The real structures of α-Al2O3 – δ anion-deficient corundum crystals characterized by δ ~ 0.001 lack-stoichiometry level allowed to use these crystals in X-Ray, gamma and beta dosimetry have been neutronographically investigated for the first time. The neutron scattering measurements were performed on two crystals sintered by Stepanov’s method, the anion vacancies contents were Ca = 8 × 1016 cm–3 for the radiation-sensitive crystal and Ca < 1014 cm–3 for the crystal taken after annealing on the oxygen atmosphere and lost to its sensitivity to radiation. With pronounced indications on essential fragmentness revealed from attestation of these two crystals, in both cases the corundum structure was recognized, the lattice parameters and atomic coordinates were found. Three approaches are considered to process the neutron scattering data obtained from the smallest oxygen deficient crystal (Ca < 1014 cm–3), with measured intensities corrected by different ways. The best results being numerically identity in the frame over all three considered approaches are extracted from the “ideal crystal” model. The obtained results were verified for the structure characterized by Ca = 8 × 1016 cm–3.