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X-ray investigation of the incommensurate modulated structure of Bi2.08Sr1.84CuO6-δ

Authors:

Leligny, H.; Durcok, S.; Labbe, P.; Ledesert, M.; Raveau, B.

Journal:

Acta Cryst. B 48 407-418 (1992)

DOI:

https://doi.org/10.1107/S0108768192002143

B-IncStrDB ID: 292E132Gb Entry date: 2010-11-08 Last revision: 2021-12-30

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Bi2_08

Chemical data

Structural Formula Sum: Bi2.076 Cu1 O5.482 Sr1.84 [ Help ]

Formula weight: 746.3 Da [ Help ]

Crystallographic data and experimental details

a: 5.3791(6) Å [ Help ]

b: 5.3811(9) Å [ Help ]

c: 24.589(3) Å [ Help ]

α: 90 ° [ Help ]

β: 89.93(1) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 711.74(17) Å3 [ Help ]

Z: 4 [ Help ]

μ: 119.428 mm-1 [ Help ]

Cell measurement temperature: 294 K [ Help ]

Crystal system: monoclinic [ Help ]

Superspace group name (WJJ): P:A 2/a:-1 1 [ Help ]

Superspace group name: A2/a(α0γ)00 [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4
2 1/2-x1,x2,-x3,-x4
3 -x1,-x2,-x3,-x4
4 1/2+x1,-x2,x3,x4
5 x1,1/2+x2,1/2+x3,x4
6 1/2-x1,1/2+x2,1/2-x3,-x4
7 -x1,1/2-x2,1/2-x3,-x4
8 1/2+x1,1/2-x2,1/2+x3,x4

Space group name (H-M): A 1 2/a 1 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.2030(2) 0 0.467(2)

Refinement details

Refinement remarks: The incommensurate model includes atomic phason Overhauser factors. Bi/Sr not reported in published 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. Occupational modulation:Fourier series. Up to 2nd-order harmonics. [ Help ]

Structure factors calc. details: Gaussian integration [ Help ]

Nb. of observed reflections: 1117 [ Help ]

R(obs): 0.066 [ Help ]

wR(all): 0.075 [ Help ]

Structural Information

Average Structure: [ Help ]

Site description Atom site label Atom symbol Symmetry multiplicity Occupancy x y z Uiso/equiv ADP type
. Bi Bi 8 0.9579(95) -0.0006(2) 0.2754(2) 0.0654(0) ? Uani
. Sr Sr 8 0.9200(90) 0.5003(4) 0.2473(5) 0.1785(1) ? Uani
Bi on Sr sites Bi/Sr Bi 8 0.0800(90) 0.5003(4) 0.2473(5) 0.1785(1) ? Uani
. Cu Cu 4 1 0 0.25 0.25 ? Uani
. O1 O 8 1 0.2526(50) 0.0004(40) 0.2517(10) 0.004(3) Uiso
. O2 O 8 0.7410(370) 0.0147(40) 0.2003(50) 0.1499(8) 0.004(3) Uiso
. O3 O 8 1 0.5210(50) 0.3404(40) 0.0698(9) 0.013(5) Uiso

Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): [ Help ]

Wave vector code q_x q_y q_z
1 0.2030 0 0.467
2 0.4060 0 0.934

Definition of the displacive (translational) Fourier series: [ Help ]

Modulation code Atom site label Displacement axis Wave vector code
Bix1 Bi x 1
Bix2 Bi x 2
Biy1 Bi y 1
Biy2 Bi y 2
Biz1 Bi z 1
Biz2 Bi z 2
Srx1 Sr x 1
Srx2 Sr x 2
Sry1 Sr y 1
Sry2 Sr y 2
Srz1 Sr z 1
Srz2 Sr z 2
Bi/Srx1 Bi/Sr x 1
Bi/Srx2 Bi/Sr x 2
Bi/Sry1 Bi/Sr y 1
Bi/Sry2 Bi/Sr y 2
Bi/Srz1 Bi/Sr z 1
Bi/Srz2 Bi/Sr z 2
Cux1 Cu x 1
Cux2 Cu x 2
Cuy1 Cu y 1
Cuy2 Cu y 2
Cuz1 Cu z 1
Cuz2 Cu 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 2
O2z1 O2 z 1
O2z2 O2 z 2
O3x1 O3 x 1
O3x2 O3 x 2
O3y1 O3 y 1
O3y2 O3 y 2
O3z1 O3 z 1
O3z2 O3 z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Bix1 -0.0544(3) 0.0642(3)
Bix2 -0.0182(4) 0.0102(4)
Biy1 0.0054(5) 0.0055(5)
Biy2 0.0036(8) 0.0049(7)
Biz1 -0.0049(0) -0.0121(0)
Biz2 -0.0003(0) -0.0007(0)
Srx1 -0.0341(6) 0.0265(6)
Srx2 -0.0161(7) -0.0029(8)
Sry1 0.0011(12) 0.0001(11)
Sry2 0.0010(21) -0.0012(21)
Srz1 -0.0023(1) -0.0150(1)
Srz2 -0.0006(2) -0.0014(1)
Bi/Srx1 -0.0341(6) 0.0265(6)
Bi/Srx2 -0.0161(7) -0.0029(8)
Bi/Sry1 0.0011(12) 0.0001(11)
Bi/Sry2 0.0010(21) -0.0012(21)
Bi/Srz1 -0.0023(1) -0.0150(1)
Bi/Srz2 -0.0006(2) -0.0014(1)
Cux1 0 0.0132(13)
Cux2 0 -0.0018(16)
Cuy1 0 0.0000(23)
Cuy2 0 0.0024(46)
Cuz1 0 -0.0186(3)
Cuz2 0 -0.0036(4)
O1x1 -0.0148(80) 0.0103(40)
O1x2 -0.0052(90) -0.0025(50)
O1y1 -0.0008(100) 0.0026(50)
O1y2 -0.0074(100) 0.0170(80)
O1z1 0.0002(25) -0.0177(10)
O1z2 -0.0077(15) -0.0022(15)
O2x1 -0.0364(60) 0.0590(60)
O2x2 -0.0326(70) 0.0130(70)
O2y1 0.0129(120) -0.0249(110)
O2z1 -0.0038(10) -0.0161(10)
O2z2 0.0024(15) -0.0016(15)
O3x1 -0.0736(70) 0.1376(80)
O3x2 -0.0403(85) 0.0561(80)
O3y1 0.0146(80) 0.0090(85)
O3y2 -0.0003(100) 0.0143(95)
O3z1 -0.0052(14) -0.0125(10)
O3z2 0.0024(15) 0.0009(15)

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Bio1 Bi 1
Bio2 Bi 2
Sro1 Sr 1
Sro2 Sr 2
Bi/Sro1 Bi/Sr 1
Bi/Sro2 Bi/Sr 2
O2o1 O2 1
O2o2 O2 2

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Bio1 -0.0476(45) -0.0277(45)
Bio2 -0.0237(60) -0.0264(60)
Sro1 0.0200(80) 0.0090(75)
Sro2 -0.0435(120) 0.0684(95)
Bi/Sro1 -0.0200(80) -0.0090(75)
Bi/Sro2 0.0435(120) -0.0684(95)
O2o1 -0.0674(450) -0.1428(600)
O2o2 0.1518(700) -0.2025(600)

Phason model: [ Help ]

Atom site label Phason formula Phason coefficient
Bi Ovr 0.0170(28)
Sr Ovr 0.0345(80)
Cu Ovr 0.0270(200)

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Bi Bi 0.0110(6) 0.0135(4) 0.015315 0.0007(7) 0.00067 -0.00067
Sr Sr 0.0078(10) 0.0106(12) 0.03063 0.0000(13) 0.0000(7) -0.0034(7)
Bi/Sr Bi 0.0078(10) 0.0106(12) 0.03063 0.0000(13) 0.0000(7) -0.0034(7)
Cu Cu 0.010(2) 0.003(3) 0.018(3) -0.002(3) 0.001(2) 0.001(3)