Local Structure of Disordered Bi_0.5K_0.5TiO₃ Investigated by Pair Distribution Function Analysis and First-Principles Calculations

We investigate A-site cation ordering in the ferroelectric perovskite Bi 0.5 K 0.5 TiO 3 (BKT) by density functional theory (DFT) calculations and synchrotron X-ray total scattering. Using BKT as a prototypical lead-free ferroelectric perovskite with mixed A-site cations, we use a combination of theory and experiments to assess the energetics and resulting physical properties of cation ordering. Ten different Bi/K configurations in a 2 × 2 × 2 supercell were assessed by real space pair distribution functions (PDFs) and DFT calculations. None of these configurations were identified as particularly favorable from experiment or theory. Ferroelectric polarization calculated by the Berry phase method for all ten configurations yields values of 50–105 μC/cm 2 . This is significantly larger than previously reported experimental results in the range of 22–49 μC/cm 2, indicating that BKT does not possess long-range A-site cation order. Reverse Monte Carlo (RMC) modeling of the total scattering data with a 12 × 12 × 12 supercell also supports substantial A-site disorder in BKT. A 4 × 4 × 4 supercell with local cation displacements in a pseudodisordered A-site sublattice reproduces the experimentally observed polarization, implying that in a real material there are multiple local polar regions which partly cancel each other. The combination of RMC modeling of PDFs with DFT calculations should be highly applicable to other crystalline materials with sublattice disorder.