DFT study of the polarization behaviors of various distorted barium titanate crystals: The role of atomic displacements

A Local Density Approximation (LDA) was employed to investigate the influence of applied strains on valence charge distributions, atomic displacements, TiO (3) bond distances and the total polarizations in barium titanate (BaTiO₃). Four types of various strains were imposed on perfect tetragonal BaTiO₃ along the a, c, ab and abc axial directions. Electromechanical properties of BaTiO₃ were evaluated in LDA framework and a good agreement with previous results was achieved. The results show that, in the cases of a, ab strains, the values of polarization are almost constant in negative strains and increased by gradual increasing of the positive strains after a sudden enhancement at about +0.1% strain. In the case of c-strain, axial oxygen and Ti atoms underwent the highest displacements and the polarization linearly increased by applied strain. The case of abc-strain, represent the both types of features. In negative abc-strain show a similar polarization behavior like c-strain case and in positive region, polarization behavior is the same as a- and ab-strain cases. In the abc-strains of −0.3% and +0.1%, an abrupt jump in total polarization curve and a small change, are observed due to abnormal atomic displacements. In the most cases a direct relation between polarization and TiO (3) bond distance was also beheld. Finally, the effects of valence charge distributions on the atomic displacements and total polarizations are studied. It is found that there is a direct relation between polarization and Valence Charge Asymmetry of 3d -orbitals.