David Laundy

The XMaS beamline at ESRF: instrumental developments and high-resolution diffraction studies.

The beamline, which is situated on a bending magnet at ESRF, comprises a unique combination of instrumentation for high-resolution and magnetic single-crystal diffraction. White-beam operation is possible, as well as focused and unfocused monochromatic modes. In addition to an eleven-axis Huber diffractometer, which facilitates simple operation in both vertical and horizontal scattering geometries, there is an in-vacuum polarization analyser and slit system, mirrors for harmonic rejection, sub 4.2 K and 1 Tesla magnetic field sample environment, plus a diamond phase plate for polarization conditioning. The instrumentation developed specifically for this beamline is described, and its use illustrated by recent scientific results.

Energy calibration and full-pattern refinement for strain analysis using energy-dispersive and monochromatic X-ray diffraction

Precise channel-to-energy conversion is very important in full-pattern refinement in energy-dispersive X-ray diffraction. Careful examination shows that the channel-to-energy conversion is not entirely linear, which presents an obstacle to obtaining accurate quantitative data for lattice strains by pattern refinement. In order to establish an accurate quadratic channel-to-energy conversion function, a Matlab program was written to find the best quadratic coefficient and hence the whole energy conversion function. Then this energy conversion function was used to perform a whole-pattern fitting of the energy-dispersive X-ray diffraction pattern of a Ti64 sample. The strain across the Ti64 bar calculated from the fitting results has been compared with values obtained by single-wavelength X-ray diffraction utilizing a Laue monochromator.

Magnetic form factors of ferromagnetic iron by X-ray diffraction

Abstract The ratios of magnetic to charge form factors have been measured for 11 reflections in ferromagnetic α-iron by diffraction of synchrotron radiation. A novel white-beam single-crystal approach has produced data of a comparable auality to early polarized neutron work, and it seems likely that this techniaue will become a valuable new tool for studying ferromagnets.

The characterisation of multiple scattering in Compton profile measurements

Abstract Extensive Monte Carlo simulations of the multiple scattering contamination in Compton scattering studies of electron momentum density distributions are reported. Over 300 calculations were made as a function of the photon energy (60–662 keV), the atomic number of the scatterer (Z = 6 to 38) and the collimation geometry. Earlier analytical approximations for double scattering are tested and the data allow the relative magnitude of the multiple scattering to be estimated in typical experiments. When the Compton cross section dominates the absorption cross section a common function of optical thickness, which estimates the ratio of multiple to single scattering, is found.

Magnetic X-ray diffraction from ferromagnetic iron

Non-resonant magnetic diffraction of synchrotron radiation from ferromagnetic iron has been measured. The authors have used, for the first time, a white beam and single crystal sample. It is demonstrated that this combination can yield magnetic flipping ratios with small statistical and systematic errors. The technique has been used to investigate the polarization dependence of magnetic scattering.

A novel facility using a Laue focusing monochromator for high-pressure diffraction at the SRS, Daresbury, UK

A novel Laue focusing monochromator has been developed to provide intense X-radiation for high-pressure diffraction experiments. A beamline using this monochromator has been successfully developed on station 9.5 at the SRS, Daresbury Laboratory. Contributions to resolution from monochromator bandpass and divergence due to focusing have been quantified and are used to assess experimental diffraction data from diamond-anvil cells recorded using image plates with X-rays at approximately 30 keV. This optical and beamline design could be readily adapted to use X-rays from a bending magnet on a third-generation synchrotron source.

Quadrupole transitions revealed by Borrmann spectroscopy.

The Borrmann effect—a dramatic increase in transparency to X-ray beams—is observed when X-rays satisfying Bragg’s law diffract through a perfect crystal. The minimization of absorption seen in the Borrmann effect has been explained by noting that the electric field of the X-ray beam approaches zero amplitude at the crystal planes, thus avoiding the atoms. Here we show experimentally that under conditions of absorption suppression, the weaker electric quadrupole absorption transitions are effectively enhanced to such a degree that they can dominate the absorption spectrum. This effect can be exploited as an atomic spectroscopy technique; we show that quadrupole transitions give rise to additional structure at the L1, L2 and L3 absorption edges of gadolinium in gadolinium gallium garnet, which mark the onset of excitations from 2s, 2p1/2 and 2p3/2 atomic core levels, respectively. Although the Borrmann effect served to underpin the development of the theory of X-ray diffraction, this is potentially the most important experimental application of the phenomenon since its first observation seven decades ago. Identifying quadrupole features in X-ray absorption spectroscopy is central to the interpretation of ‘pre-edge’ spectra, which are often taken to be indicators of local symmetry, valence and atomic environment. Quadrupolar absorption isolates states of different symmetries to that of the dominant dipole spectrum, and typically reveals orbitals that dominate the electronic ground-state properties of lanthanides and 3d transition metals, including magnetism. Results from our Borrmann spectroscopy technique feed into contemporary discussions regarding resonant X-ray diffraction and the nature of pre-edge lines identified by inelastic X-ray scattering. Furthermore, because the Borrmann effect has been observed in photonic materials, it seems likely that the quadrupole enhancement reported here will play an important role in modern optics.

X-ray phase contrast tomography by tracking near field speckle

X-ray imaging techniques that capture variations in the x-ray phase can yield higher contrast images with lower x-ray dose than is possible with conventional absorption radiography. However, the extraction of phase information is often more difficult than the extraction of absorption information and requires a more sophisticated experimental arrangement. We here report a method for three-dimensional (3D) X-ray phase contrast computed tomography (CT) which gives quantitative volumetric information on the real part of the refractive index. The method is based on the recently developed X-ray speckle tracking technique in which the displacement of near field speckle is tracked using a digital image correlation algorithm. In addition to differential phase contrast projection images, the method allows the dark-field images to be simultaneously extracted. After reconstruction, compared to conventional absorption CT images, the 3D phase CT images show greatly enhanced contrast. This new imaging method has advantages compared to other X-ray imaging methods in simplicity of experimental arrangement, speed of measurement and relative insensitivity to beam movements. These features make the technique an attractive candidate for material imaging such as in-vivo imaging of biological systems containing soft tissue.

Surface profiling of X-ray mirrors for shaping focused beams

Grazing incidence mirrors are a standard optic for focusing X-rays. Active mirrors, whose surface profile can be finely adjusted, allow control of beam shape and size at the sample. However, progress towards their routine use for beam shaping has been hampered by the strong striations in reflected beams away from the focal plane. Re-entrant (partly concave and partly convex) surface modifications are proposed for shaping X-ray beams to a top-hat in the focal plane while reducing the striations caused by unavoidable polishing errors. A method for constructing such surfaces with continuous height and slope (but only piecewise continuous curvature) will be provided. Ray tracing and wave propagation calculations confirm its effectiveness. A mirror system is proposed allowing vertical beam sizes in the range 0.5 to 10μm. A prototype will be fabricated and is expected to have applications on many synchrotron X-ray beamlines.

Calculation of the polarisation of synchrotron radiation

Abstract The polarisation of synchrotron radiation is sensitive to the motion of the electrons within the electron beam source. This motior has been incorporated into a complete description of the beam polarisation, based on evaluation of the polarisation density matrix. Calculation of the degrees of linear and circular polarisation shows the importance of taking account of the electron beam characteristics. A solution for the degree of linear polarisation on the electron beam orbit using a series expansion is presented and is shown to agree with the same parameter calculated numerically.