Complex disorder in β-NH4Fe2(PO4)2: deciphering from a five-dimensional formalism
Authors:Perez, Olivier; Adam, Laure; Guesdon, Anne; Daturi, M.; Raveau, Bernard
Journal:Acta Crystallographica, Section B 63 521-531 (2007)
DOI:https://doi.org/10.1107/S0108768107021647
B-IncStrDB ID: WTeImKnfYJC Entry date: 2022-01-25 Last revision: 2022-01-25
I
Chemical data
Structural Formula Sum: Fe1 N0.5 O4 P1 [ Help ]
Formula weight: 157.8 Da [ Help ]
Crystallographic data and experimental details
Crystal system: orthorhombic [ Help ]
Superspace group name: Fddd(0pq,0p-) [ Help ]
Symmetry operations of the superspace group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x1,x2,x3,x4,x5 |
| 2 | 1/4+x1,1/4+x2,1/4-x3,x5,x4 |
| 3 | 1/4-x1,1/4+x2,1/4+x3,x4,x5 |
| 4 | -x1,x2,-x3,x5,x4 |
| 5 | 1/4-x1,1/4-x2,1/4-x3,-x4,-x5 |
| 6 | -x1,-x2,x3,-x5,-x4 |
| 7 | x1,-x2,-x3,-x4,-x5 |
| 8 | 1/4+x1,1/4-x2,1/4+x3,-x5,-x4 |
| 9 | x1,1/2+x2,1/2+x3,x4,x5 |
| 10 | 1/4+x1,3/4+x2,3/4-x3,x5,x4 |
| 11 | 1/4-x1,3/4+x2,3/4+x3,x4,x5 |
| 12 | -x1,1/2+x2,1/2-x3,x5,x4 |
| 13 | 1/4-x1,3/4-x2,3/4-x3,-x4,-x5 |
| 14 | -x1,1/2-x2,1/2+x3,-x5,-x4 |
| 15 | x1,1/2-x2,1/2-x3,-x4,-x5 |
| 16 | 1/4+x1,3/4-x2,3/4+x3,-x5,-x4 |
| 17 | 1/2+x1,x2,1/2+x3,x4,x5 |
| 18 | 3/4+x1,1/4+x2,3/4-x3,x5,x4 |
| 19 | 3/4-x1,1/4+x2,3/4+x3,x4,x5 |
| 20 | 1/2-x1,x2,1/2-x3,x5,x4 |
| 21 | 3/4-x1,1/4-x2,3/4-x3,-x4,-x5 |
| 22 | 1/2-x1,-x2,1/2+x3,-x5,-x4 |
| 23 | 1/2+x1,-x2,1/2-x3,-x4,-x5 |
| 24 | 3/4+x1,1/4-x2,3/4+x3,-x5,-x4 |
| 25 | 1/2+x1,1/2+x2,x3,x4,x5 |
| 26 | 3/4+x1,3/4+x2,1/4-x3,x5,x4 |
| 27 | 3/4-x1,3/4+x2,1/4+x3,x4,x5 |
| 28 | 1/2-x1,1/2+x2,-x3,x5,x4 |
| 29 | 3/4-x1,3/4-x2,1/4-x3,-x4,-x5 |
| 30 | 1/2-x1,1/2-x2,x3,-x5,-x4 |
| 31 | 1/2+x1,1/2-x2,-x3,-x4,-x5 |
| 32 | 3/4+x1,3/4-x2,1/4+x3,-x5,-x4 |
a: 17.152 Å [ Help ]
b: 7.434 Å [ Help ]
c: 10.05 Å [ Help ]
α: 90 ° [ Help ]
β: 90 ° [ Help ]
γ: 90 ° [ Help ]
Volume: 1281.455 Å3 [ Help ]
Z: 16 [ Help ]
Cell measurement temperature: 173 K [ Help ]
Modulation dimension: 2 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.00000 | 0.50000 | 0.50000 |
| 2 | 0.00000 | 0.50000 | -0.50000 |
μ: 5.044 mm-1 [ Help ]
Absorption correction type: none [ Help ]
Minimum transmission factor: 1.000 [ Help ]
Maximum transmission factor: 1.000 [ Help ]
Refinement details
Total nb. of reflections: 5543 [ Help ]
Nb. of observed reflections: 2625 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(all): 0.1277 [ Help ]
R(obs): 0.0512 [ Help ]
wR(obs): 0.0374 [ Help ]
wR(all): 0.0414 [ Help ]
S(all): 1.67 [ Help ]
Nb. of reflections: 5543 [ Help ]
Nb. of parameters: 106 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/σ2(F) [ Help ]
Δ/σ(max): 0.0011 [ Help ]
Δ/σ(mean): 0.0001 [ Help ]
Δρ(max): 2.87 e_Å-3 [ Help ]
Δρ(min): -2.64 e_Å-3 [ Help ]
Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]
Extinction coefficient: 0.014(7) [ Help ]
Structural Information
Average Structure: (Show/hide table) [ Help ]
| Atom site label | Atom symbol | x | y | z | ADP type | Uiso/equiv | Occupancy | Coords from (d)iffraction or (c)alculated | Coords restraints or constraints | Disordered cluster | Disordered group |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Fe1 | Fe | 0 | 0 | 0.5 | Uani | 0.00509(6) | 1 | d | . | . | . |
| Fe2 | Fe | 0.153522(18) | 0 | 0 | Uani | 0.00383(9) | 0.4886(12) | d | . | . | . |
| N | N | 0.0863(2) | 0 | 0 | Uani | 0.0243(9) | 0.5114(12) | d | . | . | . |
| P | P | 0.06078(2) | 0.79881(7) | 0.22655(5) | Uani | 0.00369(9) | 0.5 | d | . | . | . |
| O1 | O | 0.11587(6) | 0.0550(2) | 0.48651(15) | Uani | 0.0057(3) | 0.5 | d | . | . | . |
| O2 | O | 0.00800(4) | 0.68836(14) | 0.13945(11) | Uani | 0.0171(2) | 1 | d | . | . | . |
| O3 | O | 0.08497(7) | 0.9825(2) | 0.16789(16) | Uani | 0.0080(3) | 0.5 | d | . | . | . |
ADP components: (Show/hide table) [ Help ]
| Atom site label | U11 | U22 | U33 | U12 | U13 | U23 | Atom site symbol |
|---|---|---|---|---|---|---|---|
| Fe1 | 0.00302(7) | 0.00667(10) | 0.00289(8) | 0 | 0 | 0 | Fe |
| Fe2 | 0.00320(8) | 0.00482(11) | 0.00383(11) | 0 | 0 | -0.00061(9) | Fe |
| P | 0.00274(10) | 0.00422(13) | 0.00303(12) | -0.00038(9) | 0 | -0.00024(10) | P |
| O1 | 0.0027(3) | 0.0071(4) | 0.0061(4) | 0.0005(3) | -0.0005(2) | 0.0000(3) | O |
| O2 | 0.00567(18) | 0.0110(3) | 0.0149(4) | 0.00176(19) | -0.0043(2) | -0.0081(3) | O |
| O3 | 0.0067(3) | 0.0051(5) | 0.0091(4) | -0.0018(3) | 0.0008(3) | 0.0019(4) | O |
| N | 0.026724 | 0.020521 | 0.018782 | 0 | 0 | 0.010091 | N |
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 | 0.00000 | 0.50000 | 0.50000 |
| 2 | 0.00000 | 0.50000 | -0.50000 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Fe1x1 | Fe1 | x | 1 |
| Fe1y1 | Fe1 | y | 1 |
| Fe1z1 | Fe1 | z | 1 |
| Fe1x2 | Fe1 | x | 2 |
| Fe1y2 | Fe1 | y | 2 |
| Fe1z2 | Fe1 | z | 2 |
| Fe2x1 | Fe2 | x | 1 |
| Fe2y1 | Fe2 | y | 1 |
| Fe2z1 | Fe2 | z | 1 |
| Fe2x2 | Fe2 | x | 2 |
| Fe2y2 | Fe2 | y | 2 |
| Fe2z2 | Fe2 | z | 2 |
| Px1 | P | x | 1 |
| Py1 | P | y | 1 |
| Pz1 | P | z | 1 |
| Px2 | P | x | 2 |
| Py2 | P | y | 2 |
| Pz2 | P | 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 |
| O2x2 | O2 | x | 2 |
| O2y2 | O2 | y | 2 |
| O2z2 | O2 | z | 2 |
| O3x1 | O3 | x | 1 |
| O3y1 | O3 | y | 1 |
| O3z1 | O3 | z | 1 |
| O3x2 | O3 | x | 2 |
| O3y2 | O3 | y | 2 |
| O3z2 | O3 | z | 2 |
| Nx1 | N | x | 1 |
| Ny1 | N | y | 1 |
| Nz1 | N | z | 1 |
| Nx2 | N | x | 2 |
| Ny2 | N | y | 2 |
| Nz2 | N | z | 2 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Fe1x1 | 0.00053(2) | 0 |
| Fe1y1 | 0 | -0.00678(7) |
| Fe1z1 | 0 | -0.00049(5) |
| Fe1x2 | -0.00053(2) | 0 |
| Fe1y2 | 0 | -0.00678(7) |
| Fe1z2 | 0 | 0.00049(5) |
| Fe2x1 | -0.00098(4) | 0 |
| Fe2y1 | 0 | -0.00400(13) |
| Fe2z1 | 0 | 0.00228(9) |
| Fe2x2 | -0.00016(8) | 0 |
| Fe2y2 | 0 | -0.00170(14) |
| Fe2z2 | 0 | 0.00074(10) |
| Px1 | -0.00142(5) | -0.00025(5) |
| Py1 | 0.00193(17) | -0.00025(17) |
| Pz1 | 0.00028(11) | 0.00053(12) |
| Px2 | -0.00012(5) | 0 |
| Py2 | -0.00066(18) | -0.0009(3) |
| Pz2 | 0.00035(12) | 0.0005(2) |
| O1x1 | 0.00076(13) | 0.00040(16) |
| O1y1 | -0.0026(5) | 0 |
| O1z1 | 0.0009(4) | 0 |
| O1x2 | 0 | 0.0003(2) |
| O1y2 | 0.0007(5) | 0.0012(8) |
| O1z2 | 0 | -0.0012(6) |
| O2x1 | 0.00034(8) | -0.00047(8) |
| O2y1 | 0.0034(3) | -0.0022(3) |
| O2z1 | -0.0026(2) | 0.0016(2) |
| O2x2 | -0.00043(8) | 0.00225(8) |
| O2y2 | -0.0018(3) | 0.0096(3) |
| O2z2 | 0.0017(3) | -0.01541(19) |
| O3x1 | -0.00247(16) | -0.00176(16) |
| O3y1 | 0.0046(5) | 0.0028(5) |
| O3z1 | 0.0011(4) | 0.0019(4) |
| O3x2 | 0 | -0.00037(18) |
| O3y2 | -0.0053(8) | 0.0019(7) |
| O3z2 | 0.0012(5) | 0 |
| Nx1 | 0.0031 | 0 |
| Ny1 | 0 | -0.005 |
| Nz1 | 0 | 0.0017 |
| Nx2 | 0 | 0 |
| Ny2 | 0 | 0 |
| Nz2 | 0 | 0 |
Definition of the occupation Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Wave vector code |
|---|---|---|
| Fe2o1 | Fe2 | 1 |
| Fe2o2 | Fe2 | 2 |
| Po1 | P | 1 |
| Po2 | P | 2 |
| O1o1 | O1 | 1 |
| O1o2 | O1 | 2 |
| O2o1 | O2 | 1 |
| O2o2 | O2 | 2 |
| O3o1 | O3 | 1 |
| O3o2 | O3 | 2 |
| No1 | N | 1 |
| No2 | N | 2 |
Occupation Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Fe2o1 | 0 | 0 |
| Fe2o2 | -0.4461 | 0 |
| Po1 | 0.0053(18) | 0.004(2) |
| Po2 | -0.1067(19) | 0.459(3) |
| O1o1 | 0 | 0.015(6) |
| O1o2 | 0.085(5) | -0.420(6) |
| O2o1 | 0 | 0 |
| O2o2 | 0 | 0 |
| O3o1 | 0 | 0.009(5) |
| O3o2 | -0.396(5) | 0.263(5) |
| No1 | 0 | 0 |
| No2 | 0.4461 | 0 |