Prediction of the [Na1/2Bi1/2]TiO3 ground state

The Vienna Ab-initio Simulation Package (VASP) was used to perform fully relaxed, planewave pseudopotential calculations of formation energies (DeltaE(VASP)) for a large number of ordered supercells in the perovskite based system NaTiO3 - BiTiO3, including 38 supercells with the [Na1/2Bi1/2]TiO3 (NBT) composition. The DeltaE(VASP) were used to fit a cluster expansion Hamiltonian to verify that the no other superstructure is predicted to have lower energy than the lowest DeltaE(VASP), which is a 40 atom supercell with space group symmetry P11m. Its chemical ordering is characterized by pseudocubic doubling of the cell constants, with alternating [100] rows of Na and Bi atoms in (hk0) planes plus alternating [010] rows in (hk1/2) planes. Chemical ordering alone reduces space group symmetry from cubic, Pm3m, to tetragonal, P4(2)/mmc, and octahedral tilting (a(-)a(-)c(+) system) further reduces it to monoclinic, P11m.