The Vienna Ab-initio Simulation Package (VASP) was used to perform fully relaced, planeware psudopotential calculations of formation energies (δEVASP) for a large number of ordered supercells in the perovskite based system NaTiO3 - BiTiO3, including 36 supercells with the [Na1/2Bi1/2] TiO3 (NBT) composition. The δEVASP were used to fit a cluster expansion Hamiltonian to verify that the no other superstructure is predicted to have lower energy than the lowest δEv ^ASP^, which is a 40 atom supercell with space group symmetry Pm. Its chemical ordering is characterized by pseudocubic doubling of the cell constants, with alternating  rows of Na and Bi atoms in (hk0) planes plus alternating  rows in (hk1/2) 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, Pm.
Workshop on Fundamental Physics of Ferroelectrics | 11th | Fundamental Physics of Ferroelectrics 2001: 11th Williamsburg Workshop | AIP
and Cockayne, E.
Prediction of the [Na<sub>1/2</sub>Bi<sub>1/2</sub>] TiO<sub>3</sub> Ground State, Workshop on Fundamental Physics of Ferroelectrics | 11th | Fundamental Physics of Ferroelectrics 2001: 11th Williamsburg Workshop | AIP
(Accessed December 4, 2023)