Modulated structure of Zirconium Titanate
Authors:Yamamoto, A.; Yamada, T.; Ikawa, H.; Fukunaga, O.; Tanaka, K.; Marumo, F.
Journal:Acta Cryst. C 47 1588-1591 (1991)
DOI:https://doi.org/10.1107/S0108270191001804
B-IncStrDB ID: 922EXbUZU Entry date: 2010-11-08 Last revision: 2021-12-30
ZrTi
Chemical data
Structural Formula Sum: Hf0.008 O4 Ti1 Zr0.992 [ Help ]
Formula weight: 203.8 Da [ Help ]
Crystallographic data and experimental details
a: 4.821(2) Å [ Help ]
b: 5.341(7) Å [ Help ]
c: 5.022(3) Å [ Help ]
α: 90 ° [ Help ]
β: 90 ° [ Help ]
γ: 90 ° [ Help ]
Volume: 129.31(19) Å3 [ Help ]
Z: 2 [ Help ]
μ: 7.187 mm-1 [ Help ]
Cell measurement temperature: 298 K [ Help ]
Crystal system: orthorhombic [ Help ]
Superspace group name (WJJ): P:P b c 21:-1 1 -1 [ Help ]
Superspace group name: Pbc21(α00)000 [ Help ]
Symmetry operations of the superspace group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x1,x2,x3,x4 |
| 2 | x1,-x2,1/2+x3,x4 |
| 3 | 1/2-x1,1/2-x2,1/2+x3,-x4 |
| 4 | 1/2-x1,1/2+x2,x3,-x4 |
Space group name (H-M): P b c 21 [ Help ]
Symmetry operations of the space group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x,y,z |
| 2 | x,-y,1/2+z |
| 3 | 1/2-x,1/2-y,1/2+z |
| 4 | 1/2-x,1/2+y,z |
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.43 | 0 | 0 |
Refinement details
Refinement remarks: Occupational parameters restricted by penalty functions. The amount of Hf was detected by energy-dispersive X-ray analysis Hf/Zr=0.008/0.992. WARNING: The published thermal displacement parameters, Biso, have been converted to Uiso. [ Help ]
Modulation functions description: Displacive modulation:Fourier series. 1st-order harmonics. Occupational modulation:Fourier series. 1st-order harmonics. [ Help ]
Structure factors calc. details: Gaussian integration [ Help ]
Nb. of observed reflections: 1647 [ Help ]
R(obs): 0.093 [ Help ]
wR(all): 0.094 [ Help ]
Structural Information
Average Structure: (Show/hide table) [ Help ]
| Site description | Atom site label | Atom symbol | Symmetry multiplicity | Occupancy | x | y | z | Uiso/equiv | ADP type |
|---|---|---|---|---|---|---|---|---|---|
| Common site for Hf and Zr atoms | Zr/Hf | Zr | 4 | 0.45(1) | 0.027(1) | 0.285(1) | 0.25 | 0.0029(3) | Uani |
| . | Ti | Ti | 4 | 0.55 | -0.021(1) | 0.267(1) | 0.211(2) | 0.0105(4) | Uani |
| . | O1 | O | 4 | 0.55(3) | 0.278(6) | 0.100(5) | 0.061(5) | 0.0090(3) | Uani |
| . | O2 | O | 4 | 0.45 | 0.241(12) | 0.085(11) | 0.014(12) | 0.0067(3) | Uani |
| . | O3 | O | 4 | 0.48(5) | 0.759(7) | 0.569(6) | 0.450(7) | 0.0076(3) | Uani |
| . | O4 | O | 4 | 0.52 | 0.774(6) | 0.615(6) | 0.366(7) | 0.0046(1) | Uani |
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 | 0.43 | 0 | 0 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Zr/Hfx1 | Zr/Hf | x | 1 |
| Zr/Hfy1 | Zr/Hf | y | 1 |
| Zr/Hfz1 | Zr/Hf | z | 1 |
| Tix1 | Ti | x | 1 |
| Tiy1 | Ti | y | 1 |
| Tiz1 | Ti | z | 1 |
| O1x1 | O1 | x | 1 |
| O1y1 | O1 | y | 1 |
| O1z1 | O1 | z | 1 |
| O2x1 | O2 | x | 1 |
| O2y1 | O2 | y | 1 |
| O2z1 | O2 | z | 1 |
| O3x1 | O3 | x | 1 |
| O3y1 | O3 | y | 1 |
| O3z1 | O3 | z | 1 |
| O4x1 | O4 | x | 1 |
| O4y1 | O4 | y | 1 |
| O4z1 | O4 | z | 1 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Zr/Hfx1 | -0.009(1) | -0.014(1) |
| Zr/Hfy1 | -0.005(1) | -0.020(1) |
| Zr/Hfz1 | -0.027(1) | -0.039(1) |
| Tix1 | -0.004(1) | -0.005(1) |
| Tiy1 | 0.005(1) | -0.014(1) |
| Tiz1 | 0.066(2) | 0.037(1) |
| O1x1 | 0.008(7) | 0.030(7) |
| O1y1 | 0.016(5) | 0.012(6) |
| O1z1 | 0.031(5) | 0.043(7) |
| O2x1 | -0.010(7) | 0.028(14) |
| O2y1 | 0.009(5) | -0.015(14) |
| O2z1 | 0.013(8) | -0.085(14) |
| O3x1 | -0.030(9) | 0.014(6) |
| O3y1 | -0.002(8) | -0.006(5) |
| O3z1 | -0.002(9) | -0.008(6) |
| O4x1 | -0.001(8) | -0.003(4) |
| O4y1 | -0.008(8) | -0.013(4) |
| O4z1 | 0.057(9) | 0.004(6) |
Definition of the occupation Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Wave vector code |
|---|---|---|
| Zr/Hfo1 | Zr/Hf | 1 |
| Tio1 | Ti | 1 |
| O1o1 | O1 | 1 |
| O2o1 | O2 | 1 |
| O3o1 | O3 | 1 |
| O4o1 | O4 | 1 |
Occupation Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Zr/Hfo1 | 0.30(1) | 0.37(1) |
| Tio1 | -0.30 | -0.37 |
| O1o1 | 0.11(1) | -0.49(2) |
| O2o1 | -0.11 | 0.49 |
| O3o1 | 0.45(7) | -0.17(4) |
| O4o1 | -0.45 | 0.17 |