B-IncStrDB

Modulated structure of Lu₄AlCu₂B₉O₂₃ from low temperature single-crystal X-ray data

Authors:

Bolotina, Nadezhda; Plachinda, Paul; Belokoneva, Elena

Journal:

Acta Crystallographica, Section B 69 329-335 (2013)

DOI:

https://doi.org/10.1107/S2052519213014231

B-IncStrDB ID: 8012ELVkXA Entry date: 2013-07-23 Last revision: 2021-12-12

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Chemical data

Structural Formula Sum: Al1 B9 Cu2 Lu4 O23 [ Help ]

Formula weight: 1319.2 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: P21212(00γ)00s [ 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+1/2
3	-x1+1/2,x2+1/2,-x3,-x4+1/2
4	x1+1/2,-x2+1/2,-x3,-x4

a: 12.591(1) Å [ Help ]

b: 12.591(1) Å [ Help ]

c: 4.7144(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 747.413 Å³ [ Help ]

Modulation dimension: 1 [ Help ]

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

Wave vector id	q_x	q_y	q_z
1	0.000000	0.000000	0.132000

Z: 2 [ Help ]

Cell measurement temperature: 110 K [ Help ]

μ: 29.12 mm^-1 [ Help ]

Absorption correction type: gaussian [ Help ]

Absorption correction remarks: Jana2006 (Petricek, Dusek & Palatinus, 2000) [ Help ]

Minimum transmission factor: 0.0408 [ Help ]

Maximum transmission factor: 0.1349 [ Help ]

Refinement details

Total nb. of reflections: 6076 [ Help ]

Nb. of observed reflections: 3378 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0386 [ Help ]

wR(obs): 0.0500 [ Help ]

R(all): 0.0530 [ Help ]

wR(all): 0.0526 [ Help ]

S(all): 1.19 [ Help ]

S(obs): 1.53 [ Help ]

Nb. of reflections: 6076 [ Help ]

Nb. of parameters: 217 [ Help ]

Number of constraints: 9 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(F)+0.0004F²) [ Help ]

Δ/σ(max): 0.0461 [ Help ]

Δ/σ(mean): 0.0091 [ Help ]

Δρ(max): 2.27 e_Å^-3 [ Help ]

Δρ(min): -2.60 e_Å^-3 [ Help ]

Extinction method: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974) [ Help ]

Extinction coefficient: 3400(120) [ Help ]

Absolute structure remarks: 2663 of Friedel pairs used in the refinement [ 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
Lu	Lu	0.65032(4)	0.35435(4)	0.00313(13)	Uani	0.01138(17)	4	1	d	?	?	?
Lu'	Lu	0.35243(4)	0.35148(4)	-0.00254(13)	Uani	0.01254(19)	4	1	d	?	?	?
Cu	Cu	0.8807(3)	0.5713(2)	-0.0292(10)	Uiso	0.0115(2)	4	0.5	d	?	?	?
Cu'	Cu	0.9158(3)	0.6093(3)	-0.0270(8)	Uiso	0.0115(2)	4	0.5	d	?	?	?
Al	Al	0.5	0.5	0.4931(16)	Uiso	0.0101(4)	2	1	d	?	?	?
B1	B	0.7158(10)	0.4979(10)	0.525(3)	Uiso	0.0103(8)	4	1	d	?	?	?
B1'	B	0.4970(11)	0.2845(8)	0.448(3)	Uiso	0.0103(8)	4	1	d	?	?	?
B2	B	0.8511(9)	0.6453(10)	0.4656(15)	Uiso	0.0118(11)	4	1	d	?	?	?
B3	B	0.8208(10)	0.3250(10)	0.4787(15)	Uiso	0.0116(11)	4	1	d	?	?	?
B4	B	0	0.5	0.502(2)	Uiso	0.0157(17)	2	1	d	?	?	?
O1	O	0.6929(8)	0.5024(8)	0.249(2)	Uiso	0.0136(5)	4	1	d	?	?	?
O1'	O	0.4994(9)	0.3068(8)	0.757(2)	Uiso	0.0136(5)	4	1	d	?	?	?
O2	O	0.6159(8)	0.4982(7)	0.715(2)	Uiso	0.0140(6)	4	1	d	?	?	?
O2'	O	0.5048(7)	0.3856(7)	0.286(2)	Uiso	0.0140(6)	4	1	d	?	?	?
O3	O	0.7663(7)	0.3998(7)	0.650(2)	Uiso	0.0111(6)	4	1	d	?	?	?
O3'	O	0.6038(6)	0.7678(7)	0.370(2)	Uiso	0.0111(6)	4	1	d	?	?	?
O4	O	0.7763(7)	0.5924(7)	0.650(2)	Uiso	0.0121(6)	4	1	d	?	?	?
O4'	O	0.4088(7)	0.7785(7)	0.367(2)	Uiso	0.0121(6)	4	1	d	?	?	?
O5	O	0.7995(7)	0.3024(7)	0.2108(9)	Uiso	0.0096(7)	4	1	d	?	?	?
O6	O	0.9321(6)	0.5619(7)	0.3552(9)	Uiso	0.0140(8)	4	1	d	?	?	?
O7	O	0.8088(7)	0.6856(7)	0.1982(9)	Uiso	0.0130(9)	4	1	d	?	?	?
O8	O	0	0.5	0.7858(14)	Uiso	0.0213(15)	2	1	d	?	?	?

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

Atom site label	Atom site symbol	U11	U22	U33	U12	U13	U23
Lu	Lu	0.0128(3)	0.0113(3)	0.0100(2)	0.00030(12)	0.0024(2)	0.0000(2)
Lu'	Lu	0.0135(4)	0.0110(3)	0.0131(2)	-0.00014(12)	0.0013(2)	-0.0028(2)

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

Table: (Show/hide table) [ Help ]

_jana_atom_site_occ_Fourier_absolute_site_label	_jana_atom_site_occ_Fourier_absolute
Cu	0.5
Cu'	0.5

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

Modulation code	Atom site label	Wave vector code
Cuo1	Cu	1
Cu'o1	Cu'	1

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

Modulation code	Cosine coefficient	Sine coefficient
Cuo1	0.287(11)	0.215(13)
Cu'o1	-0.287(11)	-0.215(13)

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Lux1	Lu	x	1
Luy1	Lu	y	1
Luz1	Lu	z	1
Lu'x1	Lu'	x	1
Lu'y1	Lu'	y	1
Lu'z1	Lu'	z	1
Cux1	Cu	x	1
Cuy1	Cu	y	1
Cuz1	Cu	z	1
Cu'x1	Cu'	x	1
Cu'y1	Cu'	y	1
Cu'z1	Cu'	z	1
Alx1	Al	x	1
Aly1	Al	y	1
Alz1	Al	z	1
B1x1	B1	x	1
B1y1	B1	y	1
B1z1	B1	z	1
B1'x1	B1'	x	1
B1'y1	B1'	y	1
B1'z1	B1'	z	1
B2x1	B2	x	1
B2y1	B2	y	1
B2z1	B2	z	1
B3x1	B3	x	1
B3y1	B3	y	1
B3z1	B3	z	1
B4x1	B4	x	1
B4y1	B4	y	1
B4z1	B4	z	1
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O1'x1	O1'	x	1
O1'y1	O1'	y	1
O1'z1	O1'	z	1
O2x1	O2	x	1
O2y1	O2	y	1
O2z1	O2	z	1
O2'x1	O2'	x	1
O2'y1	O2'	y	1
O2'z1	O2'	z	1
O3x1	O3	x	1
O3y1	O3	y	1
O3z1	O3	z	1
O3'x1	O3'	x	1
O3'y1	O3'	y	1
O3'z1	O3'	z	1
O4x1	O4	x	1
O4y1	O4	y	1
O4z1	O4	z	1
O4'x1	O4'	x	1
O4'y1	O4'	y	1
O4'z1	O4'	z	1
O5x1	O5	x	1
O5y1	O5	y	1
O5z1	O5	z	1
O6x1	O6	x	1
O6y1	O6	y	1
O6z1	O6	z	1
O7x1	O7	x	1
O7y1	O7	y	1
O7z1	O7	z	1
O8x1	O8	x	1
O8y1	O8	y	1
O8z1	O8	z	1

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

Modulation code	Cosine coefficient	Sine coefficient
Lux1	0.00110(8)	-0.00118(9)
Luy1	0.00132(5)	-0.00230(6)
Luz1	-0.00091(17)	0.00118(19)
Lu'x1	-0.00091(11)	-0.00084(8)
Lu'y1	0.00181(6)	-0.00132(7)
Lu'z1	-0.00373(13)	-0.00234(13)
Cux1	0.0012(3)	0.0024(3)
Cuy1	0.0035(3)	-0.0011(3)
Cuz1	-0.0025(11)	0.0012(9)
Cu'x1	-0.0044(4)	-0.0061(4)
Cu'y1	-0.0063(4)	-0.0042(3)
Cu'z1	0.0000(10)	0.0033(9)
Alx1	0.0012(4)	-0.0008(7)
Aly1	0.0007(5)	-0.0022(3)
Alz1	0	0
B1x1	-0.0005(12)	-0.0018(15)
B1y1	0.0001(12)	-0.0020(10)
B1z1	0.007(5)	-0.004(4)
B1'x1	0.0012(12)	-0.0001(17)
B1'y1	-0.0009(11)	-0.0004(9)
B1'z1	0.001(4)	-0.002(3)
B2x1	0.0017(9)	0.0021(13)
B2y1	0.0011(10)	-0.0003(9)
B2z1	0.001(3)	-0.003(3)
B3x1	-0.0008(12)	0.0004(12)
B3y1	-0.0002(11)	-0.0006(10)
B3z1	0.009(4)	0.005(3)
B4x1	-0.0007(18)	-0.001(3)
B4y1	-0.001(2)	-0.0009(13)
B4z1	0	0
O1x1	0.0032(7)	0.0012(8)
O1y1	0.0007(5)	-0.0010(5)
O1z1	0.005(2)	0.004(2)
O1'x1	0.0015(7)	-0.0007(7)
O1'y1	-0.0010(5)	-0.0011(5)
O1'z1	0.0014(18)	-0.0010(19)
O2x1	0.0016(8)	-0.0004(8)
O2y1	0.0012(5)	-0.0011(5)
O2z1	0.000(2)	0.001(2)
O2'x1	0.0021(6)	-0.0013(6)
O2'y1	-0.0011(5)	-0.0006(5)
O2'z1	0.000(2)	-0.004(2)
O3x1	0.0014(5)	-0.0014(6)
O3y1	-0.0002(5)	-0.0027(5)
O3z1	0.003(2)	-0.001(2)
O3'x1	0.0002(5)	0.0000(6)
O3'y1	0.0010(5)	-0.0009(5)
O3'z1	-0.001(2)	0.001(2)
O4x1	0.0037(6)	0.0016(6)
O4y1	-0.0011(5)	-0.0013(5)
O4z1	0.005(2)	0.002(2)
O4'x1	-0.0010(5)	0.0005(6)
O4'y1	-0.0037(5)	-0.0005(5)
O4'z1	0.003(2)	-0.003(2)
O5x1	0.0013(6)	-0.0008(6)
O5y1	-0.0007(5)	-0.0020(5)
O5z1	0.008(2)	-0.007(2)
O6x1	0.0028(6)	0.0002(6)
O6y1	0.0032(5)	-0.0005(5)
O6z1	0.002(2)	-0.001(2)
O7x1	0.0008(6)	-0.0002(6)
O7y1	-0.0009(5)	-0.0013(5)
O7z1	0.004(2)	-0.010(2)
O8x1	-0.0149(11)	-0.0082(13)
O8y1	-0.0143(10)	-0.0096(11)
O8z1	0	0

Modulated structure of Lu4AlCu2B9O23 from low temperature single-crystal X-ray data