X-ray resonant exchange scattering of rare-earth nickel borocarbides

Investigations of the physical properties of the recently discovered rare-earth nickel borocarbides, RNi2B2C, continue to provide further insight into the interplay between superconductivity and magnetism. In several of these materials, long range magnetic order coexists with superconductivity over some temperature range, and the large variety of magnetic structures observed in neutron and x-ray experiments indicate long range order of localized magnetic moments coupled via a RKKY-type interaction. The strong anisotropic behavior present in some members of the family indicates that crystalline electric field energies also play an important role in the formation of the magnetically ordered state;We performed x-ray resonant exchange (XRES) scattering experiments on NdNi2B2C, SmNi2B2C, GdNi2B2C, HoNi2B2C and ErNi2B2C. For temperatures below 5 K, the Ho compound orders in a simple antiferromagnetic state with modulation wave vector q = (0, 0, 1), while between 5 K and 6.1 K an incommensurate antiferromagnetic phase with two modulation wave vectors, qa = (0.59, 0, 0) and qc = (0, 0, 0.92) is observed. GdNi2B2C orders antiferromagnetically below TN = 19.4 K with q = (0.55, 0, 0). Between 19.4 K and 13.6 K, the magnetic moments are aligned along the b-axis of the crystal, while below 13.6 K and additional component along the c-axis develops. In ErNi2B2C, the paramagnetic-to-antiferromagnetic phase transition at TN approx 6 K is accompanied by a lowering of the lattice symmetry from tetragonal to orthorhombic. The antiferromagnetic structures of the Nd and Sm compounds are characterized by a modulation wave vector q = (1[over]2, 0, 1[over]2), while the moment directions were determined as (1, 0, 0) and (0, 0, 1), respectively;Our measurements of these materials have not only demonstrated that high resolution synchrotron x-rays measurements can confirm and refine magnetic structure determinations originally carried out by neutron diffraction, but also that XRES is a tool capable of ab initio structure determinations. In particular, we have shown that by measuring the integrated intensity of selected magnetic Bragg reflections and comparing them with model calculations of their Q-dependence, it is possible to determine the orientation of moments in antiferromagnetically ordered phases

X-ray diffraction microscopy based on refractive optics

We describe a diffraction microscopy technique based on refractive optics to study structural variations in crystals. The X-ray beam diffracted by a crystal was magnified by beryllium parabolic refractive lenses on a 2D X-ray camera. The microscopy setup was integrated into the 6-circle Huber diffractometer at the ESRF beamline ID06. Our setup allowed us to visualize structural imperfections with a resolution of approximately 1 micrometer. The configuration, however, can easily be adapted for sub-micrometer resolution.Comment: 9 pages, 4 figures. Submitted to Journal of Synchrotron Radiation on April 4th 2012. Rejecte

Full-field hard x-ray microscopy with interdigitated silicon lenses

Full-field x-ray microscopy using x-ray objectives has become a mainstay of the biological and materials sciences. However, the inefficiency of existing objectives at x-ray energies above 15 keV has limited the technique to weakly absorbing or two-dimensional (2D) samples. Here, we show that significant gains in numerical aperture and spatial resolution may be possible at hard x-ray energies by using silicon-based optics comprising 'interdigitated' refractive silicon lenslets that alternate their focus between the horizontal and vertical directions. By capitalizing on the nano-manufacturing processes available to silicon, we show that it is possible to overcome the inherent inefficiencies of silicon-based optics and interdigitated geometries. As a proof-of-concept of Si-based interdigitated objectives, we demonstrate a prototype interdigitated lens with a resolution of ~255 nm at 17 keV.Comment: 10 pages, 5 figure. Submitted to Applied Physics Letters 31st March 2015, rejected 17th June 201

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

The fractional Fourier transform (FrFT) is introduced as a tool for numerical simulations of X-ray wavefront propagation. By removing the strict sampling requirements encountered in typical Fourier optics, simulations using the FrFT can be carried out with much decreased detail, allowing, for example, on-line simulation during experiments. Moreover, the additive index property of the FrFT allows the propagation through multiple optical components to be simulated in a single step, which is particularly useful for compound refractive lenses (CRLs). It is shown that it is possible to model the attenuation from the entire CRL using one or two effective apertures without loss of accuracy, greatly accelerating simulations involving CRLs. To demonstrate the applicability and accuracy of the FrFT, the imaging resolution of a CRL-based imaging system is estimated, and the FrFT approach is shown to be significantly more precise than comparable approaches using geometrical optics. Secondly, it is shown that extensive FrFT simulations of complex systems involving coherence and/or non-monochromatic sources can be carried out in minutes. Specifically, the chromatic aberrations as a function of source bandwidth are estimated, and it is found that the geometric optics greatly overestimates the aberration for energy bandwidths of around 1%.</jats:p

Simulating and optimizing compound refractive lens-based X-ray microscopes

A comprehensive optical description of compound refractive lenses (CRLs) in condensing and full-field X-ray microscopy applications is presented. The formalism extends ray-transfer matrix analysis by accounting for X-ray attenuation by the lens material. Closed analytical expressions for critical imaging parameters such as numerical aperture, spatial acceptance (vignetting), chromatic aberration and focal length are provided for both thin- and thick-lens imaging geometries. These expressions show that the numerical aperture will be maximized and chromatic aberration will be minimized at the thick-lens limit. This limit may be satisfied by a range of CRL geometries, suggesting alternative approaches to improving the resolution and efficiency of CRLs and X-ray microscopes