Prediction of the (Na 1/2 Bi 1/2 )TiO 3 Ground State

The Vienna Ab-initio Simulation Package (VASP) was used to per- form fully relaxed, planewave pseudopotential calculations of formation energies ( EV ASP) for a large number of ordered supercells in the perovskite based system NaTiO3 BiTiO3, including 38 supercells with the (Na1/2Bi1/2)TiO3 (NBT) com- position. The EV ASP were used to fit a cluster expansion Hamiltonian to verify that the no other superstructure is predicted to have lower energy than the lowest EV ASP, which is a 40 atom supercell with space group symmetry P11m. Its chemical order- ing 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 (hk 1 ) planes. Chemical ordering alone reduces space group symmetry from cubic, Pm3m, to tetragonal, P42/mmc, and octahedral tilting (a a c + system) further reduces it to monoclinic, P11m.