Tutorial on x-ray microLaue diffraction

MicroLaue diffraction combines the oldest x-ray diffraction method–Laue diffraction–with the most modern x-ray sources, optics and detectors. The combination can resolve complex materials into single-crystal-like submicron volumes. This unique ability to nondestructively map crystal structure at and below a sample surface, with high spatial and strain resolution can address long-standing fundamental issues in materials science. For example, the three-dimensional evolution of mesoscale structure and the self organization of defects can be observed nondestructively to understand the origins of inhomogeneous grain growth, deformation and fracture.     

Second order wave diffraction by large cylinders

A non-linear mathematical model of diffraction theory is formulated to evaluate the wave forces on large cylinders. An attempt is made to amend the coefficient of mass C_M arising in the Morison equation on the linear theory by introducing second-order effects on the irrotational flow part of the wave loading. Analytical solutions are obtained and compared with the experimental data collected by the Hydraulics Laboratory of the National Research Council of Canada, Ottawa. The comparison shows favourable agreement.     

Unit cell parameters of wurtzite InP nanowires determined by x-ray diffraction

High resolution x-ray diffraction is used to study the structural properties of the wurtzite polytype of InP nanowires. Wurtzite InP nanowires are grown by metal-organic vapor phase epitaxy using S-doping. From the evaluation of the Bragg peak position we determine the lattice parameters of the wurtzite InP nanowires. The unit cell dimensions are found to differ from the ones expected from geometric conversion of the cubic bulk InP lattice constant. The atomic distances along the c direction are increased whereas the atomic spacing in the a direction is reduced in comparison to the corresponding distances in the zinc-blende phase. Using core/shell nanowires with a thin core and thick nominally intrinsic shells we are able to determine the lattice parameters of wurtzite InP with a negligible influence of the S-doping due to the much larger volume in the shell. The determined material properties will enable the ab initio calculation of electronic and optical properties of wurtzite InP nanowires.     

High-resolution ab initio three-dimensional x-ray diffraction microscopy

Coherent x-ray diffraction microscopy is a method of imaging nonperiodic isolated objects at resolutions limited, in principle, by only the wavelength and largest scattering angles recorded. We demonstrate x-ray diffraction imaging with high resolution in all three dimensions, as determined by a quantitative analysis of the reconstructed volume images. These images are retrieved from the three-dimensional diffraction data using no a priori knowledge about the shape or composition of the object, which has never before been demonstrated on a nonperiodic object. We also construct two-dimensional images of thick objects with greatly increased depth of focus (without loss of transverse spatial resolution). These methods can be used to image biological and materials science samples at high resolution with x-ray undulator radiation and establishes the techniques to be used in atomic-resolution ultrafast imaging at x-ray free-electron laser sources.     

Synthesis and x-ray diffraction characterization of nanocrystalline ZnO obtained by Pechini method

Nanocrystalline zinc oxide powders were successfully prepared by Pechini method. The polymeric precursors were prepared using zinc acetate and a mixed solution of citric acid and ethylene glycol as a chelating agent and reaction medium respectively. The polymeric precursors were calcined at temperatures from 500 to 900°C for 1 h. The resulting powders were characterized by x-ray powder diffraction, thermogravimetry, and Fourier-transform infrared spectroscopy. Well-crystallized zinc oxide was obtained at low-temperature about 500°C. The average crystallite size was estimated as 47–73 nm in the range of 500–900°C and the lattice parameters were compatible with the values found in literature. The text was submitted by the authors in English.     

Determination of oxygen to metal ratio of U-Pu mixed oxides by x-ray diffraction

The possibility of measuring the oxygen-metal ratio (O/M) of U-Pu mixed oxides by x-ray diffraction technique has been explored. In single-phase U-Pu mixed oxides, the lattice parameter vs O/M plots for different plutonium concentrations are drawn by interpolation of lattice parameter values between those of UO₂, PuO₂ and Pu₂O₃. These plots are then used for determining the O/Ms of unknown samples against their experimentally measured lattice parameter values. In two-phase mixed oxides, the mole fractions of the two phases are determined from the intensities of their selected diffraction lines. The O/M of the mixed oxide is then given by the mole average of the individual O/Ms of the two phases.     

Crystallization study of chemically vapour-deposited amorphous silicon films by in situ x-ray diffraction

The solid phase crystallization kinetics of chemically vapour-deposited amorphous silicon films were studied by in situ X-ray diffraction. We determined the crystalline volume directly from the Bragg peak intensities at various times during isothermal annealing in the temperature range 578 °C < T < 658 °C. From these experiments we deduced that the crystallization was due to nucleation predominantly at the substrate-film interface followed by crystal growth perpendicular to this interface. The crystal growth rate was thermally activated with an activation energy E_v of 3.1 eV. A strong 〈111〉 preferred orientation of the growing polycrystal was observed and the grain size remained constant at about 60 nm. Evidence of stresses at the amorphous-crystalline interface during the early stages of crystallization was observed. A comparison with previous conductivity measurements is also carried out.     

Patterning-induced strain relief in single lithographic SiGe nanostructures studied by nanobeam x-ray diffraction

The continued downscaling in SiGe heterostructures is approaching the point at which lateral confinement leads to a uniaxial strain state, giving high enhancements of the charge carrier mobility. Investigation of the strain relaxation as induced by the patterning of a continuous SiGe layer is thus of scientific and technological importance. In the present work, the strain in single lithographically defined low-dimensional SiGe structures has been directly mapped via nanobeam x-ray diffraction. We found that the nanopatterning is able to induce an anisotropic strain relaxation, leading to a conversion of the strain state from biaxial to uniaxial. Its origin is fully compatible with a pure elastic deformation of the crystal lattice without involving plastic relaxation by injection of misfit dislocations.     

衍射法X射线激光分束光栅平行度测量系统(英文)

介绍了软X射线光栅分束镜Mach-Zehnder干涉等离子体诊断系统调整用双频光栅线条平行度的衍射法测量系统.该系统主要由激光器,准直镜,待测光栅,精密转台(含角度测量仪),直线工作台,光栅调节架和探测器组成.分析了系统中各种误差对测量精度的影响其中包括距离测量误差、波长误差、光栅准直误差即光栅刻线与入射光和反射光组成的平面不垂直、光栅转动过程的误差、光栅表面面型误差、探测器误差,经计算得到系统的绝对误差为minute.计算表明,该系统的测量精度满足软X射线Mach-Zehnder干涉系统对双频调整光栅的性能要求.     

Microstructure of individual grains in cold-rolled aluminium from orientation inhomogeneities resolved by electron backscattering diffraction

The deformation structure within individual grains of a deformed material is resolved by electron backscattering diffraction. The employed evaluation scheme for local orientation data is illustrated on cold-rolled aluminium. The orientation distribution of each grain is characterized by an averaged orientation spread and its anisotropy; the dependence of both parameters on grain size and grain orientation is discussed. The preferred rotation axis in each grain is determined and shows a dominant orientation spreading around the transversal direction. Characteristic features of the deformation structure (as alternating orientation differences or orientation gradients) are resolved from sign-carrying disorientation angles defined with respect to the preferred rotation axis in each grain. Five components of the dislocation density tensor – corresponding to part of the geometrically necessary dislocation content – are inferred from the local curvatures. The spatially inhomogeneous distribution of the dislocation density offers a new possibility for identifying dislocation boundaries.     

High efficiency, high quality x-ray optic based on ellipsoidally bent highly oriented pyrolytic graphite crystal for ultrafast x-ray diffraction experiments

By the use of a thin highly oriented pyrolytic graphite crystal (HOPG) bent to a high-performance ellipsoidal shape it was possible to focus monochromatic x-rays of 4.5 keV photon energy with an efficiency of 0.0033, which is 30 times larger than for previously used bent crystals. Isotropic Ti K alpha radiation of a 150 microm source was focused onto a 450 microm spot. The size of the focal spot can be explained by broadening due to the mosaic crystal rocking curve. The rocking curve width (FWHM) of the thin graphite foil was determined to 0.11 degrees. The estimated temporal broadening of an ultrashort K alpha pulse by the crystal is not larger than 300 fs. These properties make the x-ray optic very attractive for ultrafast time-resolved x-ray measurements.     

Computer-aided prediction and analysis of electron and x-ray diffraction patterns

Using a personal computer, electron and x-ray diffraction patterns are analytically generated and printed to scale. The structure factor equation is used to determine which crystalline planes diffract according to the supplied crystal lattice type, atoms present and their positions in the unit cell, lattice dimension(s), crystal orientation, and radiation wavelength. Single crystal spot and Kikuchi electron diffraction patterns as well as polycrystalline ring patterns can be generated. Powder x-ray diffraction patterns are also generated using this code. Complex composite patterns are generated by overlaying multiple patterns resulting from crystallographic orientation effects. A user friendly program with a direct approach to generate diffraction patterns for any defined crystal aids in the analysis and indexing of these patterns.     

Toward the diffraction limit with transmissive x-ray lenses in astronomy

We develop an analytical approach to refractive, blazed diffractive, and achromatic x-ray lenses of scalable dimensions for energies from 1 to 20 keV. Based on the parabolic wave equation, their wideband imaging properties are compared and optimized for a given spectral range. Low-Z lens materials for massive cores and rugged alternatives, such as polycarbonate or Si for flat Fresnel components, are investigated with respect to their suitability for diffraction-limited high-energy astronomy. Properly designed "hybrid" combinations can serve as an approach to x-ray telescopes with an enhanced efficiency throughout the whole considered band, nearly regardless of their inherent absorption.     

Residual stress measurements on chromium films by x-ray diffraction using the sin2ψ method

Residual stresses in chromium films vacuum deposited by electron beam evaporation onto beryllium substrates were measured by X-ray diffraction. A minute peak shift of the diffraction profile reveals the presence of strain and hence stress. Detection of the shift was made possible by fitting the experimental data to a modified Lorentz function and by then subjecting the fit to a regression analysis. Computer aid was utilized extensively. Stresses, both tensile and compressive, of 10⁹–10¹⁰ dyn cm^-2 were found for substrate temperatures in the range 300– 550 °C. Stress mechanisms are discussed.     

Crystallite-size distribution and dislocation structure in nanocrystalline HfNi5 determined by x-ray diffraction profile analysis

A rapidly quenched nanocrystalline Hf11Ni89 alloy was produced by melt-spinning. The x-ray phase analysis shows that the as-quenched ribbon consists mainly of nanocrystalline fcc HfNi5 although a small amount of Ni(Hf) solid solution is also detected. The crystallite size distribution and the dislocation structure of the dominant HfNi5 phase were determined by a recently developed method of diffraction profile analysis. In this procedure, by assuming spherical shape and log-normal size distribution of crystallites, the Fourier coefficients of the measured physical profiles are fitted by the Fourier coefficients of well established ab initio functions of size and strain peak profiles. The anisotropic broadening of peak profiles is accounted for by the dislocation model of the mean square strain in terms of average dislocation contrast factors. It was found that the median and the variance of the crystallite size distribution are 3.3 nm and 0.82, respectively. The dislocation density is 3.7 x 10(16) m-2 and the character of dislocations is nearly pure screw. The results obtained from x-rays were in good agreement with transmission electron microscopy observations.     

Quantitative analysis of grain size in bimodal powders by x-ray diffraction and transmission electron microscopy

In most studies related to milled powders, the grain size¹ is analyzed via X-ray diffraction (XRD) experiments, and a transmission electron microscopy (TEM) image with high magnification, if provided, is used primarily to confirm the results obtained by XRD experiments. This widely used approach is reasonable in light of the difficulties associated with TEM sample preparation. The present study, however, addresses the hypothesis that such an approach may not be valid when there is an inhomogeneous distribution of grains present. TEM examination, carried out in carefully prepared Al-7.5 wt% Mg samples, in which a global region is observable by TEM, provided the opportunity for quantitative analysis of grain size in cryomilled powders having an inhomogeneous distribution of grain sizes. The cryomilled Al-7.5 wt% Mg had a bimodal grain microstructure of 77% (area fraction) fine grains in the range of 10 to 60 nm and 23% coarse grains of approximately 1 m. The results show that the XRD analysis yields a grain size that is close to that present in the fine-grained regions (i.e., 10–60 nm). The present study also systematically investigated the influence of the nine possible combinations of the Cauchy (C) and the Gaussian (G) approximations on the calculated grain size value, and the results show that the CC-CC approximation resulted in the largest calculated grain size, the GG-GG generated the smallest one, and the CG-CG, the approximation recommended by Klug and Alexander [1], led to a calculated grain size that is approximately equal to the average one from the CC-CC and GG-GG approximations. The maximum possible fluctuation of grain size values stemming from the various approximations is 38%.     

对医用X射线机焦点检测条件的探讨

主要根据X射线机的焦点检测提出简单可行又不影响数据判断的检测方法,提出与同行探讨。     

High temperature x-ray diffraction studies on Cr-doped V2O3

X ray powder diffraction on high purity (Cr_0.01V_0.99)₂O₃ and (Cr_0.033V_0.967)₂O₃ prepared by the arc-melting technique has been carried out in the temperature range of room temperature to 500°C. The room temperature rhombohedral structure of (Cr_0.01V_0.99)₂O₃ is found to undergo, in agreement with earlier results, a gradual transition to an isomorphous, high-temperature rhombohedral structure over a temperature range of 50–200°C. The percentage of the two phases in this coexistence range has been determined at different temperatures from the relative X ray intensities. This is found to depend on the thermal history of the sample and shows considerable hysteresis between heating and cooling cycles. Annealing of the material at 1600°C is found to stabilize the low temperature form and to broaden the temperature region of the transition. The temperature interval of the electrical anomaly correlates well with the two-phase interval. The lattice parameters and their temperature coefficients have been determined for all the phases.