Local atomic structure deviation from average structure of Na0.5Bi0.5TiO3: Combined x-ray and neutron total scattering study

Abstract

The crystal structure of sodium bismuth titanate (NBT) and related compounds is of great interest, as these may form part of a new generation of ferroelectric materials used in a multitude of piezoelectric applications. This work examines the short- and long-range structure of sodium bismuth titanate in different states of synthesis using x-ray and neutron pair distribution function studies. The average structure of NBT was modeled using the monoclinic $Cc$ space group through a combined structural refinement of x-ray and neutron diffraction data via the Rietveld method. A small box approach was used to model the local structure based on the average structure of the material, as determined from the Rietveld structural refinement, and rule out the presence of local $A$-site ordering in NBT. A ``box-car fitting'' method used to analyze the neutron pair distribution function showed that bond environments change when averaged over different length scales and the calculated bond valence of Bi${}^{3+}$, in particular, is different locally from its average value. A model calculated using the reverse Monte Carlo method allowed the positions of Na${}^{+}$ and Bi${}^{3+}$ to move independently, allowing the determination of their distinctive bonding environments with O${}^{2\ensuremath{-}}$. This method revealed that Na${}^{+}$ and Bi${}^{3+}$ have slightly different atomic positions, an effect that may be the origin of the large atomic displacement parameters calculated for the $A$ site from the average structure model. The local structure described here is discussed in comparison with published long-range structure models.