  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
300K to 930K. 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 intensities of the main
XANES features. First-principles DFT calculations are performed for both
compounds. They show that the pre-edge peak originates from forbidden 1s to 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, 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.
