First-Principles Study of Structural Trend of BiMO3 and BaMO3: Relationship between Tetragonal or Rhombohedral Structure and the Tolerance Factors

Abstract

The relationship between a tetragonal or rhombohedral structure and the tolerance factors in BiMO3 and BaMO3 has been investigated using a first-principles calculation with optimized structures. BiMO3 and BaMO3, which consist of M ions with d0-state transition metals (TMs) or non-TMs, were optimized within frameworks of P4mm (tetragonal) and R3m (rhombohedral) structures, and their total energies (Etetra and Erhombo, respectively) were compared. In BiMO3, except for BiGaO3, the total energy difference ΔE (≡Erhombo-Etetra) as a function of the tolerance factor t increases monotonically and smoothly, and the critical value from negative to positive in ΔE is about 1.00. In BiGaO3 with d10-state Ga ions, the tetragonal structure is more stable despite t<1.00. This result is due to the strong Coulomb repulsion between Ga 3s, 3p, and 3d states and O 2p states, which is consistent with tetragonal BiZn0.5Ti0.5O3 recently reported. In BaMO3, on the other hand, the dependence of ΔE is more complicated, that is, positive, zero [i.e., cubic (Pm3m)], negative, and positive, as t increases. The trend of the above calculated results is consistent with that of experimantal results, and can be a principal guideline for material design. The above crystal structures of AMO3 (A=Bi or Ba) are found to be closely related to the contribution of A ions to the local electric fields at M ions by the analysis of Lorentz corrections.