Anisotropic covalent bonds in (formula presented) observed by resonant x-ray scattering

The resonant x-ray scattering technique was applied to study the directional covalent bonds (orbital ordering) in (formula presented) associated with ferroelectricity by scanning the incident x-ray energy through the K edge of niobium. The orbital ordering was determined by measuring the real part of the x-ray anomalous dispersion (formula presented) with the photon polarization parallel and perpendicular to the orbital ordering vector. The orbital characteristics were assessed through the dependence of (formula presented) on the momentum transfer, Q, since the matrix element for the quadrupolar transition into the d states is dependent on Q, while that for the dipolar transition into the p state is not.