  We determine the structural relaxations around paramagnetic impurities (Ti,
Cr, Fe) in corundum (alpha-Al2O3), by combining x-ray absorption near edge
structure (XANES) experiments and ab initio calculations. The structural
relaxations are found to be very local. We then show that XANES is sensitive to
small variations in interatomic distances within the coordination shell of the
absorbing atom. The experiments were carried out on single crystals of ruby and
sapphires. Linear dichroic signals are essential to characterize the geometry
of the impurity site. The calculations were performed within a self-consistent
``non muffin-tin'' framework, that uses pseudopotentials, plane-wave basis set,
and the continued fraction for the absorption cross section.
