Direct mapping of microscopic polarization in ferroelectric $x\left({\mathrm{BiScO}}_3\right)\text{−}(1-x)\left({\mathrm{PbTiO}}_3\right)$ throughout its morphotropic phase boundary

Pair distribution functions of ferroelectric $x{\mathrm{BiScO}}_3\text{−}\left(1-x\right){\mathrm{PbTiO}}_3$, obtained from neutron total scattering data, were examined and modeled utilizing the reverse Monte Carlo technique to depict exclusively the local structure of this compound throughout its reported morphotropic phase boundary (MPB). Microscopic polarizations due to the cation shifts have been mapped out from the refined crystal structure as a function of composition in order to reveal individual cation behavior driven by the composition. Direct evidences are provided for large static displacements of the cations $\left(\sim 0.2-0.5\AA \right)$, local cation ordering between Ti and Sc, and a categorical change of favored polarization directions of the cations at the conjuncture of the MPB. Apart from Sc, all cations have demonstrated an apparent transition from a relatively defined directional distribution to a broad and random distribution at $x=x_{\mathrm{MPB}}$, suggesting a flattening of the local potential function for them. These features can further be correlated with the general concept of structural instability of a ferroelectric system at the MPB, which is often linked to the manifestation of enhanced physical properties.

Figure 1

Partial PDFs, averaged over ten independent RMC runs, of the metal-oxygen pairs obtained from the RMC calculations as a function of composition.

Figure 2

Oxygen environment for (a) A-site cations and (b) B-site cations of a perovskite structure-type $\left({\mathrm{ABO}}_3\right)$ with the fourfold and the threefold axis along the [001] and the [111] pseudocubic axis, repectively. (c) The stereographic projection of a cubic crystal looking along the [001] direction.

Figure 3

[001] stereographic projections of the cation shifts from the center of their oxygen polyhedra.

Figure 4

Mean shifts of the cations along with their standard deviations as a function of composition.

Figure 5

Values of occupational pair-correlation function $c_{ij}$ in the $\left(xy0\right)$ plane, suggesting a B-site cation ordering.