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X-ray absorption spectroscopy (XAS) is an easy and nice method to examine the chemical and local structural properties of materials which measures the X-ray absorption coefficients with various incident X-ray energies. XAS can reveal the atomic coordination and the intersite or intrasite electron-electron interactions for each atomic species, so that it can be commonly employed for identifying the local electronic structures of condensed matter. In this talk, I would like to overview the general principles of XAS for the local structural identification, and showcase some examples of theoretical considerations for metal oxide systems including manganites, double perovskite cobaltites and hafnia-zirconia. For the simulation of soft XAS spectra, the concept of configuration interactions with atomic multiplets is employed. For the simulation of hard XAS spectra (so-called XANES), the ab-initio real space multiplet scattering calculation (FEFF) is employed.