Antiferroelectric (Pb,Bi)1-xFe1+xO3-y Perovskites Modulated by Crystallographic Shear Planes
Authors:Abakumov, Artem M.; Batuk, Dmitry; Hadermann, Joke; Rozova, Martina G.; Sheptyakov, Denis V.; Tsirlin, Alexander A.; Niermann, Daniel; Waschkowski, Florian; Hemberger, Joachim; Van Tendeloo, Gustaaf; Antipov, Evgeny V.
Journal:Chemistry of Materials 23 255-265 (2011)
DOI:https://doi.org/10.1021/cm102907h
B-IncStrDB ID: 65Hw1nSlxOf Entry date: 2013-07-01 Last revision: 2022-02-12
(I)
Chemical data
Structural Formula Sum: Bi0.32 Fe1.042 O2.675 Pb0.64 [ Help ]
Formula weight: 300.5 Da [ Help ]
Absolute configuration: . [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Superspace group name: X2/m(α0γ)00 [ Help ]
Symmetry operations of the superspace group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x1,x2,x3,x4 |
| 2 | -x1,x2,-x3,-x4 |
| 3 | -x1,-x2,-x3,-x4 |
| 4 | x1,-x2,x3,x4 |
| 5 | x1+1/2,x2+1/2,x3+1/2,x4+1/2 |
| 6 | -x1+1/2,x2+1/2,-x3+1/2,-x4+1/2 |
| 7 | -x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2 |
| 8 | x1+1/2,-x2+1/2,x3+1/2,x4+1/2 |
a: 3.9082(1) Å [ Help ]
b: 3.90333(8) Å [ Help ]
c: 4.0900(1) Å [ Help ]
α: 90 ° [ Help ]
β: 91.936(2) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 62.35838 Å3 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.05013 | 0.00000 | 0.09170 |
Z: 1 [ Help ]
μ: 0.005 mm-1 [ Help ]
Refinement details
Nb. of parameters: 87 [ Help ]
Number of restraints: 0 [ Help ]
Number of constraints: 5 [ Help ]
Weighting scheme: sigma [ Help ]
Δ/σ(max): 0.1859 [ Help ]
Δ/σ(mean): 0.0456 [ Help ]
Structural Information
Average Structure: (Show/hide table) [ Help ]
| Atom site label | Atom symbol | x | y | z | ADP type | Uiso/equiv | Symmetry multiplicity | Occupancy | Coords from (d)iffraction or (c)alculated | Coords restraints or constraints | Disordered cluster | Disordered group |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Pb | Pb | 0 | 0 | 0 | Uani | 0.0295(8) | 2 | 0.6666 | d | . | . | . |
| Fe | Fe | 0 | 0 | 0 | Uiso | 0.0085(2) | 2 | 1 | d | . | . | . |
| O1 | O | 0.5 | 0 | 0 | Uiso | 0.0383(9) | 2 | 1 | d | . | . | . |
| O2 | O | 0 | 0 | 0.5 | Uiso | 0.0395(5) | 2 | 1 | d | . | . | . |
| O3 | O | 0 | 0.5 | 0 | Uiso | 0.0144(5) | 2 | 1 | d | . | . | . |
| Bi | Bi | 0 | 0 | 0 | Uani | 0.0295(8) | 2 | 0.3334 | d | . | . | . |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Pb | Pb | 0.0236(14) | 0.0384(8) | 0.0260(17) | 0 | -0.0052(11) | 0 |
| Bi | Bi | 0.0236(14) | 0.0384(8) | 0.0260(17) | 0 | -0.0052(11) | 0 |
Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): (Show/hide table) [ Help ]
| Wave vector code | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.05013 | 0.00000 | 0.09170 |
| 2 | 0.10025 | 0.00000 | 0.18340 |
| 3 | 0.15038 | 0.00000 | 0.27510 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Pbx1 | Pb | x | 1 |
| Pby1 | Pb | y | 1 |
| Pbz1 | Pb | z | 1 |
| Pbx2 | Pb | x | 2 |
| Pby2 | Pb | y | 2 |
| Pbz2 | Pb | z | 2 |
| Pbx3 | Pb | x | 3 |
| Pby3 | Pb | y | 3 |
| Pbz3 | Pb | z | 3 |
| Fex1 | Fe | x | 1 |
| Fey1 | Fe | y | 1 |
| Fez1 | Fe | z | 1 |
| Fex2 | Fe | x | 2 |
| Fey2 | Fe | y | 2 |
| Fez2 | Fe | z | 2 |
| O1x1 | O1 | x | 1 |
| O1y1 | O1 | y | 1 |
| O1z1 | O1 | z | 1 |
| O1x2 | O1 | x | 2 |
| O1y2 | O1 | y | 2 |
| O1z2 | O1 | z | 2 |
| O2x1 | O2 | x | 1 |
| O2y1 | O2 | y | 1 |
| O2z1 | O2 | z | 1 |
| O3x1 | O3 | x | 1 |
| O3y1 | O3 | y | 1 |
| O3z1 | O3 | z | 1 |
| O3x2 | O3 | x | 2 |
| O3y2 | O3 | y | 2 |
| O3z2 | O3 | z | 2 |
| Bix1 | Bi | x | 1 |
| Biy1 | Bi | y | 1 |
| Biz1 | Bi | z | 1 |
| Bix2 | Bi | x | 2 |
| Biy2 | Bi | y | 2 |
| Biz2 | Bi | z | 2 |
| Bix3 | Bi | x | 3 |
| Biy3 | Bi | y | 3 |
| Biz3 | Bi | z | 3 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Pbx1 | 0 | 0.0204(6) |
| Pby1 | 0 | 0 |
| Pbz1 | 0 | -0.0353(4) |
| Pbx2 | 0 | 0.0428(11) |
| Pby2 | 0 | 0 |
| Pbz2 | 0 | -0.0455(11) |
| Pbx3 | 0 | 0.0187(13) |
| Pby3 | 0 | 0 |
| Pbz3 | 0 | 0.0083(12) |
| Fex1 | 0 | -0.0098(4) |
| Fey1 | 0 | 0 |
| Fez1 | 0 | 0.0249(3) |
| Fex2 | 0 | 0.0225(5) |
| Fey2 | 0 | 0 |
| Fez2 | 0 | -0.0391(5) |
| O1x1 | 0 | 0 |
| O1y1 | 0 | 0 |
| O1z1 | 0 | 0 |
| O1x2 | 0 | 0.015(2) |
| O1y2 | 0 | 0 |
| O1z2 | 0 | -0.0180(16) |
| O2x1 | 0 | 0 |
| O2y1 | 0 | 0 |
| O2z1 | 0.0184(15) | 0 |
| O3x1 | 0 | -0.0047(7) |
| O3y1 | 0 | 0 |
| O3z1 | 0 | 0.0095(8) |
| O3x2 | 0 | 0.0463(8) |
| O3y2 | 0 | 0 |
| O3z2 | 0 | -0.0298(8) |
| Bix1 | 0 | 0.0204(6) |
| Biy1 | 0 | 0 |
| Biz1 | 0 | -0.0353(4) |
| Bix2 | 0 | 0.0428(11) |
| Biy2 | 0 | 0 |
| Biz2 | 0 | -0.0455(11) |
| Bix3 | 0 | 0.0187(13) |
| Biy3 | 0 | 0 |
| Biz3 | 0 | 0.0083(12) |
Displacive sawtooth coefficients: (Show/hide table) [ Help ]
| Atom site label | Ax | Ay | Az | Center (x0) | Width |
|---|---|---|---|---|---|
| Pb | 0.047 | 0 | -0.1337 | 0.5 | 0.4792 |
| Fe | 0.047 | 0 | -0.0072 | 0 | 0.5208 |
| O1 | 0.047 | 0 | 0.1533 | 0 | 0.3875 |
| O2 | 0.047 | 0 | 0.1294 | 0 | 0.4291 |
| O3 | 0.049 | 0 | 0.2298 | 0 | 0.5208 |
| Bi | 0.047 | 0 | -0.1337 | 0.5 | 0.4792 |