Good agreement between the high-resolution experimental results for (222, 113) three-beam diffraction in Ge and computer simulations based on the dynamical multiple diffraction theory are presented.
The results of high-resolution analysis of the (222, >113) three-beam diffraction in Ge are presented. For monochromatization and angular collimation of the incident synchrotron beam a multi-crystal arrangement in a dispersive setup in both vertical and horizontal planes was used in an attempt to experimentally approach plane-wave incident conditions. Using this setup, for various azimuthal angles the polar angular curves which are very close to theoretical computer simulations for the plane monochromatic wave were measured. The effect of the strong two-beam 222 diffraction was observed for the first time with the maximum reflectivity close to 60% even though the total reflection of the incident beam into a forbidden reflection was not achieved owing to absorption. The structure factor of the 222 reflection in Ge was experimentally determined.
dynamical diffraction; multiple diffraction; synchrotron radiation; plane waves; X-ray optics
A high-resolution study of (002, 113, 11−1) four-beam diffraction in Si was performed both experimentally and theoretically. Excellent coincidence between theory and experiment was achieved. The forbidden two-beam 002 reflection was excited with the maximum reflectivity of 80%.
The results of a high-resolution study of the (002, 113, ) four-beam diffraction in Si are presented. The incident synchrotron radiation beam was highly monochromated and collimated with a multi-crystal arrangement in a dispersive setup in both vertical and horizontal planes, in an attempt to experimentally approach plane-wave incident conditions. The Renninger scheme was used with the forbidden reflection reciprocal-lattice vector 002 normal to the crystal surface. The azimuthal and polar rotations were performed in the crystal surface plane and the vertical plane correspondingly. The polar angular curves for various azimuthal angles were measured and found to be very close to theoretical computer simulations, with only a small deviation from the plane monochromatic wave. The effect of the strong two-beam 002 diffraction was observed for the first time with the maximum reflectivity close to 80%. The structure factor of the 002 reflection in Si was experimentally determined as zero.
X-ray multiple diffraction; silicon; high resolution; forbidden reflections
Three-wave diffraction has been experimentally studied for a set of III–nitride and ZnO epitaxial films differing in thickness and structural perfection. Properties of the multiple diffraction pattern in highly distorted layers are analyzed.
Three-wave diffraction has been measured for a set of GaN, AlN, AlGaN and ZnO epitaxial layers grown on c-sapphire. A Renninger scan for the primary forbidden 0001 reflection was used. For each of the three-wave combinations, θ-scan curves were measured. The intensity and angular width of both ϕ- and θ-scan three-wave peaks were analyzed. The experimental data were used to determine properties of the multiple diffraction pattern in highly distorted layers. It is shown that the FWHM of θ scans is highly sensitive to the structural perfection and strongly depends on the type of three-wave combination. The narrowest peaks are observed for multiple combinations with the largest l index of the secondary hkl reflection. An influence of the type of the dislocation structure on the θ-scan broadening was revealed. These experimental facts are interpreted by considering the scanning geometry in the reciprocal space and taking into account the disc-shaped reciprocal-lattice points. The total integrated intensities of all the three-wave combinations were determined and their ratios were found to be in only a qualitative agreement with the theory. For AlGaN layers, the presence of the nonzero 0001 reflection was revealed, in contrast to AlN and GaN films.
X-ray diffraction; multiple diffraction; epitaxial layers; structural defects; wurtzite structure
The spatial structure of an X-ray beam focused by a planar refractive lens and Bragg diffracted from perfect silicon crystals has been studied experimentally and theoretically.
The spatial structure of a beam focused by a planar refractive lens and Bragg diffracted from perfect silicon crystals was experimentally studied at the focal plane using a knife-edge scan and a high-resolution CCD camera. The use of refractive lenses allowed for a detailed comparison with theory. It was shown that diffraction leads to broadening of the focused beam owing to the extinction effect and, for a sufficiently thin crystal, to the appearance of a second peak owing to reflection from the back surface. It was found that the spatial structure of the diffracted beam depends on whether the crystal diffracts strongly (dynamically) or weakly (kinematically). The results help to understand the physical origin of the diffracted intensity recorded in a typical microbeam diffraction experiment.
X-rays; focusing; refractive lenses; X-ray diffraction; extinction effect
To test the efficacy of phase-sensitive x-ray imaging for intact synovial joints, whereby refraction effects, along with the attenuation of conventional radiography, can be exploited.
Intact cadaveric human knee joints were imaged, in the computed tomographic mode, using an analyzer based x-ray system at the National Synchrotron Light Source, Brookhaven National Laboratory. A collimated fan beam of 51 keV X-rays was prepared by a silicon [1,1,1 reflection] double-crystal monochromator. The x-ray beam transmitted through the specimen was imaged after diffraction in the vertical plane by means of the analyzer crystal with the analyzer crystal tuned to its half-reflectivity point (6.5 microradians). A two-dimensional filtered backprojection (FBP) algorithm was used for reconstructing transverse slices of images.
The resulting images demonstrate simultaneous soft-tissue and bone contrast at a level that has not been achieved previously. Identifiable structures include articular cartilage, cruciate ligaments, loose connective tissue, menisci, and chondrocalcinosis.
Phase-sensitive x-ray imaging using an analyzer-based system renders exceptionally high quality images of soft and hard tissues within synovial joints, with high contrast and resolution, and thus holds promise for the eventual clinical utility.
A three-dimensional Bragg diffraction imaging technique, which combines rocking curve imaging with ‘pinhole’ and ‘section’ diffraction topography in the transmission case, allows three-dimensional lattice distortion in the bulk of an ice crystal under compression to be measured.
Rocking curve imaging (RCI) is a quantitative version of monochromatic beam diffraction topography that involves using a two-dimensional detector, each pixel of which records its own ‘local’ rocking curve. From these local rocking curves one can reconstruct maps of particularly relevant quantities (e.g. integrated intensity, angular position of the centre of gravity, FWHM). Up to now RCI images have been exploited in the reflection case, giving a quantitative picture of the features present in a several-micrometre-thick subsurface layer. Recently, a three-dimensional Bragg diffraction imaging technique, which combines RCI with ‘pinhole’ and ‘section’ diffraction topography in the transmission case, was implemented. It allows three-dimensional images of defects to be obtained and measurement of three-dimensional distortions within a 50 × 50 × 50 µm elementary volume inside the crystal with angular misorientations down to 10−5–10−6 rad. In the present paper, this three-dimensional-RCI (3D-RCI) technique is used to study one of the grains of a three-grained ice polycrystal. The inception of the deformation process is followed by reconstructing virtual slices in the crystal bulk. 3D-RCI capabilities allow the effective distortion in the bulk of the crystal to be investigated, and the predictions of diffraction theories to be checked, well beyond what has been possible up to now.
rocking curve imaging (RCI); 3D-RCI; ice crystals; crystal distortion; crystal defects
Computer control of beam tilt and image capture allows the collection of electron diffraction patterns over a large angular range, without any overlap in diffraction data and from a region limited only by the size of the electron beam. This results in a significant improvement in data volumes and ease of interpretation.
The advantages of convergent-beam electron diffraction for symmetry determination at the scale of a few nm are well known. In practice, the approach is often limited due to the restriction on the angular range of the electron beam imposed by the small Bragg angle for high-energy electron diffraction, i.e. a large convergence angle of the incident beam results in overlapping information in the diffraction pattern. Techniques have been generally available since the 1980s which overcome this restriction for individual diffracted beams, by making a compromise between illuminated area and beam convergence. Here a simple technique is described which overcomes all of these problems using computer control, giving electron diffraction data over a large angular range for many diffracted beams from the volume given by a focused electron beam (typically a few nm or less). The increase in the amount of information significantly improves the ease of interpretation and widens the applicability of the technique, particularly for thin materials or those with larger lattice parameters.
electron diffraction; symmetry determination; CBED; LACBED; computer control
Several ways of tuning a higher asymmetry factor (>10) in V-channel X-ray monochromators, for metrological and imaging applications, were analysed. A more than sixfold intensity increase for compositionally and thermally tuned cases was achieved.
While channel-cut crystals, in which the diffracting surfaces in an asymmetric cut are kept parallel, can provide beam collimation and spectral beam shaping, they can in addition provide beam compression or expansion if the cut is V-shaped. The compression/expansion ratio depends in this case on the total asymmetry factor. If the Ge(220) diffraction planes and a total asymmetry factor in excess of 10 are used, the rocking curves of two diffractors will have a sufficient overlap only if the second diffractor is tuned slightly with respect to the first one. This study compares and analyses several ways of overcoming this mismatch, which is due to refraction, when the Cu Kα1 beam is compressed 21-fold in a V21 monochromator. A more than sixfold intensity increase was obtained if the matching was improved either by a compositional variation or by a thermal deformation. This provided an intensity gain compared with the use of a simple slit in a symmetrical channel-cut monochromator. The first attempt to overcome the mismatch by introducing different types of X-ray prisms for the required beam deflection is described as well. The performance of the V-shaped monochromators is demonstrated in two applications. A narrow collimated monochromatic beam obtained in the beam compressing mode was used for high-resolution grazing-incidence small-angle X-ray scattering measurements of a silicon sample with corrupted surface. In addition, a two-dimensional Bragg magnifier, based on two crossed V15 channel monochromators in beam expansion mode and tuned by means of unequal asymmetries, was successfully applied to high-resolution imaging of test structures in combination with a Medipix detector.
metrology; Montel optics; Bragg magnifier; channel-cut crystal
Nanopore-based sensing has emerged as a promising candidate for affordable and powerful DNA sequencing technologies. Herein, we demonstrate that nanopores can be successfully fabricated in Mg alloys via focused electron beam (e-beam) technology. Employing in situ high-resolution transmission electron microscopy techniques, we obtained unambiguous evidence that layer-by-layer growth of atomic planes at the nanopore periphery occurs when the e-beam is spread out, leading to the shrinkage and eventual disappearance of nanopores. The proposed healing process was attributed to the e-beam-induced anisotropic diffusion of Mg atoms in the vicinity of nanopore edges. A plausible diffusion mechanism that describes the observed phenomena is discussed. Our results constitute the first experimental investigation of nanopores in Mg alloys. Direct evidence of the healing process has advanced our fundamental understanding of surface science, which is of great practical importance for many technological applications, including thin film deposition and surface nanopatterning.
Recently developed microscopy techniques, such as 4Pi, break the Abbe diffraction limit and allow for imaging at unprecedented resolution. The effective focal volume is also reduced, leading to more sensitive measurements in fluorescence microphotolysis or correlation spectroscopy. In 4Pi microscopy, the improvement is due to the utilization of two interfering laser beams for illumination, rather than a single one as in conventional microscopy. We study theoretically the possibility of further reduction of the focal volume with employment of three or more interfering beams, including the limiting case of an inifinite number of beams. The volume is indeed reduced, but reaches a limit quickly as beams are added. The volume obtained in the setups with three or four beams is about half of that in the 4Pi case and is close to the volume computed for the limit of an infinite number of beams. The setups suggested employ purely optical principles, and, thus, the considered limiting case arguably represents the maximal reduction in focal volume possible for a purely optical far-field setup.
Crystallization of human membrane proteins in lipidic cubic phase often results in very small but highly ordered crystals. Advent of the sub-10 µm minibeam at the APS GM/CA CAT has enabled the collection of high quality diffraction data from such microcrystals. Herein we describe the challenges and solutions related to growing, manipulating and collecting data from optically invisible microcrystals embedded in an opaque frozen in meso material. Of critical importance is the use of the intense and small synchrotron beam to raster through and locate the crystal sample in an efficient and reliable manner. The resulting diffraction patterns have a significant reduction in background, with strong intensity and improvement in diffraction resolution compared with larger beam sizes. Three high-resolution structures of human G protein-coupled receptors serve as evidence of the utility of these techniques that will likely be useful for future structural determination efforts. We anticipate that further innovations of the technologies applied to microcrystallography will enable the solving of structures of ever more challenging targets.
lipidic cubic phase; G protein-coupled receptor; minibeam; microcrystallography
The 19ID undulator beamline of the Structure Biology Center has been designed and built to take full advantage of the high flux, brilliance and quality of X-ray beams delivered by the Advanced Photon Source. The beamline optics are capable of delivering monochromatic X-rays with photon energies from 3.5 to 20 keV (3.5–0.6 Å wavelength) with fluxes up to 8–18 × 1012 photons s−1 (depending on photon energy) onto cryogenically cooled crystal samples. The size of the beam (full width at half-maximum) at the sample position can be varied from 2.2 mm × 1.0 mm (horizontal × vertical, unfocused) to 0.083 mm × 0.020 mm in its fully focused configuration. Specimen-to-detector distances of between 100 mm and 1500 mm can be used. The high flexibility, inherent in the design of the optics, coupled with a κ-geometry goniometer and beamline control software allows optimal strategies to be adopted in protein crystallographic experiments, thus maximizing the chances of their success. A large-area mosaic 3 × 3 CCD detector allows high-quality diffraction data to be measured rapidly to the crystal diffraction limits. The beamline layout and the X-ray optical and endstation components are described in detail, and the results of representative crystallographic experiments are presented.
X-ray beamline; protein crystallography; MAD/SAD; X-ray optics
The currently largest perfect-crystal neutron interferometer with six beam splitters and two interference loops offers novel applications in neutron interferometry. The two additional lamellas can be used for quantitative measurements of a phase shift due to crystal diffraction in the vicinity of a Bragg condition. The arising phase, referred to as “Laue phase,” reveals an extreme angular sensitivity, which allows the detection of beam deflections of the order of 10−6 s of arc. Furthermore, a precise measurement of the Laue phase at different reflections might constitute an interesting opportunity for the extraction of fundamental quantities like the neutron–electron scattering length, gravitational short-range interactions in the sub-micron range and the Debye Waller factor. For that purpose several harmonics can be utilized at the interferometer instrument ILL-S18.
Perfect crystal interferometer; Dynamical diffraction; Beam deflection; High angular resolution; Short-range interaction; Coriolis force
Characterization of PILATUS single-photon-counting X-ray detector modules regarding charge sharing, energy resolution and rate capability is presented. The performance of the detector was tested with surface diffraction experiments at the synchrotron.
PILATUS is a silicon hybrid pixel detector system, operating in single-photon-counting mode, that has been developed at the Paul Scherrer Institut for the needs of macromolecular crystallography at the Swiss Light Source (SLS). A calibrated PILATUS module has been characterized with monochromatic synchrotron radiation. The influence of charge sharing on the count rate and the overall energy resolution of the detector were investigated. The dead-time of the system was determined using the attenuated direct synchrotron beam. A single module detector was also tested in surface diffraction experiments at the SLS, whereby its performance regarding fluorescence suppression and saturation tolerance were evaluated, and have shown to greatly improve the sensitivity, reliability and speed of surface diffraction data acquisition.
hybrid pixel detector; single photon counting; energy resolution; charge sharing; dead-time; surface X-ray diffraction
The sonar beam of an echolocating bat forms a spatial window restricting the echo information returned from the environment. Investigating the shape and orientation of the sonar beam produced by a bat as it flies and performs various behavioral tasks may yield insight into the operation of its sonar system. This paper presents recordings of vertical and horizontal cross-sections of the sonar beam produced by Eptesicus fuscus (big brown bats) as they fly and pursue prey in a laboratory flight-room. In the horizontal plane the sonar beam consists of one large lobe and in the vertical plane the beam consists of two lobes of comparable size oriented frontally and ventrally. In level flight, the bat directs its beam such that the ventral lobe is pointed forward and down toward the ground ahead of its flight path. The bat may utilize the downward directed lobe to measure altitude without the need for vertical head movements.
echolocation; sonar; side-lobe; altimeter
Diamond transmission-mode white-beam position monitors installed at undulator beamline X25 at the National Synchrotron Light Source are described.
Two transmission-mode diamond X-ray beam position monitors installed at National Synchrotron Light Source (NSLS) beamline X25 are described. Each diamond beam position monitor is constructed around two horizontally tiled electronic-grade (p.p.b. nitrogen impurity) single-crystal (001) CVD synthetic diamonds. The position, angle and flux of the white X-ray beam can be monitored in real time with a position resolution of 500 nm in the horizontal direction and 100 nm in the vertical direction for a 3 mm × 1 mm beam. The first diamond beam position monitor has been in operation in the white beam for more than one year without any observable degradation in performance. The installation of a second, more compact, diamond beam position monitor followed about six months later, adding the ability to measure the angular trajectory of the photon beam.
diamond; detector; monitor; position-sensitive; quadrant; white beam; BPM; photon; undulator
Beam-induced damage on diffractive hard X-ray optics is studied by means of X-ray diffraction and scanning electron microscopy.
The issue of beam-induced damage on diffractive hard X-ray optics is addressed. For this purpose a systematic study on the radiation damage induced by a high-power X-ray beam is carried out in both ambient and inert atmospheres. Diffraction gratings fabricated by three different techniques are considered: electroplated Au gratings both with and without the polymer mold, and Ir-coated Si gratings. The beam-induced damage is monitored by X-ray diffraction and evaluated using scanning electron microscopy.
diffractive X-ray optics; radiation damage
Beamline ID23-2, the first dedicated and highly automated high-throughput monochromatic macromolecular crystallography microfocus beamline, is described.
The first phase of the ESRF beamline ID23 to be constructed was ID23-1, a tunable MAD-capable beamline which opened to users in early 2004. The second phase of the beamline to be constructed is ID23-2, a monochromatic microfocus beamline dedicated to macromolecular crystallography experiments. Beamline ID23-2 makes use of well characterized optical elements: a single-bounce silicon (111) monochromator and two mirrors in Kirkpatrick–Baez geometry to focus the X-ray beam. A major design goal of the ID23-2 beamline is to provide a reliable, easy-to-use and routine microfocus beam. ID23-2 started operation in November 2005, as the first beamline dedicated to microfocus macromolecular crystallography. The beamline has taken the standard automated ESRF macromolecular crystallography environment (both hardware and software), allowing users of ID23-2 to be rapidly familiar with the microfocus environment. This paper describes the beamline design, the special considerations taken into account given the microfocus beam, and summarizes the results of the first years of the beamline operation.
macromolecular crystallography; automation; microfocus
Using a convergent X-ray beam having continuously varying energy and glancing angle as a function of direction, the whole profile of a specular X-ray reflectivity curve is measured with no need for any mechanical motion during the measurement.
An X-ray reflectometer has been developed, which can simultaneously measure the whole specular X-ray reflectivity curve with no need for rotation of the sample, detector or monochromator crystal during the measurement. A bent-twisted crystal polychromator is used to realise a convergent X-ray beam which has continuously varying energy E (wavelength λ) and glancing angle α to the sample surface as a function of horizontal direction. This convergent beam is reflected in the vertical direction by the sample placed horizontally at the focus and then diverges horizontally and vertically. The normalized intensity distribution of the reflected beam measured downstream of the specimen with a two-dimensional pixel array detector (PILATUS 100K) represents the reflectivity curve. Specular X-ray reflectivity curves were measured from a commercially available silicon (100) wafer, a thin gold film coated on a silicon single-crystal substrate and the surface of liquid ethylene glycol with data collection times of 0.01 to 1000 s using synchrotron radiation from a bending-magnet source of a 6.5 GeV electron storage ring. A typical value of the simultaneously covered range of the momentum transfer was 0.01–0.45 Å−1 for the silicon wafer sample. The potential of this reflectometer for time-resolved X-ray studies of irreversible structural changes is discussed.
X-ray reflectivity curve; time-resolved measurement; bent-twisted polychromator crystal; simultaneous measurement
The crystalline structure of single free-standing GaAs nanowires, grown by molecular beam epitaxy on a GaAs substrate at specific positions defined by focused ion beams, and the substrate regions close to the Au-implanted regions are investigated through grazing-incidence X-ray diffraction.
Grazing-incidence X-ray diffraction measurements on single GaAs nanowires (NWs) grown on a (111)-oriented GaAs substrate by molecular beam epitaxy are reported. The positions of the NWs are intentionally determined by a direct implantation of Au with focused ion beams. This controlled arrangement in combination with a nanofocused X-ray beam allows the in-plane lattice parameter of single NWs to be probed, which is not possible for randomly grown NWs. Reciprocal space maps were collected at different heights along the NW to investigate the crystal structure. Simultaneously, substrate areas with different distances from the Au-implantation spots below the NWs were probed. Around the NWs, the data revealed a 0.4% decrease in the lattice spacing in the substrate compared with the expected unstrained value. This suggests the presence of a compressed region due to Au implantation.
semiconductor nanowires; growth; grazing-incidence X-ray diffraction; GaAs
SPring-8 BL41XU provides a high-flux X-ray beam of size 10–50 µm, and enables high-quality diffraction data to be obtained from various types of protein crystals. Details of this beamline and an upgrade project are described.
SPring-8 BL41XU is a high-flux macromolecular crystallography beamline using an in-vacuum undulator as a light source. The X-rays are monochromated by a liquid-nitrogen-cooling Si double-crystal monochromator, and focused by Kirkpatrick–Baez mirror optics. The focused beam size at the sample is 80 µm (H) × 22 µm (V) with a photon flux of 1.1 × 1013 photons s−1. A pinhole aperture is used to collimate the beam in the range 10–50 µm. This high-flux beam with variable size provides opportunities not only for micro-crystallography but also for data collection effectively making use of crystal volume. The beamline also provides high-energy X-rays covering 20.6–35.4 keV which allows ultra-high-resolution data to be obtained and anomalous diffraction using the K-edge of Xe and I. Upgrade of BL41XU for more rapid and accurate data collection is proceeding. Here, details of BL41XU are given and an outline of the upgrade project is documented.
macromolecular crystallography; micro-crystallography; high-flux beam; high-energy beam; SPring-8
Precession electron diffraction has seen a fast increase in its adoption as a technique for solving crystallographic structures as well as an alternative to conventional selected-area and converged-beam diffraction methods. One of the key issues of precession is the pivot point alignment, as a stationary apparent beam does not guarantee a fixed pivot point. A large precession tilt angle, along with pre-field and post-field misalignment, induces shift in the image plane. We point out here that the beam should be aligned to the pre-field optic axis to keep the electron illumination stationary during the rocking process. A practical alignment procedure is suggested with the focus placed on minimizing the beam wandering on the specimen, and is demonstrated for a (110)-oriented silicon single crystal and for a carbide phase (~20 nm in size) within a cast cobalt–chromium–molybdenum alloy.
Precession electron diffraction; CoCrMo alloy; M23C6 carbide; Alignment
A novel design is described for an aperture that blocks a half-plane of the electron diffraction pattern out to a desired scattering angle, and then – except for a narrow support beam – transmits all of the scattered electrons beyond that angle. Our proposed tulip-shaped design is thus a hybrid between the single-sideband (ssb) aperture, which blocks a full half-plane of the diffraction pattern, and the conventional (i.e. fully open) double-sideband (dsb) aperture. The benefits of this hybrid design include the fact that such an aperture allows one to obtain high-contrast images of weak-phase objects with the objective lens set to Scherzer defocus. We further demonstrate that such apertures can be fabricated from thin-foil materials by milling with a focused ion beam (FIB), and that such apertures are fully compatible with the requirements of imaging out to a resolution of at least 0.34 nm. As is known from earlier work with single-sideband apertures, however, the edge of such an aperture can introduce unwanted, electrostatic phase shifts due to charging. The principal requirement for using such an aperture in a routine data-collection mode is thus to discover appropriate materials, protocols for fabrication and processing, and conditions of use such that the hybrid aperture remains free of charging over long periods of time.
Phase contrast; single-sideband aperture; charging
Laguerre-Gaussian (LG) beams have been extensively studied due to their unique structure, characterized by a phase singularity at the center of the beam. Common methods for generating such beams include the use of diffractive optical elements and spatial light modulators, which although offering excellent versatility, suffers from several drawbacks, including in many cases a low power damage threshold as well as complexity and expense. This paper presents a simple, low cost method for the generation of high-fidelity LG beams using rapid prototyping techniques. Our approach is based on a fluidic-hologram concept, whereby the properties of the LG beam can be finely controlled by varying the refractive-index of the fluid that flows through the hologram. This simple approach, while optimized here for LG beam generation, is also expected to find applications in the production of tunable fluidic optical trains.
Anomalous extra spots visible in electron diffraction patterns of silicon nanowires and silicon thin films are explained by the presence of micro- and nanotwins.
Odd electron diffraction patterns (EDPs) have been obtained by transmission electron microscopy (TEM) on silicon nanowires grown via the vapour–liquid–solid method and on silicon thin films deposited by electron beam evaporation. Many explanations have been given in the past, without consensus among the scientific community: size artifacts, twinning artifacts or, more widely accepted, the existence of new hexagonal Si phases. In order to resolve this issue, the microstructures of Si nanowires and Si thin films have been characterized by TEM, high-resolution transmission electron microscopy (HRTEM) and high-resolution scanning transmission electron microscopy. Despite the differences in the geometries and elaboration processes, the EDPs of the materials show great similarities. The different hypotheses reported in the literature have been investigated. It was found that the positions of the diffraction spots in the EDPs could be reproduced by simulating a hexagonal structure with c/a = 12(2/3)1/2, but the intensities in many EDPs remained unexplained. Finally, it was established that all the experimental data, i.e. EDPs and HRTEM images, agree with a classical cubic silicon structure containing two microstructural defects: (i) overlapping Σ3 microtwins which induce extra spots by double diffraction, and (ii) nanotwins which induce extra spots as a result of streaking effects. It is concluded that there is no hexagonal phase in the Si nanowires and the Si thin films presented in this work.
silicon nanowires; silicon thin films; artifacts; twinning