Crystals In Laue Geometry Research Articles

Dynamical focusing by bent, asymmetrically cut perfect crystals in Laue geometry.

A semi-analytical approach based on the influence functions of a point source located on the crystal surface has been adopted to show that the focusing ability of cylindrically bent Laue crystals may be strongly enhanced by replacing symmetrically cut crystals with asymmetrically cut crystals. This approach is generally applicable to any distance between the X-ray source and the focusing bent crystal. A mathematically straightforward method to simplify the derivation of the already known expression of the influence functions in the case of deformed crystals with a constant strain gradient (e.g. cylindrically bent crystals) is also presented.

Hard X-ray Laue monochromator

Experimental studies of X-ray diffraction from reflecting atomic planes (10̄11) of X-cut quartz single crystal in Laue geometry influenced by the temperature gradient were carried out. It is shown that by using the temperature gradient it is possible to reflect a hard X- ray beam with photon energy near the 100 keV with high efficiency. It has been experimentally proved that the intensity of the reflected beam can be increased by more than order depending on the value of the temperature gradient.

Interference absorption coefficient of X-rays in crystals in the presence of temperature gradient

We investigate experimentally and theoretically the behavior of the interference coefficient of absorption of X-ray radiation of a quartz single crystal in Laue geometry in the presence of temperature gradient. The total intensity of transmitted X-ray radiation and that reflected from different families of reflecting atomic planes of the quartz single crystal has been recorded. It was shown that with the increase in temperature gradient the coefficient of absorption of X-ray radiation decreases abruptly reaching its minimal value at a certain value of the temperature gradient.

PARAMETRIC X-RAY AND DIFFRACTED TRANSITION RADIATION OF 4.5 GEV ELECTRONS IN DIAMOND

Recently using the theory of Afanasev-Aginian (1977-1978) it has been reconsidered theoretically the properties of the contributions of PXR, DTR and their interference into the radiation intensity produced by particles in single crystals in Laue geometry, essentially differing from those of Bragg geometry. After a short review of theoretical and experimental works devoted to DTR in this work we discuss the properties of Laue geometry and make comparison of the predictions of the above theory with the results of the second experiment performed by Avakian et al in 1987 with the help of 4.5 GeV electrons.

Study of angular width of an X-ray beam fully pumped from quartz single crystal in the presence of temperature gradient

We investigate the cross section of transmitted X-ray beam diffracted by reflecting atomic planes (10–11) of a SiO2 single crystal in Laue geometry for different values of temperature gradient applied to the crystal. It is shown that the angular width of a fully pumped X-ray beam depends on the distance between the source and the studied sample and decreases with the increase in this distance.

Experimental verification of dynamical diffraction focusing by a bent crystal wedge in Laue geometry

Recent X-ray optical experiments have validated previous theoretical work on focusing by bent crystals in Laue geometry. It was shown that a suitable choice of the crystal thickness significantly improves the focusing performance of the crystal by combining the dynamical focusing of the Borrmann triangle with the geometrical focusing obtained by the crystal bending. The best focus size achieved during the experiments was less than 5 µm and is in practice limited by the source demagnification for the considered setup.

Birefringence in multiple X-ray scatterings deduced from the alternative theory of Pendelloesung beat

The study of the inner structure of the weak-absorbing noncrystalline materials as well as the biological objects is carried out by the method of the X-ray phase contrast which at present is substantially in progress. In the present work the possibility of reconstructing the inner structure of the one-dimensional phase objects under the diffraction focusing of the X-ray spherical wave is reported.The fact that with the incidence of the monochromatic X-ray spherical wave on the crystal in Laue geometry the diffracted radiation is focused inside the crystal is used. The focal line is perpendicular to the diffraction plane. Before entering the crystal the radiation is supposed to pass through the phase object where the inhomogeneities have one-dimensional distribution along the perpendicular diffraction plane.With the wave transmission trough the phase object the conditions of the focusing are broken: because of the refraction on the inhomogeneities the X-rays change their directions and the wave front is deformed. The intensity distribution analysis in the image diffracted from a strong-absorbing wedge-like crystal with rib parallel to the diffraction vector shows that the focusing is possible for every point of the phase object if one compensates the deviation from Bragg condition along the diffraction vector and the wave front deformation along the perpendicular diffraction plane. The focusing is possible if the source-crystal distance is smaller than the ratio of the inhomogeneity size and the difference of the index of refraction from the unit. m35.p03

The formation of the X-ray phase contrast under the diffraction focusing of the spherical wave

The study of the inner structure of the weak-absorbing noncrystalline materials as well as the biological objects is carried out by the method of the X-ray phase contrast which at present is substantially in progress. In the present work the possibility of reconstructing the inner structure of the one-dimensional phase objects under the diffraction focusing of the X-ray spherical wave is reported.The fact that with the incidence of the monochromatic X-ray spherical wave on the crystal in Laue geometry the diffracted radiation is focused inside the crystal is used. The focal line is perpendicular to the diffraction plane. Before entering the crystal the radiation is supposed to pass through the phase object where the inhomogeneities have one-dimensional distribution along the perpendicular diffraction plane. With the wave transmission trough the phase object the conditions of the focusing are broken: because of the refraction on the inhomogeneities the X-rays change their directions and the wave front is deformed. The intensity distribution analysis in the image diffracted from a strong-absorbing wedge-like crystal with rib parallel to the diffraction vector shows that the focusing is possible for every point of the phase object if one compensates the deviation from Bragg condition along the diffraction vector and the wave front deformation along the perpendicular diffraction plane. The focusing is possible if the source-crystal distance is smaller than the ratio of the inhomogeneity size and the difference of the index of refraction from the unit.

A flexible configuration for a high-energy phase-contrast imaging beamline involving in-line focusing crystal optics

We discuss a new optical configuration for a hard X-ray imaging beamline that allows one to obtain a secondary source of variable size by using two asymmetrically cut bent silicon crystals in Laue geometry. A feature of this set-up is that radiation from the secondary source propagates parallel to the direction of the incident radiation. Preliminary aspects of the design for the imaging beamline are discussed.

Bent crystals in Laue geometry: dynamical focusing of a polychromatic incident beam

The main limitation of Laue geometry for the achievement of a small focus size is the focus broadening caused by the intrinsic Darwin width and the spread of the beam in the Borrmann triangle, resulting from propagation inside the crystal. A method, based on dynamical focusing, is suggested that allows improvement of the quality of high-energy polychromatic focusing by bent crystals in Laue geometry.

Initial results on logarithmic spiral bent Laue analyzer for fluorescence x-ray absorption spectroscopy (abstract)

We have previously described [Z. Zhong, D. Chapman, B. A. Bunker, G. B. Bunker, R. Fischetti, and C. U. Segre, J. Synchrotron Radiat. 6, 212 (1999); C. Karanfil et al., AIP Conf. Proc. 521, 178 (2000)] a novel concept of using highly bent single crystals in Laue geometry for wide bandwidth monochromatization of fluorescence x rays emerging from a point source, such as the sample in fluorescence x-ray absorption spectroscopy (XAFS) experiments. In this article we describe the first measurements (summer 2000) of the fluorescence XAFS of millimolar solutions of several elements. The potential of this type of analyzer is clearly demonstrated.

The nuclear-resonance-scattering station at the PETRA II undulator beamline

PETRA II, a 12 GeV accelerator at DESY, Hamburg, is used to produce synchrotron radiation (SR) for experiments in the hard X-ray regime when it is not running as injector for HERA. The beam from an undulator is split by a diamond crystal in Laue geometry to feed two experimental stations, one of which is now dedicated for nuclear resonance experiments. The X-ray energy may be chosen in the range from 5 to 55 keV covering all isotopes already observed with SR and many interesting candidates for new resonances. Tuning may be performed by optimising the magnetic gap and the storage ring energy. In particular, the opportunities for timing experiments are unique due to a very flexible filling mode of the storage ring. The flux at the sample position is comparable to undulator beams at ESRF. The second beamline covers higher energies up to some 300 keV and may also be used for nuclear resonance experiments.

Focusing characteristics of diamond crystal x-ray monochromators. An experimental and theoretical comparisona)

Perfect crystals in transmission (Laue) geometry can be used effectively for x-ray monochromators, and moreover, perfect Laue crystals show an interesting focusing effect when the incident beam is white and divergent. This focusing is directly dependent on the incident beam divergence and on the diffraction profile width of the crystal. The aim of this work is to study whether this property can be used for focusing a synchrotron x-ray beam, and to obtain quantitatively the dimensions of the resulting monochromatic beam. We have experimentally measured the size of an undulator beam after diffraction from a diamond crystal in Laue geometry, and we analyze and explain the results by comparison with ray-tracing simulations.

Focusing characteristics of diamond crystal x-ray monochromators. An experimental and theoretical comparison (abstract)a)

Perfect crystals in transmission (Laue) geometry can effectively be used for x-ray monochromators. Perfect Laue crystals show an interesting focusing effect when the incident beam is white and divergent. This focusing is highly dependent on the beam divergence and on the energy bandpass of the crystal. The aim of this work is to study whether this property can be used for focusing a synchrotron x-ray beam, and to obtain quantitatively the beam dimensions of the resulting monochromatic beam. We have experimentally measured the size of an undulator beam after diffraction from a diamond crystal in Laue geometry, and we analyzed and explained the results by comparison with ray tracing.

Gamma-ray focusing concentrators for astrophysical observations by crystal diffraction in Laue geometry

The diffraction and optical properties of several crystal concentrator configurations which could be adopted in hard x-ray astrophysical observations are discussed and compared in terms of effective area, focusing characteristics, and overall dimensions. First, a concentrator consisting of a set of circular rings covered with asymmetric mosaic crystals in Laue geometry is considered; focusing is achieved by an appropriate choice of the geometrical parameters and the asymmetry angles. Specific effective areas larger than 600 cm2 can be obtained in the energy range 120–190 keV by using Si (422) Bragg reflections in a device with a diameter of 2.5 m and a focal length of 13.5 m. Afterwards, a spherical-zone crystal concentrator is analyzed where asymmetric Laue geometry leads to focusing. With a focal length of 8 m and Si (422) reflections, the mean effective area in the energy range 100–300 keV is about 6500 times larger than the focal spot while the separation power of the concentrator is of the order of 10 arcsec. Finally, a concentrator consisting of several coaxial focusing paraboloids is analyzed. The surfaces of the paraboloids are covered by mosaic crystal tiles with lattice planes disposed normally to the meridians. By using Ge crystals with a mosaic width of ≊350 μrad and assuming a focal length f=10 m with a total aperture 2α=16 deg, it is possible to obtain effective areas larger than 1000 cm2 for energies smaller than about 150 keV. On the other hand, the ratio between the mean effective area and the size of the focal spot in the energy range 200–500 keV is higher than 10 000.

Perfect crystal X-ray phase retarders

Abstract X-ray phase retarders of perfect crystals are discussed on the basis of a dynamic theory of diffraction. Although all conceivable diffraction geometries can be used for a phase retarder, transmission of less absorptive crystals in both Laue and Bragg geometries as well as reflection and transmission of absorptive crystals in Laue geometry give practical solutions for circularly polarized X-ray generation with synchrotron radiation (SR). Some SR beamline optics using these phase retarders are presented.

X-ray beam sheet deflection for liquid surface spectrometry

An x-ray beam incident on a liquid surface at glancing angles may be specularly reflected (XR), diffracted (GID), or yield fluorescent radiation (GIF). The three mechanisms, encompassing liquid surface x-ray spectrometry, give complementary information about the liquid surface structure. In common is the incident monochromatic beam: It has the shape of a downward sloping thin sheet with the sheet normal and the propagation direction ideally spanning a vertical plane. Methods to produce such a beam from a horizontal, polychromatic synchrotron radiation beam are discussed. For a high brilliance undulator source the simplest solution turns out to be Bragg reflection from a single tilted monochromator crystal in Laue geometry.

Applications of perfect crystal X-ray optics

Recent progress in perfect crystal X-ray optics at the Photon Factory is described. As an application of the ultra-plane-wave X-ray optics, experimental observations of nearly intrinsic rocking curves for a parallel-sided perfect crystal in Laue geometry and their thickness dependence are shown. Applications to X-ray polarization optics are also described.

Multibeam calculation of the intensity distribution for an imperfect crystal in Laue geometry

A computer experiment is performed to calculate the intensity distribution for an imperfect crystal in Laue geometry. The computational procedure is based on the scattering matrix formalism of the multibeam dynamical X-ray theory. The numerical solution of this problem is presented. The structure of the GaAs crystal with antiphase domain boundaries is employed as a model for the calculation. The results suggest that this method can be useful for detailed studies of imperfect structures. Es wird ein Computerexperiment zur Berechnung der Intensitatsverteilung fur einen defektbehafteten Kristall in Laue-Geometrie durchgefuhrt. Dieses Berechnungsverfahren beruht auf dem Formalismus der Streumatrix der dynamischen Rontgen-Mehrstrahl-Theorie. Die numerische Losung dieses Problems wird vorgestellt. Die Struktur des GaAs-Kristalls mit Antiphasen-Domanengrenzen wird als Modell fur die Berechnung benutzt. Die Ergebnisse weisen darauf hin, das diese Methode fur detaillierte Untersuchungen der Defektstrukturen nutzlich sein konnen.

Diffractometer alignment and polarization determination of X-ray beams by means of the Borrmann effect

The Borrmann effect, that is, the anomalous transmission of X-ray beams through sufficiently thick perfect crystals in Laue geometry, is a sensitive diffraction tool which has many fundamental and practical applications: the accurate alignment of any full four-circle instrument (equipped with a cradle in asymmetric design) with respect to the incident beam, measurement of the divergence of any X-ray beam, and the precise determination of the beam polarization, incident or diffracted. For these applications, it is shown that no modifications to the diffractometer are required. The measurements simply consist of measuring φ and χ rocking curves of the anomalous transmitted beam where the ω angle is used as a parameter. The analyses require the findings of the peak centroid positions, the full widths at half maximum and the rocking-curve integrated intensities. Some results are presented as illustrations of the method. These Borrmann-effect applications promise to be more helpful for diffractometers installed at synchrotrons than for in-house laboratories.