Incommensurately Modulated Crystal Structure of α' (O'3)-type Sodium Cobalt Oxide NaxCoO2 (x ∼ 0.78)
Authors:Miyazaki, Yuzuru; Igawa, Naoki; Yubuta, Kunio
Journal:Acta Crystallographica Section B 77 371-377 (2021)
DOI:https://doi.org/10.1107/S205252062100370X
B-IncStrDB ID: 16942E6CXxJ Entry date: 2022-01-10 Last revision: 2022-01-25
I
Chemical data
Structural Formula Sum: Na0.779 Co1 O2 [ Help ]
Formula weight: 108.84 Da [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Superspace group name: C2/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,x4 |
| 6 | -x1+1/2,x2+1/2,-x3,-x4 |
| 7 | -x1+1/2,-x2+1/2,-x3,-x4 |
| 8 | x1+1/2,-x2+1/2,x3,x4 |
a: 4.88979(17) Å [ Help ]
b: 2.86782(8) Å [ Help ]
c: 5.78034(19) Å [ Help ]
α: 90 ° [ Help ]
β: 111.8897(16) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 75.214(4) Å3 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.3458(3) | 0.000000 | -0.2624(3) |
Z: 2 [ Help ]
Cell measurement temperature: 293 K [ Help ]
μ: 0.101 mm-1 [ Help ]
Refinement details
R(obs): 0.0303 [ Help ]
wR(obs): 0.0344 [ Help ]
R(all): 0.0329 [ Help ]
wR(all): 0.0347 [ Help ]
S(all): 1.81 [ Help ]
Nb. of parameters: 42 [ Help ]
Number of restraints: 0 [ Help ]
Number of constraints: 0 [ Help ]
Weighting scheme: sigma [ Help ]
Δ/σ(max): 0.0487 [ Help ]
Δ/σ(mean): 0.0146 [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Na | Na | 0 | 0.5 | 0.5 | Uiso | 0.0086(13) | 4 | 0.5 | d | . | . | . |
| Co | Co | 0 | 0 | 0 | Uiso | 0.0110(9) | 2 | 1 | d | . | . | . |
| O | O | 0.2544(3) | 0 | 0.8162(2) | Uiso | 0.0104(4) | 4 | 1 | d | . | . | . |
Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): (Show/hide table) [ Help ]
| Wave vector code | q_1 |
|---|---|
| 1 | 1 |
| 2 | 2 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Nax1 | Na | x | 1 |
| Nay1 | Na | y | 1 |
| Naz1 | Na | z | 1 |
| Nax2 | Na | x | 2 |
| Nay2 | Na | y | 2 |
| Naz2 | Na | z | 2 |
| Cox1 | Co | x | 1 |
| Coy1 | Co | y | 1 |
| Coz1 | Co | z | 1 |
| Cox2 | Co | x | 2 |
| Coy2 | Co | y | 2 |
| Coz2 | Co | z | 2 |
| Ox1 | O | x | 1 |
| Oy1 | O | y | 1 |
| Oz1 | O | z | 1 |
| Ox2 | O | x | 2 |
| Oy2 | O | y | 2 |
| Oz2 | O | z | 2 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Nax1 | 0 | -0.040(5) |
| Nay1 | 0 | 0 |
| Naz1 | 0 | 0.043(4) |
| Nax2 | 0 | 0 |
| Nay2 | 0 | 0 |
| Naz2 | 0 | 0 |
| Cox1 | 0 | 0.0309(15) |
| Coy1 | 0 | 0 |
| Coz1 | 0 | 0.0500(12) |
| Cox2 | 0 | 0.005(3) |
| Coy2 | 0 | 0 |
| Coz2 | 0 | -0.004(2) |
| Ox1 | 0.0175(5) | 0.0308(4) |
| Oy1 | 0 | 0 |
| Oz1 | -0.0058(5) | 0.0508(3) |
| Ox2 | 0.0032(10) | -0.0048(9) |
| Oy2 | 0 | 0 |
| Oz2 | 0.0024(7) | -0.0024(5) |
Displacive sawtooth coefficients: (Show/hide table) [ Help ]
| Atom site label | Ax | Ay | Az | Center (x0) | Width |
|---|---|---|---|---|---|
| Na | 0.234(7) | 0 | -0.013(5) | 0.051(4) | 0.779(6) |