Deriving the magnitude of niobium off-center displacement in ferroelectric niobates from infrared spectroscopy

A KSr2Nb5O15 nanopowder was synthesized by a chemical route based on a modified polyol method. The nanopowder exhibits the space group P4bm (ferroelectric) ascribed to the displacement of Nb from the central position of an [NbO6] octahedron, parallel to the c-axis (polarization axis). The magnitude of the niobium off-center, a dagger z, was determined by X-ray diffraction and mid-infrared spectroscopy (FTIR). Analysis of the infrared spectrum carried out using curve fitting based on Gaussian functions has revealed a very strong vibration at 413 cm(-1), ascribed to a bond of the Nb off-center with apical oxygen. A classical molecular theory was applied to derive the force constant of this bond from the vibrational frequency. Using the calculus of energies for the wavelength and the harmonic oscillator, we alternatively derived the a dagger z parameter.