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X-ray investigation of the incommensurate modulated structure of Bi2+xSr3-xFe2O9+δ

Authors:

Perez, O.; Leligny, H.; Grebille, D.; Labbe, Ph.; Groult, D.; Raveau, B.

Journal:

J. Phys.:Condens. Matter 7 10003-10014 (1995)

DOI:

https://doi.org/10.1088/0953-8984/7/50/030

B-IncStrDB ID: 272EhrsaN Entry date: 2010-11-08 Last revision: 2023-09-29

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Bi2px

Chemical data

Structural Formula Sum: Bi2.409 Fe2 O11 Sr2.591 [ Help ]

Formula weight: 1018.1 Da [ Help ]

Crystallographic data and experimental details

a: 5.488(1) Å [ Help ]

b: 5.475(1) Å [ Help ]

c: 31.509(5) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 946.7(3) Å3 [ Help ]

Z: 4 [ Help ]

μ: 65.183 mm-1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

Crystal system: orthorhombic [ Help ]

Superspace group name (WJJ): N:F m m m:1 -1 s [ Help ]

Superspace group name: Xmmm(0β0)00s [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4
2 -x1,x2,x3,x4
3 x1,x2,-x3,1/2+x4
4 -x1,x2,-x3,1/2+x4
5 -x1,-x2,-x3,-x4
6 x1,-x2,-x3,-x4
7 -x1,-x2,x3,1/2-x4
8 x1,-x2,x3,1/2-x4
9 x1,1/2+x2,1/2+x3,1/2+x4
10 -x1,1/2+x2,1/2+x3,1/2+x4
11 x1,1/2+x2,1/2-x3,x4
12 -x1,1/2+x2,1/2-x3,x4
13 -x1,1/2-x2,1/2-x3,1/2-x4
14 x1,1/2-x2,1/2-x3,1/2-x4
15 -x1,1/2-x2,1/2+x3,-x4
16 x1,1/2-x2,1/2+x3,-x4
17 1/2+x1,x2,1/2+x3,1/2+x4
18 1/2-x1,x2,1/2+x3,1/2+x4
19 1/2+x1,x2,1/2-x3,x4
20 1/2-x1,x2,1/2-x3,x4
21 1/2-x1,-x2,1/2-x3,1/2-x4
22 1/2+x1,-x2,1/2-x3,1/2-x4
23 1/2-x1,-x2,1/2+x3,-x4
24 1/2+x1,-x2,1/2+x3,-x4
25 1/2+x1,1/2+x2,x3,x4
26 1/2-x1,1/2+x2,x3,x4
27 1/2+x1,1/2+x2,-x3,1/2+x4
28 1/2-x1,1/2+x2,-x3,1/2+x4
29 1/2-x1,1/2-x2,-x3,-x4
30 1/2+x1,1/2-x2,-x3,-x4
31 1/2-x1,1/2-x2,x3,1/2-x4
32 1/2+x1,1/2-x2,x3,1/2-x4

Space group name (H-M): F m m m [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0 0.212(1) 0

Refinement details

Refinement remarks: Bi/Sr1 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. Modulation of temperature factors:Fourier series. Up to 2nd-order harmonics. [ Help ]

Structure factors calc. details: Gaussian integration [ Help ]

Nb. of observed reflections: 632 [ Help ]

R(obs): 0.068 [ Help ]

wR(all): 0.083 [ 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 16 0.5 0.0221(6) 0 0.2028(0) ? Uani
Sr on Sr sites Sr1 Sr 8 0.7955(120) 0.5 0 0.1176(1) ? Uani
Bi on Sr sites Bi/Sr1 Bi 8 0.2045(120) 0.5 0 0.1176(1) ? Uani
. Sr2 Sr 4 1 0.5 0 0 ? Uani
. Fe Fe 8 1 0 0 0.0607(2) ? Uani
. O1 O 16 1 0.25 0.25 0.668(6) 0.0171(1) Uiso
. O3 O 8 1 0 0 0.1389(10) 0.025(4) Uiso
. O4 O 4 1 0 0 0 0.0277(5) Uiso
. O5 O 16 1 0.6917(101) 0 0.01973(11) 0.070(3) 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 0.212 0
2 0 0.414 0

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

Modulation code Atom site label Displacement axis Wave vector code
Biy1 Bi y 1
Biy2 Bi y 2
Biz1 Bi z 1
Biz2 Bi z 2
Sr1y1 Sr1 y 1
Sr1y2 Sr1 y 2
Sr1z1 Sr1 z 1
Sr1z2 Sr1 z 2
Bi/Sr1y1 Bi/Sr1 y 1
Bi/Sr1y2 Bi/Sr1 y 2
Bi/Sr1z1 Bi/Sr1 z 1
Bi/Sr1z2 Bi/Sr1 z 2
Sr2y2 Sr2 y 2
Sr2z1 Sr2 z 1
Fey1 Fe y 1
Fey2 Fe y 2
Fez1 Fe z 1
Fez2 Fe z 2
O1y1 O1 y 1
O1y2 O1 y 2
O1z1 O1 z 1
O1z2 O1 z 2
O3y1 O3 y 1
O3y2 O3 y 2
O3z1 O3 z 1
O3z2 O3 z 2
O4z1 O4 z 1
O5x1 O5 x 1
O5x2 O5 x 2
O5y1 O5 y 1
O5y2 O5 y 2
O5z1 O5 z 1
O5z2 O5 z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Biy1 0.0764(5) 0
Biy2 0 -0.0105(7)
Biz1 0 -0.0045(0)
Biz2 -0.0006(1) 0
Sr1y1 0.0383(10) 0
Sr1y2 0 0.0013(13)
Sr1z1 0 -0.0098(2)
Sr1z2 -0.0022(2) 0
Bi/Sr1y1 0.0383(10) 0
Bi/Sr1y2 0 0.0013(13)
Bi/Sr1z1 0 -0.0098(2)
Bi/Sr1z2 -0.0022(2) 0
Sr2y2 0 -0.0005(19)
Sr2z1 0 -0.0121(3)
Fey1 0.0176(19) 0
Fey2 0 0.0026(24)
Fez1 0 -0.0134(3)
Fez2 -0.0008 0
O1y1 0.0154(60) 0
O1y2 0 0.0000(71)
O1z1 0 -0.0101(9)
O1z2 -0.0035(13) 0
O3y1 0.0815(116) 0
O3y2 0 -0.0455(139)
O3z1 0 -0.0027(15)
O3z2 0.0023(25) 0
O4z1 0 -0.0079(20)
O5x1 0 -0.0772(171)
O5x2 0.0218(173) 0
O5y1 0.2791(133) 0
O5y2 0 -0.0994(120)
O5z1 0 0.0021(18)
O5z2 0.0026(21) 0

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Sr1o1 Sr1 1
Sr1o2 Sr1 2
Bi/Sr1o1 Bi/Sr1 1
Bi/Sr1o2 Bi/Sr1 2

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Sr1o1 0 -0.0433(154)
Sr1o2 -0.0788(224) 0
Bi/Sr1o1 0 0.0433(154)
Bi/Sr1o2 0.0788(224) 0

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Bi Bi 0.0160(12) 0.0194(14) 0.010059 0 -0.0018(9) 0
Sr1 Sr 0.016174 0.0049(11) 0.040237 0 0 0
Bi/Sr1 Bi 0.016174 0.0049(11) 0.040237 0 0 0
Sr2 Sr 0.0198(12) 0.0046(14) 0.025148 0 0 0
Fe Fe 0.0122(14) 0.0076(12) 0.010059 0 0 0

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
BiU111 Bi U11 1
BiU221 Bi U22 1
BiU331 Bi U33 1
BiU121 Bi U12 1
BiU131 Bi U13 1
BiU231 Bi U23 1
BiU112 Bi U11 2
BiU222 Bi U22 2
BiU332 Bi U33 2
BiU122 Bi U12 2
BiU132 Bi U13 2
BiU232 Bi U23 2
Sr1U111 Sr1 U11 1
Sr1U221 Sr1 U22 1
Sr1U331 Sr1 U33 1
Sr1U121 Sr1 U12 1
Sr1U131 Sr1 U13 1
Sr1U231 Sr1 U23 1
Sr1U112 Sr1 U11 2
Sr1U222 Sr1 U22 2
Sr1U332 Sr1 U33 2
Sr1U122 Sr1 U12 2
Sr1U132 Sr1 U13 2
Sr1U232 Sr1 U23 2
Bi/Sr1U111 Bi/Sr1 U11 1
Bi/Sr1U221 Bi/Sr1 U22 1
Bi/Sr1U331 Bi/Sr1 U33 1
Bi/Sr1U121 Bi/Sr1 U12 1
Bi/Sr1U131 Bi/Sr1 U13 1
Bi/Sr1U231 Bi/Sr1 U23 1
Bi/Sr1U112 Bi/Sr1 U11 2
Bi/Sr1U222 Bi/Sr1 U22 2
Bi/Sr1U332 Bi/Sr1 U33 2
Bi/Sr1U122 Bi/Sr1 U12 2
Bi/Sr1U132 Bi/Sr1 U13 2
Bi/Sr1U232 Bi/Sr1 U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
BiU111 0 -0.002(3)
BiU221 0 -0.016(2)
BiU331 0 -0.00503
BiU121 0.006(3) 0
BiU131 0 0.006(3)
BiU231 -0.0017(9) 0
BiU112 -0.004(5) 0
BiU222 -0.007(3) 0
BiU332 -0.00503 0
BiU122 0 -0.002(4)
BiU132 -0.003(4) 0
BiU232 0 0.0017(9)
Sr1U111 0 0.0006(17)
Sr1U221 0 0.0009(15)
Sr1U331 0 -0.015089
Sr1U121 0 0
Sr1U131 0 0
Sr1U231 0.0044(9) 0
Sr1U112 0.001(4) 0
Sr1U222 0.0017(17) 0
Sr1U332 -0.010059 0
Sr1U122 0 0
Sr1U132 0 0
Sr1U232 0 0.0000(9)
Bi/Sr1U111 0 0.0006(17)
Bi/Sr1U221 0 0.0009(15)
Bi/Sr1U331 0 -0.015089
Bi/Sr1U121 0 0
Bi/Sr1U131 0 0
Bi/Sr1U231 0.0044(9) 0
Bi/Sr1U112 0.001(4) 0
Bi/Sr1U222 0.0017(17) 0
Bi/Sr1U332 -0.010059 0
Bi/Sr1U122 0 0
Bi/Sr1U132 0 0
Bi/Sr1U232 0 0.0000(9)