First-Principles Study of Structural Trend of BiMO 3 and BaMO 3 : Relationship between Tetragonal or Rhombohedral Structure and the Tolerance Factors

The relationship between a tetragonal or rhombohedral structure and the tolerance factors in Bi M O 3 and Ba M O 3 has been investigated using a first-principles calculation with optimized structures. Bi M O 3 and Ba M O 3 , which consist of M ions with d 0 -state transition metals (TMs) or non-TMs, were optimized within frameworks of P 4 m m (tetragonal) and R 3 m (rhombohedral) structures, and their total energies ( E tetra and E rhombo , respectively) were compared. In Bi M O 3 , except for BiGaO 3 , the total energy difference Δ 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 Δ E is about 1.00. In BiGaO 3 with d 10 -state Ga ions, the tetragonal structure is more stable despite t