First-Principles Study of Structural Trend of BiMO_3 and BaMO_3: Relationship between Tetragonal or Rhombohedral Structure and the Tolerance Factors

摘要

The relationship between a tetragonal or rhombohedral structure and the tolerance factors in BiMO_3 and BaMO_3 has been investigated using a first-principles calculation with optimized structures. BiMO_3 and BaMO_3, which consist of M ions with d~0-state transition metals (TMs) or non-TMs, were optimized within frameworks of P4mm (tetragonal) and R3m (rhombohedral) structures, and their total energies (E_(tetra) and E_(rhombo), respectively) were compared. In BiMO_3, except for BiGaO_3, the total energy difference △E (≡ E_(rhombo) - E_(tetra)) as a function of the tolerance factor t increases monotonically and smoothly, and the critical value from negative to positive in △E is about 1.00. In BiGaO_3 with d~(10)-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 BiZn_(0.5)Ti_(0.5)O_3 recently reported. In BaMO_3, on the other hand, the dependence of △E 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 AMO_3 (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.