Higher-order Bragg Reflections Research Articles

Taking Bragg Coherent Diffraction Imaging to Higher Energies at Fourth Generation Synchrotrons: Nanoscale Characterization

High-energy Bragg coherent diffraction imaging (BCDI) can enable three-dimensional imaging of atomic structure within individual crystallites in complex environments. Here, we show that sufficient coherent photon flux is available to extend the BCDI technique to higher energies to (1) obtain improved strain information and sensitivity at the nanoscale with higher order Bragg reflections, (2) exploit BCDI in embedded materials or complex operando environments, (3) reduce X-ray induced sample modification, and (4) minimize dynamical scattering effects. We demonstrate the nanoscale imaging technique on the same sub-micrometer sized crystal at 8.5, 19.9, and 33.4 keV by taking advantage of the brilliance and coherence of the fourth generation Extremely Brilliant Source of the ID01 beamline at ESRF - The European Synchrotron (Grenoble, France). The photon flux, data quality, resolution and strain information are compared. We also show the first coherent diffraction measurements performed at the ID31-EBS beamline at an energy of 41 keV.

A Compact Ultrafast Electron Diffractometer with Relativistic Femtosecond Electron Pulses

We have developed a compact relativistic femtosecond electron diffractometer with a radio-frequency photocathode electron gun and an electron lens system. The electron gun generated 2.5-MeV-energy electron pulses with a duration of 55 ± 5 fs containing 6.3 × 104 electrons per pulse. Using these pulses, we successfully detected high-contrast electron diffraction images of single crystalline, polycrystalline, and amorphous materials. An excellent spatial resolution of diffraction images was obtained as 0.027 ± 0.001 Å−1. In the time-resolved electron diffraction measurement, a laser-excited ultrafast electronically driven phase transition in single-crystalline silicon was observed with a temporal resolution of 100 fs. The results demonstrate the advantages of the compact relativistic femtosecond electron diffractometer, including access to high-order Bragg reflections, single shot imaging with the relativistic femtosecond electron pulse, and the feasibility of time-resolved electron diffraction to study ultrafast structural dynamics.

Diameter measurement of optical nanofiber based on high-order Bragg reflections using a ruled grating.

A convenient method using a commercially available ruled grating for precise and overall diameter measurement of optical nanofibers (ONFs) is presented. We form a composite Bragg reflector with a micronscale period by dissolving aluminum coating, slicing the grating along ruling lines, and mounting it on an ONF. The resonant wavelengths of high-order Bragg reflections possess fiber diameter dependence, enabling nondestructive measurement of the ONF diameter profile. This method provides an easy and economic diagnostic tool for wide varieties of ONF-based applications.

ADF-STEM Imaging of Nascent Phases and Extended Disorder Within the Mo–V–Nb–Te–O Catalyst System

Materials investigated for their potential use as heterogeneous selective oxidation catalysts may sometimes show highly ordered regions at the nanoscale which are embedded within highly disordered matrices from which they nucleate. These are often referred to as X-ray amorphous due to the lack of higher-order Bragg reflections; however, here we use annular dark-field scanning transmission electron microscopy (ADF-STEM) real space imaging to characterize the local structure of nanometer size domains of compositionally and structurally complex nascent oxide phases present in multi-phase disordered solids. These images have been obtained using aberration-corrected scanning transmission electron microscopy and point to its potential for local structural characterization where the synthesis conditions for a particular phase are not optimized or where self-assembly to extended structures has been locally hindered. Such studies may lead to identification of new catalysts, provided their targeted synthesis can be scaled up.

Reflection spectra of distorted cholesteric liquid crystal structures in cells with interdigitated electrodes

We studied the appearance of second- and third-order Bragg reflections in cholesteric liquid crystals (CLCs) in cells where the electric field was perpendicular to the helical axis. Second-order reflections with reflectance values as large as 80% of the first-order one were observed in the gap regions of alignment cells with interdigitated electrodes for CLC mixtures with pitches in the range 0.5-1.0 μm upon application of a field. The characterization was enabled by local probing of the CLC using a microspectrophotometer. LC cells that are transparent in the visible spectrum in the off-state and become colored upon application of a field due the second- or third-order reflection band appearance were demonstrated. The spectral position of the higher-order Bragg reflections can also be tuned by adjusting the magnitude of the electric field.

Neutron–electron scattering length deduced from Pendellösung interferometry in neutron Bragg reflections on silicon

A new method to deduce the neutron–electron scattering length from high-precision thermal-neutron measurements of the nuclear scattering length and of the scattering amplitudes of Bragg reflections is proposed. It consists of an extension of a Pendellösung interferometric technique proposed by Shull in 1968 to higher-order Bragg reflections in silicon. Error-bar estimates show that it could solve the ambiguity between disagreeing experimental values of the neutron–electron scattering length and provide a very precise temperature factor of silicon.

Time-of-flight implementation of an ultra-small-angle neutron scattering instrument

We report calculations describing the Bonse-Hart ultra-small-angle neutron scattering (USANS) instrument with triple-bounce Si channel-cut crystals, which show that significant gains in Q-resolution and neutron flux can be achieved using multiple high-order Bragg reflections. These reflections become usable only after combining the Bonse-Hart and time-of-flight (t-o-f) techniques, thus this variant of the USANS camera needs a pulsed neutron source. We demonstrate that t-o-f USANS instruments installed, for example, at the SNS water moderator will improve the current state of the art. Through the use of multiple wavelengths, these will provide means to detect multiple scattering effects.

Neutron charge radius deduced from Bragg reflection technique

The possibility of the determination of the neutron mean square charge radius from high-precision thermal-neutron measurements of the nuclear scattering length and of the scattering amplitudes of Bragg reflections is considered. Making use of the same interferometric technique as Shull in 1968, the scattering amplitudes of about eight higher-order Bragg reflections in silicon could be measured without contamination problem. This would provide a value of the neutron charge radius as precise as the disagreeing Argonne-Garching and Dubna values, as well as a Debye-Waller factor of silicon ten times more precise than presently available.

A perfect crystal X-ray analyser with meV energy resolution

We present a new method to construct a spherical crystal X-ray energy analyser. The energy analysis is based on high order Bragg reflections from a silicon perfect crystal at angles very close to 90°. In order to preserve the perfect crystal properties in a focusing optics, necessary for meV energy resolution and large angular acceptance, we developed a procedure to mount ≈12 000 small crystals, obtained from the same silicon wafer, on a spherical substrate. The method is based on computer controlled glueing and cycles of etching for each crystal. We obtained analysers with an energy resolution of 1.7±0.5 meV for 21.75 keV X-rays, using the Si(11 11 11) reflection, and with 25 mrad 2 angular acceptance. These analysers have been specifically developed for high energy resolution inelastic X-ray scattering.

Recording of efficient high-order Bragg reflectors in optical fibres by mask image projection and single pulse exposure with an excimer laser

A technique using high resolution mask projection for creating efficient Bragg grating reflectors in optical fibres by single excimer laser pulse exposure is described. Using a deep UV projection system with a large image field size and micrometre resolution, gratings with periods between 1 and 6 µm have been recorded in Ge-doped fused silica fibres that produce high order Bragg reflections in the wavelength range 1.43–1.65 µm.

A Laboratory EXAFS Study with Higher-Order Bragg Reflection by Means of the Fluorescence Monitoring Technique

A Laboratory EXAFS study has been tested by using higher-order Bragg reflections of Ge(440), Ge(333) and Ge(444). A single crystal spectrometer was employed and the incident x-ray intensity was monitored by measuring the fluorescent radiation from a suitable material placed in front of a sample. Good EXAFS spectra were obtained for relatively heavy elements of Se, Y and Zr with this technique. In addition, high intensity photon fluxes have been obtained, which are 6 and 3 times stronger than the case of double-crystal spectrometer at photon energies of 12 and 16 keV, respectively.

Adaptive crystal optics for high power synchrotron sources

Abstract We report successful operation of the first X-ray monochromator with built-in correction for the thermal strain field created by a high power X-ray beam. The 27 pole wiggler magnet at the National Synchrotron Light Source provides a total power load of 330 W in a beam 60 mm wide. A (220) silicon monochromator system has been tested; the compensated deformation field contributes only 2 arc sec full width at half maximum intensity to the monochromator Darwin width of high order Bragg reflections.

Effect of Higher-Order Spherical Aberration Term on Transfer Function in Electron Microscopy

The effect of the higher-order spherical aberration coefficient on the transfer function in transmission electron microscopy was calculated. In order to simplify the system, the optical illumination system was assumed to be perfectly coherent and axially symmetric. The result shows that the effect of the fifth-order spherical aberration coefficient, C5, on the usual transfer function with the third-order spherical aberration coefficient C5≡C3=0.5 mm for 100 keV electrons cannot be neglected, if high-order Bragg reflections from net planes with smaller lattice spacings than 0.1 nm are utilized for lattice imaging. The effect of the higher-order term due to the defocussing on the transfer function is also discussed.

Electron diffraction in porous silicon

Electron diffraction patterns, obtained in a high-voltage electron microscope (HVEM), of silicon containing a high density of small pores (diameter ca. 5 nm) produced by anodic etching show an enhancement of high-order Bragg reflections at the expense of low-order Bragg reflections. A theory of this effect is developed based on multiple scattering of Bloch waves at the pores. The theory allows the determination of the volume fraction of the pores from quantitative diffraction data. The results of this analysis are in good agreement with those obtained from HVEM images.

Theory of multilayer neutron monochromators

The theory of the reflecting properties of multilayer monochromators is developed on the basis of both the kinematical and the dynamical theory of neutron scattering with emphasis on the way in which the flux and polarization of the reflected beam depends on the parameters that characterize the multilayer. The effect of random variations in layer thickness is investigated using a cumulant expansion method. The contamination of the reflected beam due to both higher-order Bragg reflections and specular reflection is also discussed.

Analysis of high resolution electron microscope images of the Pd 2Si-Si interface

High resolution electron micrographs have been obtained from Pd 2Si-Si(111) interfaces viewed edge on and a detailed analysis of the interface structure has been carried out using computer simulations of the images. Since the stacking sequence of hexagonal Pd 2Si is AαAαAα…, the question whether the interface plane of Pd 2Si is silicon rich, A, or silicon deficient, α, has been investigated. An advancing interface cannot be planar at all stages of growth; therefore the question of interface roughness along the direction of the electron beam and twinning orientations has been considered. This has been modeled by Fourier shift techniques incorporated into multislice dynamical theory and, of course, is complicated by the dynamical diffraction conditions of the structure and the contributions of high order Bragg reflections to image detail. It has been possible to access the image features present in Pd 2Si/Si micrographs and to point out the difficulties which are encountered not only in this system but in a wide variety of interface structures by high resolution electron microscopy. Perhaps the most important finding of this study is that the interface region contains a mixture of silicon-rich and silicon-deficient Pd 2Si planes adjacent to the silicon side of the interface.

Analysis of High Resolution Electron Microscope Images of the Pd2Si-Si Interface

High resolution electron micrographs have been obtained from Pd2Si-Si(111) interfaces viewed edge on and a detailed analysis of the interface structure has been carried out using computer simulations of the images. Since the stacking sequence of hexagonal Pd2Si is AαAαAα..., the question whether the interface plane of Pd2Si is silicon rich, A, or silicon deficient, α, has been investigated. An advancing interface cannot be planar at all stages of growth; therefore the question of interface roughness along the direction of the electron beam and twinning orientations has been considered. This has been modeled by Fourier shift techniques incorporated into multislice dynamical theory and, of course, is complicated by the dynamical diffraction conditions of the structure and the contributions of high order Bragg reflections to image detail. It has been possible to access the image features present in Pd2Si/Si micrographs and to point out the difficulties which are encountered not only in this system but in a wide variety of interface structures by high resolution electron microscopy. Perhaps the most important finding of this study is that the interface region contains a mixture of silicon-rich and silicon-deficient Pd2Si planes adjacent to the silicon side of the interface.

Disorder is characteristic of nerve myelin

An X-ray diffraction pattern from the myelin in frog sciatic nerve has been obtained using the intense synchrotron radiation from the storage ring, SPEAR. Data with good statistical accuracy are obtained in a few minutes by using a scintillation counter or position-sensitive detector. The same indications for stacking disorder are seen as in previous conventional exposures which required one to two days. Thus, the stacking disorder is characteristic of myelin in a freshly dissected nerve. The present data, obtained with a more nearly monochromatic X-ray beam than in the previous study, remove one of two ambiguities which bear on the possible phasing of the higher order Bragg reflections.

Optical Characteristics of a Mechanical Neutron Monochromator with Helical Slots

The expression of the function f(λ) defining the transmission of a mechanical monochromator with helical slots when the incident neutron beam is limited by a Soller collimator has been calculated. The influence of the total reflection from the collimator walls upon the function f(λ) was also studied. The paper describes a mechanical monochromator with helical slots devised for the suppression of the higher-order Bragg reflections from a crystal. Measurements with this monochromator have served to check the calculations.