Double-crystal Diffractometers Research Articles

The promise of GaAs 200 in small-angle neutron scattering for higher resolution.

The Q resolution in Bonse-Hart double-crystal diffractometers is determined for a given Bragg angle by the value of the crystallographic structure factor. To date, the reflections Si 220 or Si 111 have been used exclusively in neutron scattering, which provide resolutions for triple-bounce crystals of about 2 × 10-5 Å-1 (FWHM). The Darwin width of the GaAs 200 reflection is about a factor of 10 smaller, offering the possibility of a Q resolution of 2 × 10-6 Å-1 provided crystals of sufficient quality are available. This article reports a feasibility study with single-bounce GaAs 200, yielding a Q resolution of 4.6 × 10-6 Å-1, six times superior in comparison with a Si 220 setup.

Remarkable precision of the 90-year-old dynamic diffraction theories of Darwin and Ewald

The reflectivity functions calculated by Bonse and Hart for a multi-bounce channel-cut single crystal, following the 90-year-old theories of Darwin and Ewald, exhibit extremely narrow nearly rectangular profiles. This feature provides ultra-high angular resolution and sensitivity for the double-crystal diffractometers now widely used for the observation of large-scale structures in condensed matter. However, the experimental results are several orders of magnitude poorer than the theoretical prediction, the `wings problem'. The reason for this discrepancy has remained unidentified for more than 40 years, creating problems for both theory and practice. A solution to this problem for neutron diffraction in Si channel-cut crystals is presented here. The results enable nearly theoretical functions of multiple reflectivity to be obtained, demonstrate the remarkable precision of the Darwin and Ewald theories in the range of the wings, and give rise to much improved sensitivity for the next generation of Bonse–Hart double-crystal diffractometers.

X-ray diffractometry and electron microscopy of porous silicon layers at different stages of oxidation in air

Porous silicon layers prepared by anodic etching under different conditions have been systematically studied in the course of their natural oxidation (aging) in air by many-crystal X-ray diffractometry and transmission electron microscopy. Quantitative information on the strains and crystal structure of layers has been obtained using a combination of measurements of the 004 symmetric and 224 asymmetric reflections in the Bragg geometry on double-crystal and triple-crystal X-ray diffractometers. It has been revealed that the aging of porous silicon is accompanied by an increase in macrostrains and microstrains, as well as in micro-misorientations of crystal fragments, which lead to gradual destruction of porous layers up to their complete amorphization.

Differential phase contrast and dark field neutron imaging

Differential phase contrast imaging resolves angular deviations of a beam due to phase shifts induced by a sample and thereby enables the visualisation and three-dimensional reconstruction of the refractive index distribution of a sample additional to the attenuation coefficient addressed by conventional radiography and tomography. Two instrumental techniques, namely double crystal diffractometers and a grating interferometer setup, are suitable to detect this kind of contrast. According to the high angular resolution of these methods they are suited to additionally detect dark field contrast, i.e. (ultra) small angle scattering contrast. Magnetic fields add to the refractive index for neutrons and consequently magnetic structures can in principle also be imaged by these methods. Relations between the methods will be discussed and an overview of current developments will be given.

The new V12 ultra-small-angle neutron scattering and tomography instrument at the Hahn–Meitner Institut

The new V12 instrument at the Hahn–Meitner Institute in Berlin is a multiple setup combining several techniques to investigate the internal structure of bulk samples. It consists of two double-crystal diffractometers (DCDs) and an attenuation tomography device operating with monochromatic neutrons. The three instrument parts can be used independently at the same time. The DCDs are mainly used in the ultra-small-angle neutron scattering (USANS) regime, where they overlap the accessible range of small-angle neutron scattering instruments, while tomographic methods collect real-space information on a macroscopic scale. Together they enable structural investigations over six orders of magnitude (50 nm to 5 cm). Scattering and tomographic methods can even be combined by means of diffraction and scattering-enhanced imaging. The sample environment can be varied over a large range of temperatures and pressures for USANS measurements and a polarized USANS option is available.

Scattering-related contrast signals in neutron computerized tomography and the new V12 instrument at HMI Berlin

Double-crystal diffractometers (DCD) are widely used for structural investigations at the limit between macroscopic and microscopic inner structures of sample materials. Operating in an ultra-small-angle scattering q-range between 10 −4 and 10 −1 nm −1 structures between 50 nm and nearly 100 μm can be resolved. Hence the DCD connects the resolvable ranges of small-angle neutron scattering (SANS) instruments and neutron tomography facilities. However, the DCD does not only link the resolvable size ranges but can also be operated to yield both, q-space information on microscopic structures combined with real space information in the range of macroscopic inner structures. This method was developed in recent years at the V12 DCD at HMI by introducing refraction and ultra-small-angle neutron scattering (USANS) contrast for tomography. The new V12 DCD set-up has now been optimized to exploit all the opportunities of USANS, refraction and USANS contrast tomography and conventional attenuation contrast tomography with an intense monochromatic neutron beam. The new contrast methods will be introduced as well as the final set-up of the V12 instrument. Additionally, several examples and results achieved by the new techniques and instrument will be given.

Neutron tomography in double crystal diffractometers

Using a double crystal diffractometer (DCD) for tomographic imaging introduces the possibility to use various signals for image contrast. In conventional neutron and X-ray radiography and tomography the contrast signal for imaging arises just from the attenuation in the sample. Due to recent developments in digital imaging tomography gained a lot of importance in medicine and non-destructive testing (NDT). But not all materials deliver an useful contrast concerning attenuation neither in the case of X-rays nor for neutrons. In a DCD attenuation but also other interactions between penetrating radiation and sample can be registered. Besides the common attenuation there are especially refraction and small-angle scattering effects. It will be shown at least for neutrons that from each of these signals recorded as tomographic projections in a DCD an image of the sample can be reconstructed by the means of common filtered back projection (FBP) algorithm. Additionally, all the signals can be registered in one measurement and can be used for independent reconstructions resulting in different images expressing different characteristics of the sample.

Optimisation of a crystal design for a Bonse–Hart camera

Bonse-Hart double-crystal diffractometers (DCDs) with multi-bounce channel-cut crystals show rocking curves that depart dramatically from dynamical diffraction theory in their wings. The intrinsic background is many orders of magnitude higher than the predictions of dynamical diffraction theory. This effect was studied at the ultra-small-angle neutron scattering facility at the Atominstitut in Wien and at facilities in Grenoble, Jülich and Villigen. The scattering intensity contains Bragg reflections from the front and the back faces, and thermal diffuse scattering from the internal volume. The aim of this study was to eliminate this contamination and develop a new crystal design which provides optimal resolution. Therefore different ways were tested. In the first step the contamination was eliminated by cutting a groove in the middle of the back plate of the channel-cut crystals and inserting a cadmium absorber in this groove. With this modification an additional suppression of the wings of the rocking curve of about one order of magnitude was achieved. After this, we developed a new design for a DCD. The concept for this new crystal design was to avoid the back reflection and the thermal diffuse scattering. The different steps on the way to produce these crystals are presented in a detailed way. The crystal preparation and the different instruments where these crystals have been tested are also described.

Comparative study of porosity in 3Y-TZP superplastic ceramics by ultra-small-angle neutron scattering and scanning electron microscopy image analysis

Recent measurements of cavitation in superplastically strained 3Y-TZP ceramics by scanning electron microscopy and ultra small-angle neutron scattering (USANS) led to systematic differences in volume fractions of cavities determined by both methods. We show that the scattering curves measured by double crystal USANS diffractometers can be calculated directly from scanning electron micrographs taken from a single section of the material, without any assumptions of cavity shape or distribution. This technique was used to compare the USANS measurements with electron micrographs and showed that the calculated and measured curves agree well for medium scattering vectors. This result confirms that the electron micrographs represent well the microstructure of small cavities up to about 0.6 μm in radius. On the contrary, the calculations resulted in systematically larger intensities for small scattering vectors. This indicates that large cavities are responsible for the observed differences in volume fraction for the samples with nominal strain above 100%. An explanation by an inhomogeneous distribution of large cavities generated at high strains in the bulk of the tensile specimen and/or by surface artifacts is suggested.

Analysis of neutron double-crystal diffractometer scattering curves including multiple scattering

Double-crystal diffractometers (DCD) of the Bonse–Hart type are used for small-angle neutron scattering (SANS) experiments with very high resolution. Scattering from inhomogeneities in the size range of typically 100 nm to 10 µm can be detected with a DCD. The evaluation of DCD scattering curves is more complicated than for conventional SANS instruments with point collimation for two reasons: first, a DCD operates with a long-slit geometry, and second, owing to the high scattering power of large inhomogeneities, multiple small-angle scattering is likely to play a significant role in many DCD experiments. A numerical procedure is proposed for the determination of particle size distributions from DCD scattering curves influenced by multiple scattering. This procedure is based on ann-fold convolution of single-scattering cross sections, wherendepends on the degree of multiple scattering. It makes use of the indirect Fourier transformation method and thus, firstly, size distributions of arbitrary shape can be determined, and secondly, the calculation is fast, allowing an interactive analysis. The procedure is demonstrated with scattering from latex particles with different degrees of multiple scattering. The results show that the size and volume fraction of the latex spheres can be determined with a reasonable error even from scattering curves that are strongly influenced by multiple small-angle scattering.

Ultra-Small-Angle Neutron Scattering Study of Colloidal Alloys. 1. Contrast Variation Experiments for Mixtures of Hydrogenated and Deuterated Polystyrene Latices in H2O/D2O

Ultra-small-angle neutron scattering (USANS) experiments on one- and two-component aqueous colloidal dispersions were carried out at the Bonse-Hart double crystal diffractometers installed at the High Flux Isotope Reactor (Oak Ridge, TN) and at the JRR-3M reactor (Tokai, Japan). The USANS curves from low-concentration suspensions of hydrogenated poly(methyl methacrylate) (h-PMMA) latices in D 2 O show scattering patterns typical for isolated solid spheres, which change dramatically after adding the ion-exchange resin to remove ionic impurities. This additive significantly enhances electrostatic interaction between particles, and thus the diffraction pattern from 2.5% h-PMMA latices in D 2 O + ion-exchange resin corresponds to a colloidal crystal with the fcc structure. The USANS from hydrogenated and deuterated component of the colloidal alloy ofh- and d-polystyrene (h-PS and d-PS) latices was measured separately by matching the scattering length density of h-PS and d-PS particles in H 2 O/D 2 O mixture. It was found that the minority component of large diameter latices were randomly distributed in the alloy dispersion, whereas the majority component of small diameter particles formed colloidal crystals.

Annealing behaviors of lattice misfit in YIG and La-doped YIG films grown on GGG substrates by LPE method

By the LPE method using the PbO–B 2O 3 flux system, YIG and La-doped YIG films were grown on GGG substrates. Lattice misfit and defect formation could be controlled by Pb ions which were incorporated into the garnet film. The lattice misfits of as-grown and annealed samples were investigated by double and triple crystal X-ray diffractometers. Films grew pseudomorphically regardless of stress types. When the film with high Pb content was annealed, the misfit and the FWHM of the rocking curve increased. It is supposed that the increase in misfit occurs as a result of the reduction of Pb 4+ to Pb 2+, which is compensated by the formation of oxygen vacancies. During heat treatment, PbO precipitates were formed in the film, which increased FWHM of the film. For the low Pb content films, no annealing-induced change occurred.

Surface-Induced Parasitic Scattering in Bonse–Hart Double-Crystal Diffractometers

Bonse–Hart double-crystal diffractometers (DCD) with multibounce channel-cut crystals show rocking curves which depart dramatically in their wings from dynamical diffraction theory. This intrinsic background is many orders of magnitude higher than the predictions of dynamical diffraction theory. This effect has been studied at the ultra-small-angle neutron scattering (USANS) facility at Oak Ridge National Laboratory by the measurement of rocking curves from different volume elements of a thick single-bounce Si(111) perfect crystal and from triple-bounce channel-cut Si(111) crystals. Analysis of these data, together with the rocking curves from an X-ray Bonse–Hart DCD, allows it to be established that the rocking curve of the multibounce channel-cut crystals contains parasitic scattering generated at the surface of the crystals. The intensity of this component can be reduced by very deep etching of the crystal surface. Using this technique, the signal-to-noise ratio of the Bonse–Hart DCD at the ORNL USANS facility has been improved by one order of magnitude to ~5 x 105 [I(0)/I(θ = 10′′)].

Absolute Calibration of Small-Angle Neutron Scattering Data of a Double-Crystal Diffractometer

Small-angle neutron scattering (SANS) experiments generally provide the absolute SANS cross sections and this allows quantitative results to be obtained; however, data collected at double-crystal diffractometers are frequently not normalized to absolute cross sections and they are used only for qualitative analysis. In point-geometry diffractometers, the normalization is done by comparing the scattered intensities to those of samples of known cross sections or by measuring the direct-beam intensity; in the double-crystal diffractometer, the incident flux information is contained in the rocking curve measured without a sample and this feature can therefore be used to normalize the scattered intensities to the SANS cross sections. A sample of thickness 1 mm of the Ni-based superalloy UDIMET 520 was analyzed at a double-crystal diffractometer; the SANS cross section obtained by the proposed procedure compares well with the SANS cross section found for similar materials by using conventional point-geometry diffractometers and calibrated by light water.

Characterization of quantum wells by X-ray diffraction

Measurements of the intensity distribution in diffraction space yield information far beyond that available by simple profiles. This paper briefly reviews the parameters obtainable from quantum well structures, when using conventional double-crystal and slit-based diffractometers, and shows how further structural parameters can be extracted by diffraction space mapping. To interpret subtle features a ' delta -function like' diffraction probe has been used to be sure of the origin of some of the features observed. The influence of layer tilting and lattice relaxation on the diffraction process can lead to imprecise fits, but from a diffraction space map, and including the diffuse scattering, further valuable information is extracted. The interpretation of these features has required additional modification to dynamical theory and the use of multiple-crystal topography. Examples of some unusual diffraction effects with possible explanations are also given.

The resolution function of single-crystal diffractometers at a synchrotron-radiation source: the influence of absorption and extinction on the FWHM

For the input of the correct intensity-data-collection parameters – the scan width and the number of steps – the expected full widths at half-maximum of the Bragg intensity profiles (FWHM) for the whole θ range under consideration must be known. These FWHMs depend on the divergence of the incident synchrotron beam, on the monochromator and on the mosaic structure of the sample used. They are also affected by absorption and extinction. A simple but very effective resolution function for a triple-crystal diffractometer, applicable also to single- and double-crystal diffractometers, is given, taking all the dependences mentioned above into account. The calculated FWHMs are compared with the measured ones of three different single-crystal samples, namely the FWHMs of a YIG sphere and an Si sphere, obtained at various wavelengths in the range 0.3 to 2.2 A with the new Huber four-circle diffractometer set up at HASYLAB and the FWHMs of a CaF2 sphere, given in the literature and measured with the old five-circle Stoe diffractometer at HASYLAB (DESY, Hamburg, Germany). It is shown that, with use of the proposed resolution function, the beam characteristics – divergence and wavelength spread – as well as the characteristics of the samples – mosaic spread and mosaic block size – can be determined from comparison with experimental FWHMs, measured at different wavelengths.

Tomographic methods for 2D reconstruction with the double crystal diffractometer

High-resolution double crystal diffractometers are used to determine the internal ferromagnetic structure of crystals, e.g., FeSi samples. The measured data correspond to the Radon tranform of the 2D scattering distribution of the crystal. We develop and compare tomographic methods, such as the algebraic reconstruction technique and the filtered backprojection algorithm, for this application. This method allows us to image scattering patterns in the very low Q-range of Q ∼ 10 5 A ̊ −1 which is about two orders of magnitude lower than conventional small angle techniques.

Alignment of double-crystal diffractometers

A rapid method is described for aligning a double-crystal diffractometer based on the design of Hart (Characterization of Crystal Growth Defects by X-ray Methods, edited by Tanner & Bowen, pp. 483–485. Plenum Press, London, 1980). The theoretical intensity profiles are derived for variations in crystal tilt and rotation, and a method is described that uses these profiles to align any double-crystal diffractometer in a systematic way, suitable for computer automation. The alignment requirements for simple mismatch measurements are also given.

X-ray diffraction

Four hundred and fourteen references concerning x-ray diffraction occurring in published literature from mid 1977 through late 1979 are cited in this review. The review places emphasis on new developments in applications and instrumentation in both single crystal and powder diffraction; however, the topic of crystal structure analysis has been ignored except in the area of new instrumentation. Compound analysis has also been omitted where emhasis was on the compound rather than the method. Some topics covered in the review are synchrotron radiation applications, x-ray sources, flash x-ray techniques, detectors, image intensifiers, double-crystal diffractometers, precision diffractometers, single-crystal devices, x-ray topography, computer automation, diffractometry, low-temperature diffractometry, high-temperature diffractometry, special-handling techniques or equipment, quantitative analysis, line profile theory, profile analysis, stress analysis, crystallographic texture, computer programs, powder pattern indexing, computer/search/match techniques, powder cameras, and powder pattern in general. (BLM)