First-Principles Study of Structural Trend of Bi$M$O3 and Ba$M$O3: Relationship between Tetragonal or Rhombohedral Structure and the Tolerance Factors

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The relationship between a tetragonal or rhombohedral structure and the tolerance factors in Bi$M$O3 and Ba$M$O3 has been investigated using a first-principles calculation with optimized structures. Bi$M$O3 and Ba$M$O3, 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 ($E_{\text{tetra}}$ and $E_{\text{rhombo}}$, respectively) were compared. In Bi$M$O3, except for BiGaO3, the total energy difference $\Delta E$ ($\equiv E_{\text{rhombo}}-E_{\text{tetra}}$) as a function of the tolerance factor $t$ increases monotonically and smoothly, and the critical value from negative to positive in $\Delta E$ 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 Ba$M$O3, on the other hand, the dependence of $\Delta E$ is more complicated, that is, positive, zero [i.e., cubic ($Pm\bar{3}m$)], 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 $AM$O3 ($A=\text{Bi}$ 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.
2010-03-25

First-Principles Study of Structural Trend of Bi$M$O3 and Ba$M$O3: Relationship between Tetragonal or Rhombohedral Structure and the Tolerance Factors

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