Anisotropic covalent bonds inKNbO3observed by resonant x-ray scattering

Abstract

The resonant x-ray scattering technique was applied to study the directional covalent bonds (orbital ordering) in ${\mathrm{KNbO}}_{3}$ 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 ${f}^{\ensuremath{'}},$ with the photon polarization parallel and perpendicular to the orbital ordering vector. The orbital characteristics were assessed through the dependence of ${f}^{\ensuremath{'}}$ 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.