Y. M. Chang, H. F. Wang, and C. Rudowicz, "Crystal-field energy levels for deep Fe centers at orthorhombic and higher symmetry sites in BaTiO3," J. Opt. Soc. Am. B 12, 544-552 (1995)
We calculate the crystal-field energy levels for Fe3+, Fe4+, and Fe2+ ions in BaTiO3 by diagonalizing the complete matrices for the electrostatic term, the Trees correction, and the crystal-field interaction. We use the superposition model to determine the crystal-field parameters for Fe3+, Fe4+, and Fe2+ ions in each of the three phases, i.e., cubic, tetragonal, and orthorhombic, of BaTiO3. We use a recently developed computer package to diagonalize the full Hamiltonian within the whole configuration 3d4(Fe4+), 3d5(Fe3+), and 3d6(Fe2+). The absorption spectra and the charge-transfer process of deep Fe centers in BaTiO3 are investigated, and possible mechanisms for the photorefractive effects in BaTiO3 are discussed.
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Polar Positions (R, θ, ϕ) of Oxygens around Iron Centers Doped at Titanium Sites in the Three Phases in BaTiO3 Calculated from the Crystallographic Data of Ref. 29 and 30a
Phase
Cubic
Tetragonal
Orthorhombic
O1
(2.0046, 90, 0)
(1.996, 91.22, 0)
(1.9286, 44.12, 90)
O2
(2.0046, 90, 90)
(1.996, 91.22, 90)
(1.9286, 44.12, −90)
O3
(2.0046, 90, 180)
(1.996, 91.22, 180)
(2.0898, 134.04, 90)
O4
(2.0046, 90, 270)
(1.996, 91.22, 270)
(2.0898, 134.04, −90)
O5
(2.0046, 0, 0)
(1.9191, 0, 0)
(1.9944, 91.47, 0)
O6
(2.0046, 180, 0)
(2.1161, 180, 0)
(1.9944, 91.47, 180)
Equivalent oxygen
O1 – O6
O1 – O4
O1, O2
O5, O6
O3, O4
O5, O6
The values of R are in angstroms, and the angles are in degrees.
Table 2
Crystal-Field Parameters (inverse centimeters) for Fe3+, Fe4+, and Fe2+ in BaTiO3 in the Three Phases Calculated from the Superposition Model Data Given in the Texta
Sites
B20
B22
B40
B42
B44
Fe3+
Cubic
I
32 872
19 645
II
−8218
−25988
14 734
Tetragonal
−846
33 057
19 984
Orthorhombic
−83
448
−8 169
−26 365
14 981
S6
590.2
173.2
33 447.5
−88.8
−19 837.9
Fe4+
Cubic
I
35 700
21 335
II
−8925
−28223
16001
Tetragonal
−1020
36 097
21 781
Orthorhombic
−100
541
−8 936
−28 829
16 348
S6
712.6
209.3
36 537.5
−69.1
−21697.8
Fe2+
Cubic
I
16 800
10 040
II
−4200
−13281
7530
Tetragonal
−480
16 988
10 250
Orthorhombic
−47
255
−4 205
−13 566
7 693
S6
335.8
98.7
17 177.5
−32.4
−10 210.3
For orthorhombic sites the standardized Bkq (using the transformation S6; see Ref. 38) are also provided.
Table 3
3d Energy Levels (103 cm−1) of Fe4+ in BaTiO3 for the Three Phases: Cubic (Oh), Tetragonal (C4V), and Orthorhombic (C2V)a
Only the possible levels lying in the band gap are listed here. The experimental data for Fe4+ in SrTiO3 are given for comparison. Ref. 52. Ref. 53. Ref. 19. Ref. 54. Ref. 61. Ref. 55.
Table 4
3d Energy Levels (103 cm−1) of Fe3+ in BaTiO3 for the Three Phases: Cubic (Oh) Tetragonal (C4V), and Orthorhombic (C2V)a
Only the possible levels lying in the band gap are listed here. The experimental data for Fe3+ in other similar crystals are given for comparison. Ref. 56. Ref. 57. Ref. 54. Ref. 58. Ref. 59.
Table 5
3d Energy Levels (103 cm−1) of Fe2+ in BaTiO3 for the Three Phases: Cubic (Oh), Tetragonal (C4V), and Orthorhombic (C2V)a
Only the possible levels lying in the band gap are listed here. The experimental data for Fe2+ in other similar crystals are given for comparison. Ref. 19. Ref. 6. Ref. 60.
Tables (5)
Table 1
Polar Positions (R, θ, ϕ) of Oxygens around Iron Centers Doped at Titanium Sites in the Three Phases in BaTiO3 Calculated from the Crystallographic Data of Ref. 29 and 30a
Phase
Cubic
Tetragonal
Orthorhombic
O1
(2.0046, 90, 0)
(1.996, 91.22, 0)
(1.9286, 44.12, 90)
O2
(2.0046, 90, 90)
(1.996, 91.22, 90)
(1.9286, 44.12, −90)
O3
(2.0046, 90, 180)
(1.996, 91.22, 180)
(2.0898, 134.04, 90)
O4
(2.0046, 90, 270)
(1.996, 91.22, 270)
(2.0898, 134.04, −90)
O5
(2.0046, 0, 0)
(1.9191, 0, 0)
(1.9944, 91.47, 0)
O6
(2.0046, 180, 0)
(2.1161, 180, 0)
(1.9944, 91.47, 180)
Equivalent oxygen
O1 – O6
O1 – O4
O1, O2
O5, O6
O3, O4
O5, O6
The values of R are in angstroms, and the angles are in degrees.
Table 2
Crystal-Field Parameters (inverse centimeters) for Fe3+, Fe4+, and Fe2+ in BaTiO3 in the Three Phases Calculated from the Superposition Model Data Given in the Texta
Sites
B20
B22
B40
B42
B44
Fe3+
Cubic
I
32 872
19 645
II
−8218
−25988
14 734
Tetragonal
−846
33 057
19 984
Orthorhombic
−83
448
−8 169
−26 365
14 981
S6
590.2
173.2
33 447.5
−88.8
−19 837.9
Fe4+
Cubic
I
35 700
21 335
II
−8925
−28223
16001
Tetragonal
−1020
36 097
21 781
Orthorhombic
−100
541
−8 936
−28 829
16 348
S6
712.6
209.3
36 537.5
−69.1
−21697.8
Fe2+
Cubic
I
16 800
10 040
II
−4200
−13281
7530
Tetragonal
−480
16 988
10 250
Orthorhombic
−47
255
−4 205
−13 566
7 693
S6
335.8
98.7
17 177.5
−32.4
−10 210.3
For orthorhombic sites the standardized Bkq (using the transformation S6; see Ref. 38) are also provided.
Table 3
3d Energy Levels (103 cm−1) of Fe4+ in BaTiO3 for the Three Phases: Cubic (Oh), Tetragonal (C4V), and Orthorhombic (C2V)a
Only the possible levels lying in the band gap are listed here. The experimental data for Fe4+ in SrTiO3 are given for comparison. Ref. 52. Ref. 53. Ref. 19. Ref. 54. Ref. 61. Ref. 55.
Table 4
3d Energy Levels (103 cm−1) of Fe3+ in BaTiO3 for the Three Phases: Cubic (Oh) Tetragonal (C4V), and Orthorhombic (C2V)a
Only the possible levels lying in the band gap are listed here. The experimental data for Fe3+ in other similar crystals are given for comparison. Ref. 56. Ref. 57. Ref. 54. Ref. 58. Ref. 59.
Table 5
3d Energy Levels (103 cm−1) of Fe2+ in BaTiO3 for the Three Phases: Cubic (Oh), Tetragonal (C4V), and Orthorhombic (C2V)a
Only the possible levels lying in the band gap are listed here. The experimental data for Fe2+ in other similar crystals are given for comparison. Ref. 19. Ref. 6. Ref. 60.
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