Rocking-curve width of sagittally bent Laue crystals

Characterization and on-line adjustment of the sagittal-bent Laue crystal profile

The sagittal-bent Laue monochromator can provide an ideal way to focus high-energy X-ray beams. However, the anticlastic curvature induced by sagittal bending has a great influence on the crystal performance. Thus, characterizing the bent-crystal shape is very important for predicting the performance of the bent-crystal monochromator. In this paper the crystal profile is measured by off-line optical metrology and on-line X-ray experiments. The off-line results showed that the bent-crystal surface could be well fitted to a saddle surface apart from a redundant cubic term which was related to the different couples applied on the crystal. On-line characterization of the meridional and the sagittal radius of the bent crystal includes double-crystal topography and ray-tracing measurement. In addition, the double-crystal topography experiment could be used as a quick diagnostic method for the bending condition adjustment. The sagittal radius of the bent crystal was characterized through a ray-tracing experiment by using a particularly designed tungsten mask. Moreover, rocking curves under different bending conditions were measured as well. The results were highly consistent with analytical results derived from the elastic theory. Furthermore, radii along different vertical positions under various bending conditions were measured and showed a quadratic relationship between the vertical positions and the meridional radii.

The high-energy x-ray diffraction and scattering beamline at the Canadian Light Source

The optical design for the high-energy x-ray diffraction and scattering beamline of the Brockhouse sector at the Canadian Light Source is described. The design is based on a single side-bounce silicon focusing monochromator that steers the central part of a high-field permanent magnet wiggler beam into the experimental station. Two different configurations are proposed: a higher energy resolution with vertical focusing and a lower energy resolution with horizontal and vertical focusing. The monochromator will have the possibility of mounting three crystals: one crystal optimized for 35 keV that focuses in the horizontal and vertical directions using reflection (1,1,1) and two other crystals both covering the energies above 40 keV: one with only vertical focusing and another one with horizontal and vertical focusing. The geometry of the last two monochromator crystals was optimized to use reflections (4,2,2) and (5,3,3) to cover the broad energy range from 40 to 95 keV.

Bent Bragg–Laue monochromator for high-energy X-rays

A bent Bragg–Laue monochromator (BLM) is proposed for high-energy X-ray (∼25–60 keV) beamlines. The BLM has the unique feature of bi-directional focusing. A sagittally bent Laue crystal can focus the large horizontal fan of a bending magnet or wiggler source. A meridionally bent Bragg crystal focuses the beam vertically and corrects for the anticlastic bending effects of the Laue crystal. This monochromator geometry relies on the crystal orientations being optimized. It is shown that the focusing condition and Rowland condition can be simultaneously satisfied at a given energy. Detailed ray tracings indicate that a BLM can provide similar energy resolution and higher flux density compared to a sagittally bent double-Laue monochromator configuration. A prototype BLM with a symmetric Bragg crystal and an asymmetric Laue crystal was tested. Matching of the bend radii of the two crystals in the meridional direction was demonstrated. In general, the horizontal acceptance of the sagittally bent Laue crystal is limited by the large curvature. This horizontal BLM acceptance could be increased by translating the Laue crystal along its sagittal bending axis.

Anisotropic elasticity of silicon and its application to the modelling of X-ray optics

The crystal lattice of single-crystal silicon gives rise to anisotropic elasticity. The stiffness and compliance coefficient matrix depend on crystal orientation and, consequently, Young's modulus, the shear modulus and Poisson's ratio as well. Computer codes (in Matlab and Python) have been developed to calculate these anisotropic elasticity parameters for a silicon crystal in any orientation. These codes facilitate the evaluation of these anisotropy effects in silicon for applications such as microelectronics, microelectromechanical systems and X-ray optics. For mechanically bent X-ray optics, it is shown that the silicon crystal orientation is an important factor which may significantly influence the optics design and manufacturing phase. Choosing the appropriate crystal orientation can both lead to improved performance whilst lowering mechanical bending stresses. The thermal deformation of the crystal depends on Poisson's ratio. For an isotropic constant Poisson's ratio, ν, the thermal deformation (RMS slope) is proportional to (1 + ν). For a cubic anisotropic material, the thermal deformation of the X-ray optics can be approximately simulated by using the average of ν12 and ν13 as an effective isotropic Poisson's ratio, where the direction 1 is normal to the optic surface, and the directions 2 and 3 are two normal orthogonal directions parallel to the optical surface. This average is independent of the direction in the optical surface (the crystal plane) for Si(100), Si(110) and Si(111). Using the effective isotropic Poisson's ratio for these orientations leads to an error in thermal deformation smaller than 5.5%.

Performance calculations of the X-ray powder diffraction beamline at NSLS-II

The X-ray Powder Diffraction (XPD) beamline at the National Synchrotron Light Source II is a multi-purpose high-energy X-ray diffraction beamline with high throughput and high resolution. The beamline uses a sagittally bent double-Laue crystal monochromator to provide X-rays over a large energy range (30-70 keV). In this paper the optical design and the calculated performance of the XPD beamline are presented. The damping wiggler source is simulated by the SRW code and a filter system is designed to optimize the photon flux as well as to reduce the heat load on the first optics. The final beamline performance under two operation modes is simulated using the SHADOW program. For the first time a multi-lamellar model is introduced and implemented in the ray tracing of the bent Laue crystal monochromator. The optimization and the optical properties of the vertical focusing mirror are also discussed. Finally, the instrumental resolution function of the XPD beamline is described in an analytical method.

Surface curvatures and diffraction profiles of sagittally bent Laue crystals

The performance of a bent Laue crystal monochromator crucially depends on the sagittal and meridional bending curvatures of the crystal. To optimize the design of monochromator crystals, the surface curvatures and diffraction profiles of a set of sagittally bent Laue crystals with different aspect ratios have been studied experimentally by optical metrology and X-ray measurements. The results were confirmed with finite-element analysis using large-deformation theory. The nonlinear relationship between the curvatures necessitates an experimentally determined parameter in the theoretical modeling of the diffraction profiles. By taking into account the local stress and the aspect ratio of the sagittally bent Laue crystal, the modified analytical approach successfully predicts the rocking-curve width and the integrated reflecting power. The effect of extreme sagittal bending on the rocking curve is also discussed. To retain high reflectivity, the bending curvature should not exceed its critical value for the specified crystal geometry. Furthermore, the uniformity of the bending curvatures across the crystal surface has been examined, which suggests that the minimum crystal dimension should be approximately twice the size of the beam footprint.

The real structure of Na3BiO4 by electron microscopy, HR-XRD and PDF analysis

The real stucture of a new crystalline high temperature phase, metastable at room temperature, in the system sodium – bismuth – oxygen, β-Na3BiO4, was determinated using high resolution X-ray powder diffraction, pair distribution function analysis, and high resolution transmission electron microscopy. β-Na3BiO4 was synthesized by anodic oxidation of bismuth(III)-oxide in a sodium hydroxide – lithium hydroxide melt. The average crystal structure of β-Na3BiO4 at ambient conditions (R3m, a = 3.32141(9) Å, c = 16.4852(5) Å) is structurally related to α-NaFeO2 with metal layers almost statistically occupied in a Na:Bi ratio of 3:1. Analysis of the long-range order on the bulk material by Rietveld refinement led to approximately Na:Bi ratios of 2:1 and 4:1, in consecutive metal layers, while a detailed analysis of the local order by means of the pair distribution function revealed the existence of almost pure sodium layers and mixed 1:1 – sodium:bismuth layers. Complementary studies on single crystallites using high resolution transmission electron miscroscopy exhibited a complex domain structure with short-range ordered, partially ordered, and long-range ordered domains.