Theoretical analysis of the possibilities of Zernike phase contrast method in hard X rays for nondestructive imaging of micropipes in a silicon carbide single crystal

The possibilities of using Zernike phase contrast in hard X rays for imaging micropipes in a silicon carbide single crystal are analyzed by numerical simulation. Calculations are performed for the experimental conditions characteristic of third-generation synchrotron radiation sources. A scheme is considered where the focusing element is a parabolic refracting lens and the phase-shifting element is mounted at the point of the source image. It is shown that micropipe cross sections by a beam with a longitudinal diameter reaching 10 μm are imaged by the lens without distortions. At the same time, the lens makes it possible to magnify the image several tens of times. The cross sections that are significantly elongated along the beam are imaged with artifacts; however, their structure can also be recovered. It is shown that polychromaticity of radiation does not significantly affect the object imaging.     

Numerical modeling of optical properties of a system of two zone plates for focusing hard synchrotron radiation

Results of numerical experiments on focusing of a monochromatic spherical wave by a system of two linear zone plates are reported. Calculations were performed for a photon energy of 12.3985 keV and zone plates with a radius of the first zone of 5 μm, a number of zones of 628, and an aperture of 250 μm. To calculate the Kirchhoff integrals, the double Fourier transform method was used and the fast Fourier transform procedure on a grid with a number of points 65 536 = 2¹⁶ was applied. On the basis of the calculation results, a conclusion was drawn that two zone plates operate as one with a doubled phase shift in zones with a material if the longitudinal distance between them is smaller than 1/3 of the focus depth and the transverse displacement is smaller than 1/3 of the outermost zone width (the focus size). If the distance (displacement) exceeds the focus depth (size), the two zone plates operate independently, similar to refracting lenses with a set of different focusing orders, including the zero order. The nature of the moiré pattern at a transverse displacement of the zone plates is discussed.     

Diffraction reflection of a focused X-ray wave by a multilayer crystal

The Bragg diffraction of a narrow X-ray beam in a multilayer crystal is studied in the reflection geometry. It is shown by computer simulation of the experiment that strong integrated kinematic reflection occurs at any boundary of a multilayer crystal at the point of intersection of a narrow beam with the boundary. In contrast to the dynamic diffraction of a plane wave, attenuation of a narrow incident beam due to the reflection is small in comparison with the conventional absorption. As an example of a multilayer crystal, a Fabry-Perot interferometer is considered, which consists of two 70-μm-thick crystal Si layers separated by a 100-μm-thick air layer. The 12 4 0 reflection is studied at a photon energy of 15 keV. Three methods of formation of a narrow beam are considered: wavefront limitation by a slit, focusing with a parabolic lens, and focusing with a zone plate. It is shown that, for a local analysis of the thickness of layers and scattering parameters, the method of parabolic lens focusing has some advantages in comparison with the other methods.     

Determination of the Cholesteric Screw Sense

If a cholesteric liquid crystal is placed between a glass plate with planar alignment and a spherical lens with concentric surface alignment, a double spiral disclination line appears. The spiral rotation sense depends on the helix screw sense of the cholesteric phase and the radial distance between the disclination lines on the pitch magnitude. A theoretical calculation of the form of the spiral disclination lines is given and compared with experimental results.     

A method for implementing the diffraction of a widely divergent X-ray beam

A method for implementing the diffraction of a widely divergent characteristic X-ray beam from a standard X-ray tube with a linear focal spot was improved. X rays, passing through a diaphragm 30 μm in diameter, diffract from a crystal adjacent to the diaphragm. The crystal, together with a photographic plate, rotates around the axis perpendicular to the plate. It is shown that the diffraction image is a set of hyperbolas in this case. The equations of the hyperbolas are obtained and investigated. A method for interpreting the diffraction images in the case of small crystal asymmetry is proposed.     

Nucleation and polymorphism explored via an easy-to-use microfluidic tool

We present an easy-to-use microfluidic set-up, easily transferable to the laboratory and determine an accurate method for metastable zone width measurement. We clearly define a zone in the phase diagram where nucleation is mononuclear. We nucleate a single crystal of metastable phase, which turns out to be stable. This approach holds promise for the control and the study of crystallization processes.     

Computer simulation of images of photonic crystals for hard X rays in a transmission scheme. Near field

We have developed a method of calculation of transmission of hard x-ray radiation through a perfect and well oriented photonic crystal consisting of closely packed spheres of matter. The method is based on using an approximate solution of paraxial equation for small distances. The recurrent formula is obtained for a transmission of radiation on one period of crystal. A computer program is elaborated for a simulation of images of photonic crystals in a near field, particularly, just behind the crystal. The calculation is performed for silica spheres of 500 nm diameter. It is shown that the standard phase contrast technique is not valid for these objects, because a strong change of intensity takes place inside the volume of crystal due to a scattering of radiation by separate spheres.     

Study of the diffraction contrast of dislocations in X-ray topo-tomography: A computer simulation and image analysis

Oblique X-ray diffraction images of individual dislocations in the symmetric Laue geometry from a plane-parallel silicon plate have been calculated based on the Takagi-Taupin equations and analyzed. Computer simulation is used to develop a general mathematical model of the formation of oblique images which correspond to sample rotation around the diffraction vector h in X-ray topo-tomography. The results of numerical calculations and analysis of different oblique images of straight-line dislocations, where the dislocation line vector τ lies in a plane parallel to input surface of {111}Si plate with a diffraction vector h 〈220〉, are presented.     

The effect of minor additions of P2O5 on some phase transformations of plate glass

The effects of additions of several tenths of a per cent of P₂O₅ on the devitrification behavior of plate glass with the primary phase of tridymite are different from that with the primary phase of wollastonite. But they still follow the phase equilibrium relationship of multicomponents. By examinations with TEM, and measurements of electrical resistivities, it is indicated that phase separation of plate glass may be promoted with a minor addition of P₂O₅. Through XPS measurements it is further suggested that such an addition causes a certain change in the structure of the plate glass.     

Crystal growth and dopant segregation of Ce:LiSrAlF6 and Eu:LiSrAlF6 crystals with high dopant concentrations

Ce:LiSrAlF₆ and Eu:LiSrAlF₆ crystals with different dopant concentrations were grown by the micro-pulling-down method. The crystals with high dopant crystal included the secondary phase as clusters with the plate shape in BSE images. The secondary phases were identified CeF₃ and EuF₂, respectively, by the EDS analysis and powder-XRD measurement. Eu concentration against the Sr sites in the Eu 2% doped LiSAF crystal were most uniform in the range 0.9–1.6 atm% using the EPMA.     

The features of identifying lines in a diffraction image formed by a widely divergent X-ray beam

A method for identifying lines in a diffraction image formed by a widely divergent X-ray beam and a technique for measuring the crystal structure parameters in the case of asymmetric crystal position have been developed. It is established that, once the distances between a crystal and a photographic plate and between the points of intersection of the hyperbola branches in a diffraction image are known, one can determine the angle between the crystal’s zone axis and the wave vector, which leads to multiwave diffraction. Relations linking this angle with the parameters of two atomic planes are obtained. It is found that, to measure the parameters of atomic planes belonging to a given zone, one can use different sets of crossed hyperbolas formed by radiations K _α and K _β. The measurements and calculations performed for the same sample (Si crystal), mounted symmetrically and asymmetrically, confirm the reliability of the proposed method.     

Investigation of the effect of coefficient of thermal expansion on prediction of refractive index of thermally formed glass lenses using FEM simulation

During the cooling phase of thermal forming processes, the properties of glass undergo minor changes. These changes are a result of structural relaxation near the glass transition region. One such property, refractive index, is the most important material property that governs the optical performance of a glass lens. Therefore, it must be properly considered prior to manufacturing. A finite element model is established in this research to simulate structural relaxation behavior of glass during cooling. This is done in order to accurately predict the refractive index change which occurs during and after the forming process. This study shows that the success of the simulation model depends largely on the accuracy of material information available to the lens manufacturers. Specifically, the comparison between simulated and experimental data demonstrates that the published information for the generic coefficient of thermal expansion is inadequate for precisely predicting volume change. To resolve the issue, a reverse calculation method was presented. In addition, simulated finite element results showed that the value of the liquid coefficient of thermal expansion has a major effect on the simulated results, as compared to fraction parameter.     

Microscopy with an ellipsometric arrangement

A method is given to observe a sample with an ellipsometer equipment allowing a microscopical observation of a reflecting surface. The microscopical images are contrasted by the elliptical polarization and reflect the inhomogeneity of the optical properties of the surface. The contrast is of the high resolution of the ellipsometrical method registrating very low variations of optical properties of the reflecting sample. In this paper we give par example an observation of a step of a native oxide film on GaAs of only three Ångstroms.     

Solidification characteristics of textured 123 phase in YBCO by laser floating zone leveling (LFZL) method

Because of incongruent melting in YBa₂Cu₃O_7-x, it is difficult to grow the textured 123 phase directly from the laser-heated molten zone in the laser floating zone (LFZ) method. To overcome this problem, the laser floating zone leveling (LFZL) method was utilized following a pseudo-binary diagram along the Y₂BaCuO₅−YBa₂Cu₃O_7−x tie line and a crystal rod of textured 123 phases was directly grown from the molten zone. Experimental results indicate that the orientation of the textured tetragonal 123 phases is perpendicular to the c-axis and that the T_c of the grown crystal rod is 91.2 K after annealing at 550°C for 40 h in flowing oxygen. Also, the solidified morphologies of some crystal rods grown at different growth rates were observed.     

Liquid phase epitaxy of SiC in the system Tb?Si?SiC by temperature gradient zone melting (III). Epitaxial layer properties

In the present work the electrophysical and structural properties of the SiC epitaxial layers grown by the temperature gradient zone melting method in vacuum conditions is considered. Some correlations between the epitaxial layer properties and the process conditions are observed. It is shown that the performence of the growth process in vacuum leads to a significant improvement of the layer quality, if one observes some requirements – how to decrease significantly the number of the second phase inclusions and how to improve the structural perfection of the layers.     

基于人工微纳结构的平板衍射透镜

现代显微镜中的物镜受限于瑞利衍射极限,其分辨率不能满足生物成像、材料科学以及光刻等领域的需求。目前,突破瑞利衍射极限的方法可分为近场(如扫描近场光学显微镜、超透镜、微球透镜)和远场(如受激辐射损耗显微镜、光激活定位显微镜、随机光学重建显微镜)方法。然而,前者利用纳米探针散射物体表面一个波长范围内的倏逝波,极具挑战性;而后者对样品有选择性,只适用于荧光分子样品,且会对样品造成损伤。近年来,平板透镜利用波带片、光子筛以及梯度超构表面等人工微纳结构来控制光的衍射,具有小型化、高数值孔径、大焦深、亚衍射极限聚焦等功能,为远场无标记超分辨率成像提供了一个可行的解决方案。本文从衍射聚焦光学的统一理论出发,总结平面衍射透镜的最新进展,揭示基于光场调控实现纳米聚焦的物理机制,介绍平板衍射透镜的设计原理、光学性能、微纳结构特性和材料影响,详细讨论平板衍射透镜的光学像差(如离轴像差和色差)及其校正,平板衍射透镜在纳米成像、光刻以及光电子能谱仪中的应用,最后展望其未来的发展方向和机遇。     

On the Kinetics of Solid-Liquid-Solid. Phase Transformation

Solid-solid phase transformation of different hydrates or polymorphs in suspension proceeds in such a way that the metastable phase dissolves and the stable phase precipitates from the solution. If the starting point lies within the metastable zone of the stable phase, the transformation starts only after elapse of the corresponding induction period. In the case when the starting point is situated outside the metastable zone of the stable solute, the transformation proceeds without any delay. These theoretical considerations are illustrated by an example with recrystallization of calcium sulphate in presence of phosphoric acid; a small concentration change of the acid changes the kinetics significantly.     

Phase dispersion X-ray imaging of murine soft tissue

The generation of phase-contrast (PC) images in the phase-dispersion introscopy (PDI) technique is the subject of this paper. Conditions for extreme sensitivity to murine soft-tissue anatomy are discussed. The unique information content and good contrast of the minutest details of anatomy, together with the high brilliance of X-ray optics, give the authors confidence that the PDI method can be successfully applied for medical diagnostics.     

Nanoscale phase separation of CuI-Cu2MoO4 superionic conducting glass studied by analytical transmission electron microscopy

Microstructures of CuI-Cu₂MoO₄ superionic conducting glasses have been studied by analytical transmission electron microscopy equipped with high angle annular detector dark field (HAADF) detector and energy dispersive X-ray spectroscopy (EDS). Structural inhomogeneities of 5-10 nm in size are observed from HAADF images in the glass. Deference of composition between bright and dark contrast regions is clearly confirmed by EDS experiments. The nanoscale phase separation of 5-10 nm in size has been clarified by HAADF and EDS experiments.