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The modulated structure of the calcium aluminate Ca6(AlO2)12.Bi2O3

Authors:

Perez, O.; Malo, S.; Hervieu, M.

Journal:

Acta Crystallographica, Section B 66 585-593 (2010)

DOI:

https://doi.org/10.1107/S0108768110035792

B-IncStrDB ID: 3652EYAidb Entry date: 2010-12-01 Last revision: 2022-01-02

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CaAlBiO

Chemical data

Structural Formula Sum: Al12 Bi2 Ca6 O27 [ Help ]

Formula weight: 1414.2 Da [ Help ]

Crystallographic data and experimental details

Crystal system: trigonal [ Help ]

Superspace group name: X-3(00γ)0 [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4
2 -x2,x1-x2,x3,x4
3 -x1,-x2,-x3,-x4
4 -x1+x2,-x1,x3,x4
5 x2,-x1+x2,-x3,-x4
6 x1-x2,x1,-x3,-x4
7 x1+2/3,x2+1/3,x3+1/3,x4+2/3
8 -x2+2/3,x1-x2+1/3,x3+1/3,x4+2/3
9 -x1+2/3,-x2+1/3,-x3+1/3,-x4+2/3
10 -x1+x2+2/3,-x1+1/3,x3+1/3,x4+2/3
11 x2+2/3,-x1+x2+1/3,-x3+1/3,-x4+2/3
12 x1-x2+2/3,x1+1/3,-x3+1/3,-x4+2/3
13 x1+1/3,x2+2/3,x3+2/3,x4+1/3
14 -x2+1/3,x1-x2+2/3,x3+2/3,x4+1/3
15 -x1+1/3,-x2+2/3,-x3+2/3,-x4+1/3
16 -x1+x2+1/3,-x1+2/3,x3+2/3,x4+1/3
17 x2+1/3,-x1+x2+2/3,-x3+2/3,-x4+1/3
18 x1-x2+1/3,x1+2/3,-x3+2/3,-x4+1/3

a: 17.3892(16) Å [ Help ]

b: 17.3892(16) Å [ Help ]

c: 6.986(6) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 120 ° [ Help ]

Volume: 1829.4(3) Å3 [ Help ]

Z: 3 [ Help ]

Cell determination reflection Nb.: 45 [ Help ]

θ(min) for cell determination: 5 ° [ Help ]

θ(max) for cell determination: 20 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0 0 0.045

μ: 17.213 mm-1 [ Help ]

Absorption correction type: gaussian [ Help ]

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

Minimum transmission factor: 0.1572 [ Help ]

Maximum transmission factor: 0.2895 [ Help ]

Refinement details

Total nb. of reflections: 7371 [ Help ]

Nb. of observed reflections: 5668 [ Help ]

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

Refinement based on: F [ Help ]

R(all): 0.0628 [ Help ]

R(obs): 0.043 [ Help ]

wR(obs): 0.0451 [ Help ]

wR(all): 0.0464 [ Help ]

S(all): 2.82 [ Help ]

Nb. of reflections: 7371 [ Help ]

Nb. of parameters: 134 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0335 [ Help ]

Δ/σ(mean): 0.0019 [ Help ]

Δρ(max): 5.13 e_Å-3 [ Help ]

Δρ(min): -5.37 e_Å-3 [ Help ]

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

Structural Information

Average Structure: [ Help ]

Atom symbol Atom site label x y z Uiso/equiv ADP type Coords from (d)iffraction or (c)alculated Coords restraints or constraints Occupancy Disordered cluster Disordered group
Bi Bi1 0.666667 0.333333 0.12054(2) 0.01411(8) Uani d ? 1 ? ?
Ca Ca1 0.10864(3) 0.85819(3) 0.09306(6) 0.00953(12) Uani d ? 1 ? ?
Al Al1 0.2078(4) 0.74193(4) 0.12913(9) 0.00504(17) Uani d ? 1 ? ?
Al Al2 0.04921(4) 0.64322(4) 0.39897(8) 0.00485(18) Uani d ? 1 ? ?
O O1 0.12444(10) 0.73896(10) 0.2747(2) 0.0081(4) Uani d ? 1 ? ?
O O2 0.22609(10) 0.81531(10) -0.0572(2) 0.0094(4) Uani d ? 1 ? ?
O O3 0.18036(11) 0.63511(10) 0.0498(2) 0.0113(5) Uani d ? 1 ? ?
O O4 -0.05848(9) 0.59733(10) 0.30701(19) 0.007(4) Uani d ? 1 ? ?
O O5 0.0934(2) 0.0917(2) -0.0124(5) 0.0141(8) Uani d ? 0.5 ? ?

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
Bi1 0.01176(10) 0.01176(10) 0.01882(15) 0.00588(5) 0 0 Bi
Ca1 0.00837(15) 0.00917(16) 0.00992(13) 0.00353(13) -0.00114(11) -0.00239(11) Ca
Al1 0.0046(2) 0.0038(2) 0.0064(2) 0.0018(17) 0.00066(16) 0.00049(16) Al
Al2 0.0049(2) 0.0053(2) 0.0046(2) 0.00266(19) -0.00011(16) -0.00034(16) Al
O1 0.0071(5) 0.0055(5) 0.0109(5) 0.0026(4) 0.0033(4) 0.0015(4) O
O2 0.0103(6) 0.0056(5) 0.0076(5) 0.0005(5) -0.0014(4) 0.0021(4) O
O3 0.0146(6) 0.0056(5) 0.0124(6) 0.0042(5) 0.0054(5) 0.0011(4) O
O4 0.0058(5) 0.0088(6) 0.0056(4) 0.0031(5) -0.0009(4) 0.0009(4) O
O5 0.0119(10) 0.0129(10) 0.0103(8) 0.0007(9) 0.0004(7) -0.0013(7) O

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

Wave vector code q_x q_z
1 0 0.045
2 0 0.09

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

Modulation code Atom site label Displacement axis Wave vector code
Bi1x1 Bi1 x 1
Bi1y1 Bi1 y 1
Bi1z1 Bi1 z 1
Ca1x1 Ca1 x 1
Ca1y1 Ca1 y 1
Ca1z1 Ca1 z 1
Al1x1 Al1 x 1
Al1y1 Al1 y 1
Al1z1 Al1 z 1
Al2x1 Al2 x 1
Al2y1 Al2 y 1
Al2z1 Al2 z 1
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O4x1 O4 x 1
O4y1 O4 y 1
O4z1 O4 z 1
O5x1 O5 x 1
O5y1 O5 y 1
O5z1 O5 z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Bi1x1 0 0
Bi1y1 0 0
Bi1z1 -0.01137(6) 0.0079(7)
Ca1x1 0.00343(5) -0.0054(5)
Ca1y1 0.0038(5) -0.00561(5)
Ca1z1 0.0002(8) 0.00311(8)
Al1x1 0.00058(7) -0.00317(7)
Al1y1 0.00207(7) -0.00282(7)
Al1z1 -0.00606(12) -0.00254(12)
Al2x1 0.00541(7) -0.0004(7)
Al2y1 0.004(7) -0.00447(7)
Al2z1 0.0009(11) 0.00125(12)
O1x1 0.00469(16) -0.00237(17)
O1y1 0.0047(16) -0.00345(16)
O1z1 0.003(3) 0.0017(3)
O2x1 -7e-05(17) -0.00433(17)
O2y1 0.00496(16) -0.0012(16)
O2z1 0.0003(3) 0.0027(3)
O3x1 -0.00392(19) -0.00295(19)
O3y1 0.00116(17) -0.00243(17)
O3z1 -0.0101(3) -0.0058(3)
O4x1 0.00616(16) -0.00061(16)
O4y1 0.00372(16) -0.00553(16)
O4z1 -0.0021(3) 0.0012(3)
O5x1 0.0006(16) 0.0011(5)
O5y1 0.0012(17) -0.0013(5)
O5z1 0.002(3) -0.0002(8)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
BiU111 Bi1 U11 1
BiU221 Bi1 U22 1
BiU331 Bi1 U33 1
BiU121 Bi1 U12 1
BiU131 Bi1 U13 1
BiU231 Bi1 U23 1
BiU112 Bi1 U11 2
BiU222 Bi1 U22 2
BiU332 Bi1 U33 2
BiU122 Bi1 U12 2
BiU132 Bi1 U13 2
BiU232 Bi1 U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
BiU111 -0.00014(6) 0(6)
BiU221 -0.00014(6) 0(6)
BiU331 0.00023(8) 0.00204(9)
BiU121 -7e-05(3) 0(3)
BiU131 0 0
BiU231 0 0
BiU112 -0.0024(5) 0.0086(4)
BiU222 -0.0024(5) 0.0086(4)
BiU332 -0.0054(3) 0.0119(3)
BiU122 -0.0012(2) 0.00432(19)
BiU132 0 0
BiU232 0 0

Displacive sawtooth coefficients: [ Help ]

Atom site label Ax Ay Az Center (x0) Width
. . . . . .

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
O5 0.25 0.5