Complementary evaluation of structure stability of perovskite oxides using bond-valence and density-functional-theory calculations

Figures & data

Figure 1. Global instability index for typical ABO₃-type metal oxides in cubic perovskite structure.

Figure 2. Global instability index and discrepancy factors for selected ABO₃-type metal oxides in cubic perovskite structure; (a) SrTiO₃, (b) BaZrO₃, (c) CaTiO₃, and (d) BaTiO₃.

Table 1. Tolerance factor (t), ionic radius of A- and B-ions, GII for cubic (GII _cubic) and distorted perovskite structures (GII _exp), a ₀, and crystal structure at room temperature determined by experiment for selected ABO₃-type oxides.

Oxide	t	r A (Å)	r B (Å)	GII cubic (v.u.)	a 0 (Å)	GII exp (v.u.)	Crystal system, space group, and lattice constants (Å) determined by experiment
CaTiO3	0.966	1.34	0.605	0.273	3.870	0.128	Orthorhombic (Pbnm); a = 5.3789, b = 5.4361, c = 7.6388 [32]
SrTiO3	1.001	1.44	0.605	0.006	3.930	0.102	Cubic (Pm $\overline{3}$ m); a = 3.9049 [33]
BaTiO3	1.062	1.61	0.605	0.362	4.045	0.410	Tetragonal (P4mm); a = 3.9925, c = 4.0365 [34]
CaZrO3	0.914	1.34	0.72	0.521	4.085	0.140	Orthorhombic (Pbnm); a = 5.5890, b = 5.7586, c = 8.0140 [35]
SrZrO3	0.947	1.44	0.72	0.309	4.110	0.156	Orthorhombic (Pbnm); a = 5.7862, b = 5.8151, c = 8.1960 [36]
BaZrO3	1.004	1.61	0.72	0.003	4.175	0.049	Cubic (Pm $\overline{3}$ m); a = 4.1879 [37]
NaTaO3	0.967	1.39	0.64	0.102	3.960	0.103	Orthorhombic (Pbnm); a = 5.48109, b = 5.52351, c = 7.79483 [38]
LaAlO3	1.009	1.36	0.535	0.027	3.805	0.078	Rhombohedral (R $\overline{3}$ c); a = 5.48109, c = 7.79483 [39]

Figure 3. Square of global instability index (red circles) and relative total energy (blue squares) as a function of a for (a) SrTiO₃ and (b) BaZrO₃ in cubic perovskite structure. The curves represent the fitting results using quadratic function.

Table 2. Fitting results of GII ² and relative total energy using quadratic function for SrTiO₃ and BaZrO₃.

	k 1 [v.u.^2/Å^2]	k 2 [eV/(Å^2 f.u.)]	k 2 /k 1 [eV/(v.u.^2 f.u.)]
SrTiO3	14.41(14)	19.44(10)	1.349
BaZrO3	14.34(14)	17.69(8)	1.234

Figure 4. Comparison of structure instability between total energy and GII. The line represents the linear fitting result.

Yashima M , Ali R . Structural phase transition and octahedral tilting in the calcium titanate perovskite CaTiO3 . Solid State Ionics. 2009;180:120–126.10.1016/j.ssi.2008.11.019

 Web of Science ®Google Scholar

Luo W-Q , Shen Z-Y , Li Y-M , et al . Structural characterizations, dielectric properties and impedance spectroscopy analysis of Nd x Sr1–1.5x TiO3 ceramics. J Electroceram. 2013;31:117–123.10.1007/s10832-013-9805-0

 Web of Science ®Google Scholar

Kwei GH , Lawson AC , Billinge SJL , et al . Structures of the ferroelectric phases of barium titanate. J Phys Chem. 1993;97:2368–2377.10.1021/j100112a043

 Web of Science ®Google Scholar

Stoch P , Szczerba J , Lis J , et al . Crystal structure and ab initio calculations of CaZrO3 . J Eur Ceram Soc. 2012;32:665–670.10.1016/j.jeurceramsoc.2011.10.011

 Web of Science ®Google Scholar

Ahtee A , Ahtee M , Glazer AM , et al . The structure of orthorhombic SrZrO3 by neutron powder diffraction. Acta Crystallogr Sect B. 1976;32:3243–3246.10.1107/S0567740876010029

 Web of Science ®Google Scholar

Ahmed I , Eriksson SG , Ahlberg E , et al . Proton conductivity and low temperature structure of In-doped BaZrO3 . Solid State Ionics. 2006;177:2357–2362.10.1016/j.ssi.2006.05.030

 Web of Science ®Google Scholar

Mitchell RH , Liferovich RP . A structural study of the perovskite series Ca1−x Na x Ti1−x Ta x O3 . J Solid State Chem. 2004;177:4420–4427.10.1016/j.jssc.2004.09.031

 Web of Science ®Google Scholar

Christopher JH , Brendan JK , Bryan CC . Neutron powder diffraction study of rhombohedral rare-earth aluminates and the rhombohedral to cubic phase transition. J Phys Condens Matter. 2000;12:349.

 Web of Science ®Google Scholar