International Tables for Crystallography

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Finite-difference method for the calculation of X-ray spectroscopies
Y. Joly, A. Y. Ramos and O. Bunău. International Tables for Crystallography (2022). Vol. I [ doi:10.1107/S1574870722001598 ]

Abstract

All of the ingredients of the finite-difference method (FDM) for the calculation of X-ray near-edge absorption and emission as well as X-ray resonant diffraction peaks are presented. Solution of the relativistic Schrödinger equation is performed on a dense grid of points inside a sphere surrounding a cluster of atoms containing the absorber (or resonant) atom. The most important point is that this simple scheme allows a free description of the potential shape, which most often offers a good reproduction of the experimental spectra without additional parameters. It is shown how the center of the atoms, where a classical expansion in spherical waves takes place, is embedded in the grid. The continuity with the region of the outer sphere is performed in the same way and ensures convenient normalization of the states. Thanks to the appropriate algorithms, the calculation of all states of photoelectrons can now be performed using standard personal computers. The core–unoccupied state transitions are then calculated, finally giving the absorption or emission cross sections or the resonant diffracted beam intensities. Some examples with light and heavy chemical elements, both magnetic and nonmagnetic, demonstrate the possibility of FDM, which is at the heart of the FDMNES software.


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About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The multi-volume series comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.