Both magnetic and nonmagnetic x-ray diffraction has been studied near the Fe K-edge of hematite ͑␣-Fe 2 O 3 ͒ and the Cr K-edge of eskolaite ͑Cr 2 O 3 ͒ and compared to the symmetry-based calculations. These crystals have identical atomic structures but different magnetic orderings. The observed "forbidden" 111 and 333 reflections in both crystals show a resonant peak only in the pre-edge energy region. In eskolaite, the azimuthal angle dependence of the resonant 111 and 333 reflections exhibits threefold symmetry, which is in good agreement with the calculated curves based on electric dipole-quadrupole and quadrupole-quadrupole scattering channels. This threefold symmetry is the first reliable evidence for antisymmetric terms in dipolequadrupole scattering and hence for local chirality of atoms in centrosymmetric crystals. In hematite, nonresonant and resonant scattering has been observed for the forbidden reflections. The azimuth dependence of the nonresonant intensity shows the twofold symmetry. From the azimuthal symmetry and temperature dependence of the nonresonant diffraction, it is revealed that the nonresonant intensity is due to magnetic scattering caused by the antiferromagnetic structure. The azimuth dependence of the 111 resonant peak in hematite shows almost threefold symmetry similar to eskolaite. On the other hand, the resonant 333 reflection in hematite shows complicated azimuth dependence, nearly mirror symmetry, at room temperature. As a result of least-squares analysis of the azimuth dependence and the low-temperature measurement, we conclude that the nonresonant magnetic scattering has a significant influence on the resonant electric scattering though its intensity is much smaller. Thus the interference between the magnetic and electric scatterings plays a very important role in hematite and opens new ways for studying additional details of the magnetic structure.

Symmetric and antisymmetric dipole-quadrupole contributions to the Ti scattering factor are determined via the "forbidden" 002 reflection excited at the Ti K absorption edge in the TiO 2 polymorph anatase. Both contributions are separated by studying different azimuthal orientations of the crystal. The simulation of the forbidden resonant scattering performed within the full multiple-scattering method reveals the relevant Ti electronic states resulting from the p-d hybridization of parity-odd and parity-even orbitals. A thermal-motioninduced anisotropy of the atomic scattering factor is found negligible below ambient temperatures.