Experimental evidence of thermal fluctuations on the x-ray absorption near-edge structure at the aluminumKedge

Abstract

After a review of temperature-dependent experimental x-ray absorption near-edge structure (XANES) and related theoretical developments, we present the Al $K$-edge XANES spectra of corundum and beryl for temperature ranging from 300 to 930 K. These experimental results provide a first evidence of the role of thermal fluctuation in XANES at the Al $K$ edge, especially, in the pre-edge region. The study is carried out by polarized XANES measurements of single crystals. For any orientation of the sample with respect to the x-ray beam, the pre-edge peak grows and shifts to lower energy with temperature. In addition, temperature induces modifications in the position and intensity of the main XANES features. First-principles DFT calculations are performed for both compounds. They show that the pre-edge peak originates from forbidden 1$s$$\ensuremath{\rightarrow}$$3s$ transitions induced by vibrations. Three existing theoretical models are used to take vibrations into account in the absorption cross-section calculations: (i) an average of the XANES spectra over the thermal displacements of the absorbing atom around its equilibrium position, (ii) a method based on the crude Born-Oppenheimer approximation where only the initial state is averaged over thermal displacements, and (iii) a convolution of the spectra obtained for the atoms at the equilibrium positions with an approximate phonon spectral function. The theoretical spectra so obtained permit to qualitatively understand the origin of the spectral modifications induced by temperature. However, the correct treatment of thermal fluctuation in XANES spectroscopy requires more sophisticated theoretical tools.