B-IncStrDB

Structures of incommensurate and commensurate composite crystals Na_xCuO₂ (x = 1.58, 1.6, 1.62)

Authors:

van Smaalen, Sander; Dinnebier, Robert ; Sofin, Mikhail; Jansen,Martin

Journal:

Acta Crystallographica, Section B 63 17-25 (2007)

DOI:

https://doi.org/10.1107/S0108768106039462

B-IncStrDB ID: N9lhzei9O8t Entry date: 2022-01-28 Last revision: 2022-01-28

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I

Chemical data

Full Name: sodium copper oxide [ Help ]

Structural Formula Sum: Cu1 Na1.57664 O2 [ Help ]

Formula weight: 661.6 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: C2/m(0β0)s0 [ 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,-x3,1/2+x4
3	-x1,-x2,-x3,-x4
4	x1,-x2,x3,1/2-x4
5	1/2+x1,1/2+x2,x3,x4
6	1/2-x1,1/2+x2,-x3,1/2+x4
7	1/2-x1,1/2-x2,-x3,-x4
8	1/2+x1,1/2-x2,x3,1/2-x4

a: 8.24153(4) Å [ Help ]

b: 2.78589(2) Å [ Help ]

c: 5.71687(3) Å [ Help ]

α: 90 ° [ Help ]

β: 111.9698(5) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 121.7270(10) Å³ [ Help ]

Z: 2 [ Help ]

Cell measurement temperature: 293 K [ Help ]

Modulation dimension: 1 [ Help ]

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1-st subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 2 [ Help ]

Subsystem description: 2-nd subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	0.0	0.0	1.0
0.0	0.0	1.0	0.0
0.0	1.0	0.0	0.0

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.00000	0.78832(2)	0.00000

μ: 17.561 mm^-1 [ Help ]

Absorption correction type: none [ Help ]

Absorption correction remarks: (Jana2000; Petricek, Dusek & Palatinus, 2000) [ Help ]

Refinement details

R(all): 0.0482 [ Help ]

R(obs): 0.0468 [ Help ]

wR(obs): 0.0454 [ Help ]

wR(all): 0.0455 [ Help ]

Nb. of parameters: 36 [ Help ]

Number of restraints: 0 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.2946 [ Help ]

Δ/σ(mean): 0.0323 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom symbol	Atom site label	Subsystem	x	y	z	Uiso/equiv	ADP type	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Occupancy	Disordered cluster	Disordered group
Cu	Cu1	1	0	0.5	0	0.0038(2)	Uiso	d	.	1	.	.
O	O1	1	0.0493(3)	0	0.2416(3)	0.0091(7)	Uiso	d	.	1	.	.
Na	Na1	2	-0.1512(3)	0.25	0.3832(4)	0.0141(6)	Uiso	d	.	1	.	.

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	0.78832	0.00000
2	0.00000	1.57664	0.00000

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Cu1x1	Cu1	x	1
Cu1y1	Cu1	y	1
Cu1z1	Cu1	z	1
Cu1x2	Cu1	x	2
Cu1y2	Cu1	y	2
Cu1z2	Cu1	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
Na1x1	Na1	x	1
Na1y1	Na1	y	1
Na1z1	Na1	z	1
Na1x2	Na1	x	2
Na1y2	Na1	y	2
Na1z2	Na1	z	2

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Cu1x1	0	-0.01696(19)
Cu1y1	0	0
Cu1z1	0	-0.0291(3)
Cu1x2	0	0
Cu1y2	0	-0.0041(10)
Cu1z2	0	0
O1x1	0	0.0117(7)
O1y1	0.0323(19)	0
O1z1	0	0.0232(8)
O1x2	0.0037(12)	0
O1y2	0	0.021(3)
O1z2	0.0074(18)	0
Na1x1	-0.0358(5)	0
Na1y1	0	0.1111(9)
Na1z1	-0.0233(7)	0
Na1x2	-0.0201(9)	0
Na1y2	0	0.0160(15)
Na1z2	-0.0177(12)	0

II

Chemical data

Structural Formula Sum: Cu5 Na8 O10 [ Help ]

Formula weight: 661.6 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: C2/m(0β0)s0 [ 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,-x3,1/2+x4
3	-x1,-x2,-x3,-x4
4	x1,-x2,x3,1/2-x4
5	1/2+x1,1/2+x2,x3,x4
6	1/2-x1,1/2+x2,-x3,1/2+x4
7	1/2-x1,1/2-x2,-x3,-x4
8	1/2+x1,1/2-x2,x3,1/2-x4

a: 8.228(1) Å [ Help ]

b: 2.7858(4) Å [ Help ]

c: 5.707(1) Å [ Help ]

α: 90 ° [ Help ]

β: 111.718(2) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 121.528 Å³ [ Help ]

Z: 2 [ Help ]

Modulation dimension: 1 [ Help ]

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1-st subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 2 [ Help ]

Subsystem description: 2-nd subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	0.0	0.0	1.0
0.0	0.0	1.0	0.0
0.0	1.0	0.0	0.0

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.00000	0.80000	0.00000

μ: 22.317 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: 5656 [ Help ]

Nb. of observed reflections: 4523 [ Help ]

Intense reflections threshold: I>3σ(I) [ Help ]

Refinement based on: F [ Help ]

R(all): 0.0418 [ Help ]

R(obs): 0.0347 [ Help ]

wR(obs): 0.0332 [ Help ]

wR(all): 0.0334 [ Help ]

S(all): 2.95 [ Help ]

Nb. of reflections: 5656 [ Help ]

Nb. of parameters: 107 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/σ²(F) [ Help ]

Δ/σ(max): 0.0018 [ Help ]

Δ/σ(mean): 0.0002 [ Help ]

Refinement remarks: Dubious amplitudes of some ADP modulations. [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom symbol	Atom site label	Subsystem	x	y	z	Uiso/equiv	ADP type	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Occupancy	Disordered cluster	Disordered group
Cu	Cu1	1	0	0.5	0	0.0107	Uani	d	.	1	.	.
O	O1	1	0.05204	0	0.242277	0.0161	Uani	d	.	1	.	.
Na	Na1	2	-0.154182	0.25	0.377855	0.0268	Uani	d	.	1	.	.

ADP components: (Show/hide table) [ Help ]

Atom site label	U11	U22	U33	U13	Atom site symbol
Cu1	0.012659	0.010929	0.008165	0.003339	Cu
O1	0.023003	0.014862	0.009429	0.004993	O
Na1	0.021659	0.042864	0.016004	0.007236	Na

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	0.80000	0.00000
2	0.00000	1.60000	0.00000
3	0.00000	2.40000	0.00000
4	0.00000	3.20000	0.00000

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Cu1x1	Cu1	x	1
Cu1y1	Cu1	y	1
Cu1z1	Cu1	z	1
Cu1x2	Cu1	x	2
Cu1y2	Cu1	y	2
Cu1z2	Cu1	z	2
Cu1x3	Cu1	x	3
Cu1y3	Cu1	y	3
Cu1z3	Cu1	z	3
Cu1x4	Cu1	x	4
Cu1y4	Cu1	y	4
Cu1z4	Cu1	z	4
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O1x2	O1	x	2
O1y2	O1	y	2
O1z2	O1	z	2
O1x3	O1	x	3
O1y3	O1	y	3
O1z3	O1	z	3
O1x4	O1	x	4
O1y4	O1	y	4
O1z4	O1	z	4
Na1x1	Na1	x	1
Na1y1	Na1	y	1
Na1z1	Na1	z	1
Na1x2	Na1	x	2
Na1y2	Na1	y	2
Na1z2	Na1	z	2
Na1x3	Na1	x	3
Na1y3	Na1	y	3
Na1z3	Na1	z	3
Na1x4	Na1	x	4
Na1y4	Na1	y	4
Na1z4	Na1	z	4

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Cu1x1	0	-0.0143
Cu1y1	0	0
Cu1z1	0	-0.0286
Cu1x2	0	0
Cu1y2	0	-0.0062
Cu1z2	0	0
Cu1x3	0	0.0042
Cu1y3	0	0
Cu1z3	0	0.0027
Cu1x4	0	0
Cu1y4	0	-0.0014
Cu1z4	0	0
O1x1	0	0.0119
O1y1	0.0239	0
O1z1	0	0.0243
O1x2	-0.0061	0
O1y2	0	0.0204
O1z2	-0.0075	0
O1x3	0	0.0076
O1y3	-0.0082	0
O1z3	0	0.0043
O1x4	0.0013	0
O1y4	0	0.0048
O1z4	0.0003	0
Na1x1	-0.0364	0
Na1y1	0	0.0985
Na1z1	-0.0256	0
Na1x2	-0.0082	0
Na1y2	0	-0.0018
Na1z2	-0.0097	0
Na1x3	0.0042	0
Na1y3	0	-0.0179
Na1z3	-0.0007	0
Na1x4	0.0024	0
Na1y4	0	0
Na1z4	0.0004	0

Definition of the ADP Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Tensor element	Wave vector code
Cu1U111	Cu1	U11	1
Cu1U221	Cu1	U22	1
Cu1U331	Cu1	U33	1
Cu1U121	Cu1	U12	1
Cu1U131	Cu1	U13	1
Cu1U231	Cu1	U23	1
Cu1U112	Cu1	U11	2
Cu1U222	Cu1	U22	2
Cu1U332	Cu1	U33	2
Cu1U122	Cu1	U12	2
Cu1U132	Cu1	U13	2
Cu1U232	Cu1	U23	2
Cu1U113	Cu1	U11	3
Cu1U223	Cu1	U22	3
Cu1U333	Cu1	U33	3
Cu1U123	Cu1	U12	3
Cu1U133	Cu1	U13	3
Cu1U233	Cu1	U23	3
Cu1U114	Cu1	U11	4
Cu1U224	Cu1	U22	4
Cu1U334	Cu1	U33	4
Cu1U124	Cu1	U12	4
Cu1U134	Cu1	U13	4
Cu1U234	Cu1	U23	4
O1U111	O1	U11	1
O1U221	O1	U22	1
O1U331	O1	U33	1
O1U121	O1	U12	1
O1U131	O1	U13	1
O1U231	O1	U23	1
O1U112	O1	U11	2
O1U222	O1	U22	2
O1U332	O1	U33	2
O1U122	O1	U12	2
O1U132	O1	U13	2
O1U232	O1	U23	2
O1U113	O1	U11	3
O1U223	O1	U22	3
O1U333	O1	U33	3
O1U123	O1	U12	3
O1U133	O1	U13	3
O1U233	O1	U23	3
O1U114	O1	U11	4
O1U224	O1	U22	4
O1U334	O1	U33	4
O1U124	O1	U12	4
O1U134	O1	U13	4
O1U234	O1	U23	4
Na1U111	Na1	U11	1
Na1U221	Na1	U22	1
Na1U331	Na1	U33	1
Na1U121	Na1	U12	1
Na1U131	Na1	U13	1
Na1U231	Na1	U23	1
Na1U112	Na1	U11	2
Na1U222	Na1	U22	2
Na1U332	Na1	U33	2
Na1U122	Na1	U12	2
Na1U132	Na1	U13	2
Na1U232	Na1	U23	2
Na1U113	Na1	U11	3
Na1U223	Na1	U22	3
Na1U333	Na1	U33	3
Na1U123	Na1	U12	3
Na1U133	Na1	U13	3
Na1U233	Na1	U23	3
Na1U114	Na1	U11	4
Na1U224	Na1	U22	4
Na1U334	Na1	U33	4
Na1U124	Na1	U12	4
Na1U134	Na1	U13	4
Na1U234	Na1	U23	4

ADP Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Cu1U111	0	0
Cu1U221	0	0
Cu1U331	0	0
Cu1U121	-0.002292	0
Cu1U131	0	0
Cu1U231	-0.001951	0
Cu1U112	-0.000938	0
Cu1U222	-0.001233	0
Cu1U332	-0.000409	0
Cu1U122	0	0
Cu1U132	0.000089	0
Cu1U232	0	0
Cu1U113	0	0
Cu1U223	0	0
Cu1U333	0	0
Cu1U123	0.001153	0
Cu1U133	0	0
Cu1U233	0.001033	0
Cu1U114	-0.00367	0
Cu1U224	-0.00013	0
Cu1U334	-0.001985	0
Cu1U124	0	0
Cu1U134	-0.001894	0
Cu1U234	0	0
O1U111	0	-0.007726
O1U221	0	-0.001137
O1U331	0	0.000357
O1U121	0.004968	0
O1U131	0	-0.000565
O1U231	0.002039	0
O1U112	0.000177	0
O1U222	0.005123	0
O1U332	-0.00091	0
O1U122	0	-0.000235
O1U132	0.000452	0
O1U232	0	0.000425
O1U113	0	-0.000164
O1U223	0	-0.000637
O1U333	0	-0.000686
O1U123	0.003843	0
O1U133	0	-0.000386
O1U233	0.000288	0
O1U114	-0.001578	0
O1U224	0.002843	0
O1U334	0.001428	0
O1U124	0	0.000814
O1U134	0.000707	0
O1U234	0	-0.00006
Na1U111	0.005322	0
Na1U221	0.035756	0
Na1U331	0.002385	0
Na1U121	0	0.019492
Na1U131	0.001318	0
Na1U231	0	0.008364
Na1U112	-0.004723	0
Na1U222	0.001838	0
Na1U332	0.00038	0
Na1U122	0	0.018063
Na1U132	-0.000804	0
Na1U232	0	0.009998
Na1U113	-0.011063	0
Na1U223	-0.022437	0
Na1U333	0.004784	0
Na1U123	0	0.008346
Na1U133	-0.002286	0
Na1U233	0	0.006811
Na1U114	0.000236	0
Na1U224	-0.015349	0
Na1U334	-0.004909	0
Na1U124	0	-619.6094
Na1U134	-0.001531	0
Na1U234	0	-6.237483

III

Chemical data

Structural Formula Sum: Cu1 Na1.61689 O2 [ Help ]

Formula weight: 661.6 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: C2/m(0β0)s0 [ 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,-x3,1/2+x4
3	-x1,-x2,-x3,-x4
4	x1,-x2,x3,1/2-x4
5	1/2+x1,1/2+x2,x3,x4
6	1/2-x1,1/2+x2,-x3,1/2+x4
7	1/2-x1,1/2-x2,-x3,-x4
8	1/2+x1,1/2-x2,x3,1/2-x4

a: 8.23682(15) Å [ Help ]

b: 2.79269(4) Å [ Help ]

c: 5.71224(10) Å [ Help ]

α: 90 ° [ Help ]

β: 111.6696(9) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 122.112(5) Å³ [ Help ]

Z: 2 [ Help ]

Modulation dimension: 1 [ Help ]

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1-st subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 2 [ Help ]

Subsystem description: 2-nd subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	0.0	0.0	1.0
0.0	0.0	1.0	0.0
0.0	1.0	0.0	0.0

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.00000	0.80844(3)	0.00000

μ: 32.162 mm^-1 [ Help ]

Absorption correction remarks: (Jana2000; Petricek, Dusek & Palatinus, 2000) [ Help ]

Refinement details

R(all): 0.0556 [ Help ]

R(obs): 0.0546 [ Help ]

wR(obs): 0.0589 [ Help ]

wR(all): 0.0589 [ Help ]

Nb. of parameters: 37 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0489 [ Help ]

Δ/σ(mean): 0.0098 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom symbol	Atom site label	Subsystem	x	y	z	Uiso/equiv	ADP type	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Occupancy	Disordered cluster	Disordered group
Cu	Cu1	1	0	0.5	0	0.0024(4)	Uiso	d	.	1	.	.
O	O1	1	0.0526(3)	0	0.2465(5)	0.0208(10)	Uiso	d	.	1	.	.
Na	Na1	2	-0.1566(4)	0.25	0.3717(5)	0.0183(9)	Uiso	d	.	1	.	.

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	0.80844	0.00000
2	0.00000	1.61688	0.00000

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Cu1x1	Cu1	x	1
Cu1y1	Cu1	y	1
Cu1z1	Cu1	z	1
Cu1x2	Cu1	x	2
Cu1y2	Cu1	y	2
Cu1z2	Cu1	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
Na1x1	Na1	x	1
Na1y1	Na1	y	1
Na1z1	Na1	z	1
Na1x2	Na1	x	2
Na1y2	Na1	y	2
Na1z2	Na1	z	2

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Cu1x1	0	-0.0182(3)
Cu1y1	0	0
Cu1z1	0	-0.0309(4)
Cu1x2	0	0
Cu1y2	0	-0.0023(13)
Cu1z2	0	0
O1x1	0	0.0037(9)
O1y1	0.022(2)	0
O1z1	0	0.0180(11)
O1x2	-0.0037(14)	0
O1y2	0	0.010(4)
O1z2	0.007(2)	0
Na1x1	-0.0396(5)	0
Na1y1	0	0.1009(12)
Na1z1	-0.0332(9)	0
Na1x2	-0.0210(9)	0
Na1y2	0	0.003(2)
Na1z2	-0.0190(15)	0

Structures of incommensurate and commensurate composite crystals NaxCuO2 (x = 1.58, 1.6, 1.62)

van Smaalen, Sander; Dinnebier, Robert ; Sofin, Mikhail; Jansen,Martin

Acta Crystallographica, Section B 63 17-25 (2007)

https://doi.org/10.1107/S0108768106039462

Download CIF

Open in JSmol

I

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

II

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

III

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

Structures of incommensurate and commensurate composite crystals Na_xCuO₂ (x = 1.58, 1.6, 1.62)