Mechanism of the incommensurate phase in lead oxide α-PbO

Abstract

We report detailed studies of the incommensurate phase of lead oxide \ensuremath{\alpha}-PbO using neutron and x-ray scattering as well as electron-diffraction techniques. Comparison of the structural evolution of \ensuremath{\alpha}-PbO with those of two isostructural compounds, ${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{TiO}}_{\mathit{x}}$O (4.5x8 mol %) and tin oxide SnO, has been made. The experimental results clearly suggest that the incommensurate phase observed in \ensuremath{\alpha}-PbO is of the displacive type, induced by the softening of a lattice phonon mode. Using a simple ionic approximation we have studied the localization of the lone pairs inside the structures of the three isotypic compounds using a simple model of competing Coulomb interactions which leads to unstable positions of ${\mathrm{Pb}}^{2+}$ and ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ ions in the average structure. The stability of the incommensurate phase down to the lowest temperatures seems to be favored by the frustration arising from the next-nearest-neighbor Coulomb interaction.