blazed grating (BMG) in the tender X-ray range (2.5-3 keV photon energy). The key feature consists of depositing a 70 nm thick B4C film on the BMG surface with subsequent removal of the saw-tooth relief by polishing. Such a design allows suppressing the low-energy parasitic radiation intensity by a factor exceeding 104 on the grating surface through reflection from the film in the total external reflection conditions. A high diffraction efficiency of 8-21% for the -2nd order can be achieved at the same time.

Grating optics lie in the heart of X-ray spectroscopy instruments. The low efficiency and angular dispersion of conventional single-layer-coated gratings significantly limit the transmission and energy resolution of monochromators and spectrometers, particularly in the tender X-ray region (E = 1-5 keV). Multilayer-coated blazed gratings (MLBGs) operating at high diffraction orders offer the advantage of achieving both high efficiency and high dispersion simultaneously. Tender X-ray monochromators and spectrometers using different high-order MLBGs have been designed, all demonstrating one to two orders of magnitude higher transmission compared to conventional systems. By employing a 2400 l/mm MLBG at the -4th or -8th diffraction order, the theoretical energy resolution of the instrument is improved by two to three times at 2.5 keV. Two MLBGs operating at the -2nd and -4th orders have been fabricated, showcasing remarkable efficiencies of 34%-12% at 2.5 keV, surpassing that of single-layer-coated gratings by an order of magnitude. Further optimization of manufacturing accuracy can yield even higher efficiencies. The measured angular dispersion agrees well with theoretical predictions, supporting the potential for high resolution. High-order MLBG optics pave the way for a new generation of tender X-ray monochromators/spectrometers that offer both high transmission and high resolution. (c) 2025 Chinese Laser Press

An analytic theory of X-ray (E∼0.04-4 keV) diffraction from wideband multilayer coated gratings is developed. It is found that the wideband blazed gratings can operate in the single-order regime when only one diffraction wave is effectively excited. The diffraction efficiency achieves the reflectivity of conventional depth-graded multilayer mirrors in a wide spectral range. The physical reasons and the conditions of the single-order regime of wideband multilayer grating operation are discussed. A simple and clear design procedure is developed to suppress undesirable diffraction orders. The way to achieve a high diffraction efficiency plateau of 25% throughout the E = 2-3 keV interval is demonstrated.

The universal approach was originally developed to design wideband multilayer coated blazed gratings operating in the tender X-ray region (E = 2-3 keV), realizing different diffraction geometries including constant incidence angle, constant Cff-factor, and constant deviation angle, while retaining high diffraction efficiency in a wide spectral range.The designed gratings coated by depth-graded Cr/C multilayer structures and operating in the -1st diffraction order are demonstrated to provide the constant factor Cff = 2.52 or the constant deviation angle ψ = 4.75° with the diffraction efficiency of 29% ± 2% or 17.5% ± 1.5%, respectively, throughout the 2-3 keV spectral range.

Usability of the Névot-Croce (NC) formula for calculation of the reflectivity from a surface with high-frequency roughness is critically analyzed. First, the necessary conditions of the NC factor applicability are identified quantitatively in the limiting case of vanishingly small correlation length of roughness. Second, the conditions are established, when the nonzero correlation length of real surface roughness can be reckoned as vanishingly small. Third, these conditions are compared with the experimental values of the correlation length of high-frequency roughness. The final conclusions concerning applicability of the NC formula for hard X-ray to extreme ultraviolet radiation are formulated.

Coating nano/micro-structured elements with a single or multi-layered film can greatly enhance their functionality. The experimental enhancement, however, is significantly limited by the smoothing and distortion of the structural profile after coating. This requires a comprehensive understanding of the layer growth behavior on nanoscale non-isotropic surface with a proper model to analyze and predict the structure evolution. Here, a simplified linear growth model with single free parameter was successfully used for analysis of the smoothening of grating grooves. The model enables a quantitative description of the evolution of surface morphology from substrate to the top surface with sub-nanometer accuracy. Based on this, the smoothing behavior of single-Si layer and W/Si multilayer growth on nanoscale gratings (period similar to 40 nm) and flat substrates were studied experimentally, for applications in X-ray optics. The smoothing effect of the W/Si multilayer coating is more pronounced than that of the single Si layer for both substrate types. The corrugated nanogratings suppressed the smoothing effect as compared to the flat isotropic surface. These works provide new guidance to predict and control the growth of layers on nanostructures.

The wax appearance temperature (WAT), being one of the key characteristics of waxy crude oil and other waxy substances, is used for the necessary assessment of the phase stability of materials during various technological processes. However, the determination of this parameter as well as peculiarities of wax formation under high gas pressure suffers from the lack of suitable techniques for this task. To address this issue, an attenuated total reflection Fourier transform infrared spectroscopy (ATR FT-IR) method has been applied for the first time to measure the WAT of waxy crude oil under high gas pressure. Carbon dioxide (CO2), nitrogen, and natural gas were used in the study due to their widespread applicability as injection gases in enhanced oil recovery methods. The S2/S1 versus temperature method based on changes in the band of rocking vibrations of the CH2 group was applied to determine WAT. It was found that the ATR FT-IR method based on the proposed dependence S2/S1 versus temperature gives lower WAT values compared to those observed by viscometry, magnetic resonance imaging inspection, and cross-polarized microscopy methods for the waxy crude oil studied. A detailed analysis was carried out using variable-temperature ATR FT-IR spectra of waxy crude oil in the temperature region near the WAT. Essentially different dynamics of wax crystal formation in waxy oil sample and model paraffin solution were demonstrated during the cooling process. The results obtained by high-pressure ATR FT-IR showed that CO2 and natural gas reduce the WAT, while nitrogen has virtually no effect. In addition, for the studied oil, it was found that high pressure of CO2 and natural gases leads to a visual decrease in the amount of wax crystals precipitated, but not to the complete disappearance of microcrystals at a certain temperature and pressure. The results obtained proved that ATR FT-IR can be an effective method for proper determinations of WAT under high-pressure conditions similar to those met in practice.

The work demonstrates the results of the first experimental PFG NMR study in situ of the complex phase behavior of asphaltenes in the presence of high-pressure CO2. To perform the experiments, a series of sealed, thick-walled quartz capillaries were prepared with a mixture of CO2 and asphaltenes dissolved either in chloroform or benzene at different initial concentrations. Then, the temperature dependence of the diffusion coefficients of the asphaltene aggregates was measured for each sample after the mixture reached its equilibrium state, at which, in accordance with the solubility limit, only part of the initial asphaltenes remained dissolved. Despite quite low residual asphaltene concentrations in solution, experimental data clearly demonstrated the presence of aggregated structures (up to 70-80 wt %) attributed solely to nanoaggregates, with no signs of the presence of macroaggregates in the samples. Temperature dependencies of aggregate diffusivity clearly showed that the scenario, according to which the evolution of the asphaltene aggregates will develop, strongly depends on the initial asphaltene concentration, mass fraction of CO2 loaded into the system, and chemical nature of the solvent used. In particular, the most diluted asphaltene solution, expected to be the most resistive to the aggregation processes in a high-pressure CO(2 )environment, revealed the most pronounced aggregation-dependent translational dynamics as compared to those with a moderate initial asphaltene concentration. Contrarily, the concentrated asphaltene solution may not show drastic aggregation processes if the mass fraction of the CO2 loaded will not appear to be so high. Finally, the experimental results provide evidence that the temperature-triggered structural transformation of asphaltene aggregates due to the noncovalent bond breakup is not hindered under high-pressure CO2, but instead becomes more emphasized. The results obtained shed new light on asphaltene aggregate dynamics and brought new knowledge about the fundamental behavior of asphaltene in high-pressure CO2 conditions.

The reflection and transmission of a wave falling onto a stratified medium is analyzed in terms of the RT-matrixes establishing a relation between the wave amplitudes in the asymptotic regions z→±∞. The RT-matrixes are considered as a generalization of the characteristic matrixes introduced by Abelès with elements expressed via the amplitude reflectance and transmittance of a wave falling onto the medium from the right and left sides. If the medium is divided into several parts, the product of their RT-matrixes is equal to the matrix of the whole medium, whose reflectance and transmittance are thus expressed via the reflectance and transmittance of its parts. The easy use of the RT-matrix in practical calculations was shown through analysis of the wave reflection from periodic and aperiodic multilayer structures with abrupt or smooth interfaces.

An original method for direct synthesis of tetramethyl orthosilicate from SiO2 raw minerals and supercritical methanol was developed for the first time in a flow mode. The process promoted by KOH was performed at 270 degrees C and 100 atm using 3 angstrom zeolite molecular sieves to shift the reversible reaction toward TMOS formation by removing released water. The equilibrium constant K-eq of the reaction was determined as 0.839E-08. Silica gel (100 wt% SiO2), quartz sand (97 wt% SiO2), expanded perlite (73 wt% SiO2) and vermiculite (38 wt% SiO2) were tested as SiO2 minerals. The highest equilibrium concentration of TMOS equal to 20.4 g/L was achieved for silica gel that can be increased using larger amount of water adsorbent.

We demonstrate a theoretical approach whereby light backscattering toward the incident beam can be suppressed entirely for a high-reflectivity, rough-surfaced multilayer mirror fabricated using oblique deposition, such that the interface relief is replicated at a certain angle β to the sample normal. The mirror comprises two parts: a main (lower) multilayer consisting of N identical bi-layers growing at the angle βML to the mirror normal, and an additional bi- or tri-layer forming the topmost section of the mirror, which grows at another angle βBL. We show that choosing appropriate growth angles βML and βBL results in a disappearance of backscattering toward the incident beam due to the destructive interference of waves scattered from the main multilayer and uppermost bi- or tri-layer. The conditions for the scattering suppression are formulated, and the suitability of different mirror materials is discussed.

The low efficiency of conventional single layer gratings at the tender X-ray region (E=1~5 keV) significantly limits the photon flux of the beamline and the development of related imaging and spectroscopy experiments in this region. To overcome this issue, multilayer coated gratings have been proposed and developed. The diffraction behavior of a multilayer grating is more complex than a single layer grating. To understand the diffraction behavior and exert the maximum potential of this new optics, we have built an analytical theory based on coupled wave theory. A high efficiency single order diffraction regime was first identified which means only one diffraction order will be excited with a certain incidence angle and structure parameters. This is applicable to blazed multilayer gratings (BMGs). To achieve maximum efficiency, the optimum grating and multilayer structures were analyzed. The highest theoretical efficiency of a BMG can reach the same value of the coated multilayer reflectance. Moreover, blazed multilayer gratings exhibit the advantage of high harmonics suppression. For the BMG, the conventional condition of maximal diffraction efficiency, Dsinα = nd, where D and d is the grating period and multilayer period, respectively, α is blaze angle, n is diffraction order, has been proved invalid. This is due to the contribution of anti-blaze facets to diffraction and effect of strongly asymmetric diffraction. Based on these, a Cr/C BMG was fabricated in collaboration with the Department for Nanometer Optics and Technology in BESSY-II. Maximum efficiency of up to 60% was demonstrated at 3 keV which is close to the theoretical prediction.

The problem of X-ray diffraction from multilayer-coated blazed diffraction gratings is analyzed. Invalidity of the conventional condition of maximal diffraction efficiency observed in previous experiments is explained theoretically. This is attributed to two factors: contribution of anti-blaze facets to diffraction efficiency and effect of strongly asymmetric diffraction. We demonstrate that a proper choice of the multilayer d-spacing allows to design grating with the diffraction efficiency close to the maximal possible one throughout the tender X-ray range (E∼1-5 keV). An optimization procedure is suggested for the first time to choose the optimal grating parameters and the operation diffraction order to obtain a high fix-focus constant and high diffraction efficiency simultaneously in a wide spectral range.

Abstract. Effective area is one of the most important parameters of x-ray telescopes. It can be increased by enlarging the entrance aperture or maximizing the reflectivity through the proper designing and optimization of the reflecting coating. A method to increase the reflectivity of grazing incidence x-ray mirrors in the 0.5- to 8-keV energy region is analyzed. The idea consists in the use of a trilayer reflecting coating instead of single-layer one (e.g., C/Ni/Pt mirror instead of Pt one). Deposition of low-absorbing medium-Z and low-Z layers onto the top of strongly absorbing high-Z material results in essential increase in the reflectivity while keeping the same width of the reflectivity plateau. In particular, C/Ni/Pt trilayer mirror demonstrates enhancement of the double reflection coefficient by a factor achieving 1.5 to 3.5 compared to that of Pt-coated mirror. The effective area of a telescope is also considerably increased. The experimental results are in a very good agreement with the theoretical predictions. In addition, the C/Ni/Pt trilayer mirror exhibits a reasonable thermal stability and a relatively low compressive stress of about −550  MPa.

We present a general method for designing XUV aperiodic multilayer mirrors that can mimic a given target spectrum, specifically, the spectral transmission of an XUV optical system. The method is based on minimizing a merit function and using fidelity parameters that quantify the matching of the multilayer reflectivity spectrum with that of the target spectrum. To assess the feasibility of fabricating such a system, we show how to reduce the layer-to-layer thickness variations throughout the aperiodic layer stack. We demonstrate the design method using an example of an EUV optical system composed of 12 identical Mo/Si multilayer mirrors having a reflectivity peak at 13.5 nm. We found that the target spectrum can be mimicked with high fidelity either with a single reflection at an aperiodic multilayer mirror combined with standard absorbing filters or, if required, with two subsequent reflections at a mimic mirror. These examples demonstrate the applicability for metrology at XUV sources, including spectrally proper source imaging. Because our approach is of general applicability, the process can be used to mimic any other narrowband, single-peaked target spectrum in the XUV region.

The optimized design of multilayer-coated blazed gratings (MLBG) for high-flux tender X-ray monochromators was systematically studied by numerical simulations. The resulting correlation between the multilayer d-spacing and grating blaze angle significantly deviated from the one predicted by conventional equations. Three high line density gratings with different blaze angles were fabricated and coated by the same Cr/C multilayer. The MLBG with an optimal blaze angle of 1.0° showed a record efficiency reaching 60% at 3.1 keV and 4.1 keV. The measured efficiencies of all three gratings were consistent with calculated results proving the validity of the numerical simulation and indicating a more rigorous way to design the optimal MLBG structure.

To develop highly efficient narrow-bandwidth multilayer optics for the soft x-ray ( SXR) spectroscopy, a low optical contrast MoSi2/Si lamellar multilayer grating ( LMG) was proposed and developed. The low contrast LMG allows for a large lamel width which can potentially achieve higher resolution than the conventional LMG and simplify the fabrication. As a first demonstration, a MoSi2/Si multilayer with a d-spacing of 5 nm and 180 bilayers was deposited. The lamellar grating structure with a period of 614 nm, lamel-to-period ratio of 0.38, and lamel height of 670 nm was fabricated in the multilayer with reactive ion etching process. The SXR measurements show a high 0th-order diffraction efficiency of 16%-33% at 876 eV-1648 eV, which reaches around 80% of the unetched multilayer reflectivity. A maximal bandwidth reduction of 2.2 times was obtained compared with the multilayer mirror, indicating an energy resolution of E/Delta E = 108 at 1183 eV. The resolution can be further improved by reducing the multilayer d-spacing and increasing the etching depth.

Cr/V multilayer mirrors are suitable for applications in the “water window” spectral ranges. To study factors influencing the internal microstructure of Cr/V multilayers, multilayers with different vanadium layers thicknesses varying from 0.6 nm to 4.0 nm, and a fixed thickness (1.3 nm) of chromium layers, were fabricated and characterized with a set of experimental techniques. The average interface width characterizing a cumulative effect of different structure irregularities was demonstrated to exhibit non-monotonous dependence on the V layer thickness and achieve a minimal value of 0.31 nm when the thickness of the V layers was 1.2 nm. The discontinuous growth of very thin V films increased in roughness as the thickness of V layers decreased. The columnar growth of the polycrystalline grains in both materials became more pronounced with increasing thickness, resulting in a continuous increase in the interface width to a maximum of 0.9 nm for a 4 nm thickness of the V layer.