On the resolution function for powder diffraction with area detectors

In a powder diffraction experiment the resolution function defines the instrumental contribution to the peak widths as a function of the Bragg angle. The Caglioti formula is frequently applied to model the instrumental broadening and used in structural refinement. The parameters in the Caglioti formula are linked to physically meaningful parameters for most diffraction geometries. However, this link is lost for the now very popular powder diffraction geometry using large 2D area detectors. Here we suggest a new physical model for the instrumental broadening specifically developed for powder diffraction data measured with large 2D area detectors. The model is verified using data from two synchrotron diffraction beamlines with the Pilatus2M and MAR345 detectors. Finally, a functional form is proposed to replace the Caglioti formula for this geometry in the Rietveld method and profile refinements.

X-ray dynamical diffraction Talbot effect behind a crystal in free space

The dynamical diffraction Talbot effect takes place inside a crystal, when a periodic object is illuminated by a plane or spherical X-ray wave which then falls on the crystal at an angle close to the Bragg angle for some reflection. Both theoretical consideration and numerical calculations show that the dynamical diffraction Talbot effect also takes place behind the crystal. The effect is accompanied by the dynamical diffraction pendulum effect and wave focusing. Expressions are found for the dynamical diffraction Talbot distance for areas before and after focusing. The spatial Fourier spectrum of the periodic object is obtained on the focusing plane. Detailed analysis when the periodic object is illuminated by a plane wave has shown new features of this effect. The dynamical diffraction Talbot effect in free space can be used to determine the structure of a periodic object, to determine the structure of an arbitrary object placed before or after the periodic object, and to determine structural defects and deformations of the crystal.

Side-bounce beamlines using single-reflection diamond monochromators at Cornell High Energy Synchrotron Source

The design and implementation of new beamlines featuring side-bounce (single-reflection) diamond monochromators at Cornell High Energy Synchrotron Source (CHESS) are described. Undulator radiation is monochromated using an interchangeable set of diamond crystal plates reflecting radiation in the horizontal (synchrotron) plane, where each crystal plate is set to one of the low-index Bragg reflections (111, 220, 311 and 400) in either Bragg or Laue reflection geometries. At the nominal Bragg angle of 18° these reflections deliver monochromated X-rays with photon energies of 9.7, 15.9, 18.65 and 22.5 keV, respectively. An X-ray mirror downstream of the diamond monochromator is used for rejection of higher radiation harmonics and for initial focusing of the monochromated beam. The characteristics of the X-ray beam entering the experimental station were measured experimentally and compared with the results of simulations. A reasonable agreement is demonstrated. It is shown that the use of selected high-dislocation-density `mosaic' diamond single-crystal plates produced using the chemical vapor deposition method yields a few-fold enhancement in the flux density of the monochromated beam in comparison with that delivered by perfect crystals under the same conditions. At present, the Functional Materials Beamline at CHESS, which is used for time-resolved in situ characterization of soft materials during processing, has been outfitted with the described setup.

Acousto-Optic Cells with Phased-Array Transducers and Their Application in Systems of Optical Information Processing

This paper presents the results of theoretical and experimental studies of anisotropic acousto-optic interaction in a spatially periodical acoustic field created by a phased-array transducer with antiphase excitation of adjacent sections. In this case, contrary to the nonsectioned transducer, light diffraction is absent when the optical beam falls on the phased-array cell at the Bragg angle. However, the diffraction takes place at some other angles (called “optimal” here), which are situated on the opposite sides to the Bragg angle. Our calculations show that the diffraction efficiency can reach 100% at these optimal angles in spite of a noticeable acousto-optic phase mismatch. This kind of acousto-optic interaction possesses a number of interesting regularities which can be useful for designing acousto-optic devices of a new type. Our experiments were performed with a paratellurite (TeO2) cell in which a shear acoustic mode was excited at a 9∘ angle to the crystal plane (001). The piezoelectric transducer had to nine antiphase sections. The efficiency of electric to acoustic power conversion was 99% at the maximum frequency response, and the ultrasound excitation band extended from 70 to 160 MHz. The experiments have confirmed basic results of the theoretical analysis.

Design simulations of a horizontally deflecting high-heat-load monochromator

The performance of a liquid-nitrogen-cooled high-heat-load monochromator with a horizontal scattering plane has been analysed, aiming to preserve the high quality of the X-ray beam in the vertical plane for downstream optics. Using finite-element analysis, height profiles of the crystal surface for various heat loads and the corresponding slope errors in the meridional and sagittal planes were calculated. Then the angular distortions of the reflected beam in both meridional and sagittal planes were calculated analytically and also modelled by ray tracing, revealing a good agreement of the two approaches. The results show that with increasing heat load in the crystal the slope errors of the crystal surface reach their smallest values first in the sagittal and then in the meridional plane. For the considered case of interest at a photon energy of 14.412 keV and the Si(111) reflection with a Bragg angle of 7.88°, the angular distortions of the reflected beam in the sagittal plane are an order of magnitude smaller than in the meridional one. Furthermore, they are smaller than the typical angular size of the beam source at the monochromator position. For a high-heat-load monochromator operating in the horizontal scattering plane, the sagittal angular distortions of the reflected beam appear in the vertical plane. Thus, such an instrument perfectly preserves the high quality of the X-ray beam in the vertical plane for downstream optics. Compared with vertical scattering, the throughput of the monochromatic beam with the horizontal scattering plane is reduced by only 3.3% for the new EBS source, instead of 34.3% for the old ESRF-1 machine. This identifies the horizontal-scattering high-heat-load monochromator as a device essentially free of the heat-load effects in the vertical plane and without significant loss in terms of throughput.

A study on the limit of application of kinematical theory of X-ray diffraction

In this work, the limit of application of the kinematical theory of X-ray diffraction was calculate integrated intensities was evaluated as a function of perfect crystal thickness, when compared with the Ewald–Laue dynamical theory. The percentual difference between the dynamical and kinematical integrated intensities was calculated as a function of unit cell volume, Bragg angle, wavelength, module, and phase of structure factor and linear absorption coefficient. A critical thickness was defined to be the value for which the intensities differ 5%. We show that this critical thickness is 13.7% of the extinction length, which a specific combination of the parameters mentioned before. Also, we find a general expression, for any percentage of the difference between both theories, to determine the validity of the application of the kinematical theory. Finally, we also showed that the linear absorption decreases this critical thickness.

SURFACE-COVERED 1×3 GRATING WITH DIELECTRIC-METAL SLABS UNDER SECOND BRAGG INCIDENCE

This paper designed a novel three-port reflective surface-covered grating with a connecting layer. The grating can be used as a splitter, and the polarized light can be divided into zero order, first order and second order. Through rigorous coupled-wave analysis, the efficiency of the three orders of diffraction light is close to 33% under the condition that the incident light at 1550 nm is incident at the second Bragg angle and the given duty cycle is 0.5. The efficiency and bandwidth of the surface-covered grating are improved compared with that of the surface-relief grating reported in the past. Especially for transverse magnetic polarized light, the beam splitting effect is more uniform, the efficiency ratio of the zeroth order to first order can reach 1.01, and the efficiency ratio of the first order to second order can reach 1.

Performance of nearly fixed offset asymmetric channel-cut crystals for X-ray monochromators

X-ray double-crystal monochromators face a shift of the exit beam when the Bragg angle and thus the transmitted photon energy changes. This can be compensated for by moving one or both crystals accordingly. In the case of monolithic channel-cut crystals, which exhibit utmost stability, the shift of the monochromated beam is inevitable. Here we report performance tests of novel, asymmetrically cut, channel-cut crystals which reduce the beam movements by more than a factor of 20 relative to the symmetric case over the typical energy range of an EXAFS spectrum at the Cu K-edge. In addition, the presented formulas for the beam offset including the asymmetry angle directly indicate the importance of this value, which has been commonly neglected so far in the operation of double-crystal monochromators.

Research on reflective three-output by packaged grating under second Bragg angle

This paper designed a novel three-output reflective packaged grating. The optimized parameters such as the period and depth of the high-efficiency three-output grating with an incident wavelength of 1550 nm can be calculated by rigorous coupled-wave analysis (RCWA). According to the optimized result, the grating can diffract the incident light energy into three orders with an efficiency of nearly 33% under the premise of second Bragg angle incidence and the given duty ratio of 0.5. The diffraction efficiency of the packaged grating is improved compared to the surface-relief three-output grating under second Bragg angle incidence, especially for TE-polarized light.