Table of contents

The 7th Biennial Conference on High Resolution X-Ray Diffraction and Imaging (XTOP 2004) was held in the Prague suburb of Pruhonice, Czech Republic, during 7–10 September 2004. It was organized by the Czech and Slovak Crystallographic Association in cooperation with the Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Masaryk University, Brno, and Charles University, Prague. XTOP 2004 took place just after EPDIC IX (European Powder Diffraction Conference) organised in Prague by the same Association during 2–5 September 2004. The Organizing Committee was supported by an International Programme Committee including about 20 prominent scientists from several European and overseas countries, whose helpful suggestions for speakers are acknowledged. The conference was sponsored by the International Union of Crystallography and by several industrial sponsors; this sponsorship allowed us to support about 20 students and young scientists.

In total, 147 official delegates and 8 accompanying persons from 16 countries of three continents attended our conference. The scientific programme of the conference was divided into 11 half-day sessions and 2 poster sessions. The participants presented 147 accepted contributions; of these 9 were 45-minute long invited talks, 34 were 20-minute oral presentations and 104 were posters. All posters were displayed for the whole meeting to ensure maximum exposure and interaction between delegates.

We followed the very good experience from the previous conference, XTOP 2002, and also organized pre-conference tutorial lectures presented by experts in the field: `Imaging with hard synchrotron radiation' (J Härtwig, Grenoble), `High-resolution x-ray diffractometry: determination of strain and composition' (J Stangl, Linz), `X-ray grazing-incidence scattering from surfaces and nanostructures' (U Pietsch, Potsdam) and `Hard x-ray optics' (J Hrdý, Prague).

According to the recommendation of the International Program Committee, the invited lectures covered a broader field than the original conference subject, namely coherent speckle diffraction (I Robinson, Urbana), scattering from soft-matter films (W de Jeu, Amsterdam), femtosecond diffraction (J Wark, Oxford), magnetic soft x-ray microscopy (P Fischer, Stuttgart), x-ray standing-wave imaging (J Zegenhagen, Grenoble), new trends in hard x-ray imaging (J Baruchel, Grenoble), anomalous x-ray scattering from nanostructures, (T Schülli, Grenoble), in-situ x-ray scattering (G Renaud, Grenoble) and x-ray waveguides (W Jark, Trieste).

The topics of the oral presentations and posters can be divided into two large groups, namely x-ray imaging and x-ray diffraction. In the first group, the contributions concentrated on new developments in methods and instrumentation, including in-situ imaging, phase-contrast imaging and three-dimensional imaging. In the second group, attention was paid to anomalous scattering methods and scattering from thin films and nanostructures. The full list of all contributions together with their abstracts are available at the website http://www.xray.cz/xtop.

During one session, Professor Andrew Lang, one of the pioneers of x-ray topography who gave his name to the popular topographic technique, and honorary guest of XTOP 2004, celebrated his 80th birthday. In a celebration address Professor A Authier reviewed Professor Lang's career and his invaluable contribution to the development of our field.

We continue the tradition of previous XTOPs and publish a selection of original contributions from the conference in this special issue of Journal of Physics D: Applied Physics. The papers have been subject to peer review according to the normal practice of the journal.

Generally, we observed that a new generation of young and very talented scientists has appeared, who are publishing very interesting and important papers. Therefore, the future prospects of x-ray imaging and high-resolution diffraction are bright and we all look forward to the next XTOP conference, organized by Tilo Baumbach and his group, which will take place in Karlsruhe, Germany, in 2006.

This paper briefly chronicles a long-standing and productive collaboration between the Institute of Physics, Czech Academy of Science and the H H Wills Physics Laboratory. It began in early 1962 with a brief visit to Bristol by Milena Polcarová. The initial aim, successfully achieved, was the mapping by transmission topography of dislocations in melt-grown single crystals of a Fe–Si alloy. A novel by-product was the x-ray topographic observation of internal magnetic domain structures in specimen plates prepared in both (110) and (112) orientations. In the alloy studied, which contained about 3 wt% Si, the directions of easy magnetization are ⟨ 100 ⟩, and domain boundaries are either 180° or 90° Bloch walls. The latter walls can generate strong x-ray diffraction contrast, but no contrast from 180° walls is expected. In the (110) plates x-ray topography revealed complex internal domain structures containing 90° walls, some previously unsuspected on evidence of optical micrography of colloid patterns (Bitter patterns). Certain details of these structures remain a puzzle to this day! In (112) specimens, in which no direction of easy magnetization lies in the plate surface, the specimen is filled with a hierarchy of domains, diminishing in scale towards the surfaces in order to minimize magnetostatic energy due to free poles. However, in (112) plate thicknesses less than ∼20 µm, x-ray topographs recorded internal domain structures sufficiently uncomplicated for their main features to be interpreted. This was achieved by F C Frank in the early 1960s, but not published till 1993! During a 1968 visit to Bristol by Polcarová it was discovered that under appropriate diffraction conditions x-ray topographic contrast from 180° Bloch walls was just detectable. This finding was not published till 1991. More recent work with Prague specimens has applied synchrotron x-ray reticulography at Daresbury, showing that this technique can be informatively used with lightly-deformed Fe–Si bicrystals.

A very different enterprise was the Bristol method of producing x-ray moiré patterns by superposing one crystal plate upon another, achieved in 1967. This project gained from Czech collaboration through the skilful participation of J Brádler, on leave from Prague.

The coherent x-ray diffraction (CXD) method is particularly attractive for understanding structures that can be represented as phase objects. Diffraction from a crystal acquires a phase whenever atoms are displaced from lattice sites, even by small fractions of an angstrom, so CXD measured around a Bragg peak is ideal for studying strain. We have succeeded in using these coherent beams to study the strain field arising from individual misfit dislocations located at an interface between a GeSi thin film and its Si(001) substrate. The data have not yet been inverted to images, but we show how the asymmetric CXD diffraction patterns can be explained qualitatively by a model phase structure.

The propagation of transverse coherence with a stationary phase object is discussed. Models of phase objects are constructed from refractive contrast imaging of Be windows using a Fresnel diffraction calculation. Numerical simulations of coherence propagation with the objects are performed. The simulated results are compared with those experimentally measured by intensity interferometry, and the level of agreement is reasonable.

We have studied the propagation and elimination of dislocations generated at the early stage of Czochralski silicon crystal growth using synchrotron white x-ray topography combined with a topo-tomographic technique. Two silicon crystals with [001] growth-axes were examined. One was intentionally grown without enlarging its diameter to easily observe the features of the dislocation propagation, and the other was grown with Dash necking, followed by a 2 inch enlargement of its diameter in order to observe the elimination of the dislocations. The three-dimensional structure of the individual dislocation, i.e. the direction of the dislocation line, its Burgers vector and the glide plane, were determined. These investigations revealed that dislocation half loops, which were generated from tangled dislocations, were expanded on their glide planes and were often deformed by their interaction, cross slip and collision with the crystal surface, followed by a gradual decrease in their density. The dislocation-elimination effect of the Dash necking was caused by the expansion of the dislocation half loops being terminated within the crystal and by their pinning on the crystal surface.

Plane-wave x-ray topography was used to characterize grown-in defects in silicon crystals grown by the Czochralski method at a slow speed. The 220 reflection rocking curves of the sample crystal were measured in a symmetric Laue case. Oscillatory profiles were clearly observed in the rocking curves and were in good agreement with those calculated from the dynamical theory of x-ray diffraction. Images of the grown-in defects were observed in the plane-wave x-ray topographs of the 220 reflection. The density of the defects was determined as 300 cm⁻³. The lattice strain around the defects was evaluated as 10⁻⁶ from the dependence of the defect image contrast on the x-ray incident angles. The defect images are discussed using a grown-in defect model of entangled dislocation loop clusters.

We present results obtained at the ID19 beamline of the European Synchrotron Radiation Facility (ESRF) by synchrotron x-ray radiography during the solidification of Al–Ni alloys. We focus on columnar dendritic and equiaxed solidification, and the transition between the two regimes. The columnar to equiaxed transition is a critical and still pending issue in metallurgy. By making use of the high potential of synchrotron experimental tools for in situ and real-time characterization of the solid–liquid interface during directional solidification, we were able to provide insight into key physical phenomena, in particular, sedimentation, interaction and arrangement of equiaxed grains.

The study of migration of well-characterized grain boundaries (GBs) in bicrystals of an Fe–Si alloy by in situ synchrotron radiation (SR) topography is described. The differences in migration behaviour of the (100)/(110) asymmetrical tilt GB and {hk0} symmetrical tilt GB in the 45° [001] bicrystal at 1293 K are evidently connected with intersections of the GB with low angle subgrain boundaries or changes of the circular shape of migrating GB to a straight one (faceting on low-index GB planes). From reliable data the product of GB mobility and energy was determined which is comparable with that obtained previously by optical measurements after annealing experiments.

To characterize diamond monochromators for synchrotron radiation beamlines, images for a region 25 µm below the surface were obtained. Topographical images of a Bragg-diffracted beam having a scattering angle (twice the Bragg angle) of 90° were obtained from asymmetric reflections with a CCD area detector. A 25 µm incident slit was used to section the sample topographically. Patchwork images for the full surface area, but limited in depth to the slit size, were assembled from microbeam images. The small extinction depths provided by the asymmetric reflection geometry, namely, 2.8 µm and 3.5 µm for ideal diamond crystals set for the (224) and (044) reflections, respectively, permitted data analyses for a region near the surface. The diamonds were synthetic type Ib (yellowish due to nitrogen impurities). They were in the shape of plates sized 6 × 5 mm and were 0.5 mm thick. Measurements were made using monochromatic bending magnet radiation at the Advanced Photon Source at 12.04 keV and 13.90 keV. Data obtained before and after chemical etching demonstrate that damage visible as contrast from saw grooves is largely removed by etching. Dislocation etch pits were observed after etching for the (111) surface but not for the (100) surface.

A novel white-beam synchrotron radiography/topography substrate curvature technique has been used to study stress development in situ during annealing of Al–Cu–Fe quasicrystalline and approximant coatings, as well as to image their failure modes in real time. Single crystal Si and sapphire substrates were coated with a 2.55 µm precursor coating by RF sputtering from an Al₆₅Cu₂₃Fe₁₂ powder composite target and subsequently annealed at 585°C while stress and imaging data were acquired. After the initial ramp to the annealing temperature, a stress plateau was reached for coatings on both Si and sapphire substrates, although the magnitude of the stress plateau was different in each case. A tensile stress developed in the coatings during cooling due to differential thermal expansion between the coating and substrate, allowing for calculation of both the coefficient of thermal expansion and elastic modulus of the film. During cooling, the films exhibited different stress evolution above and below 470°C, a temperature of interest in Al–Cu–Fe quasicrystal and approximant phase development. The Al–Cu–Fe coating on the Si substrate fractured at approximately 954 MPa, while the coating on the sapphire substrate fractured at approximately 431 MPa. From these values the fracture toughness was calculated to be 1.9 MPa m^1/2 and 0.76 MPa m^1/2 for the coatings on Si and sapphire, respectively.

We report on recent advances in spatially resolved x-ray diffraction, extending the technique known as rocking curve imaging down to 1–2 µm spatial resolution. Application to a set of gallium nitride samples grown by epitaxial lateral overgrowth (ELO) shows the potential of the technique. Quantitative information on crystallographic misorientations and lattice quality can be obtained by direct imaging with high lateral resolution. Results from two samples of ELO-GaN grown on different substrates are compared. Tilt in individual lateral periods of the ELO structure can be quantified. Local tilt fluctuations are distinguished from macroscopic variations (curvature). The local lattice quality can be investigated via the peak width of diffraction profiles recorded in individual camera pixels. The peak broadening previously observed in laboratory x-ray diffraction measurements is found to have (at least) two different reasons. In both cases, peak broadening does not indicate a degradation in local crystalline quality.

The behaviour of a (001) slice of initially single-domain rubidium titanyl arsenate (RbTiOAsO₄, RTA) crystal, when prepared with a periodic Ag electrode of period 38 µm, as for periodic poling in nonlinear optics, is investigated for applied voltages of up to ±1.5 kV. The method of investigation is by synchrotron x-ray section topography with electric fields applied in situ, while under white-beam x-ray illumination at the ID19 topography beamline of the ESRF, Grenoble. An increasing expansion of the width of section topographs is observed with increasing voltage resulting from a corresponding bending of the lattice planes in the near-surface region, with angles ranging between 4–200 µrads. This behaviour is explained by the formation of a Schottky barrier, which results from a semiconductor–metal contact interaction between RTA and the Ag film, in the near-surface region beneath the high voltage electrode. This restricts the depth of the electric field to a near-surface depletion layer. The actual bending of the planes is by the electrostrictive strain that acts only in the depletion layer where the field is non-zero.

Synthetic type IIa diamonds were characterized using rocking curve measurements and x-ray topography with quasi-plane-wave incidence, and high resolution reciprocal space mapping. The rocking curves of the (111) crystals were comparable to the theoretical ones. Some crystals had wider rocking curves because of the higher density of stacking faults. Even the highest quality crystal did not give the theoretical rocking curve due to dislocations and strain bands. On the other hand, the (100) crystals had nearly perfect area. The difference was attributed to the orientation of the seed crystal.

The coexistence of the ferromagnetic and fan phases in a (001) MnP crystal, under a magnetic field applied along the b direction, is investigated in real time, by synchrotron radiation diffraction topography, at T ≈ 48 K. The ferromagnetic–fan interface includes bulk transition regions, elongated along a, and thick enough along the b direction (in the 10⁻⁴ m range) to produce a substantial contribution to diffraction. The Bragg condition changes continuously across these regions. This configuration, which involves magnetic charge distribution, is in sharp distinction with the usual two-dimensional character of magnetic walls and phase boundaries. The thick interface is likely to comprise a set of intermediate magnetic states.

Self-detection of x-ray diffraction has been accomplished by measuring the electrical behaviour of a semiconductor single-crystal of a commercial detector when it is in and out of the x-ray diffraction condition. A decrease in the photocurrent or in the photocounting is measured when the detector is set in the diffraction condition. The self-detection of x-ray diffraction was imaged using a CCD detector diffracting the Si(400) in a non-dispersive set-up with an external monochromator. The depletion layer of the CCD is about 30 µm thick, which makes it a finite crystal for the energies used in terms of the dynamical theory of x-ray diffraction. The profile, referred to here as the anti-h peak, was obtained from images taken at different diffraction angular positions of the CCD. These profiles are in agreement with those calculated for finite crystals. An application of this effect, where the CCD is used as a detector and an analyser crystal in an analyser-based x-ray phase contrast imaging set-up, is realized here. It could be useful for Multiple Imaging Radiography and related mathematical image processing with the Schlieren method.

Some elements of the study of fibrous structure are presented in this paper. X-ray synchrotron microtomography is used to provide information about the three-dimensional structure. In this context a segmentation method is proposed to separate the different components of the porous material considered (paper).

Cataract is a disease that degrades the transparency of crystalline lenses. The crystalline lens is a cellular structure that has a unique shape and protein composition. Cataract is associated with changes in the structure and composition of the lenses. Analyser-based x-ray phase contrast imaging (PCI) is a non-destructive technique that presents images with more contrast and details than the images acquired with conventional synchrotron radiography. Here, an analyser-based x-ray PCI set-up was optimized in the XRD2 beamline at Brazilian Synchrotron Light Laboratory for comparative studies on PCI and conventional synchrotron radiography, for non-cataractous (healthy tissue) and cataractous crystalline (diseased tissue) lenses. Refraction angle and apparent absorption contrast images (diffraction enhanced imaging—DEI) were also obtained. The present PCI and DEI images indicate that the healthy tissue shows enhanced shell structures, while in the diseased tissue these are almost absent. This is associated with the clinical case of total opacity of the cataractous crystalline lenses when it is exposed to visible light.

In the last decade, the III-N compounds have attracted much interest because of their applications in blue, violet and ultraviolet optoelectronics. Most of the devices and research use sapphire as a substrate for epitaxy of nitrides. However, these epi-structures contain a very high dislocation density induced by the 16% lattice mismatch between GaN and sapphire. In our laboratory, we grow single crystals of GaN at a high hydrostatic pressure of 10 kbar of nitrogen. These crystals have an ultra-low dislocation density and are successfully used for construction of violet laser diodes. This work presents experimental data of high resolution x-ray diffractometry and photoluminescence. This work consist of three parts: (i) comparison between GaN substrates and GaN/sapphire templates; (ii) influence of AlGaN layers on bowing of samples; (iii) microstructure of InGaN/GaN multiple quantum wells.

Equations governing scans along arbitrary directions in reciprocal space were developed and used to map reciprocal lattice points (RLPs) with radial raster patterns to study mosaic structure in GaN thin films deposited on semi-insulating 4H-SiC substrates using AlN nucleation layers (NLs). The films were grown by molecular beam epitaxy, keeping the GaN growth conditions the same, but using different AlN NL growth conditions. Mosaic tilt angles determined from symmetric RLP breadth measurements were similar for all samples measured, consistent with screw and mixed dislocation densities determined from transmission electron microscopy (TEM) measurements. Mosaic twist was determined using off-axis skew-symmetric high resolution x-ray diffraction measurements of asymmetric RLP breadths, yielding results consistent with grazing incidence in-plane x-ray diffraction twist measurements. A clear correlation between the twist angle and the edge and mixed dislocation densities determined by TEM was not observed, warranting careful consideration of dislocation structure.

We have studied a series of GaN films grown with a range of dislocation densities by atomic force microscopy (AFM), transmission electron microscopy (TEM) and high resolution x-ray diffraction (HRXRD). The (002), (004), (006), (105), (204), (302), (100), (110), (200) and (300) reflections were measured as reciprocal space maps (RSMs) or scans in ω and ω/2θ. The latter 4 in-plane reflections were measured using a low, or glancing, incident angle with respect to the film surface. We have used a variety of different methods to try and obtain reliable measurements for mosaic tilt, twist, crystallite size and microstrain both in- and out-of plane. From (hk0) data in-plane twist angles were measured ranging from 0.37° to 0.078° and in-plane microstrains from 3.5 × 10⁻⁴ to 1.8 × 10⁻⁴. The improvements in the quality of the GaN layers relate to the increased island coalescence time, which reduces in particular the number of edge-type threading dislocations. The first three samples had a much larger tilt ∼0.09° than the last three ∼0.04°. However, the latter samples were bowed, so results from a single measurement on the (002) peak are too large. Beam restriction on the (002) or an extrapolation from several (00l) reflections gives more reliable results. The values obtained for in-plane crystallite size are in general variable or unreliable. For some samples the sizes are considered to be too large to be accessible by XRD; in most cases the peak broadening is dominated by tilt or twist or microstrain and the results are sensitive to assumptions about the peak shape. For the samples with smaller measurable crystallite sizes, the (hk0) peaks were too weak to measure reliably. The cell parameters showed more compressive strain with fewer dislocations. The trends observed by HRXRD are consistent with AFM and TEM results.

Nitrogen doping during crystal growth is used to create nitrogen–vacancy(–oxygen) complexes. These complexes enhance the nucleation of silicon oxide precipitates. The precipitates and other volume defects in silicon wafers serve as gettering centres for metal impurities during the device processing. We have studied nitrogen-doped silicon wafers (001) from the origin, middle and end of the ingot, annealed at low (750°C) and high (1050°C) temperatures, using triple-axis high-resolution x-ray diffraction. The reciprocal space intensity distributions from clusters, stacking faults and dislocation loops were modelled using the Krivoglaz theory and a continuum model of the defect deformation field. Good agreement of the theory with the experimental data was achieved for the model of dislocation loops. The symmetry of measured reciprocal space maps determines the type of dislocation loops and from extracted linear scans in the ⟨111⟩ direction we can obtain the radius and concentration of the loops. These parameters were combined with the results from selective etching and infrared absorption spectroscopy. Concentration of interstitial oxygen, shape, stoichiometry and volume fraction of precipitates were obtained from absorption spectra taken at room and liquid nitrogen temperature.

A combination of x-ray diffraction methods and electron microscopy was used for the structural study of Czochralski silicon crystals highly doped by As. For as-grown crystals a weak strain field and probable clustering of As-impurity atoms follow from section topography and a reduction in the Borrmann effect intensity. For annealed crystals, it is shown that precipitates and dislocation loops are formed during annealing. The defects are located in highly distorted stripes lying nearly parallel to the crystal surface with period 200–300 µm. The concentration of the defects drastically decreases along the crystal radius from the centre to the periphery and along the growth axis from the seed. The average size of the defects obtained from the diffuse scattering increases with increasing distance from the centre to the periphery and along the growth axis from the seed. One concludes that the dependence of the defect parameters observed is associated with the change in oxygen concentration along the crystal radius and growth axis.

As a part of the International Avogadro Project we have utilized a state-of-the-art lattice comparator at the National Institute of Standards and Technology (NIST) to measure relative lattice parameter differences that are of the order of 10⁻⁸. Samples have been prepared from NRLM3, NRLM4, WASO04 and WASO17 material, which are of great importance in terms of a precise determination of the silicon d₂₂₀ lattice parameter. The experimental set-up at NIST consists of a two-source, two-crystal Laue x-ray diffractometer. It uses a heterodyne interferometer to control the position of the first crystal with an uncertainty of 2 × 10⁻⁹ rad. From a least-squares fit we estimate the measurement uncertainty for a relative lattice parameter comparison at about 3 × 10⁻⁹. The measured lattice parameter variation across each individual sample indicates that the lattice uniformity of a particular specimen has to be carefully considered in view of comparing similar, though physically different, samples made out of the same material.

We have investigated strain compensated Si/Si_0.2Ge_0.8 multilayers, which were grown pseudomorphically on relaxed Si_0.5Ge_0.5 pseudosubstrates by molecular beam epitaxy. The stability of these highly strained Si/SiGe structures upon in situ annealing has been measured by means of x-ray reflectivity (XRR) up to 830°C. The temporal evolution of XRR reciprocal space maps was recorded, and a gradual disappearance of the multilayer structure was detected after annealing for 7 h at a temperature of 790°C. From the temporal evolution of the optical constants of the layers, deduced from the simulations and fits of the specular reflectivity, we obtained an interdiffusion coefficient D = (1.01 ± 0.03) × 10⁻²¹ m² s⁻¹ at 790°C.

The effect of in situ photoexcitation on the generation of structure defects in Si crystals implanted by Ar⁺ and Ne⁺ ions was studied using high-resolution x-ray diffraction. Photoexcitation was found to decrease the residual concentration of radiation-induced point defects in the case of low radiation damage (low doses, high energies) leading to annihilation of Frenkel pairs. For heavy damage (high doses, low implantation temperatures, low energies), photoexcitation contributes to amorphization of the damaged layer, which manifests itself as the formation and growth of clusters of radiation-induced point defects. Thus, in situ photoexcitation speeds up secondary processes, and the predominance of one or other process is stipulated by the degree of supersaturation of the solid solution of radiation-induced point defects.

In order to better understand interdiffusion in quantum well based optoelectronic Al_xGa_1−xAs/GaAs devices, we have performed rapid thermal processing on similar periodic superlattices (SLs) grown by solid source molecular beam epitaxy. The interdiffusion has been studied by x-ray diffraction measurements. The intermixing of the atoms at the barrier–well interfaces in the temperature range between 800°C and 950°C shifts the energy levels of the bound states and thus the photoluminescence wavelength of the structures. X-ray ω–2θ scans confirm Al–Ga interdiffusion at the barrier–well interfaces and are quantitatively investigated by fitting the envelope function of the SL satellites. A fit to the data yields diffusion lengths in the range 0.2–2.7 nm. Diffusion coefficients and activation energies can be derived from the temperature dependence of diffusion lengths. In the samples that exhibit rougher interfaces, the early stages of interdiffusion at up to 800°C for 1 min show the narrowing and increasing of satellite peak intensities followed by their broadening and decrease of peak maxima at higher temperatures above 850°C. The observation correlates with the initial smoothing of the interfaces

We have studied a possible generalization of the so-called iso-strain method that would allow for the characterization of strain fields in buried quantum dots (QDs) from x-ray grazing incidence diffraction data. In particular, the method allows us to determine the vertical position of a sub-volume of QDs of a certain lattice constant. The principle of the method is illustrated with a simulation and its precision is estimated. The method is applied for the analysis of buried InAs/GaAs QDs.

A new method based on measurement of the absorption of an x-ray beam diffracted from a substrate has been used to determine the film composition in an InGaAs/InP nearly-lattice-matched single heterostructure.

The absorption coefficient, μ_InGaAs, of the InGaAs alloy was obtained by accurately measuring the InGaAs layer thickness and the integrated intensities of several diffractions of the InP substrate compared with the integrated intensities of the equivalent peaks of an InP reference crystal. By using the tabulated Ga, As and In absorption factors, the In content was then determined. It is shown that in the case of an InGaAs alloy the accuracy in In content determination can reach 1%. The absolute In content of the InGaAs epilayer was found to be 4%–5% larger than expected from the linear dependence of the lattice parameter on the alloy composition as stated by the Vegard law.

This result has been confirmed by a diffraction profile auto-fitting software; with the assumption of the Vegard law the best fit of the 004 diffraction profile of the InGaAs/InP heterostructure could only be obtained with a 4.6% larger InGaAs thickness, to compensate for the larger In content as determined by the absorption measurement.

We have characterized the structure of AlAs/GaAs atomic-layer superlattices by x-ray diffraction. We show that when the superlattice layers are only a few monolayers (MLs) thick, lateral domains of vertical extent of 1–2 MLs exist. The small layer thickness also magnifies the growth error, leading to periodic compositional stacking faults in the growth direction. As the layer thickness increases, the lateral domain structures tend to behave like interfacial roughness. Growth interruption between successive layers enlarges the lateral domains, but does not remove the vertical stacking faults.

X-ray diffuse scattering from a 17-fold InGaAs/GaAs quantum dot (QD) multilayer grown by an advanced molecular beam epitaxy process was investigated. The QDs in each layer form extended chains that are oriented along the planar direction. A prominent three-dimensional satellite structure in the x-ray diffuse scattering is found, which is caused by a strong lateral chain–chain correlation and vertical correlation of the lateral chain positions in the multilayer. In contrast, the dot–dot correlation within the chains are comparatively small. Numerical x-ray scattering simulations have been carried out. A comparison with corresponding experimental intensity patterns provides information on the QD size and QD spatial distribution.

Very weak Bragg reflections have already been used successfully to investigate dopant positions in the structure of the host lattice. The intensity of the x-ray diffracted beam is a function of the structure factor, F, which in turn is modified by the presence of the additional dopant atoms in the lattice. That change can be measured by carefully analysing the integrated intensity of the relevant weak reflections. New materials like low temperature GaMnAs layers are the subject of recent vigorous investigations into their various properties. A theoretical model based on detailed calculations of the structure factor is a way of answering the basic question about the lattice arrangements of the Mn atoms in the host lattice of the GaAs layer. Understanding the structural properties of these materials is essential, and investigations into the local arrangements around the dopant atoms are vital. One can do this through measurements of the quasi-forbidden (very weak) x-ray reflections. Our evaluation clearly indicates the need for the highest possible temperature control and stability of the growth process of such materials.

We study the strain evolution during molecular beam epitaxy growth of MnAs on GaAs(113)A, its change during postgrowth annealing and the interfacial structure by in situ grazing incidence x-ray diffraction. A MnAs peak is detected at a coverage as low as 0.5 monolayer (ML). The film is compressively strained at the onset of growth and relaxes as the thickness increases. The in-plane grain size increases in two distinct stages: a fast increase up to 4 ML nominal thickness is followed by a slow increase. Postgrowth annealing of the layer improves the crystal quality and leads to a further relaxation of the layer. An ordered array of misfit dislocations is found at the interface.

We present an analysis of the relaxation of thin MnAs films on GaAs(001) by x-ray grazing incidence diffraction during molecular beam epitaxy. Separate in-plane peaks of the MnAs layer and the GaAs substrate are detected for average thicknesses starting from ≈1 monolayer indicating the formation of a relaxed MnAs lattice. The variation of position of the MnAs peaks during growth yields the time dependence of relaxation. MnAs domains of different orientations are detected. A line broadening due to size and strain effects is observed. We find a regular arrangement of misfit dislocations at the interface. The range of twist of the domains reduces during growth indicating an improvement of the epitaxy.

Specular and diffuse x-ray reflectivity measurements were employed for wafer bonding studies of surface and interfacial reactions in ∼800 Å thick SiN films deposited on III–V substrates. CuK_α1 radiation was employed for these measurements. The as-deposited films show very low surface roughness and uniform, high density SiN. Reflectivity measurements show that an oxygen plasma treatment converts the nitride surface to a somewhat porous SiO_x layer (67 Å thick, at 80% of SiO₂ density), with confirmation of the oxide formation from x-ray photoelectron spectroscopy. Reactions at the bonded interface of two oxygen plasma treated SiN layers were examined using a bonded structure from which one of the III–V wafers is removed. Reflectivity measurements of bonded structures annealed at 150°C and 300°C show an increase in the SiO_x layer density and thickness and even a density gradient across this interface. The increase in density is correlated with an increase in bond strength, where after the 300°C anneal, a high interfacial bond strength, exceeding the bulk strength, was achieved.

Different x-ray techniques are used to characterize Pr₂O₃ layers epitaxially grown on Si substrates. X-ray reflectometry is the preferred technique to determine the layer thickness and to detect and characterize possible interface layers. With standard x-ray diffraction (XRD), we found for 100 Si substrates that Pr₂O₃ grows in its cubic phase with the 110 direction perpendicular to the surface, while the hexagonal phase in 0001 orientation is preferred for 111 Si. In the thickness range of microelectronics applications, Pr₂O₃ layers can be considered as well-ordered heteroepitaxial structures. The relaxation of the oxide layer from pseudomorphism to bulk behaviour was studied in the technologically important thickness range (1–10 nm) by synchrotron radiation grazing incidence XRD.

High-resolution x-ray diffraction and high-resolution scanning electron microscopy have been applied to characterize BaTiO₃ films of different thicknesses, metal–organic chemical vapour deposition grown on MgO substrates. We found a strong correlation between the strain state of the films and the amount of specific material discontinuities, the latter serving as an effective channel of strain relaxation. The results obtained are explained by considering the structural misfit arising at the interface between in-plane oriented 90° domains.

Grazing incidence small angle x-ray scattering has been used to probe the in-plane length scale and scaling behaviour of the conformal interface roughness of sputtered Co/Pd multilayers. Scaling was seen in the intensity distribution through the Bragg sheets for large out-of-plane wavevectors. The scaling exponent showed power law variation with multilayer repeat number, the extreme values being close to those predicted by the Kardar–Parisi–Zhang and Tang–Alexander–Bruinsma models of film growth. The wavevector at which scaling broke down increased linearly with repeat number. A power law increase as a function of bilayer repeat number was found in the in-plane correlation length defined by fitting the scattering in the incidence plane to the Sinha model. Both approaches showed that the multilayer interfaces tended towards a two-dimensional character as the number of repeats increased.

This paper presents the results of a study of elastoplastic deformation of titanium alloy Ti-6Al-4V subjected to four point bending prior to residual elastic strain measurements by high energy synchrotron diffraction. Both white-beam and monochromatic x-rays were used at the SRS Station 16.3 in order to record diffraction patterns as a function of beam position across the sample. This allowed the comparison between the two techniques to be readily made. Residual (elastic) strain was calculated as a function of position across the sample, based on different reflections of hcp titanium. Inelastic bending analysis was used to extract the plastic strains. The results demonstrate that (i) the level of plastic deformation can be deduced from the x-ray diffraction profile, (ii) the asymmetry of the material response to plastic deformation in tension and compression can be identified and (iii) differences in the behaviour of different grain groups can be seen.

High-resolution diffraction using synchrotron x-ray radiation was applied to study γ' precipitates with an L1₂ superlattice crystal structure in the single crystal superalloy SC16 after creep deformation at 1223 K with a creep strain of ±0.5% for tensile and compressive loads, respectively. The measurements of full width at half maximum (FWHM) of 001 and 100 γ' superlattice reflections were performed at various temperatures from ambient temperature to 1173 K in vacuum. The experimental results revealed that the FWHM of both reflections decrease with increasing temperature. It is well-known that changes in particle size and lattice distortion in materials could lead to a variation of FWHM. The observed behaviour is discussed in the light of both the above-mentioned aspects. The decrease in the peak width is mainly attributed to the temperature dependence of the internal strain state.

Laser- and light-induced charge density variations in organic molecular single crystals of 2-benzyl-5-benzylidene-cyclopentanone (BBCP) have been investigated using high resolution x-ray diffraction and spectroscopic methods.

In BBCP single crystals a cyclobutane ring is formed from two parallel double bonds of neighbouring molecules by light irradiation. Due to this photodimerization, the bond lengths, bond angles and electron density are strongly changed near the C = C double bonds in the molecules, as has been shown by spectroscopic techniques and diffraction methods.

Also, the overall transformation of the crystals from the reactant to the product state via a transient structure with a picosecond lifetime has been found by time-resolved x-ray diffraction, and by the time-correlated single-photon counting measurements.

Using asymmetric diffraction in grazing incidence or in grazing emergence it is possible to expand or compress an x-ray beam in one dimension. Combining two asymmetric diffractions with non-coplanar planes of diffraction it is possible to obtain two-dimensional beam expansion or compression. This paper reports on a monolithic two-dimensional x-ray beam compressor consisting of two non-coplanar asymmetrically inclined {311} diffractors prepared in one silicon crystal block and tested at Optics beamline BM05 at ESRF, Grenoble. The design of the x-ray beam compressor, the results of beam tracing image simulation, the experimental arrangement used for testing and the properties of the x-ray microbeams formed are presented. For the beam energy of 9.5 keV 10- and 13-times beam compression in two directions was observed. Using a metal grid in the incident beam more than 400 microbeams smaller than 10 µm and separated by less than 5 µm were obtained in the outgoing beam. A gain of up to 100 times in intensity per unit area was obtained in comparison with the x-ray beam magnifier geometry, demonstrating a real two-dimensional beam compression.

A planar x-ray waveguide (WG) consisting of a diamond-like carbon layer sandwiched between two Ni layers is used to demonstrate for the first time the possibility of using WGs as optical elements with standard laboratory sources. The exit beam profile for the first two guided modes has been measured and analysed to demonstrate the high degree of beam coherence. The exit divergence and the beam size are reported and compared with theoretical predictions. Other relevant parameters, such as efficiency and gain, have been measured. This opens up interesting perspectives for the production of nanometre-sized x-ray beams with table-top laboratory sources.

Parabolic refractive x-ray lenses are novel optical components for the hard x-ray range from about 5 keV to about 120 keV. They are compact, robust, and easy to align and to operate. They can be used like glass lenses are used for visible light, the main difference being that the numerical aperture is much smaller than 1 (of the order of 10⁻⁴–10⁻³). They have been developed at Aachen University and are made of beryllium, boron, aluminium and silicon. Their main applications are in micro- and nanofocusing, in imaging by absorption and phase contrast. In combination with tomography they allow for three-dimensional imaging of opaque media with sub-micrometre resolution. Finally, they can be used in speckle spectroscopy by means of coherent x-ray scattering. References to a number of applications are given.

One of the factors influencing the focus size in diffractive–refractive optics is the quality of diffracting surface. If the surface is uneven, as it is when the silicon crystal surface is only etched, then the diffraction at each point of the surface is a combination of an asymmetric and inclined diffraction (general asymmetric diffraction). This somewhat deviates and spreads the diffracted beam. The integration over the surface hit by an incident beam gives the angular spread of the diffracted beam. It is shown theoretically that in some cases (highly asymmetric, highly inclined cut) the etched surface may create the spread of the diffracted beam such that it causes a significant broadening of the focus. In this case a mechanical–chemical polishing is necessary. This has been verified by us earlier in a preliminary experiment with synchrotron radiation. In this work the new experiment with the same crystals is performed using double crystal (+, −) arrangement and a laboratory x-ray source (CuKα radiation). We compared two samples; one of them is mechanically–chemically (MC) polished and thus the diffracting surface is almost perfect; the other is only etched. This experiment allows a better comparison of the result with the theory. The difference between the measured rocking curve widths for the etched and MC polished crystals (10'') roughly agrees with theory (7''), which supports the correctness of the theoretical approach.

Structural investigations of synthesized crystals of diamond have been carried out by means of multiple coplanar diffraction. The x-ray divergent-beam technique and the method of numerical solution of Takagi's equations have been used. It has been shown that diamond crystals synthesized in the Ni–Mn–C system contain laminated segregations in the form of growth regions due to the inhomogeneous capture of nitrogen or boron impurities during the crystal growth and the quasiperiodic strain fields generated.

The resonance concept is extended for x-ray interbranch scattering by a bent crystal with a uniform strain gradient. Splitting each of the branches of the dispersion surface follows from these considerations. It is shown that interbranch crossover is due to interference of the waves corresponding to 'new' branches, making up the 'new' Bloch-modes.

The classic scheme of the genetic algorithm is extended to improve the robustness and efficiency of the genetic technique. New genetic operators implemented in this paper are shown to increase the convergence speed and reliability of the optimization process. A complex model function with multiple local extrema and real x-ray reflectivity and diffraction data have been used to prove the modified algorithm. The effectiveness of the new technique is compared with the effectiveness of various optimization methods.

A novel simulation program in the MATLAB format for x-ray diffraction profiles in multilayers was developed, which can be applied to any multilayered structure with no limitations. The simulation algorithm (nickname DIWAS) is based on direct summation of waves, scattered by individual atomic planes. It takes into account strain and concentration-induced fluctuations of interplanar spacings, interface roughness and buried amorphous layers, and enables the addition of diffuse scattering profiles.

The program allows handling of asymmetric reflections as well as symmetric ones, taking special care of the effective layer thickness. The summation over individual layers can be done coherently or incoherently, depending on the interface structure. To make the fitting procedure comprehensible, the contribution of every layer can be plotted separately.

In this paper, the direct wave summation (DIWAS) routine is described in detail and is applied to fit experimental diffraction profiles taken from MOVPE grown heterostructures and superlattices of practical importance, such as InGaN/GaN/AlGaN/sapphire, GaAsN/GaAs, InGaAsP/InP and InGaAs/InP.