La1.16Mo8O16:a Hollandite-related compound with an incommensurate modulated structure
Authors:Leligny, H; Labbe, Ph.; Ledesert, M.; Raveau, B.; Valdez, C.; McCarrol, W.H.
Journal:Acta Cryst. B 48 134-144 (1992)
DOI:https://doi.org/10.1107/S0108768191013101
B-IncStrDB ID: 512EBsCa5 Entry date: 2010-11-08 Last revision: 2021-12-30
La1_16
Chemical data
Structural Formula Sum: La1.16 Mo8 O16 [ Help ]
Formula weight: 1184.6 Da [ Help ]
Crystallographic data and experimental details
a: 9.983(1) Å [ Help ]
b: 9.983(1) Å [ Help ]
c: 2.8890(5) Å [ Help ]
α: 90 ° [ Help ]
β: 90 ° [ Help ]
γ: 90 ° [ Help ]
Volume: 287.92(6) Å3 [ Help ]
Z: 1 [ Help ]
μ: 12.706 mm-1 [ Help ]
Cell measurement temperature: 294 K [ Help ]
Crystal system: tetragonal [ Help ]
Superspace group name (WJJ): P:I 4:1 [ Help ]
Superspace group name: I4(00γ)0 [ Help ]
Symmetry operations of the superspace group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x1,x2,x3,x4 |
| 2 | -x2,x1,x3,x4 |
| 3 | -x1,-x2,x3,x4 |
| 4 | x2,-x1,x3,x4 |
| 5 | 1/2+x1,1/2+x2,1/2+x3,x4 |
| 6 | 1/2-x2,1/2+x1,1/2+x3,x4 |
| 7 | 1/2-x1,1/2-x2,1/2+x3,x4 |
| 8 | 1/2+x2,1/2-x1,1/2+x3,x4 |
Space group name (H-M): I 4 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0 | 0 | 0.608(1) |
Refinement details
Refinement remarks: Atomic occupancies constrained with penalty functions. WARNING: The published thermal displacement parameters have been converted to U,s. The calculated standard uncertainties (s.u.) have been based uniquely on the published ones without considering the s.u. of any other quantity involved in such conversion. [ Help ]
Modulation functions description: Displacive modulation:Fourier series. Up to 2nd-order harmonics. Occupational modulation:Fourier series. Up to 2nd-order harmonics. [ Help ]
Structure factors calc. details: Gaussian integration [ Help ]
Nb. of observed reflections: 1145 [ Help ]
R(obs): 0.041 [ Help ]
Structural Information
Average Structure: (Show/hide table) [ Help ]
| Atom site label | Atom symbol | Symmetry multiplicity | Occupancy | x | y | z | Uiso/equiv | ADP type |
|---|---|---|---|---|---|---|---|---|
| La | La | 2 | 0.5800(50) | 0 | 0 | 0 | ? | Uani |
| Mo | Mo | 8 | 1 | 0.3188(1) | 0.1614(1) | 0.0346(33) | ? | Uani |
| O1 | O | 8 | 1 | 0.3282(10) | 0.3681(10) | 0.0364(60) | ? | Uani |
| O2 | O | 8 | 1 | 0.0399(8) | 0.3313(8) | 0.0289(55) | ? | 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 | 0 | 0.608 |
| 2 | 0 | 0 | 1.216 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Laz1 | La | z | 1 |
| Laz2 | La | z | 2 |
| Mox1 | Mo | x | 1 |
| Mox2 | Mo | x | 2 |
| Moy1 | Mo | y | 1 |
| Moy2 | Mo | y | 2 |
| Moz1 | Mo | z | 1 |
| Moz2 | Mo | z | 2 |
| O1x1 | O1 | x | 1 |
| O1x2 | O1 | x | 2 |
| O1y1 | O1 | y | 1 |
| O1y2 | O1 | y | 2 |
| O1z1 | O1 | z | 1 |
| O1z2 | O1 | z | 2 |
| O2x1 | O2 | x | 1 |
| O2x2 | O2 | x | 2 |
| O2y1 | O2 | y | 1 |
| O2y2 | O2 | y | 2 |
| O2z1 | O2 | z | 1 |
| O2z2 | O2 | z | 2 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Laz1 | 0 | -0.1576(14) |
| Laz2 | -0.0282(29) | 0.0053(33) |
| Mox1 | 0.0023(0) | 0.0018(2) |
| Mox2 | 0.0010(4) | 0.0056(1) |
| Moy1 | -0.0090(0) | -0.0010(4) |
| Moy2 | 0.0033(2) | -0.0029(3) |
| Moz1 | 0.0187(21) | 0.0485(7) |
| Moz2 | 0.0122(40) | 0.0388(14) |
| O1x1 | -0.0121(8) | 0.0090(14) |
| O1x2 | 0.0010(19) | 0.0026(15) |
| O1y1 | -0.0083(9) | 0.0114(13) |
| O1y2 | 0.0057(19) | 0.0001(15) |
| O1z1 | -0.0072(81) | 0.0018(39) |
| O1z2 | -0.0246(67) | 0.0013(104) |
| O2x1 | 0.0057(4) | -0.0021(10) |
| O2x2 | 0.0023(11) | 0.0076(7) |
| O2y1 | -0.0038(4) | -0.0007(12) |
| O2y2 | 0.0032(9) | -0.0007(12) |
| O2z1 | -0.0130(53) | 0.0026(25) |
| O2z2 | -0.0174(64) | 0.0017(40) |
Definition of the occupation Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Wave vector code |
|---|---|---|
| Lao1 | La | 1 |
| Lao2 | La | 2 |
Occupation Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Lao1 | 0.5414(44) | -0.0938(159) |
| Lao2 | -0.0841(52) | 0.0358(96) |
Phason model: (Show/hide table) [ Help ]
| Atom site label | Phason formula | Phason coefficient |
|---|---|---|
| La | Ovr | 0.1440(42) |
| Mo | Ovr | 0.3313(46) |
| O1 | Ovr | 0.3539(452) |
| O2 | Ovr | 0.0149(383) |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| La | La | 0.007573 | 0.007573 | 0.0078(6) | 0 | 0 | 0 |
| Mo | Mo | 0.004039 | 0.004544 | 0.0007(2) | -0.000505 | -0.0016(3) | 0.0013(3) |
| O1 | O | 0.0050(10) | 0.0045(10) | 0.0072(18) | -0.0015(5) | 0.006(2) | 0.001(2) |
| O2 | O | 0.0015(5) | 0.0086(5) | 0.0065(16) | -0.0010(5) | -0.005(2) | -0.003(2) |