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

X-ray focusing by bent crystals: focal positions as predicted by the crystal lens equation and the dynamical diffraction theory

The location of the beam focus when monochromatic X-ray radiation is diffracted by a thin bent crystal is predicted by the `crystal lens equation'. This equation is derived in a general form valid for Bragg and Laue geometries. It has little utility for diffraction in Laue geometry. The focusing effect in the Laue symmetrical case is discussed using concepts of dynamical theory and an extension of the lens equation is proposed. The existence of polychromatic focusing is considered and the feasibility of matching the polychromatic and monochromatic focal positions is discussed.

Wide field imaging energy dispersive X-ray absorption spectroscopy

A new energy dispersive X-ray absorption spectroscopy (EDXAS) method is presented for simultaneous wide-field imaging and transmission X-ray absorption spectroscopy (XAS) to enable rapid imaging and speciation of elements. Based on spectral K-Edge Subtraction imaging (sKES), a bent Laue imaging system diffracting in the vertical plane was developed on a bend magnet beamline for selenium speciation. The high flux and small vertical focus, forming a wide horizontal line beam for projection imaging and computed tomography applications, is achieved by precise matching of lattice plane orientation and crystal surface (asymmetry angle). The condition generating a small vertical focus for imaging also provides good energy dispersion. Details for achieving sufficient energy and spatial resolution are demonstrated for both full field imaging and computed tomography in quantifying selenium chemical species. While this system has lower sensitivity as it uses transmission and may lack the flux and spatial resolution of a dedicated focused beamline system, it has significant potential in rapid screening of heterogeneous biomedical or environmental systems to correlate metal speciation with function.

Energy flow of Bloch waves in X-ray dynamical diffraction in the Laue case for perfect crystals

The direction of energy flow for Bloch waves during X-ray dynamical diffraction in perfect crystals is investigated. The energy flow is spread uniformly within the Borrmann fan in the conventional Laue case where the imaginary part of the crystal structure factor is much smaller than the real part. However, when the imaginary part is large, as in the case of X-rays with energies close to the absorption edge for single atoms in crystals, the energy flow direction is found to be restricted, and the results are discussed in relation to the Bragg case.

A finite-element approach to dynamical diffraction problems in reflection geometry

A finite-element approach to the numerical solution of the Takagi–Taupin equations expressed in a weak form is presented and applied to simulate the X-ray reflectivity curves, spatial intensity distributions and focusing properties of bent perfect crystals in symmetric reflection geometry. The proposed framework encompasses a new formulation of the Takagi–Taupin equations, which appears to be promising in terms of robustness and stability and supports the Fresnel propagation of the diffracted waves. The presented method is very flexible and has the potential of dealing with dynamical X-ray or neutron diffraction problems related to crystals of arbitrary shape and deformation. The reference implementation based on the commercial COMSOLMultiphysicssoftware package is available to the relevant user community.