  The local environment and oxidation state of the Fe impurity in strontium
titanate are studied using XAFS spectroscopy. The influence of annealing
temperature and deviation from stoichiometry on the possibility of
incorporation of the impurity into the $A$ and $B$ sites of the perovskite
structure is studied. The results obtained from the X-ray diffraction, XANES
spectra, and EXAFS spectra suggest that at high annealing temperature the iron
atoms, at least partially (up to 30%), enter the $A$ sites in SrTiO$_3$. The
obtained results agree with results of first-principles calculations, according
to which the iron at the $A$ site exhibits strong off-centering (the
displacement of $\sim$1 {\AA}), similar to that previously established in
SrTiO$_3$ samples doped with Mn and Co.
