B-IncStrDB

Ordered vacancy distribution in 2/1 mullite: A superspace model

Authors:

Klar, Paul Benjamin; de la Pinta, Noelia; Lopez, Gabriel Alejandro; Etxebarria, Inigo; Breczweski, Tomasz; Madariaga, Gotzon

Journal:

Acta Crystallographica, Section B 73 377-388 (2017)

DOI:

https://doi.org/10.1107/S2052520617001652

B-IncStrDB ID: 13172EtfBj9 Entry date: 2017-06-06 Last revision: 2021-12-12

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I

Chemical data

Common Name: Mullite [ Help ]

Formula moiety: 2.1(Al2 O3), (Si O2) [ Help ]

Structural Formula Sum: Al4.847 O9.577 Si1.153 [ Help ]

Formula weight: 316.4 Da [ Help ]

Compound Source: Sigma Aldrich [ 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: 7.5817(6) Å [ Help ]

b: 7.6752(7) Å [ Help ]

c: 2.8843(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 167.84(3) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

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

Wave vector id	q_x	q_y	q_z
1	0.300100	0.000000	0.500000

Z: 1 [ Help ]

Cell determination reflection Nb.: 2808 [ Help ]

θ(min) for cell determination: 3.77 ° [ Help ]

θ(max) for cell determination: 39.54 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 1.06 mm^-1 [ Help ]

Absorption correction type: numerical [ Help ]

Absorption correction remarks: STOE X-Red32 [ Help ]

Minimum transmission factor: 0.9650 [ Help ]

Maximum transmission factor: 0.9810 [ Help ]

Refinement details

Total nb. of reflections: 864 [ Help ]

Nb. of observed reflections: 516 [ Help ]

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

Refinement based on: Fsqd [ Help ]

R(obs): 0.0354 [ Help ]

wR(obs): 0.0886 [ Help ]

R(all): 0.0629 [ Help ]

wR(all): 0.1115 [ Help ]

S(all): 0.98 [ Help ]

S(obs): 1.03 [ Help ]

Nb. of reflections: 864 [ Help ]

Nb. of parameters: 52 [ Help ]

Number of constraints: 12 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(I)+0.0049000001I²) [ Help ]

Refinement of hydrogen atoms: constr [ Help ]

Δ/σ(max): 0.0008 [ Help ]

Δ/σ(mean): 0.0001 [ Help ]

Δρ(max): 1.18 e_Å^-3 [ Help ]

Δρ(min): -1.02 e_Å^-3 [ 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
Al1	Al	0	0	0	Uani	0.00645(18)	2	0.25	d	?
Al2	Al	0.1492(2)	0.3407(2)	0.5	Uani	0.00716(16)	4	0.317127	d	?
Si2	Si	0.1492(2)	0.3407(2)	0.5	Uani	0.00716(16)	4	0.182873	d	?
Al3	Al	0.2629(3)	0.2050(3)	0.5	Uani	0.0068(4)	4	0.5	d	?
O1	O	0.35872(15)	0.42222(18)	0.5	Uani	0.0082(6)	4	0.5	d	?
O2	O	0.12751(16)	0.21796(17)	0	Uani	0.0132(4)	4	0.5	d	?
O3a	O	0	0.5	0.5	Uani	0.0195(18)	2	0.25	d	?
O3b	O	0	0.5	0.5	Uani	0.0195(18)	4	0.5	d	?
O4	O	0.4514(9)	0.0492(8)	0.5	Uani	0.0112(14)	4	0.5	d	?

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

Atom site label	Atom site symbol	U11	U22	U33	U12
Al1	Al	0.0084(2)	0.0065(2)	0.0044(4)	0.00029(17)
Al2	Al	0.0065(3)	0.0071(3)	0.0079(2)	-0.0014(2)
Si2	Si	0.0065(3)	0.0071(3)	0.0079(2)	-0.0014(2)
Al3	Al	0.0059(7)	0.0078(8)	0.0066(8)	0.0010(6)
O1	O	0.0113(8)	0.0073(15)	0.0059(4)	-0.0011(9)
O2	O	0.0164(5)	0.0141(4)	0.0091(9)	-0.0069(4)
O3a	O	0.018(3)	0.015(3)	0.025(3)	0.002(2)
O3b	O	0.018(3)	0.015(3)	0.025(3)	0.002(2)
O4	O	0.012(3)	0.008(3)	0.015(2)	0.0014(18)

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

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

Atom site label	Center (x0)	Width
Al2	0.04477(7)	0.7883
Si2	0.04477(7)	0.788(2)
Al3	0.57888(12)	0.212(2)
O3a	0	0.088(2)
O3b	0.325(2)	0.138(4)
O4	0.6355(3)	0.212(2)

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
Al1x2	Al2	x	1
Al1y2	Al2	y	1
Al1z2	Al2	z	1
Si2x1	Si2	x	1
Si2y1	Si2	y	1
Si2z1	Si2	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

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

Modulation code	Cosine coefficient	Sine coefficient
Al1x1	0	0
Al1y1	0	0
Al1z1	0	-0.020(2)
Al1x2	0.0011(8)	-0.0041(5)
Al1y2	-0.0015(9)	-0.0057(6)
Al1z2	0	0
Si2x1	0.0011(8)	-0.0041(5)
Si2y1	-0.0015(9)	-0.0057(6)
Si2z1	0	0
O1x1	-0.0064(11)	-0.0094(11)
O1y1	0.0165(10)	0.0099(12)
O1z1	0	0
O2x1	0	0
O2y1	0	0
O2z1	-0.025(3)	-0.013(3)

II

Chemical data

Common Name: 2/1 Mullite [ Help ]

Formula moiety: (Al2 O8),(Si0.8 O0.4),(Al0.4 Si0.4 O0.4),(Al2.4 O0.8) [ Help ]

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

Crystallographic data and experimental details

a: 75.8170(6) Å [ Help ]

b: 7.6752(7) Å [ Help ]

c: 5.7686(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 3356.8(4) Å³ [ Help ]

Z: 10 [ Help ]

Crystal system: orthorhombic [ Help ]

Space group name (H-M): B b 21 m [ Help ]

Space group nb.: 36 [ Help ]

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

Operation code	Operation in algebraic form
1	x, y, z
2	-x, y+1/2, -z
3	-x, y+1/2, z
4	x, y, -z
5	x+1/2, y, z+1/2
6	-x+1/2, y+1/2, -z+1/2
7	-x+1/2, y+1/2, z+1/2
8	x+1/2, y, -z+1/2

Refinement details

Structural Information

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

Atom site label	Occupancy	x	y	z	ADP type	Uiso/equiv	Atom symbol
Al11	1.0	0.025000	0.500000	0.245409	Uiso	0.006463	Al
Al12	1.0	0.075000	0.000000	0.259987	Uiso	0.006463	Al
Al13	1.0	0.125000	0.500000	0.242850	Uiso	0.006463	Al
Al14	1.0	0.175000	0.000000	0.248418	Uiso	0.006463	Al
Al15	1.0	0.225000	0.500000	0.259009	Uiso	0.006463	Al
Al21	1.0	0.010357	0.836560	0.000000	Uiso	0.007123	Al
Al22	1.0	0.040259	0.156979	0.000000	Uiso	0.007123	Al
Al23	1.0	0.109786	0.841865	0.000000	Uiso	0.007123	Al
Al24	1.0	0.139725	0.163262	0.000000	Uiso	0.007123	Al
Al25	1.0	0.160411	0.663215	0.000000	Uiso	0.007123	Al
Al26	1.0	0.190271	0.343947	0.000000	Uiso	0.007123	Al
Al27	1.0	0.259860	0.659408	0.000000	Uiso	0.007123	Al
Al28	1.0	0.289826	0.337300	0.000000	Uiso	0.007123	Al
Al29	1.0	0.389624	0.339473	0.000000	Uiso	0.007123	Al
Al210	1.0	0.460422	0.661683	0.000000	Uiso	0.007123	Al
Si21	1.0	0.310434	0.837391	0.000000	Uiso	0.007123	Si
Si22	1.0	0.340249	0.155447	0.000000	Uiso	0.007123	Si
Si23	1.0	0.359888	0.655400	0.000000	Uiso	0.007123	Si
Si24	1.0	0.409956	0.839326	0.000000	Uiso	0.007123	Si
Si25	1.0	0.439936	0.161809	0.000000	Uiso	0.007123	Si
Si26	1.0	0.490194	0.344778	0.000000	Uiso	0.007123	Si
Al31	1.0	0.048714	0.795047	0.000000	Uiso	0.006733	Al
Al32	1.0	0.101286	0.204953	0.000000	Uiso	0.006733	Al
Al33	1.0	0.198714	0.704953	0.000000	Uiso	0.006733	Al
Al34	1.0	0.251286	0.295047	0.000000	Uiso	0.006733	Al
O111	1.0	0.010083	0.428592	0.000000	Uiso	0.008203	O
O112	1.0	0.038006	0.596214	0.000000	Uiso	0.008203	O
O113	1.0	0.488339	0.915842	0.000000	Uiso	0.008203	O
O114	1.0	0.459750	0.059352	0.000000	Uiso	0.008203	O
O121	1.0	0.060678	0.066846	0.000000	Uiso	0.008203	O
O122	1.0	0.089657	0.937509	0.000000	Uiso	0.008203	O
O123	1.0	0.438934	0.588720	0.000000	Uiso	0.008203	O
O124	1.0	0.411402	0.406925	0.000000	Uiso	0.008203	O
O131	1.0	0.111889	0.402985	0.000000	Uiso	0.008203	O
O132	1.0	0.139627	0.577329	0.000000	Uiso	0.008203	O
O133	1.0	0.390145	0.941449	0.000000	Uiso	0.008203	O
O134	1.0	0.361371	0.078237	0.000000	Uiso	0.008203	O
O141	1.0	0.159870	0.066112	0.000000	Uiso	0.008203	O
O142	1.0	0.188011	0.906391	0.000000	Uiso	0.008203	O
O143	1.0	0.338126	0.589454	0.000000	Uiso	0.008203	O
O144	1.0	0.309756	0.438043	0.000000	Uiso	0.008203	O
O151	1.0	0.211033	0.427728	0.000000	Uiso	0.008203	O
O152	1.0	0.239941	0.559633	0.000000	Uiso	0.008203	O
O153	1.0	0.289288	0.916706	0.000000	Uiso	0.008203	O
O154	1.0	0.261685	0.095933	0.000000	Uiso	0.008203	O
O211	1.0	0.012249	0.717963	0.260814	Uiso	0.013163	O
O212	1.0	0.037751	0.282037	0.236036	Uiso	0.013163	O
O221	1.0	0.062249	0.782037	0.251251	Uiso	0.013163	O
O222	1.0	0.087751	0.217963	0.255602	Uiso	0.013163	O
O231	1.0	0.112249	0.717963	0.237715	Uiso	0.013163	O
O232	1.0	0.137751	0.282037	0.257379	Uiso	0.013163	O
O241	1.0	0.162249	0.782037	0.263191	Uiso	0.013163	O
O242	1.0	0.187751	0.217963	0.235723	Uiso	0.013163	O
O251	1.0	0.212249	0.717963	0.246778	Uiso	0.013163	O
O252	1.0	0.237751	0.282037	0.259404	Uiso	0.013163	O
O31	1.0	0.325000	0.000000	0.000000	Uiso	0.019453	O
O32	1.0	0.375000	0.500000	0.000000	Uiso	0.019453	O
O33	1.0	0.425000	0.000000	0.000000	Uiso	0.019453	O
O34	1.0	0.475000	0.500000	0.000000	Uiso	0.019453	O
O41	1.0	0.029857	0.950792	0.000000	Uiso	0.011233	O
O42	1.0	0.120143	0.049208	0.000000	Uiso	0.011233	O
O43	1.0	0.179857	0.549208	0.000000	Uiso	0.011233	O
O44	1.0	0.270143	0.450792	0.000000	Uiso	0.011233	O

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

Atom site label	U11	U22	U33	U12
Al11	0.00845	0.00652	0.00442	-0.00030
Al12	0.00845	0.00652	0.00442	0.00030
Al13	0.00845	0.00652	0.00442	-0.00030
Al14	0.00845	0.00652	0.00442	0.00030
Al15	0.00845	0.00652	0.00442	-0.00030
Al21	0.00641	0.00706	0.00790	0.00139
Al22	0.00641	0.00706	0.00790	0.00139
Al23	0.00641	0.00706	0.00790	0.00139
Al24	0.00641	0.00706	0.00790	0.00139
Al25	0.00641	0.00706	0.00790	-0.00139
Al26	0.00641	0.00706	0.00790	-0.00139
Al27	0.00641	0.00706	0.00790	-0.00139
Al28	0.00641	0.00706	0.00790	-0.00139
Al29	0.00641	0.00706	0.00790	-0.00139
Al210	0.00641	0.00706	0.00790	-0.00139
Si21	0.00641	0.00706	0.00790	0.00139
Si22	0.00641	0.00706	0.00790	0.00139
Si23	0.00641	0.00706	0.00790	-0.00139
Si24	0.00641	0.00706	0.00790	0.00139
Si25	0.00641	0.00706	0.00790	0.00139
Si26	0.00641	0.00706	0.00790	-0.00139
Al31	0.00582	0.00778	0.00660	0.00097
Al32	0.00582	0.00778	0.00660	0.00097
Al33	0.00582	0.00778	0.00660	-0.00097
Al34	0.00582	0.00778	0.00660	-0.00097
O111	0.01136	0.00730	0.00595	-0.00112
O112	0.01136	0.00730	0.00595	-0.00112
O113	0.01136	0.00730	0.00595	0.00112
O114	0.01136	0.00730	0.00595	0.00112
O121	0.01136	0.00730	0.00595	0.00112
O122	0.01136	0.00730	0.00595	0.00112
O123	0.01136	0.00730	0.00595	-0.00112
O124	0.01136	0.00730	0.00595	-0.00112
O131	0.01136	0.00730	0.00595	-0.00112
O132	0.01136	0.00730	0.00595	-0.00112
O133	0.01136	0.00730	0.00595	0.00112
O134	0.01136	0.00730	0.00595	0.00112
O141	0.01136	0.00730	0.00595	0.00112
O142	0.01136	0.00730	0.00595	0.00112
O143	0.01136	0.00730	0.00595	-0.00112
O144	0.01136	0.00730	0.00595	-0.00112
O151	0.01136	0.00730	0.00595	-0.00112
O152	0.01136	0.00730	0.00595	-0.00112
O153	0.01136	0.00730	0.00595	0.00112
O154	0.01136	0.00730	0.00595	0.00112
O211	0.01631	0.01407	0.00911	0.00693
O212	0.01631	0.01407	0.00911	0.00693
O221	0.01631	0.01407	0.00911	-0.00693
O222	0.01631	0.01407	0.00911	-0.00693
O231	0.01631	0.01407	0.00911	0.00693
O232	0.01631	0.01407	0.00911	0.00693
O241	0.01631	0.01407	0.00911	-0.00693
O242	0.01631	0.01407	0.00911	-0.00693
O251	0.01631	0.01407	0.00911	0.00693
O252	0.01631	0.01407	0.00911	0.00693
O31	0.01835	0.01503	0.02498	-0.00171
O32	0.01835	0.01503	0.02498	0.00171
O33	0.01835	0.01503	0.02498	-0.00171
O34	0.01835	0.01503	0.02498	0.00171
O41	0.01165	0.00752	0.01453	0.00144
O42	0.01165	0.00752	0.01453	0.00144
O43	0.01165	0.00752	0.01453	-0.00144
O44	0.01165	0.00752	0.01453	-0.00144