Air-coupled ultrasonic investigation of stacked cylindrical rods

Measurement of the periodicities of diffraction gratings composed of stacked cylindrical rods is explored using an air-coupled ultrasonic technique. Acoustic Bragg scattering from three periodic structures is investigated by means of a polar scan. Consequently, Bragg angles and corresponding frequencies are obtained from angular spectrograms, using two different data acquisition approaches. According to the principle of Bragg scattering, the periodicities of the three periodic structures, which are equal to the diameter of the cylindrical rods, are determined. In order to evaluate the reliability of the technique and its accuracy, the obtained diameters are compared with those directly measured with a digital caliber. To show the robustness of the technique measurements are done with transducers of different quality.     

Fine structure of the diffraction image of an edge dislocation in high-resolution section topography

The propagation of an x-ray wave field in an elastic field of an edge dislocation crossing a scattering triangle exactly along the bisector of the scattering angle has been considered. The scattering of the x-ray wave field by a complex elastic field of the edge dislocation has been analyzed using the methods of geometrical optics. It has been established that the fine structure of a diffraction image of defects in thick crystals is determined by the differences in scattering of the normal and anomalous modes of the x-ray wave field in the vicinity of the Bragg reflection. In the case of thick crystals, the x-ray diffraction image of defects can have a symmetry different from the symmetry of the function of local misorientations of the crystal lattice. X-ray wave scattering by local distortions of the crystal lattice can occur according to two different mechanisms depending on the gradient of space changes in the deformation field. In the crystal regions where the elastic field varies slowly with a change in the distance, the x-ray wave field has had time to adjust itself to follow the course of deviations of the crystal lattice from the exact Bragg condition. In the crystal region where the elastic field changes significantly at distances of the order of the extinction length, this region leaves the reflecting position and interference scattering occurs at the interface of the region. It is important that the form of the deformation field in this case is of no significance.     

Soft X-ray resonant magnetic diffraction

We have conducted the first soft x-ray diffraction experiments from a bulk single crystal, studying the bilayer manganite La2-2xSr1+2xMn2O7 with x=0.475 in which we were able to access the (002) Bragg reflection using soft x rays. The Bragg reflection displays a strong resonant enhancement at the L(III) and L(II) manganese absorption edges. We demonstrate that the resonant enhancement of the magnetic diffraction of the (001) is extremely large, indeed so large that it exceeds that of the nonresonant Bragg diffraction. Resonant soft x-ray scattering of 3d transition metal oxides is the only technique for the atomic selective measurement of spin, charge, and orbital correlations in materials, such as high temperature superconductors, colossal magnetoresistance manganites, and charge stripe nickelates.     

Determination of the mechanism for resonant scattering in LaMnO3

The resonant multiple Bragg x-ray diffraction is used to study the forbidden (104) reflection in LaMnO3. Using the interference between the three-beam scattering and resonant scattering we can determine the phase of the resonant scattering. This phase is shown to be consistent with a model in which the resonant scattering is caused by the influence of the Mn-O bond length distortion rather than directly by the orbital ordering on the Mn 4p band structure.     

Dynamic fluctuations and static speckle in critical X-ray scattering from SrTiO3

We report a study of critical x-ray scattering from SrTiO3 near the antiferrodistortive structural phase transition at T(C) approximately 105 K. A line shape analysis of the thermal diffuse scattering results in the most precise experimental determination to date of the critical exponent gamma. The microscopic mechanism behind the anomalous "central peak" critical scattering component is clarified here by the first-ever observation of a static coherent diffraction pattern (speckle pattern) within the anomalous critical scattering of SrTiO3. This observation allows us to directly attribute the origins of the central peak to Bragg diffraction from remnant static disorder above T(C).     

Manipulating the magnetic structure with electric fields in multiferroic ErMn2O5

Based on measurements of soft x-ray magnetic diffraction under in situ applied electric field, we report on significant manipulation and exciting of commensurate magnetic order in multiferroic ErMn2O5. The induced magnetic scattering intensity arises at the commensurate magnetic Bragg position whereas the initial magnetic signal almost persists. We demonstrate the possibility to imprint a magnetic response function in ErMn2O5 by applying an electric field.     

Hexagonal order in crystalline and columnar phases of hard rods

We report a study of colloidal suspensions of highly monodisperse semiflexible chiral rodlike viruses, denoted fd, in the range of high concentrations. Small angle x-ray scattering experiments reveal the existence of two hexagonal phases: the first one is crystalline and the second one is hexatic columnar, as shown by its short-range positional order. The suspension of rodlike viruses is the first experimental system showing the whole phase sequence with increasing particle concentration theoretically predicted for systems of hard rods, ranging from the chiral nematic via the smectic to columnar and crystalline phases.     

Technical Reports: A Single-photon Counting Pixel Detector for Surface Diffraction Experiments

The intense flux delivered by third-generation synchrotron sources has opened up exciting new possibilities in surface diffraction (SD) studies [1–3]. Nonetheless, practical SD experiments are plagued by several technical problems. Because the crystalline surface is typically probed down to a depth of approximately 1 or 2 nm when using subcritical-angle incident X-ray beams, the scattering volume is only about 10^-12 cm³. This is further exacerbated by the fact that the most interesting information on the surface structure is generally obtained from those regions of diffraction features known as crystal truncation rods (CTRs) where scattering is weakest, i.e., in between Bragg peaks.     

Direct determination of strain and composition profiles in SiGe islands by anomalous x-Ray diffraction at high momentum transfer

Anomalous x-ray scattering is employed for quantitative measurements of the Ge composition profile in islands on Si(001). The anomalous effect in SiGe is enhanced exploiting the dependence of the complex atomic form factors on the momentum transfer. Comparing the intensity ratios for x-ray energies below and close to the K edge of Ge at various Bragg reflections in the grazing incidence diffraction setup, the sensitivity for the Ge profile is considerably enhanced. The method is demonstrated for SiGe dome-shaped islands grown on Si(001). It is found that the composition inside the island changes rather abruptly, whereas the lattice parameter relaxes continuously.     

Framework for three-dimensional coherent diffraction imaging by focused beam x-ray Bragg ptychography

We present the framework for convergent beam Bragg ptychography, and, using simulations, we demonstrate that nanocrystals can be ptychographically reconstructed from highly convergent x-ray Bragg diffraction. The ptychographic iterative engine is extended to three dimensions and shown to successfully reconstruct a simulated nanocrystal using overlapping raster scans with a defocused curved beam, the diameter of which matches the crystal size. This object reconstruction strategy can serve as the basis for coherent diffraction imaging experiments at coherent scanning nanoprobe x-ray sources.     

Observation of the Debye-Waller factor in a colloidal single crystal

Bragg diffraction spot intensities of a colloidal single crystal were found to exhibit a DebyeWaller factor-like decay. The Lindemann parameter and the mean-square displacement after infinite times of the colloidal particles could be obtained.     

多重散射理论声光耦合波方程的龙格-库塔法数值分析

提出利用直观、方便且具有普遍性的4阶龙格-库塔(R-K)方法求解基于多重散射理论推导出的声光耦合波方程, 模拟计算布喇格衍射下衍射效率随各关键参数的变化关系, 分析入射光偏离Bragg角对Bragg衍射光效率的影响程度, 以及最佳Bragg衍射效率所需参数的选取问题. 模拟结果表明：Q（Klein-Cook参数）=4π时Bragg衍射效率可达97%, 证实了特征长度作为选取声光互作用长度的合理性.     

原子吸收限附近完整晶体内的能流方向

研究了原子吸收限附近对称劳厄和布拉格情况下完整晶体内的能流方向．发现在对称劳厄情况下，只有当原子散射因子的虚部对衍射的贡献可以与实部的贡献相比较时，晶体内与色散面上某一结点相对应的能流会偏离色散面的实部的法向；而在对称布拉格情况下，即使在原子散射因子的虚部对衍射的贡献可以忽略时，在所谓的“全反射”区内也会偏离．当衍射仅由原子的虚部引起时，这种偏离在对称劳厄情况下最大，而在对称布拉格情况下最小． 关键词：     

A discotic disguised as a smectic: A hybrid columnar bragg glass

We show that discotics, lying deep in the columnar phase, can exhibit an x-ray scattering pattern which mimics that of a somewhat unusual smectic liquid crystal. This exotic, new glassy phase of columnar liquid crystals, which we call a "hybrid columnar Bragg glass," can be achieved by confining a columnar liquid crystal in an anisotropic random environment of, e.g., strained aerogel. Long-ranged orientational order in this phase makes single-domain x-ray scattering possible, from which a wealth of information could be extracted. We give detailed quantitative predictions for the scattering pattern in addition to exponents characterizing anomalous elasticity of the system.     

Diffuse x-ray scattering near Bragg peaks from point defects in a general lattice

Using the continuum theory of linear elasticity, diffuse x-ray scattering has been calculated in the immediate neighbourhood of Bragg peaks from point defects in a lattice containing more than one atom in the unit cell. General expressions are obtained for the Debye-Waller factor, Huang diffuse scattering and the asymmetric scattering due to the defect. For lattices with one atom per unit cell, these expressions reduce to the well-known formulae of diffuse scattering.     

Microstructure and dynamics near an attractive colloidal glass transition

The microstructure and dynamics of a colloidal system interacting via short-ranged interparticle potential is studied by ultra-small-angle x-ray scattering and x-ray photon correlation spectroscopy. A colloidal gas-liquid type transition is induced when the short-ranged attractive interactions attain sufficient magnitude. The development of liquidlike structure is preceded by a systematic transition in the particle dynamics from diffusive to constrained motion and then completely frozen behavior. This demonstrates the existence of a jamming transition induced by strong short-ranged attractive interactions even at low packing fractions.     

Nonlinear BLOCH-wave interaction and bragg scattering in optically induced lattices

We study, both theoretically and experimentally, the Bragg scattering of light in optically induced photonic lattices and reveal the key physical mechanisms which govern the nonlinear self-action of narrow beams under the combined effects of Bragg scattering and wave diffraction, allowing for selecting bands with different effective dispersion.     

Multiple-wave diffraction in high energy resolution back-reflecting x-ray optics

We have studied the effects of multiple-wave diffraction in a novel optical scheme recently published by Shvyd'ko et?al. utilizing Bragg diffraction of x?rays in backscattering geometry from asymmetrically cut crystals for achieving energy resolutions beyond the intrinsic width of the Bragg reflection. By numerical simulations based on dynamic x-ray diffraction and by experimentation involving two-dimensional angular scans of the back-reflecting crystal, multiple-wave diffraction was found to contribute up to several tens percent loss of efficiency but can be avoided without degrading the energy resolution of the original scheme by careful choice of azimuthal orientation of the diffracting crystal surface and by tilting of the crystal perpendicular to the dispersion plane.     

Right handed or left handed? Forbidden x-ray diffraction reveals chirality

Enantiomers, or stereoisomers, have crystal structures that are mirror images of each other and are thus handed, like our right and left hands. The physical properties of enantiomers are identical except for optical activity, which rotates linearly polarized light by equal amounts but in opposite directions. While conventional x-ray Bragg diffraction can determine crystal structures, it does not distinguish between right- and left-handed crystals. We show resonant Bragg diffraction using circularly polarized x rays reveals the handedness of crystals by coupling x-ray helicity to a crystal screw axis. The intensity of resonantly allowed reflection of alpha-quartz is well described by an admixture of a parity-even and a parity-odd process. Our results are of general importance and demonstrate a new method to directly study chiral motifs in structures that include biomaterials, liquid crystals, magnets, multiferroics, etc.     

Peculiarities of the formation of the X-ray diffraction image of a surface acoustic wave in grazing geometry

The x-ray diffraction image of a Bluestein-Gulyaev surface acoustic wave (SAW) at grazing angles of incidence is considered in the noncoplanar symmetric Laue geometry. It is assumed that the SAW propagation direction makes a small angle with the diffraction vector. It is shown that small deviations from the Bragg angle (～0.01″) due to SAWs that do not lead to a change in the reflection coefficient result in the formation of diffraction satellites for both standing and traveling SAWs. The recorded x-ray diffraction image representing the time-averaged intensity distribution has characteristic profiles for even-and odd-order satellites.