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First (3 + 2)-dimensional superspace approach to the structure of levyclaudite-(Sb), a member of the cylindrite-type minerals

Authors:

Evain, Michel; Petricek, Vaclav; Moelo, Yves; Maurel, Colette

Journal:

Acta Crystallographica, Section B 62 775-789 (2006)

DOI:

https://doi.org/10.1107/S010876810602547X

B-IncStrDB ID: a7JwDmTmunB Entry date: 2022-01-30 Last revision: 2024-01-02

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Chemical data

Structural Formula Sum: Cu0.299 Pb0.951 S3.357 Sb0.406 Sn0.851 [ Help ]

Formula weight: 474.1 Da [ Help ]

Crystallographic data and experimental details

Crystal system: triclinic [ Help ]

Space group name (H-M): C-1 [ Help ]

Superspace group name: C-1(α1β1γ1)(α2β2γ2) [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4,x5
2 -x1,-x2,-x3,-x4,-x5
3 1/2+x1,1/2+x2,x3,x4,x5
4 1/2-x1,1/2-x2,-x3,-x4,-x5

a: 3.6733(4) Å [ Help ]

b: 6.3120(5) Å [ Help ]

c: 11.9039(12) Å [ Help ]

α: 92.484(8) ° [ Help ]

β: 90.687(9) ° [ Help ]

γ: 89.941(8) ° [ Help ]

Volume: 275.72(5) Å3 [ Help ]

Z: 2 [ Help ]

Modulation dimension: 2 [ 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
0.0 1.0 0.0 0.0 0.0
0.0 0.0 1.0 0.0 0.0
0.0 0.0 0.0 1.0 0.0
0.0 0.0 0.0 0.0 1.0

Subsystem code: 2 [ Help ]

Subsystem description: 2-nd subsystem [ Help ]

W matrix:

0.0 -1.0 0.0 -0.5 1.0
0.0 1.0 0.0 0.5 0.0
0.0 0.0 1.0 0.0 0.0
0.0 0.0 0.0 1.0 0.0
1.0 1.0 0.0 0.0 0.0

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.00338(6) 0.15278(14) -0.0138(3)
2 0.63105(7) 1.07460(17) -0.4438(3)

μ: 37.04 mm-1 [ Help ]

Absorption correction type: gaussian [ Help ]

Absorption correction remarks: (Jana2006; Petricek, Dusek & Palatinus, 2006) [ Help ]

Minimum transmission factor: 0.039 [ Help ]

Maximum transmission factor: 0.912 [ Help ]

Refinement details

Total nb. of reflections: 29574 [ Help ]

Nb. of observed reflections: 0 [ Help ]

Intense reflections threshold: I>2.5σ(I) [ Help ]

Refinement based on: F [ Help ]

R(all): 0.0741 [ Help ]

R(obs): 0.0741 [ Help ]

wR(obs): 0.0895 [ Help ]

wR(all): 0.0895 [ Help ]

S(all): 2.65 [ Help ]

Nb. of reflections: 12026 [ Help ]

Nb. of parameters: 186 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0005 [ Help ]

Δ/σ(mean): 0.0001 [ Help ]

Δρ(max): 3.34 e_Å-3 [ Help ]

Δρ(min): -3.21 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: [ 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
Sn Sn 1 0 0 0 0.01480(12) Uani d . 0.851(2) . .
Cu Cu 1 0.0029(9) 0.0057(5) 0.1147(3) 0.0229(11) Uani d . 0.149(2) . .
S S1 1 0.5033(2) 0.84278(12) 0.12342(7) 0.0177(3) Uani d . 1 . .
Pb Pb 2 0.05541(5) 0.24113(4) 0.36783(2) 0.03573(12) Uani d . 0.701(10) . .
Sb Sb 2 0.055408 0.241132 0.367832 0.03573(12) Uani d . 0.299(10) . .
S S2 2 -0.0402(3) 0.2583(2) 0.59639(13) 0.0310(4) Uani d . 1 . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
Sn 0.0137(2) 0.00983(16) 0.0208(3) -0.00043(12) -0.00029(14) 0.00055(12) Sn
Cu 0.0180(16) 0.0138(13) 0.037(2) -0.0009(10) -0.0004(12) 0.0021(11) Cu
S1 0.0193(4) 0.0133(3) 0.0205(5) -0.0005(3) -0.0005(3) 0.0008(3) S
Pb 0.0382(2) 0.03020(16) 0.0390(2) -0.00096(11) -0.00807(14) 0.00192(11) Pb
Sb 0.0382(2) 0.03020(16) 0.0390(2) -0.00096(11) -0.00807(14) 0.00192(11) Sb
S2 0.0395(8) 0.0295(6) 0.0237(7) -0.0002(5) -0.0052(6) 0.0019(5) S

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 0.00338 0.15278 -0.0138
2 0.63105 1.07460 -0.4438
3 0.00776 0.30556 -0.0276
4 0.01114 0.45834 -0.0414
5 0.01452 0.61112 -0.0552
6 0.63443 1.22738 -0.4576

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Pbo1 Pb 1
Pbo2 Pb 2
Pbo3 Pb 3
Pbo4 Pb 4
Sbo1 Sb 1
Sbo2 Sb 2
Sbo3 Sb 3
Sbo4 Sb 4

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Pbo1 -0.002(6) 0.170(4)
Pbo2 0 0
Pbo3 0.026(5) 0.002(4)
Pbo4 0.017(6) -0.042(5)
Sbo1 0.002(6) -0.170(4)
Sbo2 0 0
Sbo3 -0.026(5) -0.002(4)
Sbo4 -0.017(6) 0.042(5)

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

Modulation code Atom site label Displacement axis Wave vector code
Snx1 Sn x 1
Sny1 Sn y 1
Snz1 Sn z 1
Snx2 Sn x 2
Sny2 Sn y 2
Snz2 Sn z 2
Snx3 Sn x 3
Sny3 Sn y 3
Snz3 Sn z 3
Snx4 Sn x 4
Sny4 Sn y 4
Snz4 Sn z 4
Cux1 Cu x 1
Cuy1 Cu y 1
Cuz1 Cu z 1
Cux2 Cu x 2
Cuy2 Cu y 2
Cuz2 Cu z 2
Cux3 Cu x 3
Cuy3 Cu y 3
Cuz3 Cu z 3
S1x1 S1 x 1
S1y1 S1 y 1
S1z1 S1 z 1
S1x2 S1 x 2
S1y2 S1 y 2
S1z2 S1 z 2
S1x3 S1 x 3
S1y3 S1 y 3
S1z3 S1 z 3
Pbx1 Pb x 1
Pby1 Pb y 1
Pbz1 Pb z 1
Pbx2 Pb x 2
Pby2 Pb y 2
Pbz2 Pb z 2
Pbx3 Pb x 3
Pby3 Pb y 3
Pbz3 Pb z 3
Pbx4 Pb x 4
Pby4 Pb y 4
Pbz4 Pb z 4
Pbx5 Pb x 5
Pby5 Pb y 5
Pbz5 Pb z 5
Pbx6 Pb x 6
Pby6 Pb y 6
Pbz6 Pb z 6
Sbx1 Sb x 1
Sby1 Sb y 1
Sbz1 Sb z 1
Sbx2 Sb x 2
Sby2 Sb y 2
Sbz2 Sb z 2
Sbx3 Sb x 3
Sby3 Sb y 3
Sbz3 Sb z 3
Sbx4 Sb x 4
Sby4 Sb y 4
Sbz4 Sb z 4
Sbx5 Sb x 5
Sby5 Sb y 5
Sbz5 Sb z 5
Sbx6 Sb x 6
Sby6 Sb y 6
Sbz6 Sb z 6
S2x1 S2 x 1
S2y1 S2 y 1
S2z1 S2 z 1
S2x2 S2 x 2
S2y2 S2 y 2
S2z2 S2 z 2
S2x3 S2 x 3
S2y3 S2 y 3
S2z3 S2 z 3

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Snx1 0 -0.00159(16)
Sny1 0 -0.00481(8)
Snz1 0 -0.06455(5)
Snx2 0 0
Sny2 0 0
Snz2 0 0
Snx3 0 0.00004(18)
Sny3 0 -0.00395(8)
Snz3 0 -0.00108(5)
Snx4 0 0.0003(2)
Sny4 0 -0.00075(10)
Snz4 0 0.00042(6)
Cux1 0.0018(11) -0.0012(13)
Cuy1 0.0184(6) -0.0092(6)
Cuz1 -0.0013(4) -0.0611(4)
Cux2 0 0
Cuy2 0 0
Cuz2 0 0
Cux3 0.0002(13) 0.0003(15)
Cuy3 -0.0021(7) -0.0036(7)
Cuz3 -0.0001(4) 0.0014(4)
S1x1 0.0018(3) -0.0012(4)
S1y1 0.02435(17) -0.00397(18)
S1z1 -0.00034(11) -0.06312(12)
S1x2 0 0
S1y2 0 0
S1z2 0 0
S1x3 -0.0002(4) -0.0001(4)
S1y3 -0.00007(19) -0.00411(19)
S1z3 -0.00031(11) -0.00102(12)
Pbx1 -0.00108(7) 0.02947(8)
Pby1 -0.02618(6) -0.00518(7)
Pbz1 0.00011(3) -0.07516(4)
Pbx2 -0.0036(3) -0.0042(3)
Pby2 -0.00533(16) -0.00529(17)
Pbz2 -0.00363(9) 0.00240(9)
Pbx3 0.00007(8) -0.00043(8)
Pby3 -0.00090(7) -0.00055(7)
Pbz3 -0.00095(4) -0.00090(4)
Pbx4 -0.00031(10) -0.00143(10)
Pby4 0.00122(8) -0.00018(8)
Pbz4 0.00004(4) 0.00267(4)
Pbx5 -0.00129(15) -0.00043(15)
Pby5 -0.00002(10) 0.00106(10)
Pbz5 0.00023(6) 0.00015(6)
Pbx6 -0.0053(3) 0.0022(3)
Pby6 0.00496(16) -0.00435(17)
Pbz6 0.00287(9) 0.00189(9)
Sbx1 -0.00108(7) 0.02947(8)
Sby1 -0.02618(6) -0.00518(7)
Sbz1 0.00011(3) -0.07516(4)
Sbx2 -0.0036(3) -0.0042(3)
Sby2 -0.00533(16) -0.00529(17)
Sbz2 -0.00363(9) 0.00240(9)
Sbx3 0.00007(8) -0.00043(8)
Sby3 -0.00090(7) -0.00055(7)
Sbz3 -0.00095(4) -0.00090(4)
Sbx4 -0.00031(10) -0.00143(10)
Sby4 0.00122(8) -0.00018(8)
Sbz4 0.00004(4) 0.00267(4)
Sbx5 -0.00129(15) -0.00043(15)
Sby5 -0.00002(10) 0.00106(10)
Sbz5 0.00023(6) 0.00015(6)
Sbx6 -0.0053(3) 0.0022(3)
Sby6 0.00496(16) -0.00435(17)
Sbz6 0.00287(9) 0.00189(9)
S2x1 0.0007(4) 0.0280(4)
S2y1 0.0262(3) -0.0068(3)
S2z1 -0.00002(18) -0.07151(17)
S2x2 0 0
S2y2 0 0
S2z2 0 0
S2x3 0.0001(4) 0.0008(4)
S2y3 -0.0007(3) 0.0017(3)
S2z3 -0.00049(17) -0.00096(17)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
SnU111 Sn U11 1
SnU221 Sn U22 1
SnU331 Sn U33 1
SnU121 Sn U12 1
SnU131 Sn U13 1
SnU231 Sn U23 1
SnU112 Sn U11 2
SnU222 Sn U22 2
SnU332 Sn U33 2
SnU122 Sn U12 2
SnU132 Sn U13 2
SnU232 Sn U23 2
PbU111 Pb U11 1
PbU221 Pb U22 1
PbU331 Pb U33 1
PbU121 Pb U12 1
PbU131 Pb U13 1
PbU231 Pb U23 1
PbU112 Pb U11 2
PbU222 Pb U22 2
PbU332 Pb U33 2
PbU122 Pb U12 2
PbU132 Pb U13 2
PbU232 Pb U23 2
PbU113 Pb U11 3
PbU223 Pb U22 3
PbU333 Pb U33 3
PbU123 Pb U12 3
PbU133 Pb U13 3
PbU233 Pb U23 3
PbU114 Pb U11 4
PbU224 Pb U22 4
PbU334 Pb U33 4
PbU124 Pb U12 4
PbU134 Pb U13 4
PbU234 Pb U23 4
SbU111 Sb U11 1
SbU221 Sb U22 1
SbU331 Sb U33 1
SbU121 Sb U12 1
SbU131 Sb U13 1
SbU231 Sb U23 1
SbU112 Sb U11 2
SbU222 Sb U22 2
SbU332 Sb U33 2
SbU122 Sb U12 2
SbU132 Sb U13 2
SbU232 Sb U23 2
SbU113 Sb U11 3
SbU223 Sb U22 3
SbU333 Sb U33 3
SbU123 Sb U12 3
SbU133 Sb U13 3
SbU233 Sb U23 3
SbU114 Sb U11 4
SbU224 Sb U22 4
SbU334 Sb U33 4
SbU124 Sb U12 4
SbU134 Sb U13 4
SbU234 Sb U23 4
S2U111 S2 U11 1
S2U221 S2 U22 1
S2U331 S2 U33 1
S2U121 S2 U12 1
S2U131 S2 U13 1
S2U231 S2 U23 1

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
SnU111 0.0002(2) 0
SnU221 -0.00056(18) 0
SnU331 0.0007(3) 0
SnU121 -0.00012(17) 0
SnU131 0.0002(2) 0
SnU231 -0.00053(17) 0
SnU112 0 0
SnU222 0 0
SnU332 0 0
SnU122 0 0
SnU132 0 0
SnU232 0 0
PbU111 0.0002(3) -0.0025(3)
PbU221 0.0007(2) 0.0036(2)
PbU331 0.0019(3) -0.0110(3)
PbU121 -0.00164(15) 0.00023(15)
PbU131 -0.00019(18) 0.00244(19)
PbU231 0.00668(15) -0.00125(16)
PbU112 0 0
PbU222 0 0
PbU332 0 0
PbU122 0 0
PbU132 0 0
PbU232 0 0
PbU113 -0.0007(3) 0.0006(3)
PbU223 -0.0002(2) 0.0008(2)
PbU333 -0.0007(3) 0.0009(3)
PbU123 -0.00006(16) 0.00069(16)
PbU133 -0.00023(18) -0.0004(2)
PbU233 0.00004(15) -0.00305(16)
PbU114 0.0010(4) -0.0003(3)
PbU224 -0.0004(3) -0.0009(2)
PbU334 0.0012(4) 0.0003(4)
PbU124 0.0000(2) -0.0002(2)
PbU134 -0.0008(3) 0.0016(3)
PbU234 0.0000(2) 0.0007(2)
SbU111 0.0002(3) -0.0025(3)
SbU221 0.0007(2) 0.0036(2)
SbU331 0.0019(3) -0.0110(3)
SbU121 -0.00164(15) 0.00023(15)
SbU131 -0.00019(18) 0.00244(19)
SbU231 0.00668(15) -0.00125(16)
SbU112 0 0
SbU222 0 0
SbU332 0 0
SbU122 0 0
SbU132 0 0
SbU232 0 0
SbU113 -0.0007(3) 0.0006(3)
SbU223 -0.0002(2) 0.0008(2)
SbU333 -0.0007(3) 0.0009(3)
SbU123 -0.00006(16) 0.00069(16)
SbU133 -0.00023(18) -0.0004(2)
SbU233 0.00004(15) -0.00305(16)
SbU114 0.0010(4) -0.0003(3)
SbU224 -0.0004(3) -0.0009(2)
SbU334 0.0012(4) 0.0003(4)
SbU124 0.0000(2) -0.0002(2)
SbU134 -0.0008(3) 0.0016(3)
SbU234 0.0000(2) 0.0007(2)
S2U111 0.0006(11) 0.0098(11)
S2U221 0.0016(8) 0.0059(8)
S2U331 -0.0002(9) -0.0015(10)
S2U121 -0.0002(8) 0.0002(7)
S2U131 -0.0003(8) 0.0005(9)
S2U231 0.0015(7) -0.0006(7)