Toward a Machine\nLearning Approach to Interpreting\nX‑ray Spectra of Trace Impurities by Converting XANES to EXAFS

The fact that\nthe photoabsorption spectrum of a material contains\ninformation about the atomic structure, commonly understood in terms\nof multiple scattering theory, is the basis of the popular extended\nX-ray absorption spectroscopy (EXAFS) technique. How much of the same\nstructural information is present in other complementary spectroscopic\nsignals is not obvious. Here we use a machine learning approach to\ndemonstrate that within theoretical models that accurately predict\nthe EXAFS signal, the extended near-edge region does indeed contain\nthe EXAFS-accessible structural information. We do this by exhibiting\ndeep operator neural networks (DeepONets) that have learned the relationship\nbetween the extended and near edge portions of the X-ray absorption\nspectrum to predict the former from the latter. We find that we can\naccurately predict the EXAFS spectrum between 6 and 14 Å<sup>–1</sup> from the first 6 Å<sup>–1</sup> (≈100\neV) of the absorption spectrum of Cu<sup>2+</sup> substitutional defects\nin the Fe<sup>3+</sup> mineral hematite (α-Fe<sub>2</sub>O<sub>3</sub>). This surprising finding implies that theoretical analyses\nof X-ray absorption spectra could be implemented that extract the <i>same</i> conclusions as high-quality EXAFS studies from spectra\ncollected over a much smaller range of photon energies. This relaxes\na host of experimental limitations related to the X-ray source and\nmeasurement sample, including collection time, minimum dopant concentration,\nsource brilliance, and energy range. We describe the theoretical data\nsets and DeepONet construction and show that the resulting DeepONets\nproduce EXAFS that recovers linear combination fits to experimental\ndata with accuracy approaching the original ab initio calculations.\nWe discuss the implications of our findings for minor constituent\ncharacterization and for understanding the information content of\nspectroscopic data more broadly, including how this approach might\nbe applied to measured experimental spectra. To encourage similar\nefforts, the simulated X-ray spectra, machine learning, and fitting\ncode are publicly available.