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Revision of pyrrhotite structures within a common superspace model

Authors:

Izaola, Zunbeltz; Gonzalez, Santiago; Elcoro, Luis; Perez-Mato, J.M.; Madariaga, Gotzon; Garcia, Alberto

Journal:

Acta Crystallographica, Section B 63 693-702 (2007)

DOI:

https://doi.org/10.1107/S0108768107037275

B-IncStrDB ID: s1X7c4ujHU5 Entry date: 2022-01-25 Last revision: 2022-01-25

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Chemical data

Structural Formula Sum: Fe0.91 S1 [ Help ]

Formula weight: 82.9 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Xbnn(1/21/2γ)qq0 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 6.8920(10) Å [ Help ]

b: 11.9520(10) Å [ Help ]

c: 5.7440(10) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 473.15(11) Å3 [ Help ]

Z: 16 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.00000 0.00000 0.18050

μ: 12.539 mm-1 [ Help ]

Absorption correction type: none [ Help ]

Minimum transmission factor: 1.000 [ Help ]

Maximum transmission factor: 1.000 [ Help ]

Refinement details

Total nb. of reflections: 588 [ Help ]

Nb. of observed reflections: 391 [ Help ]

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

Refinement based on: F [ Help ]

R(all): 0.1419 [ Help ]

R(obs): 0.1152 [ Help ]

wR(obs): 0.0899 [ Help ]

wR(all): 0.0960 [ Help ]

S(all): 4.81 [ Help ]

Nb. of reflections: 588 [ Help ]

Nb. of parameters: 46 [ Help ]

Weighting scheme: unit [ Help ]

Δ/σ(max): 0.0172 [ Help ]

Δ/σ(mean): 0.0033 [ 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 Symmetry multiplicity Disordered cluster Disordered group
Fe Fe1 0.1264(4) 0.125 0 0.0120(10) Uani d . 4 . .
S S1 0.125 -0.0426(2) 0.75 0.0073(9) Uiso d . 4 . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
Fe1 0.0102(19) 0.0160(11) 0.0098(19) 0 0 0.0002(10) Fe

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 0.00000 0.00000 0.18050
2 0.00000 0.00000 0.36101
3 0.00000 0.00000 0.54151
4 0.00000 0.00000 0.72202

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

Modulation code Atom site label Displacement axis Wave vector code
Fe1x1 Fe1 x 1
Fe1y1 Fe1 y 1
Fe1z1 Fe1 z 1
Fe1x2 Fe1 x 2
Fe1y2 Fe1 y 2
Fe1z2 Fe1 z 2
Fe1x3 Fe1 x 3
Fe1y3 Fe1 y 3
Fe1z3 Fe1 z 3
Fe1x4 Fe1 x 4
Fe1y4 Fe1 y 4
Fe1z4 Fe1 z 4
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
S1x4 S1 x 4
S1y4 S1 y 4
S1z4 S1 z 4

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1x1 0.0129(5) 0.0129(5)
Fe1y1 0.00423(18) -0.00423(18)
Fe1z1 0.0062(5) -0.0062(5)
Fe1x2 0 0.0020(8)
Fe1y2 -0.0100(2) 0
Fe1z2 0.0094(6) 0
Fe1x3 0.0044(5) -0.0044(5)
Fe1y3 0.00165(19) 0.00165(19)
Fe1z3 0.0051(5) 0.0051(5)
Fe1x4 -0.0021(9) 0
Fe1y4 0 0
Fe1z4 0 0.0020(6)
S1x1 0 0
S1y1 -0.0006(3) -0.0006(3)
S1z1 0.0106(8) -0.0106(8)
S1x2 0 0
S1y2 0 -0.0008(3)
S1z2 -0.0142(9) 0
S1x3 0 0
S1y3 0 0
S1z3 0.0037(7) 0.0037(7)
S1x4 0 0
S1y4 0 0
S1z4 0 -0.0032(9)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Fe1U111 Fe1 U11 1
Fe1U221 Fe1 U22 1
Fe1U331 Fe1 U33 1
Fe1U121 Fe1 U12 1
Fe1U131 Fe1 U13 1
Fe1U231 Fe1 U23 1
Fe1U112 Fe1 U11 2
Fe1U222 Fe1 U22 2
Fe1U332 Fe1 U33 2
Fe1U122 Fe1 U12 2
Fe1U132 Fe1 U13 2
Fe1U232 Fe1 U23 2
Fe1U113 Fe1 U11 3
Fe1U223 Fe1 U22 3
Fe1U333 Fe1 U33 3
Fe1U123 Fe1 U12 3
Fe1U133 Fe1 U13 3
Fe1U233 Fe1 U23 3
Fe1U114 Fe1 U11 4
Fe1U224 Fe1 U22 4
Fe1U334 Fe1 U33 4
Fe1U124 Fe1 U12 4
Fe1U134 Fe1 U13 4
Fe1U234 Fe1 U23 4

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1U111 -0.006(2) -0.006(2)
Fe1U221 -0.0046(14) -0.0046(14)
Fe1U331 -0.006(4) -0.006(4)
Fe1U121 -0.0019(9) 0.0019(9)
Fe1U131 -0.0006(11) 0.0006(11)
Fe1U231 0.0001(11) 0.0001(11)
Fe1U112 0 -0.016(4)
Fe1U222 0 -0.0027(17)
Fe1U332 0 -0.005(4)
Fe1U122 -0.0080(13) 0
Fe1U132 -0.0077(16) 0
Fe1U232 0 0.0048(14)
Fe1U113 0.011(2) -0.011(2)
Fe1U223 0.0065(15) -0.0065(15)
Fe1U333 0.014(3) -0.014(3)
Fe1U123 0.0028(9) 0.0028(9)
Fe1U133 -0.0006(11) -0.0006(11)
Fe1U233 0 0
Fe1U114 0.016(3) 0
Fe1U224 0 0
Fe1U334 0.022(4) 0
Fe1U124 0 0.0019(14)
Fe1U134 0 -0.0026(19)
Fe1U234 0 0

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
Fe1 0.625 0.91