B-IncStrDB

Modular crystals as modulated structures: the case of the lillianite homologous series

Authors:

Elcoro, Luis; Perez-Mato, J.M.; Friese, Karen; Petricek, Vaclav; Balic-Zunic, Tonci; Olsen, Lars Arnskov

Journal:

Acta Crystallographica Section B 64 684-701 (2008)

DOI:

https://doi.org/10.1107/S0108768108031492

B-IncStrDB ID: oruL0Bft9f0 Entry date: 2021-12-15 Last revision: 2024-01-02

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3D

Chemical data

Structural Formula Sum: Pb16 S18 [ Help ]

Formula weight: 3892.1 Da [ Help ]

Absolute configuration: . [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

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

Space group name (Hall): -B -2xb;-2yb;-2z [ Help ]

Symmetry operations of the space group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x,y,z
2	-x,-y,z
3	-x,y+1/2,-z
4	x,-y+1/2,-z
5	-x,-y,-z
6	x,y,-z
7	x,-y+1/2,z
8	-x,y+1/2,z
9	x+1/2,y,z+1/2
10	-x+1/2,-y,z+1/2
11	-x+1/2,y+1/2,-z+1/2
12	x+1/2,-y+1/2,-z+1/2
13	-x+1/2,-y,-z+1/2
14	x+1/2,y,-z+1/2
15	x+1/2,-y+1/2,z+1/2
16	-x+1/2,y+1/2,z+1/2

a: 13.712 Å [ Help ]

b: 31.212 Å [ Help ]

c: 4.131 Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 1767.981 Å³ [ Help ]

Z: 34 [ Help ]

μ: 1307.66 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: 756 [ Help ]

Nb. of observed reflections: 455 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0418 [ Help ]

wR(obs): 0.0398 [ Help ]

R(all): 0.0784 [ Help ]

wR(all): 0.0448 [ Help ]

S(all): 1.51 [ Help ]

S(obs): 1.77 [ Help ]

Nb. of reflections: 756 [ Help ]

Nb. of parameters: 55 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0194 [ Help ]

Δ/σ(mean): 0.0038 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	x	y	z	ADP type	Uiso/equiv	Symmetry multiplicity	Occupancy	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Disordered cluster	Disordered group
S1-1	S	0.8625(7)	0.9734(3)	0.5	Uani	0.016(3)	8	1	d	.	.	.
S1-3	S	0.4137(7)	0.0861(3)	0.5	Uani	0.019(4)	8	1	d	.	.	.
S1-4	S	0.6748(8)	0.1466(4)	0.5	Uani	0.026(4)	8	1	d	.	.	.
S1-5	S	0.9562(7)	0.1954(3)	0.5	Uani	0.014(3)	8	1	d	.	.	.
S1-6	S	0.2198(11)	0.25	0.5	Uani	0.016(5)	4	1	d	.	.	.
Pb1-1	Pb	0.27142(11)	0.05819(5)	0	Uani	0.0167(5)	8	1	d	.	.	.
Pb1-2	Pb	0.54473(11)	0.11906(5)	0	Uani	0.0141(5)	8	1	d	.	.	.
Pb1-3	Pb	0.81792(11)	0.17492(5)	0	Uani	0.0161(5)	8	1	d	.	.	.
Pb1-4	Pb	0.07864(19)	0.25	0	Uani	0.0421(11)	4	1	d	.	.	.
Pb1-8	Pb	0	0.5	0	Uani	0.0136(7)	4	1	d	.	.	.

ADP components: (Show/hide table) [ Help ]

Atom site label	Atom site symbol	U11	U22	U33	U12
S1-1	S	0.016(5)	0.005(5)	0.027(6)	0.000(4)
S1-3	S	0.020(6)	0.026(6)	0.011(7)	0.005(5)
S1-4	S	0.035(6)	0.025(7)	0.019(7)	-0.015(5)
S1-5	S	0.014(6)	0.010(6)	0.018(7)	-0.004(4)
S1-6	S	0.027(8)	0.006(7)	0.016(9)	0
Pb1-1	Pb	0.0166(8)	0.0168(9)	0.0166(10)	-0.0015(6)
Pb1-2	Pb	0.0140(8)	0.0138(9)	0.0144(10)	0.0007(6)
Pb1-3	Pb	0.0199(8)	0.0117(9)	0.0166(10)	0.0008(7)
Pb1-4	Pb	0.0321(16)	0.064(2)	0.0306(19)	0
Pb1-8	Pb	0.0144(12)	0.0117(12)	0.0148(14)	0.0006(9)

Modulated

Chemical data

Structural Formula Sum: Pb1 S1 [ Help ]

Formula weight: 239.2 Da [ Help ]

Absolute configuration: . [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Bmmm(0β0)s00 [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

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

a: 13.737 Å [ Help ]

b: 1.7496 Å [ Help ]

c: 4.1448 Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 99.6172 Å³ [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.00000	0.05556	0.00000

Z: 16 [ Help ]

μ: 681.521 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: 756 [ Help ]

Nb. of observed reflections: 454 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0427 [ Help ]

wR(obs): 0.0437 [ Help ]

R(all): 0.0805 [ Help ]

wR(all): 0.0507 [ Help ]

S(all): 1.42 [ Help ]

S(obs): 1.60 [ Help ]

Nb. of reflections: 756 [ Help ]

Nb. of parameters: 24 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(F)+0.0001F²) [ Help ]

Δ/σ(max): 0.0492 [ Help ]

Δ/σ(mean): 0.0143 [ Help ]

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

Extinction coefficient: 243(28) [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	x	y	ADP type	Uiso/equiv	Symmetry multiplicity	Occupancy	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Disordered cluster	Disordered group
Pb0	Pb	0.92118(19)	0.5	Uani	0.0443(11)	4	0.0555	d	.	.	.
S1	S	0.5	0.5	Uani	0.0199(14)	4	0.5	d	.	.	.
Pb1	Pb	0	0	Uani	0.0174(3)	4	0.5	d	.	.	.

ADP components: (Show/hide table) [ Help ]

Atom site label	Atom site symbol	U11	U22	U33
Pb0	Pb	0.0341(16)	0.068(2)	0.0310(19)
S1	S	0.024(2)	0.018(3)	0.019(2)
Pb1	Pb	0.0184(5)	0.0163(5)	0.0175(5)

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

Wave vector code	q_x	q_y	q_z
1	0.00000	0.05556	0.00000
2	0.00000	0.11112	0.00000
3	0.00000	0.16668	0.00000
4	0.00000	0.22224	0.00000
5	0.00000	0.27780	0.00000
6	0.00000	0.33336	0.00000

Occupation crenel coefficients: (Show/hide table) [ Help ]

Atom site label	Center (x0)	Width
Pb0	0.25	0.0555

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
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
S1x5	S1	x	5
S1y5	S1	y	5
S1z5	S1	z	5
S1x6	S1	x	6
S1y6	S1	y	6
S1z6	S1	z	6
Pb1x1	Pb1	x	1
Pb1y1	Pb1	y	1
Pb1z1	Pb1	z	1
Pb1x2	Pb1	x	2
Pb1y2	Pb1	y	2
Pb1z2	Pb1	z	2
Pb1x3	Pb1	x	3
Pb1y3	Pb1	y	3
Pb1z3	Pb1	z	3
Pb1x4	Pb1	x	4
Pb1y4	Pb1	y	4
Pb1z4	Pb1	z	4
Pb1x5	Pb1	x	5
Pb1y5	Pb1	y	5
Pb1z5	Pb1	z	5
Pb1x6	Pb1	x	6
Pb1y6	Pb1	y	6
Pb1z6	Pb1	z	6

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
S1x1	0	-0.0815(4)
S1y1	0	0
S1z1	0	0
S1x2	0	0
S1y2	0	0.080(4)
S1z2	0	0
S1x3	0	0.0080(5)
S1y3	0	0
S1z3	0	0
S1x4	0	0
S1y4	0	-0.018(4)
S1z4	0	0
S1x5	0	-0.0063(5)
S1y5	0	0
S1z5	0	0
S1x6	0	0
S1y6	0	-0.054(4)
S1z6	0	0
Pb1x1	0	0.0188(2)
Pb1y1	0	0
Pb1z1	0	0
Pb1x2	0	0
Pb1y2	0	0.1414(6)
Pb1z2	0	0
Pb1x3	0	-0.0011(2)
Pb1y3	0	0
Pb1z3	0	0
Pb1x4	0	0
Pb1y4	0	-0.0298(7)
Pb1z4	0	0
Pb1x5	0	0.00085(16)
Pb1y5	0	0
Pb1z5	0	0
Pb1x6	0	0
Pb1y6	0	-0.0157(8)
Pb1z6	0	0

Displacive sawtooth coefficients: (Show/hide table) [ Help ]

Atom site label	Ax	Ay	Az	Center (x0)	Width
S1	-1.125	0	0	0	0.5
Pb1	-0.9722	0	0	0	0.3889

misfit

Chemical data

Structural Formula Sum: Pb16 S18 [ Help ]

Formula weight: 3892.1 Da [ Help ]

Absolute configuration: . [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Bbmm(0β0)s00 [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

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

a: 13.712 Å [ Help ]

b: 1.836 Å [ Help ]

c: 4.131 Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 103.9989 Å³ [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.00000	0.05882	0.00000

Number of subsystems: 3 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1st subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 2 [ Help ]

Subsystem description: 2nd subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	1.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 3 [ Help ]

Subsystem description: 3rd subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	-1.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Z: 2 [ Help ]

μ: 1307.66 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: 756 [ Help ]

Nb. of observed reflections: 455 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0405 [ Help ]

wR(obs): 0.0380 [ Help ]

R(all): 0.0780 [ Help ]

wR(all): 0.0436 [ Help ]

S(all): 1.4453 [ Help ]

S(obs): 1.6481 [ Help ]

Nb. of reflections: 756 [ Help ]

Nb. of parameters: 36 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0000 [ Help ]

Δ/σ(mean): 0.0000 [ Help ]

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

Extinction coefficient: 223.87 [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	Subsystem	x	y	z	ADP type	Uiso/equiv	Symmetry multiplicity	Occupancy	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Disordered cluster	Disordered group
S1	S	2	0.5	0.5	0	Uani	0.0193(12)	4	0.5	d	.	.	.
Pb1	Pb	3	0	0	0	Uani	0.0204(3)	4	0.5	d	.	.	.

ADP components: (Show/hide table) [ Help ]

Atom site label	Atom site symbol	U11	U22	U33	U12	U13	U23
S1	S	0.023(2)	0.017(2)	0.019(2)	0	0	0
Pb1	Pb	0.0203(4)	0.0219(5)	0.0191(4)	0	0	0

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

Wave vector code	q_x	q_y	q_z
1	0.00000	0.05882	0.00000
2	0.00000	0.11765	0.00000
3	0.00000	0.17647	0.00000
4	0.00000	0.23529	0.00000
5	0.00000	0.29412	0.00000
6	0.00000	0.35294	0.00000
7	0.00000	0.41176	0.00000
8	0.00000	0.47059	0.00000

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
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
S1x5	S1	x	5
S1y5	S1	y	5
S1z5	S1	z	5
S1x6	S1	x	6
S1y6	S1	y	6
S1z6	S1	z	6
Pb1x1	Pb1	x	1
Pb1y1	Pb1	y	1
Pb1z1	Pb1	z	1
Pb1x2	Pb1	x	2
Pb1y2	Pb1	y	2
Pb1z2	Pb1	z	2
Pb1x3	Pb1	x	3
Pb1y3	Pb1	y	3
Pb1z3	Pb1	z	3
Pb1x4	Pb1	x	4
Pb1y4	Pb1	y	4
Pb1z4	Pb1	z	4
Pb1x5	Pb1	x	5
Pb1y5	Pb1	y	5
Pb1z5	Pb1	z	5
Pb1x6	Pb1	x	6
Pb1y6	Pb1	y	6
Pb1z6	Pb1	z	6

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
S1x1	0	-0.0816(4)
S1y1	0	0
S1z1	0	0
S1x2	0	0
S1y2	0	0.080(4)
S1z2	0	0
S1x3	0	0.0083(4)
S1y3	0	0
S1z3	0	0
S1x4	0	0
S1y4	0	-0.017(4)
S1z4	0	0
S1x5	0	-0.0068(5)
S1y5	0	0
S1z5	0	0
S1x6	0	0
S1y6	0	-0.054(4)
S1z6	0	0
Pb1x1	0	-0.07096(7)
Pb1y1	0	0
Pb1z1	0	0
Pb1x2	0	0
Pb1y2	0	-0.1430(5)
Pb1z2	0	0
Pb1x3	0	0.00693(8)
Pb1y3	0	0
Pb1z3	0	0
Pb1x4	0	0
Pb1y4	0	0.0662(6)
Pb1z4	0	0
Pb1x5	0	-0.00077(8)
Pb1y5	0	0
Pb1z5	0	0
Pb1x6	0	0
Pb1y6	0	-0.0479(5)
Pb1z6	0	0

Displacive sawtooth coefficients: (Show/hide table) [ Help ]

Atom site label	Ax	Ay	Az	Center (x0)	Width
S1	-1.125	0	0	0	0.5
Pb1	-1	0	0	0	0.5

Definition of the ADP Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Tensor element	Wave vector code
Pb1U111	Pb1	U11	1
Pb1U221	Pb1	U22	1
Pb1U331	Pb1	U33	1
Pb1U121	Pb1	U12	1
Pb1U131	Pb1	U13	1
Pb1U231	Pb1	U23	1
Pb1U112	Pb1	U11	2
Pb1U222	Pb1	U22	2
Pb1U332	Pb1	U33	2
Pb1U122	Pb1	U12	2
Pb1U132	Pb1	U13	2
Pb1U232	Pb1	U23	2
Pb1U113	Pb1	U11	3
Pb1U223	Pb1	U22	3
Pb1U333	Pb1	U33	3
Pb1U123	Pb1	U12	3
Pb1U133	Pb1	U13	3
Pb1U233	Pb1	U23	3
Pb1U114	Pb1	U11	4
Pb1U224	Pb1	U22	4
Pb1U334	Pb1	U33	4
Pb1U124	Pb1	U12	4
Pb1U134	Pb1	U13	4
Pb1U234	Pb1	U23	4
Pb1U115	Pb1	U11	5
Pb1U225	Pb1	U22	5
Pb1U335	Pb1	U33	5
Pb1U125	Pb1	U12	5
Pb1U135	Pb1	U13	5
Pb1U235	Pb1	U23	5
Pb1U116	Pb1	U11	6
Pb1U226	Pb1	U22	6
Pb1U336	Pb1	U33	6
Pb1U126	Pb1	U12	6
Pb1U136	Pb1	U13	6
Pb1U236	Pb1	U23	6
Pb1U117	Pb1	U11	7
Pb1U227	Pb1	U22	7
Pb1U337	Pb1	U33	7
Pb1U127	Pb1	U12	7
Pb1U137	Pb1	U13	7
Pb1U237	Pb1	U23	7
Pb1U118	Pb1	U11	8
Pb1U228	Pb1	U22	8
Pb1U338	Pb1	U33	8
Pb1U128	Pb1	U12	8
Pb1U138	Pb1	U13	8
Pb1U238	Pb1	U23	8

ADP Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Pb1U111	0	0
Pb1U221	0	0
Pb1U331	0	0
Pb1U121	0.0006(4)	0
Pb1U131	0	0
Pb1U231	0	0
Pb1U112	-0.0058(6)	0
Pb1U222	-0.0116(7)	0
Pb1U332	-0.0035(7)	0
Pb1U122	0	0
Pb1U132	0	0
Pb1U232	0	0
Pb1U113	0	0
Pb1U223	0	0
Pb1U333	0	0
Pb1U123	0.0010(5)	0
Pb1U133	0	0
Pb1U233	0	0
Pb1U114	0.0048(6)	0
Pb1U224	0.0121(7)	0
Pb1U334	0.0038(7)	0
Pb1U124	0	0
Pb1U134	0	0
Pb1U234	0	0
Pb1U115	0	0
Pb1U225	0	0
Pb1U335	0	0
Pb1U125	-0.0003(5)	0
Pb1U135	0	0
Pb1U235	0	0
Pb1U116	-0.0028(6)	0
Pb1U226	-0.0146(8)	0
Pb1U336	-0.0038(8)	0
Pb1U126	0	0
Pb1U136	0	0
Pb1U236	0	0
Pb1U117	0	0
Pb1U227	0	0
Pb1U337	0	0
Pb1U127	-0.0009(4)	0
Pb1U137	0	0
Pb1U237	0	0
Pb1U118	0.0004(4)	0
Pb1U228	0.0059(5)	0
Pb1U338	0.0007(6)	0
Pb1U128	0	0
Pb1U138	0	0
Pb1U238	0	0

modular_2n_3

Chemical data

Structural Formula Sum: Pb S [ Help ]

Formula weight: 239.2 Da [ Help ]

Absolute configuration: . [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Bbmm(0β0)s00 [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

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

a: 13.712 Å [ Help ]

b: 1.836 Å [ Help ]

c: 4.131 Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 103.9989 Å³ [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.00000	0.05882	0.00000

Number of subsystems: 3 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1st subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 2 [ Help ]

Subsystem description: 2nd subsystem [ Help ]

W matrix:

3.0	-1.0	0.0	14.01
1.0	0.0	0.0	5.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 3 [ Help ]

Subsystem description: 3rd subsystem [ Help ]

W matrix:

3.0	1.0	0.0	-14.01
1.0	0.0	0.0	-5.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	-1.0

Z: 32 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 653.83 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: 756 [ Help ]

Nb. of observed reflections: 455 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0422 [ Help ]

wR(obs): 0.0395 [ Help ]

R(all): 0.0794 [ Help ]

wR(all): 0.0450 [ Help ]

S(all): 1.48 [ Help ]

S(obs): 1.70 [ Help ]

Nb. of reflections: 756 [ Help ]

Nb. of parameters: 30 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0189 [ Help ]

Δ/σ(mean): 0.0085 [ Help ]

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

Extinction coefficient: 225(25) [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	Subsystem	x	y	ADP type	Uiso/equiv	Symmetry multiplicity	Occupancy	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Disordered cluster	Disordered group
Pb0	Pb	1	0.92115(18)	0.25	Uani	0.0437(10)	4	0.0588	d	.	.	.
S0	S	1	0.2798(10)	0.25	Uani	0.017(4)	4	0.0588	d	.	.	.
Pb1	Pb	2	0	0	Uani	0.0171(3)	4	0.4118	d	.	.	.
S1	S	2	0	0.5	Uani	0.0200(14)	4	0.4706	d	.	.	.

ADP components: (Show/hide table) [ Help ]

Atom site label	Atom site symbol	U11	U22	U33	U12
Pb0	Pb	0.0343(15)	0.065(2)	0.0315(18)	0
S0	S	0.029(8)	0.007(7)	0.014(8)	0
Pb1	Pb	0.0176(4)	0.0163(5)	0.0174(5)	0.0013(3)
S1	S	0.020(2)	0.021(3)	0.019(2)	0.0027(19)

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

Wave vector code	q_x	q_y	q_z
1	0.00000	0.05882	0.00000
2	0.00000	0.11765	0.00000
3	0.00000	0.17647	0.00000

Occupation crenel coefficients: (Show/hide table) [ Help ]

Atom site label	Center (x0)	Width
Pb0	0.25	0.0588
S0	0.25	0.0588
Pb1	0	0.4118
S1	0	0.4706

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Pb1x1	Pb1	x	1
Pb1y1	Pb1	y	1
Pb1z1	Pb1	z	1
Pb1x2	Pb1	x	2
Pb1y2	Pb1	y	2
Pb1z2	Pb1	z	2
Pb1x3	Pb1	x	3
Pb1y3	Pb1	y	3
Pb1z3	Pb1	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

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Pb1x1	0	0.268(13)
Pb1y1	0	-0.207(9)
Pb1z1	0	0
Pb1x2	0	-0.242(13)
Pb1y2	0	0.273(9)
Pb1z2	0	0
Pb1x3	0	0.087(5)
Pb1y3	0	-0.098(3)
Pb1z3	0	0
S1x1	0	-0.02(3)
S1y1	0	-0.37(2)
S1z1	0	0
S1x2	0	0.07(3)
S1y2	0	0.43(2)
S1z2	0	0
S1x3	0	-0.041(14)
S1y3	0	-0.176(10)
S1z3	0	0

modular_2n_4

Chemical data

Structural Formula Sum: Pb S [ Help ]

Formula weight: 239.2 Da [ Help ]

Absolute configuration: . [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Bmmm(0β0)s00 [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

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

a: 13.737 Å [ Help ]

b: 1.7496 Å [ Help ]

c: 4.1448 Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 99.6172 Å³ [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.00000	0.05556	0.00000

Number of subsystems: 3 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1st subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 2 [ Help ]

Subsystem description: 2nd subsystem [ Help ]

W matrix:

3.0	-1.0	0.0	15.0
1.0	0.0	0.0	5.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 3 [ Help ]

Subsystem description: 3rd subsystem [ Help ]

W matrix:

3.0	1.0	0.0	-15.0
1.0	0.0	0.0	-5.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	-1.0

Z: 16 [ Help ]

μ: 681.521 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: 756 [ Help ]

Nb. of observed reflections: 454 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0421 [ Help ]

wR(obs): 0.0431 [ Help ]

R(all): 0.0795 [ Help ]

wR(all): 0.0499 [ Help ]

S(all): 1.41 [ Help ]

S(obs): 1.59 [ Help ]

Nb. of reflections: 756 [ Help ]

Nb. of parameters: 30 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(F)+0.0001F²) [ Help ]

Δ/σ(max): 0.0010 [ Help ]

Δ/σ(mean): 0.0003 [ Help ]

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

Extinction coefficient: 241(28) [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	Subsystem	x	y	ADP type	Uiso/equiv	Symmetry multiplicity	Occupancy	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Disordered cluster	Disordered group
Pb0	Pb	1	0.92116(19)	0.5	Uani	0.0443(11)	4	0.0556	d	.	.	.
S0	S	1	0.2799(10)	0.5	Uani	0.017(4)	4	0.0556	d	.	.	.
Pb	Pb	2	0	0	Uani	0.0174(3)	4	0.3889	d	.	.	.
S	S	2	0	0.5	Uani	0.0203(14)	4	0.4444	d	.	.	.

ADP components: (Show/hide table) [ Help ]

Atom site label	Atom site symbol	U11	U22	U33	U12
Pb0	Pb	0.0339(15)	0.068(2)	0.0314(18)	0
S0	S	0.029(8)	0.008(7)	0.014(8)	0
Pb	Pb	0.0179(5)	0.0168(5)	0.0175(5)	0.0013(3)
S	S	0.020(2)	0.021(3)	0.019(3)	0.003(2)

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

Wave vector code	q_x	q_y	q_z
1	0.00000	0.05556	0.00000
2	0.00000	0.11111	0.00000
3	0.00000	0.16667	0.00000

Occupation crenel coefficients: (Show/hide table) [ Help ]

Atom site label	Center (x0)	Width
Pb0	0.25	0.0556
S0	0.25	0.0556
Pb	0	0.3889
S	0	0.4444

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
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
Sx1	S	x	1
Sy1	S	y	1
Sz1	S	z	1
Sx2	S	x	2
Sy2	S	y	2
Sz2	S	z	2
Sx3	S	x	3
Sy3	S	y	3
Sz3	S	z	3

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Pbx1	0	0.267(13)
Pby1	0	-0.206(9)
Pbz1	0	0
Pbx2	0	-0.242(13)
Pby2	0	0.271(9)
Pbz2	0	0
Pbx3	0	0.087(5)
Pby3	0	-0.098(3)
Pbz3	0	0
Sx1	0	-0.01(3)
Sy1	0	-0.36(2)
Sz1	0	0
Sx2	0	0.06(3)
Sy2	0	0.43(2)
Sz2	0	0
Sx3	0	-0.039(14)
Sy3	0	-0.174(10)
Sz3	0	0