Maximum Diffraction Research Articles

Light diffraction from a phase grating at oblique incidence in the intermediate diffraction regime

We experimentally characterize the positions of the diffraction maxima of a phase grating on a screen, for laser light at oblique incidence (so-called off-plane diffraction or conical diffraction). We discuss the general case of off-plane diffraction geometries and derive basic equations for the positions of the diffraction maxima, in particular for their angular dependence. In contrast to previously reported work (Jetty et al. in Am J Phys 80:972, 2012), our reasoning is solely based on energy- and momentum conservation. We find good agreement of our theoretical prediction with the experiment. A detailed discussion of the diffraction maxima positions, the number of diffraction orders, and the diffraction efficiencies is provided. We assess the feasibility of an experimental test of the phenomenon for neutron matter waves.

Numerical Analysis of X-Ray Diffraction Reflection Spectra of AlGaAs/GaAs Superlattices Depending on Structural Parameters

In this paper, we study the properties of X-ray diffraction reflection spectra of multilayer periodic AlGaAs/GaAs heterostructures depending on the thickness and composition of the layer material and number of periods. The number and intensity of additional diffraction maxima on the rocking curves are shown to increase with an increase in the layer thickness and number of periods. The layer composition does not affect the number of maxima but changes their angular position and the full width at half maximum. Numerical calculations were compared with experimental spectra measured for a heterostructure grown by molecular beam epitaxy and consisting of 50 periods in which the AlxGa1–xAs barrier had a composition of x ≈ 26.7% and a thickness of d ≈ 51.6 nm while the GaAs quantum well had a thickness of d ≈ 4.6 nm. The calculated parameters are found to be in good agreement with the technological data and the results of transmission electron microscope measurements.

Анализ дифракции белого рентгеновского излучения на кристаллах методом Эвальда при определении угловых параметров кристаллической реш􀉺тки

Using the Ewald method, the analysis a diffraction pattern formation in the interaction of white xray radiation with crystals in the process of diffraction shooting by the ω-scanning method using a point counter is carried out. The influence of such parameters as x-ray voltage x-ray tube and the angular the counter position to the number and intensity of reflections on x-rays. It is shown that the angles between the diffraction maxima on the diffractograms obtained by ω-scanning using white x-ray radiation are equal to the angles between the corresponding crystallographic planes. The angles and crystallographic indices of the reflecting crystals planes of some simple substances were measured using the considered x-ray survey.

Investigation of the impact of mechanical activation on synthesis of the MgO-TiO2 system

In this study, a mixture of magnesium oxide and titanium dioxide was mechanically activated in order to investigate the possibility of mechanochemical synthesis of magnesium titanate. Mechanical activation was performed for 1000 min in a high-energy vibro mill (type MH954/3, KHD Humboldt Wedag AG, Germany). The mill is equipped with housing having a horizontally placed shutter. The cylindrical stainless steel working vessel, with inner dimensions of 40 mm in height and 170 mm in diameter, has working elements consisting of two free concentric stainless steel rings with a total weight of 3 kg. The engine power is 0.8 kW. Respecting the optimal amount of powder to be activated of 50-150 g and the stoichiometric ratio of the reactants in the equation presenting the chemical reaction of magnesium titanate synthesis, the starting amounts were 20.2 g (0.5 mol) of MgO and 39.9 g (0.5 mol) TiO2. During the experiments, X-ray diffraction analysis of the samples taken from the reaction system after 60, 180, 330, and 1000 min of mechanical activation was performed. Atomic absorption spectrophotometry was used for chemical composition analysis of samples taken at different activation times. Based on the X-ray diffraction analysis results, it can be concluded that the greatest changes in the system took place at the very beginning of the mechanical activation due to the disturbance of the crystal structure of the initial components. X-ray diffraction analysis of the sample after 1000 min of activation showed complete amorphization of the mixture, but diffraction maxima characteristic for magnesium titanate were not identified. Therefore, the mechanical activation experiments were stopped. Evidently, the energy input was not sufficient to overcome the energy barrier to form a new chemical compound - magnesium titanate. The failure to synthesize magnesium titanate is explained by the low negative Gibbs energy value of -25.8 kJ/mol (despite the theoretical possibility that the reaction will happen), as well as by the amount of mechanical energy entered into the system during activation which was insufficient to obtain the reaction product. Although the synthesis of MgTiO3 was not achieved, significant results were obtained which identify models for further investigations of the possibility of mechanochemical reactions of alkaline earth metals and titanium dioxide.

Morphology and structure characteristics of nanoscale carbon materials containing graphene

A comprehensive study of the nanostructured powders (graphite GSM-2; Taunit-M; thermally expanded graphite (TEG)) by methods of transmission electron microscopy (TEM), scanning electron microscopy (SEM), X-ray diffractometry (XRD), reflection high-energy electron diffraction (RHEED), Raman spectroscopy, was carried out. The experimental XRD halo was interpreted by superimposing theoretical diffraction maxima, and an X-ray amorphous graphite phase was revealed. It was found that the X-ray amorphous phase is characterized by the limiting degree of graphite nanostructuring. From the width of the diffraction rings, the maximum sizes of graphite nanocrystals were estimated, which do not exceed 5 and 10 nm in the [0001] and [ ] directions, respectively. Carbon nanotubes and plates of turbostratic graphene were revealed. The structural and morphological parameters of the nanostructured material “Taunit-M” have been established – multi-walled nanotubes with a diameter of up to 10 nm are combined through an interlayer of X-ray amorphous carbon into flat ribbons up to 40 nm wide. Dark-field TEM images (in reflections of ) revealed moiré patterns that appear on overlapping graphene sheets due to double diffraction of the electron beam. It was found that in thermally expanded graphite, the rotation of graphene sheets ranges from 3 to 4°. Within the graphene sheets, complete dislocations with the Burgers vector b = 1/2 were revealed [1010]. The Fourier analysis of moiré images made it possible to determine the mutual orientation of graphene sheets, to reveal regions of multilayer graphene, and to identify turbostratic graphene. It is shown that the combination of RHEED, TEM, and Fourier transformations of periodic contrast of electron microscopic images is a promising approach to the analysis of the substructure and morphology of nanoscale carbon materials containing graphene and other allotropic modifications of carbon.

Элементное и структурное картирование объемных кристаллов (Al-=SUB=-x-=/SUB=-Ga-=SUB=-1-x-=/SUB=-)-=SUB=-2-=/SUB=-O-=SUB=-3-=/SUB=-, полученных методом Чохральского

Using X-ray fluorescence and X-ray diffraction mapping, as well as scanning electron microscopy, the distribution of aluminum in the surface layer of the (AlxGa1-x) 2O3 crystal obtained by the Czochralski method using a sapphire seed was studied. It is shown that the distribution of aluminum correlates with the change in the physical broadening of the diffraction maxima of the system of planes (h00) of the crystal and is associated with the distance from the seeding zone.

Selection of location of radiators in a non-equivident antenna array

Antennas are one of the main elements of radio engineering systems. Phased antenna arrays (PAR), which make it possible to regulate the direction of radiation due to the ability to control the phases or phase differences of the emitted signal, are the most effective types of antennas. The size, design and shape of the PAR depend on the tasks to be solved, the type of emitters and the nature of their location. The article discusses the transformation of an equidistant PAR into a non-equidistant antenna array in order to reduce the level of side lobes and suppress diffraction maxima with a given minimum distance between the emitters. A model of a non-equidistant antenna array and calculation formulas for its analysis are presented. The method presented in the work based on iterative calculation methods makes it possible to select the main parameters of a non-equidistant PAR taking into account the bonds formed between neighboring radiating elements. The coordinates of the emitter elements of the non-equidistant PAR were calculated in a program using the MATLAB language. At the same time, a method was implemented to search for the optimal arrangement of emitters relative to each other, in which the directional pattern of the antenna array will have a minimum level of diffraction maxima and the required level of side lobe. According to the results of the program execution, the coordinates of the new non-equidistant PAR were obtained. The non-equidistant phased array antenna simulated according to the calculation results showed a complete absence of diffraction maxima, in contrast to the equidistant array, but it was not possible to sufficiently obtain the required level of side lobes. The calculated antenna radiation patterns presented for comparison showed the advantages of a non-equidistant antenn array.

Application of a Low-Cost Cellulose-Based Bioadsorbent for the Effective Recovery of Terbium Ions from Aqueous Solutions

The preparation of a low-cost cellulose-based bioadsorbent from cellulosic material extracted from rose stems (CRS) was carried out; rose stems are considered agricultural waste. After the required pretreatment of this waste and further treatment with an acidic mixture of acetic and nitric acids, the CRS product was produced. The resulting bioadsorbent was characterized by several techniques, such as X-ray diffraction, which revealed diffraction maxima related to the cellulose structure, whose calculated crystallinity index (CrI) was 75%. In addition, Fourier Transform Infrared spectroscopy (FTIR), 13C Nuclear Magnetic Resonance (NMR), and X-ray Photoelectron Spectroscopy (XPS) showed signs of acetylation of the sample. The thermal properties of the solid were also evaluated through Thermogravimetric Analysis (TGA). Scanning Electron Microscopy (SEM) showed cellulose fibers before and after the adsorption process, and some particles with irregular shapes were also observed. The CRS bioadsorbent was used for the effective adsorption of valuable Tb(III) from an aqueous solution. The adsorption data showed a good fit to the Freundlich isotherm and pseudo-second-order kinetic models; however, chemisorption was not ruled out. Finally, desorption experiments revealed the recovery of terbium ions with an efficiency of 97% from the terbium-loaded bioadsorbent.

ОСОБЕННОСТИ ПРОЦЕССОВ ГИДРАТАЦИИ ВЯЖУЩИХ КОМПОЗИЦИЙ С ИСПОЛЬЗОВАНИЕМ ОТХОДОВ ВСПУЧЕННОГО ПЕРЛИТОВОГО ПЕСКА

The results of studying the processes of hydration of binder compositions obtained at different ratios of cement and waste of expanded perlite sand (from 5 to 10%), in a vortex jet mill, under different modes of mechanical and chemical activation - from one to three passes are presented. Comprehensive studies of hydration products by X-ray phase analysis and electron microscopy indicate that the use of highly dispersed wastes from the production of expanded perlite sand in binding compositions allows an increase in the content of hydrated neoplasms due to an increase in the degree of hydration of the main clinker phases, as well as due to the pozzolanic activity of these wastes. The contact zone between the hydrated compounds and the remnants of the grains of the original cements has a special effect on the formation of a high-strength structure of the cement stone. The structure formation of a cement stone depends on a number of factors, which can be influenced by various technological methods. When designing compositions of cement composites, it is necessary to ensure that hydration products in the created system are present along with low-basic calcium hydrosilicates and high-basic ones. Their ratio should be such that carbonization does not reduce the volume of the formed crystalline phase of the cement stone. The composition of the hydration products determines the level of supersaturation of the solution, the type and number of impurities soluble in water, the duration of the hydration process, etc. The chemistry of the reactions of the hydrated system changes accordingly. It is found that the intensity of the diffraction maxima, indicating the presence of highly basic calcium hydrosilicates in the compositions that underwent mechanical activation, increases by 18% in comparison with the ordinary PC. The strength characteristics of Portland cements, which have undergone mechanical activation, increase up to 15% compared to the original PC. The most rational binder composition is established in terms of composition (No. 6), mechanical activation and maximum compressive strength at 28 days of age – 69.1 MPa.

Diffraction efficiency of a small-period astronomical x-ray reflection grating fabricated using thermally activated selective topography equilibration

We have fabricated a blazed x-ray reflection grating with a period of 160 nm using thermally activated selective topography equilibration (TASTE) and electron-beam (ebeam) physical vapor evaporation. TASTE makes use of grayscale ebeam lithography to create three-dimensional (3-D) structures in resist, which can then be thermally reflown into a desired profile. A blazed grating profile can be fabricated by selectively reflowing a periodic staircase structure into a wedge. This was done for the first time at a grating period of 160 nm, 2.5 times smaller than previous x-ray gratings fabricated using TASTE. The grating was patterned over a 10 mm by 60 mm area in a 147-nm-thick layer of poly(methyl methacrylate) resist and coated with 5 nm of chromium and 15 nm of gold using ebeam evaporation. The diffraction efficiency of the grating was measured using beamline 6.3.2 at Lawrence Berkeley National Laboratory’s Advanced Light Source. The results show a total absolute diffraction efficiency ≳40 % at lower energies, with maximum single-order diffraction efficiency ranging from 20% to 40%. The total diffraction efficiency was ≳30 % across the measured bandpass of 180 to 1300 eV.

Investigation of the filament spatial structure by aberration focusing in air of a femtosecond radiation pulse

The appearance conditions of two filaments propagating at an angle to each other by aberration focusing in air of femtosecond radiation pulse with a 940 nm wavelength are studied. Interest to these beams is due to the formation of highly directed radiation of the white supercontinuum in them with diffraction divergence. It is shown that the pump beam diffraction on plasma and Kerr nonlinearity in filamentation area are responsible for the formation of two additional filaments. The diffraction maxima are beginnings of high-intensity pump beams due to Kerr self-focusing of surrounding energy reservoir of pump radiation. The dynamics of these beams from foci zone till far zone is demonstrated.

Acoustic measurements of capillary-gravity water surface waves

For this work an optical method for measuring surface acoustic waves was adapted to acoustics using airborne ultrasound for measurements on water surface waves. With ultrasound incident on periodic traveling water surface waves, the reflected signal can be treated as the diffraction pattern from a moving corrugated reflection grating as long as the amplitude of the water surface waves is much less than the incident acoustic wavelength. The acoustic signal received at the first-order diffraction maxima is amplitude modulated at the frequency of the water surface wave. The intensity of this modulation is directly proportional to the amplitude of the water surface wave. Using spectral decomposition of the signal, the water surface wave amplitudes are precisely determined at sum and difference frequencies around the source peak. The transmission of water surface waves incident on a solid piercing boundary was measured using this method to understand capillary-gravity wave interactions with boundaries. [Work supported by NASA.]

Mechanisms of crack generation in high-pure tungsten exposed to high power density plasma

The mechanisms of crack formation in the tungsten divertor plates irradiated by hydrogen plasma under ITER-type steady-state and transient events are investigated. The stresses and defects of samples‘ initial structure are annealed as a result of steady-state irradiation with Falcon ion source, which generates 2 keV hydrogen ion flux of ~ 1022 m-2s−1 and power density ~ 1.7 MW × m−2. Quasi-stationary plasma accelerator QSPA Kh-50 provides pulsed hydrogen plasma loads which operating mode simulates transient events (type I ELMs) in ITER: ion impact energy is about 400 eV, maximum plasma pressure is 0.32 MPa, pulse duration is 0.25 ms. The diffraction maxima profiles, positions, intensities, half-widths, and intensity distributions are analyzed. The origin of crack formation is found to be in the plastic deformation of surface layers by the twinning mechanism. The latter is reinforced by the interaction of twins with the hydrogen-filled micro-pores. The micro-pores appear as a result of hydrogen saturation of subtraction loops formed due to the coalescence of vacancy complexes.

SOLVING MINERALOGY PROBLEMS WITH THE HELP OF THE “ORIGIN" PACKAGE

Algorithms for solving typical mineralogical problems associated with quantitative x-ray spectral analysis and quantitative x-ray phase analysis using the program “Origin” are developed. The calculation of the areas and midpoint of spectral lines using the tabular processor of the program “Origin” is considered. Various approaches to determining the parameters of spectral lines using the least squares method using the standard functions of the program “Origin” were tested. The creation of a user function for approximation of diffraction maxima by the Cauchy function taking into account the doublet character of Ka series of x-rays is also considered. Various built-in algorithms for smoothing functions (based on averaging, polynomial approximation and Fourier analysis – synthesis) were tested to find weak diffraction maxima against strong noise; optimal schemes for the application of these algorithms were found. The considered algorithms can be applied in universities when processing the results of laboratory works on the topics "Analysis of spectra of emission of atoms", "Quantitative x-ray spectral analysis" and "Quantitative x-ray phase analysis".

Tailoring diffraction of light carrying orbital angular momenta.

A unified approach to controlling the diffraction of light carrying orbital angular momenta (OAM) is developed and experimentally verified in this Letter. This approach allows one to specify not only the number of diffraction maxima, their spatial frequencies, and the intensity distribution between them, but also the OAM in each maximum. It is verified that the approach can be used for structuring both single and multiple beams carrying OAMs. Simulations reveal phase singularities in structured beams. In addition, the approach makes it possible to shape the light in regular and irregular two-dimensional arrays with addressing the OAMs at each site. This approach offers new opportunities for singular optics.

Spatial Photoresponse, Formfactor, and Requirements to Holographic Materials

Problems arising when recording holograms in volume materials and manifesting themselves, firstly, as the spatial resonance of the hologram recording field with refractive index inhomogeneities caused by this recording are considered. Secondly, they manifest themselves as cross-coupling of two nonlinearities in the process of holographic recording—nonlinearity of the diffraction efficiency and nonlinearity of the distribution of the exposure and visibility recorded by the holographic grating over the hologram field. It is noted that the appearance of one more nonlinearity—the nonlinear photoresponse of the holographic material—leads not to a decrease in the diffraction efficiency but to an increase in it under certain conditions. In this work, main classes of volume holographic materials are distinguished—relaxation free dynamic media and media with development. Restrictions of the maximum achievable diffraction efficiency for both types of the media are demonstrated. Recommendations on elimination of undesirable consequences of the revealed effects are formulated. The recommendations are based on the analysis of main regularities in the formation of the photoresponse with allowance for the spatial resonance and presence of the formfactor.

Designing Fully Populated Phased Arrays for Noninvasive Ultrasound Surgery with Controlled Degree of Irregularity in the Arrangement of Elements

When designing phased antenna arrays for use in noninvasive ultrasound surgery, it is desirable to provide the highest possible power for a given array dimensions. At the same time, it is necessary to take into account the limitations on the maximum allowable ultrasound intensity at the array elements and to ensure suppression of spurious diffraction maxima in the spatial structure of the emitted field. The problem can be solved by designing an irregular arrangement combined with the densest filling of the array surface with elements. This paper presents a modification of such a method for creating fully populated arrays with nonperiodic tessellation distribution of elements, based on the restriction of the relaxation mechanism in an iterative array design algorithm. A computer model that allows for controlling the degree of irregularity in distribution of the array elements was developed. The stability of maintaining the low level of acoustic intensity in unwanted grating lobes was tested for various random realizations of the element arrangements by analyzing a statistical ensemble of 500 model arrays. The advantages of the considered arrays in comparison with existing models of fully populated arrays are demonstrated.

Structural evolution of Lu2‐xCexTi2O7 pyrochlores under 400 keV Ne irradiation

AbstractLu2‐xCexTi2O7 (LCTO) pyrochlores were irradiated by 400 keV Ne2+ with fluences (dose) of up to 5 × 1015 ions/cm2 (1.875 dpa). The detailed damage process was investigated by combining grazing incident angle X‐ray diffraction (GIXRD) and transmission electron microscopy (TEM). Subsequent to the 2% volume swelling at a fluence of 1 × 1014 ions/cm2 (0.037 dpa), the initially swollen LCTO pyrochlore formed both a disordered fluorite phase and a nanocrystalline pyrochlore phase at a fluence of 5 × 1014 ions/cm2 (0.185 dpa). At higher fluences, the fluorite phase diminished as amorphous domains increased in volume when the dose reached a fluence of 1 × 1015 ions/cm2 (0.371 dpa), while the nanocrystalline pyrochlore phase persisted. At the highest fluence of 5 × 1015 ions/cm2 (1.854 dpa), the amorphous fraction decreased, meanwhile the degree of crystallinity of nanocrystalline pyrochlore phase was enhanced, as evidenced by the increased intensity of superlattice diffraction maxima. The phase transformation and recrystallization can be explained by the release of strain in irradiation‐induced swollen pyrochlore crystallites. The evolution of the damage process is mainly driven by the differences in the Gibb's free energies of fluorite phase as compared with the pyrochlore phase as a function of grain size. We have demonstrated that ion beam techniques can be used to manipulate the phase stability and crystallite size of pyrochlore. These results provide the basis for tailoring the mechanical strength and response of pyrochlores to extreme radiation environments.

ВЛИЯНИЕ МИКРОНАПОЛНИТЕЛЕЙ ИЗ ПРИРОДНОГО ВОЛЛАСТОНИТА НА СВОЙСТВА МЕЛКОЗЕРНИСТОГО БЕТОНА

The possibility of obtaining effective highly dispersed additives from natural wollastonite is substantiated and their influence on the properties of fine-grained concrete is investigated. On the basis of wollastonite, a complex micro-filler with particle sizes up to 100 microns was developed, obtained by joint grinding with quartz sand in a 3:1 ratio in a ball mill in the presence of an anionic surfactant naphthalene-formaldehyde type C-3 and a calcium stearate hydrophobizer technical C-17. A suspension of wollastonite with a modal particle diameter of 405 nm was obtained by pre-grinding wollastonite and anionic surfactant in a ball mill, with their further ultrasonic treatment in a bath-type activator. Mathematical models of the dependence of compression and bending strength on the content of the initial components are developed. It is established that the complex microfill leads to an increase in the strength of fine-grained concrete in bending by 2 times, in compression by 1.7 times with its content in the composition of fine-grained concrete in the amount of 10% by weight of cement. Wollastonite suspension increases the bending strength of fine-grained concrete to 3.1 MPa, compression to 57.8 MPa. The results of qualitative x-ray phase analysis showed that the total intensity of diffraction maxima of not fully hydrated alite C3S, belite C2S grains and their aggregates in cement stone with wollastonite decreases by 1.5-2 times compared to the control composition. This is most likely due to the amorphous nature of the wollastonite surface after grinding in a ball mill and ultrasonic dispersion in a bath-type activator. In addition, such particles are the centers of crystallization. Their needle-like shape contributes to the reinforcement of the structure by crystallizing new formations of cement stone.

Analysis of Phase Composition and CSR Sizes in Non-Equilibrium Nanostructured Systems Fe-Co and Ni-Cu Using Diffraction Maxima Simulations in a Doublet Radiation

The paper addresses the problem of determining phase composition, composition of mixed phases, and the CSR size in structurally similar metal systems where the most part of similar reflections of two phases overlap with each other. The overall experimental diffraction profile of overlapping reflections is decomposed into components by simulation techniques. The profile of each individual reflection is calculated as the convolution of the broadening function (in the form of the Pearson VII distribution with refined parameters) and an instrumental doublet function that is measured on a reference substance with a sufficiently large CSR size, shifted by an appropriate angle, and adapted to this position. As a result, parameters of profile components were identified and further used to determine phase compositions and compositions of mixed phases in nonequilibrium systems Fe-Co and Ni-Cu as well as the dependence of the CSR size on system’s composition.