B-IncStrDB

The modulated average structure of mullite

Authors:

Birkenstock, Johannes; Petricek, Vaclav; Pedersen, Bjoern; Schneider, Hartmut; Fischer, Reinhard X.

Journal:

Acta Crystallographica, Section B 71 358-368 (2015)

DOI:

http://dx.doi.org/10.1107/S205252061500757X

B-IncStrDB ID: 11262E9iecH Entry date: 2015-06-01 Last revision: 2021-12-12

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I

Chemical data

Structural Formula Sum: Al4.8 O9.6 Si1.2 [ Help ]

Formula weight: 316.8 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Pbam(α01/2)0ss [ 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,x3-x4+1/2
3	-x1+1/2,x2+1/2,-x3,-x4+1/2
4	x1+1/2,-x2+1/2,-x3,-x3+x4
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x3+x4+1/2
7	x1+1/2,-x2+1/2,x3,x4+1/2
8	-x1+1/2,x2+1/2,x3,x3-x4

a: 7.5911 Å [ Help ]

b: 7.6924 Å [ Help ]

c: 2.8899 Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 168.7522 Å³ [ Help ]

Modulation dimension: 1 [ Help ]

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

Wave vector id	q_x	q_y	q_z
1	0.313700	0.000000	0.500000

Z: 1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 1.057 mm^-1 [ Help ]

Absorption correction type: empirical [ Help ]

Minimum transmission factor: 0.7414 [ Help ]

Maximum transmission factor: 0.8306 [ Help ]

Refinement details

Total nb. of reflections: 1234 [ Help ]

Nb. of observed reflections: 772 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0277 [ Help ]

wR(obs): 0.0558 [ Help ]

R(all): 0.0461 [ Help ]

wR(all): 0.0572 [ Help ]

S(all): 3.01 [ Help ]

S(obs): 3.82 [ Help ]

Nb. of reflections: 1234 [ Help ]

Nb. of parameters: 106 [ Help ]

Number of constraints: 48 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0320 [ Help ]

Δ/σ(mean): 0.0063 [ Help ]

Δρ(max): 0.39 e_Å^-3 [ Help ]

Δρ(min): -0.50 e_Å^-3 [ Help ]

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

Extinction coefficient: 2000(200) [ 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
Al1	Al	0	0	0	Uani	0.00670(13)	2	1	d	?	?	?
Al2	Al	0.14887(5)	0.34028(4)	0.5	Uani	0.00720(13)	4	0.5	d	?	?	?
Si2	Si	0.14887(5)	0.34028(4)	0.5	Uani	0.00720(13)	4	0.2963	d	?	?	?
Al3	Al	0.2626(2)	0.2055(2)	0.5	Uani	0.0087(4)	4	0.2037	d	?	?	?
Si3	Si	0.2626(2)	0.2055(2)	0.5	Uani	0.0087(4)	4	0	d	?	?	?
O1	O	0.35820(9)	0.42264(10)	0.5	Uani	0.0132(2)	4	1	d	?	?	?
O2	O	0.12772(10)	0.21868(11)	0	Uani	0.0134(2)	4	1	d	?	?	?
O3	O	0	0.5	0.5	Uani	0.0198(16)	2	0.3889	d	?	?	?
O4	O	0.4523(8)	0.0457(11)	0.5	Uani	0.0119(17)	4	0.2037	d	?	?	?

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

Atom site label	Atom site symbol	U11	U22	U33	U12
Al1	Al	0.0079(2)	0.0068(2)	0.0054(2)	0.00073(11)
Al2	Al	0.0065(2)	0.0081(2)	0.0070(2)	-0.00052(10)
Si2	Si	0.0065(2)	0.0081(2)	0.0070(2)	-0.00052(10)
Al3	Al	0.0088(7)	0.0090(6)	0.0082(6)	0.0015(5)
Si3	Si	0.0088(7)	0.0090(6)	0.0082(6)	0.0015(5)
O1	O	0.0141(4)	0.0188(4)	0.0066(3)	-0.0079(3)
O2	O	0.0156(3)	0.0136(4)	0.0109(3)	-0.0063(2)
O3	O	0.007(3)	0.024(4)	0.0283(17)	-0.0002(16)
O4	O	0.005(3)	0.017(4)	0.0138(18)	-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_1
1	1

Table: (Show/hide table) [ Help ]

_jana_atom_site_occ_Fourier_absolute_site_label	_jana_atom_site_occ_Fourier_absolute
Al2	0.5
Si2	0.2963
Al3	0.2037
Si3	0
O3	0.3889
O4	0.2037

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

Modulation code	Atom site label	Wave vector code
Al2o1	Al2	1
Si2o1	Si2	1
Al3o1	Al3	1
Si3o1	Si3	1
O3o1	O3	1
O4o1	O4	1

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

Modulation code	Cosine coefficient	Sine coefficient
Al2o1	0.0254(5)	0.00766(16)
Si2o1	0.0254(5)	0.00766(16)
Al3o1	-0.0207(6)	-0.0144(6)
Si3o1	-0.0207(6)	-0.0144(6)
O3o1	0.0265(5)	0
O4o1	-0.0140(6)	-0.0210(6)

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Al1x1	Al1	x	1
Al1y1	Al1	y	1
Al1z1	Al1	z	1
Al2x1	Al2	x	1
Al2y1	Al2	y	1
Al2z1	Al2	z	1
Si2x1	Si2	x	1
Si2y1	Si2	y	1
S12z1	Si2	z	1
Al3x1	Al3	x	1
Al3y1	Al3	y	1
Al3z1	Al3	z	1
Si3x1	Si3	x	1
Si3y1	Si3	y	1
S13z1	Si3	z	1
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O1x2	O2	x	1
O1y2	O2	y	1
O1z2	O2	z	1
O1x3	O3	x	1
O1y3	O3	y	1
O1z3	O3	z	1
O1x4	O4	x	1
O1y4	O4	y	1
O1z4	O4	z	1

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

Modulation code	Cosine coefficient	Sine coefficient
Al1x1	0	0
Al1y1	0	0
Al1z1	0	-0.00392(14)
Al2x1	0.00041(5)	-0.00102(5)
Al2y1	-0.00023(5)	-0.00112(5)
Al2z1	0	0
Si2x1	0.00041(5)	-0.00102(5)
Si2y1	-0.00023(5)	-0.00112(5)
S12z1	0	0
Al3x1	0.0008(3)	-0.0001(2)
Al3y1	0.0005(2)	-0.0009(2)
Al3z1	0	0
Si3x1	0.0008(3)	-0.0001(2)
Si3y1	0.0005(2)	-0.0009(2)
S13z1	0	0
O1x1	-0.00122(11)	-0.00169(11)
O1y1	0.00270(9)	0.00192(10)
O1z1	0	0
O1x2	0	0
O1y2	0	0
O1z2	-0.0056(2)	-0.0021(2)
O1x3	0	-0.0041(7)
O1y3	0	-0.0004(9)
O1z3	0	0
O1x4	-0.0018(12)	0.0044(8)
O1y4	-0.0080(16)	-0.0028(8)
O1z4	0	0

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

Modulation code	Atom site label	Tensor element	Wave vector code
Al1U111	Al1	U11	1
Al1U221	Al1	U22	1
Al1U331	Al1	U33	1
Al1U121	Al1	U12	1
Al1U131	Al1	U13	1
Al1U231	Al1	U23	1
Al2U111	Al2	U11	1
Al2U221	Al2	U22	1
Al2U331	Al2	U33	1
Al2U121	Al2	U12	1
Al2U131	Al2	U13	1
Al2U231	Al2	U23	1
Si2U111	Si2	U11	1
Si2U221	Si2	U22	1
Si2U331	Si2	U33	1
Si2U121	Si2	U12	1
Si2U131	Si2	U13	1
Si2U231	Si2	U23	1
Al3U111	Al3	U11	1
Al3U221	Al3	U22	1
Al3U331	Al3	U33	1
Al3U121	Al3	U12	1
Al3U131	Al3	U13	1
Al3U231	Al3	U23	1
Si3U111	Si3	U11	1
Si3U221	Si3	U22	1
Si3U331	Si3	U33	1
Si3U121	Si3	U12	1
Si3U131	Si3	U13	1
Si3U231	Si3	U23	1
O1U111	O1	U11	1
O1U221	O1	U22	1
O1U331	O1	U33	1
O1U121	O1	U12	1
O1U131	O1	U13	1
O1U231	O1	U23	1
O2U111	O2	U11	1
O2U221	O2	U22	1
O2U331	O2	U33	1
O2U121	O2	U12	1
O2U131	O2	U13	1
O2U231	O2	U23	1
O3U111	O3	U11	1
O3U221	O3	U22	1
O3U331	O3	U33	1
O3U121	O3	U12	1
O3U131	O3	U13	1
O3U231	O3	U23	1
O4U111	O4	U11	1
O4U221	O4	U22	1
O4U331	O4	U33	1
O4U121	O4	U12	1
O4U131	O4	U13	1
O4U231	O4	U23	1

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

Modulation code	Cosine coefficient	Sine coefficient
Al1U111	0	0
Al1U221	0	0
Al1U331	0	0
Al1U121	0	0
Al1U131	-0.00010(18)	0
Al1U231	-0.00051(17)	0
Al2U111	-0.0022(2)	-0.0002(2)
Al2U221	-0.0019(2)	0.0008(2)
Al2U331	-0.00133(19)	-0.00015(18)
Al2U121	-0.00014(18)	-0.00030(16)
Al2U131	0	0
Al2U231	0	0
Si2U111	-0.0022(2)	-0.0002(2)
Si2U221	-0.0019(2)	0.0008(2)
Si2U331	-0.00133(19)	-0.00015(18)
Si2U121	-0.00014(18)	-0.00030(16)
Si2U131	0	0
Si2U231	0	0
Al3U111	0.0099(10)	0.0025(10)
Al3U221	0.0082(9)	0.0046(10)
Al3U331	0.0092(9)	0.0049(8)
Al3U121	0.0011(7)	-0.0007(7)
Al3U131	0	0
Al3U231	0	0
Si3U111	0.0099(10)	0.0025(10)
Si3U221	0.0082(9)	0.0046(10)
Si3U331	0.0092(9)	0.0049(8)
Si3U121	0.0011(7)	-0.0007(7)
Si3U131	0	0
Si3U231	0	0
O1U111	-0.0019(5)	-0.0009(4)
O1U221	-0.0001(4)	0.0003(5)
O1U331	0.0003(3)	0.0005(3)
O1U121	0.0014(4)	0.0005(4)
O1U131	0	0
O1U231	0	0
O2U111	0	0
O2U221	0	0
O2U331	0	0
O2U121	0	0
O2U131	-0.0003(3)	-0.0006(3)
O2U231	-0.0001(3)	0.0009(3)
O3U111	0.010(5)	0
O3U221	-0.016(6)	0
O3U331	0.000(3)	0
O3U121	0.000(3)	0
O3U131	0	0
O3U231	0	0
O4U111	-0.002(4)	0.005(3)
O4U221	0.025(5)	0.008(3)
O4U331	0.004(3)	0.008(2)
O4U121	-0.010(3)	-0.0025(19)
O4U131	0	0
O4U231	0	0

II

Chemical data

Structural Formula Sum: Al4.78 O9.61 Si1.22 [ Help ]

Formula weight: 317 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

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

Space group name (Hall): -P -2xab;-2yab;-2z [ Help ]

Space group nb.: 55 [ 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+1/2,y+1/2,-z
4	x+1/2,-y+1/2,-z
5	-x,-y,-z
6	x,y,-z
7	x+1/2,-y+1/2,z
8	-x+1/2,y+1/2,z

a: 7.5757 Å [ Help ]

b: 7.6651 Å [ Help ]

c: 2.885 Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 167.5276 Å³ [ Help ]

Z: 1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 0.00044 mm^-1 [ Help ]

Minimum transmission factor: 0.997 [ Help ]

Maximum transmission factor: 0.998 [ Help ]

Refinement details

Total nb. of reflections: 1534 [ Help ]

Nb. of observed reflections: 1516 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0497 [ Help ]

wR(obs): 0.0668 [ Help ]

R(all): 0.0504 [ Help ]

wR(all): 0.0671 [ Help ]

S(all): 2.68 [ Help ]

S(obs): 2.68 [ Help ]

Nb. of reflections: 1534 [ Help ]

Nb. of parameters: 47 [ Help ]

Number of constraints: 16 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0070 [ Help ]

Δ/σ(mean): 0.0010 [ Help ]

Δρ(max): 1.12 e_Å^-3 [ Help ]

Δρ(min): -0.69 e_Å^-3 [ Help ]

Extinction method: B-C type 1 Lorentzian anisotropic (Becker & Coppens, 1975) [ Help ]

Refinement remarks: The anisotropic components of the Type I extinction correction: -0.014(5) -0.026(2) -0.0078(8) -0.008(2) -0.001(1) -0.0009(7) [ 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
Al1	Al	0	0	0	Uani	0.0045(3)	2	1	d	?	?	?
Al2	Al	0.14897(9)	0.34022(13)	0.5	Uani	0.0049(3)	4	0.56(5)	d	?	?	?
Si2	Si	0.14897(9)	0.34022(13)	0.5	Uani	0.0049(3)	4	0.24(5)	d	?	?	?
Al3	Al	0.2619(4)	0.2066(4)	0.5	Uani	0.0054(9)	4	0.13(5)	d	?	?	?
Si3	Si	0.2619(4)	0.2066(4)	0.5	Uani	0.0054(9)	4	0.06(5)	d	?	?	?
O1	O	0.35845(5)	0.42238(8)	0.5	Uani	0.0111(2)	4	1	d	?	?	?
O2	O	0.12734(5)	0.21852(7)	0	Uani	0.0116(2)	4	1	d	?	?	?
O3	O	0.5	0	0.5	Uani	0.0194(16)	2	0.42(2)	d	?	?	?
O4	O	0.4496(11)	0.0518(9)	0.5	Uani	0.0072(9)	4	0.195(8)	d	?	?	?

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

Atom site label	Atom site symbol	U11	U22	U33	U12
Al1	Al	0.0056(4)	0.0065(4)	0.0013(5)	0.0011(3)
Al2	Al	0.0038(4)	0.0081(5)	0.0029(5)	-0.0013(2)
Si2	Si	0.0038(4)	0.0081(5)	0.0029(5)	-0.0013(2)
Al3	Al	0.0016(14)	0.0091(13)	0.0055(19)	0.0014(10)
Si3	Si	0.0016(14)	0.0091(13)	0.0055(19)	0.0014(10)
O1	O	0.0116(4)	0.0199(4)	0.0018(4)	-0.00831(17)
O2	O	0.0131(3)	0.0138(4)	0.0078(4)	-0.00698(15)
O3	O	0.018(3)	0.018(4)	0.0224(13)	-0.006(3)
O4	O	0.0094(18)	0.0047(15)	0.0073(12)	-0.0002(11)