Incommensurate modulated disorder in Ba0.85Ca2.15In6O12
Authors:Baldinozzi, G.; Goutenoire, F.; Hervieu, M.; Suard, E.; Grebille, D.
Journal:Acta Cryst. B 52 780-789 (1996)
DOI:https://doi.org/10.1107/S0108768196006519
B-IncStrDB ID: 152Eik11I Entry date: 2010-11-08 Last revision: 2021-12-30
Ba085_REFRNCE
Chemical data
Structural Formula Sum: Ba0.85 Ca2.15 In6 O12 [ Help ]
Formula weight: 1083.8 Da [ Help ]
Crystallographic data and experimental details
a: 9.8880(1) Å [ Help ]
b: 9.8880(1) Å [ Help ]
c: 3.2170(1) Å [ Help ]
α: 90 ° [ Help ]
β: 90 ° [ Help ]
γ: 120 ° [ Help ]
Volume: 272.395(9) Å3 [ Help ]
Z: 1 [ Help ]
Cell measurement temperature: 293 K [ Help ]
Crystal system: hexagonal [ Help ]
Space group name (H-M): P 63/m [ Help ]
Space group name (Hall): -P 6c [ Help ]
Symmetry operations of the space group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x,y,z |
| 2 | x-y,x,1/2+z |
| 3 | -y,x-y,z |
| 4 | -x,-y,1/2+z |
| 5 | -x+y,-x,z |
| 6 | y,-x+y,1/2+z |
| 7 | -x,-y,-z |
| 8 | -x+y,-x,1/2-z |
| 9 | y,-x+y,-z |
| 10 | x,y,1/2-z |
| 11 | x-y,x,-z |
| 12 | -y,x-y,1/2-z |
Refinement details
Refinement remarks: Rietveld refinement using X-ray and neutron data. The occupation probability of Ba sites is probably wrong. It should be 1/4 of the published value. 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. WARNING: The published thermal displacement parameters, Biso, have been converted to Uiso. [ Help ]
Structural Information
Average Structure: (Show/hide table) [ Help ]
| Atom site label | Atom symbol | Symmetry multiplicity | Occupancy | x | y | z | Uiso/equiv | ADP type |
|---|---|---|---|---|---|---|---|---|
| Ba | Ba | 4 | 0.86(1) | 0 | 0 | 0.160(12) | 0.039 | Uani |
| Ca | Ca | 2 | 1 | 0.3333 | 0.6666 | 0.25 | 0.0027(5) | Uiso |
| In | In | 6 | 1 | 0.3472(1) | -0.0044(2) | 0.25 | 0.0041(3) | Uiso |
| O1 | O | 6 | 1 | 0.1935(3) | 0.3048(3) | 0.25 | 0.0049 | Uani |
| O2 | O | 6 | 1 | 0.5316(3) | 0.3985(2) | 0.25 | 0.0058 | Uani |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Ba | Ba | .0052(15) | .0052(15) | .10(4) | .0026(7) | 0 | 0 |
| O1 | O | .0067(7) | .0241(11) | .0028(5) | .0189(15) | 0 | 0 |
| O2 | O | .0078(7) | .0011(7) | .0069(6) | .0007(11) | 0 | 0 |
Ba085_MOD
Chemical data
Structural Formula Sum: Ba0.85 Ca2.15 In6 O12 [ Help ]
Formula weight: 1083.8 Da [ Help ]
Crystallographic data and experimental details
Space group name (H-M): P 3 [ Help ]
Modulation dimension: 1 [ Help ]
a: 9.8880(1) Å [ Help ]
b: 9.8880(1) Å [ Help ]
c: 3.2170(1) Å [ Help ]
α: 90 ° [ Help ]
β: 90 ° [ Help ]
γ: 120 ° [ Help ]
Volume: 272.395(9) Å3 [ Help ]
Z: 1 [ Help ]
Cell measurement temperature: 293 K [ Help ]
Crystal system: trigonal [ Help ]
Superspace group name (ITC): P3(1/31/3g) [ Help ]
Superspace group name: P3(1/31/3g)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-x2,x3,-x2+x4 |
| 3 | -x1+x2,-x1,x3,-x1+x4 |
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.333333 | 0.333333 | 0.1385(1) |
Refinement details
Refinement remarks: Rietveld refinement using X-ray and neutron data. 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. WARNING: The published thermal displacement parameters, Biso, have been converted to Uiso. [ Help ]
Modulation functions description: Displacive modulation:Fourier series. Up to 2nd-order harmonics Ocupation modulation:Fourier series. Up to 2nd-order harmonics [ Help ]
Structure factors calc. details: neutron-S2 '2nd-order satellites,neutron experiment' [ Help ]
Structural Information
Average Structure: (Show/hide table) [ Help ]
| Atom site label | Atom symbol | Symmetry multiplicity | Occupancy | x | y | z | Uiso/equiv | ADP type |
|---|---|---|---|---|---|---|---|---|
| Ba1 | Ba | 1 | 0.35(3) | 0 | 0 | -0.295(4) | 0.0044(9) | Uiso |
| Ba2 | Ba | 1 | 0.17(2) | 0 | 0 | 0.222(7) | 0.0044(9) | Uiso |
| Ba3 | Ba | 1 | 0.31(2) | 0 | 0 | -0.064(5) | 0.0044(9) | Uiso |
| Ca0 | Ca | 1 | 0.10(2) | 0 | 0 | -0.064(5) | 0.0044(9) | Uiso |
| Ca1 | Ca | 1 | 1 | 0.3333 | 0.6666 | 0.267(5) | 0.0058(4) | Uiso |
| Ca2 | Ca | 1 | 1 | 0.6666 | 0.3333 | -0.255(7) | 0.0058(4) | Uiso |
| In1 | In | 3 | 1 | 0.3492(4) | -0.0005(4) | 0.25 | 0.0049(3) | Uiso |
| In2 | In | 3 | 1 | -0.3455(4) | 0.0068(4) | -0.253(2) | 0.0049(3) | Uiso |
| O1a | O | 3 | 1 | 0.1910(5) | 0.3040(4) | 0.250(5) | 0.0030(4) | Uiso |
| O1b | O | 3 | 1 | -0.1948(6) | -0.3024(6) | -0.241(4) | 0.0030(4) | Uiso |
| O2a | O | 3 | 1 | 0.5293(6) | 0.3970(6) | 0.248(5) | 0.0056(4) | Uiso |
| O2b | O | 3 | 1 | -0.5331(6) | -0.3997(7) | -0.246(5) | 0.0056(4) | Uiso |
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 | 0.333333 | 0.333333 | 0.1385 |
| 2 | 0.666666 | 0.666666 | 0.2770 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| In1x1 | In1 | x | 1 |
| In1y1 | In1 | y | 1 |
| In1z1 | In1 | z | 1 |
| In2x1 | In2 | x | 1 |
| In2y1 | In2 | y | 1 |
| In2z1 | In2 | z | 1 |
| O1ax1 | O1a | x | 1 |
| O1ay1 | O1a | y | 1 |
| O1ay2 | O1a | y | 2 |
| O1az1 | O1a | z | 1 |
| O1bx1 | O1b | x | 1 |
| O1bx2 | O1b | x | 2 |
| O1by1 | O1b | y | 1 |
| O1bz1 | O1b | z | 1 |
| O2ax1 | O2a | x | 1 |
| O2ay1 | O2a | y | 1 |
| O2bx1 | O2b | x | 1 |
| O2bz1 | O2b | z | 1 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| In1x1 | 0 | 0.0053(1) |
| In1y1 | 0 | 0.0061(1) |
| In1z1 | 0 | 0.0006(1) |
| In2x1 | 0 | -0.0030(1) |
| In2y1 | 0 | 0.0018(1) |
| In2z1 | 0.0124(1) | 0 |
| O1ax1 | 0 | 0.0032(1) |
| O1ay1 | 0 | 0.0089(1) |
| O1ay2 | 0 | -0.0084(1) |
| O1az1 | 0 | -0.0267(2) |
| O1bx1 | 0 | -0.0187(1) |
| O1bx2 | 0 | -0.0024(2) |
| O1by1 | 0 | -0.0339(1) |
| O1bz1 | 0 | 0.0093(3) |
| O2ax1 | -0.0095(1) | 0 |
| O2ay1 | 0 | -0.0020(1) |
| O2bx1 | 0.0061(1) | 0 |
| O2bz1 | 0 | -0.0334(2) |
Definition of the occupation Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Wave vector code |
|---|---|---|
| Ba1o1 | Ba1 | 1 |
| Ba1o2 | Ba1 | 2 |
| Ba2o1 | Ba2 | 1 |
| Ba2o2 | Ba2 | 2 |
| Ba3o1 | Ba3 | 1 |
| Ba3o2 | Ba3 | 2 |
| Ca0o1 | Ca0 | 1 |
| Ca0o2 | Ca0 | 2 |
Occupation Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Ba1o1 | 0.057(2) | 0.430(1) |
| Ba1o2 | -0.196(7) | -0.018(3) |
| Ba2o1 | 0.073(2) | -0.345(1) |
| Ba2o2 | -0.153(7) | -0.076(3) |
| Ba3o1 | -0.368(2) | 0 |
| Ba3o2 | 0.193 | 0 |
| Ca0o1 | 0.119(6) | 0 |
| Ca0o2 | 0.117(13) | 0 |