Digital processing of X-ray diffraction patterns from oriented fibers

Accurate measurement of intensity data from x-ray diffraction patterns of oriented fibers is one of the major difficulties in the determination of polymer structures. Accurate diffraction data are particularly important when discrimination between different, but similar, molecular models is required. Although digital processing of diffraction patterns has provided more accurate data than was obtainable by traditional measurements, many of the methods used have been partly subjective and restricted to well-resolved diffraction patterns. Background is a major source of error in intensity measurement. A general method of two-dimensional background removal has been developed. Objective methods of measuring the intensities of Bragg reflections from x-ray diffraction patterns of polycrystal-line fibers are described. A profile fitting method (which is an extension of the previously reported angular deconvolution procedure) for measuring diffraction data from noncrystalline oriented polymers is also presented. These methods have been used to collect data from diffraction patterns of a variety of nucleic acid polymers.     

Microstructure and strain analysis of GaN epitaxial films using in-plane grazing incidence x-ray diffraction

This paper investigates the major structural parameters,such as crystal quality and strain state of (001)-oriented GaN thin films grown on sapphire substrates by metalorganic chemical vapour deposition,using an in-plane grazing incidence x-ray diffraction technique.The results are analysed and compared with a complementary out-of-plane xray diffraction technique.The twist of the GaN mosaic structure is determined through the direct grazing incidence measurement of (100) reflection which agrees well with the result obtained by extrapolation method.The method for directly determining the in-plane lattice parameters of the GaN layers is also presented.Combined with the biaxial strain model,it derives the lattice parameters corresponding to fully relaxed GaN films.The GaN epilayers show an increasing residual compressive stress with increasing layer thickness when the two dimensional growth stage is established,reaching to a maximum level of-0.89 GPa.     

Diffraction and external reflection by dielectric faceted particles

The scattering of light by dielectric particles much larger than the wavelength of incident light is attributed to diffraction, external reflection and outgoing refracted waves. This paper focuses on diffraction and external reflection by faceted particles, which can be calculated semi-analytically based on physical optics. Three approximate methods; the surface-integral method (SIM), the volume-integral method (VIM), and the diffraction plus reflection pattern from ray optics (DPR) are compared. Four elements of the amplitude scattering matrix in the SIM and the VIM are presented in an explicit form. Of interest is that diffraction and external reflection are separable in the SIM, whereas they are combined in the VIM. A feature of zero forward reflection is noticed in the SIM. The applicability of the DPR method is restricted to particles with random orientations. In the manner of van de Hulst, we develop a new technique to compute the reflection pattern of randomly oriented convex particles using spheres with the same refractive index, resulting in an improvement in the precision of the reflection calculation in near-forward and near-backward directions. The accuracy of the aforementioned three methods is investigated by comparing their results with those from the discrete-dipole-approximation (DDA) method for hexagonal particles at the refractive index of 1.3+i1.0. For particles with fixed orientations, it is found that the SIM and the VIM are comparable in accuracy and applicable when the size parameter is on the order of 20. The ray-spreading effect on the phase function is evident from the results of various size parameters. For randomly oriented particles, the DPR is more efficient than the SIM and the VIM.     

Method of Coupled Waves in the Theory of Diffraction of Light by Elastic Waves in Crystals

Diffraction of light by elastic waves in crystals is described by the method of coupled waves in a form different from that used by other researchers. The difference is determined by the treatment of two pairs of orthogonal coordinate systems whose principal axes are oriented along the directions of phase and energy transfer of two optical waves interacting on a sound wave. Due to this, the equations of coupled waves assume the most compact form, which was previously unknown for crystals. These equations are easily solved by the conventional methods in terms of quasi-plane waves and also admit of a wider class of solutions for bounded interaction regions. Two different diffraction regimes are compared in the present work, namely, the transmission and reflection diffraction. It is indicated that the suggested approach allows one to refine the parameters that define the efficiency of diffraction of light by elastic waves in crystals.     

发散X射线晶体衍射模拟研究

根据晶体的对称性、衍射几何和衍射规律,研究了复杂的发散X射线晶体衍射。描述了模拟这种衍射的方法。由计算机产生的背射赝Kossel线花样与实验结果完全相符,并能识别出衍射图中所有线条的衍射指数。完成了一套由计算机绘制的〈100〉,〈110〉和〈111〉取向的Si单晶的发散衍射标准图谱。 关键词：     

Recovery of concentration spectra of binary solids from diffraction profiles by means of band matrices

A method for the retrieval of concentration spectra of crystalline mixtures from x-ray diffraction profiles is described. Both spectra are associated with an integral equation which can be simplified to yield a set of linear equations. Solutions are readily obtained by triangular decomposition since the equations are typically described by band matrices. The method has been tested with simulated diffraction profiles to allow for a variety of options concerning the concentration spectra. The procedure is well suited for binary alloys containing crystals of different structure and lattice parameters. The time consumption of the calculations is significantly reduced as compared to hitherto available methods.     

Resonant soft x-ray scattering from stepped surfaces of SrTiO3

We studied the resonant diffraction signal from stepped surfaces of SrTiO(3) at the Ti 2p → 3d (L(2,3)) resonance in comparison with x-ray absorption (XAS) and specular reflectivity data. The steps on the surface form an artificial superstructure suitable as a model system for resonant soft x-ray diffraction. A small step density on the surface is sufficient to produce a well defined diffraction peak. We determined the optical parameters of the sample across the resonance and found that the differences between the energy dependence of the x-ray absorption signal, the specular reflectivity and the step-related peak reflect the different quantities probed in these signals. When recorded at low incidence or detection angles, XAS and specular reflectivity spectra are strongly distorted by the changes of the angle of total reflection with energy. The resonant diffraction spectrum is less affected and can be used as a spectroscopic probe even in less favorable geometries.     

粉末衍射谱图分解的模拟退火法

将模拟退火法应用于中子和x射线粉末衍射谱图分解研究中. 该方法有两个主要优点：一是 解谱结果不依赖于峰参数初始值的选取，可以任意给定峰参数初始值而不影响收敛性，因而 能克服传统最小二乘拟合法在拟合多峰严重重叠的复杂谱图时遇到的初始解的选取困难；二 是具有寻找全局最优解的能力，可有效解决谱图分解在数学上的多解性问题，这对于因多峰 重叠而可能存在多个局部最优解的谱图分解很有益处. 详细描述了方法的计算步骤，讨论了 有关参数设置，并通过模拟谱和实际谱例子对模拟退火法与传统最小二乘拟合法进行了比较 ，阐明了前者在处理复杂谱图时的独特优越性. 原则上该方法也可应用到与粉末衍射谱类似 能用峰形函数描述的其他实验谱的拟合研究中. 关键词： 谱图分解 模拟退火法 粉末衍射 分峰     

Modelling x-ray scattering from quantum dots using Keating energy-minimised structures

In a traditional analysis of surface x-ray diffraction data, the surface unit cell can be defined by a small set of parameters, and fitting of experimental data is accomplished using well-established procedures. A quantum dot (QD), however, may contain as many as 20,000 atoms, so a different approach to data analysis is required. A method for modelling a quantum dot and relaxing the structure by minimising the Keating energy is presented, and the simulation of x-ray scattering from such models is described. A method is then developed for simulating the alloying of InAs and GaAs inside the QDs using intermediate Keating parameters. This removes the need to relax and average multiple models with randomly distributed atoms, which would increase the computation time significantly.     

Quantitative imaging of single, unstained viruses with coherent x rays

We report the recording and reconstruction of x-ray diffraction patterns from single, unstained viruses, for the first time. By separating the diffraction pattern of the virus particles from that of their surroundings, we performed quantitative and high-contrast imaging of a single virion. The structure of the viral capsid inside a virion was visualized. This work opens the door for quantitative x-ray imaging of a broad range of specimens from protein machineries and viruses to cellular organelles. Moreover, our experiment is directly transferable to the use of x-ray free electron lasers, and represents an experimental milestone towards the x-ray imaging of large protein complexes.     

Investigation of the structure of multilayer lipid membranes by real-time neutron diffraction

This paper reports on the results of neutron diffraction experiments on the study of structural changes in multilayer lipid membranes as a function of the degree of hydration. The experiments have been performed on a time-of-flight diffractometer at the IBR-2 pulsed reactor (Joint Institute for Nuclear Research, Dubna, Russia) with a dipalmitoylphosphatidylcholine (DPPC) multilayer membrane oriented on a quartz plate. The structural parameters have been determined from the simultaneously measured several (up to five) diffraction orders of reflection, which has made it possible to calculate the profile of the DPPC bilayer structure. A high rate of the measurement of diffraction patterns has allowed one to trace the evolution the lamellar structure of the lipid bilayer in the course of its hydration and dehydration. The minimum time of accumulation of the necessary statistics is 3 min, which has made it possible to determine the characteristic times of transition processes in the membrane with a high accuracy.     

热处理引起3C-ZnS结构转变的X-射线衍射分析

为了论证层错是硫化锌晶体中交流电致发光的一个必要条件,我们把3C-ZnS单晶体在1100℃热处理后引入了层错.同时,我们对热处理前后的结构,用劳埃背反射法和文献[8、13]推导的公式进行了分析.结果表明,沿3C-结构<111>四个等价方向都可以产生无序、孪晶和2H-结构,而且当热处理时间足够长时,结构转变趋向于一个<111>方向.这些实验结果,在有关的文献中尚未见到.     

Atomic structure of cadmium sulfide nanoparticles

A method for calculating the x-ray diffraction patterns of cadmium sulfide nanoparticles with a disordered internal structure, a real surface, shape, and size is proposed within the kinematic theory of scattering. A computer analysis has revealed that the characteristic shape of the experimental x-ray diffraction patterns of cadmium sulfide films and powders is determined by a specific disordered nanoparticle structure differing from the crystal structures of wurtzite and sphalerite. According to the computer simulation, cadmium sulfide nanoparticles synthesized through chemical deposition have a shape similar to a hexagonal prism with a characteristic size of approximately 5 nm.     

Testing the Possibility of Average-Color Perception from Multi-Colored Patterns

To test the possibility that an average color is perceived from a multi-colored pattern, the appearance of colored mosaic patterns as a whole was measured by the method of adjustment. As the range of color distribution in a mosaic pattern became larger, subjects matches deviated more from the photometric averages of each pattern and the subjects perceived higher brightness from mosaic patterns. Since the saliency of element colors was different in an equiluminant mosaic pattern, two possible hypotheses for selecting a color which represents a mosaic pattern was examined by using brightness match results for each element color. The results show that the mosaic element with the highest-saturation strongly influences the choice of a color to represent a mosaic pattern.     

Diamond anvil cell radial x-ray diffraction program at the National Synchrotron Light Source

During the past decade, the radial x-ray diffraction method using a diamond anvil cell (DAC) has been developed at the X17C beamline of the National Synchrotron Light Source. The detailed experimental procedure used with energy dispersive x-ray diffraction is described. The advantages and limitations of using the energy dispersive method for DAC radial diffraction studies are also discussed. The results for FeO at 135?GPa and other radial diffraction experiments performed at X17C are discussed in this report.     

Structural aspects of solid-state amorphization in Eu<Subscript>2</Subscript>(MoO<Subscript>4</Subscript>)<Subscript>3</Subscript> single crystals

X-ray diffraction studies of Eu₂(MoO₄)₃ single crystals were performed, which demonstrate that, in contrast to polycrystalline samples, these crystals do not exhibit amorphous-like diffraction patterns during the reverse transition from the high-pressure phase into the initial β phase; rather, the diffracted intensity in their diffraction patterns decreases significantly to the background. Such a diffraction pattern can be explained under the assumption that a single crystal is divided into small (nanoscopic) regions inside which the lattice parameters of the high-pressure phase and the initial β phase change continuously. The simultaneous recovery of the single-crystal state of the β phase from this intermediate state in all nanoscopic regions as the annealing temperature increases indicates that nanocrystals in this state are structurally correlated with each other. This result suggests that the halo-type diffraction patterns of polycrystalline samples reflect an intermediate state between the high-pressure phase and the β phase in every initial crystallite (as in the single crystals) rather than being caused by an amorphous structure of the sample. In this case, the total diffraction pattern of differently oriented crystallites gives an amorphous-like diffraction pattern reflecting the contributions from numerous various crystallographic planes involved in diffraction.     

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.