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Homogeneous and inclusion-free single crystals of 2:1 mullite (Al4.8Si1.2O9.6) grown by the Czochralski technique were examined by X-ray and neutron diffraction methods. The observed diffuse scattering together with the pattern of satellite reflections confirm previously published data and are thus inherent features of the mullite structure. The ideal composition was closely met as confirmed by microprobe analysis (Al4.82 (3)Si1.18 (1)O9.59 (5)) and by average structure refinements. 8 (5) to 20 (13)% of the available Si was found in the T* position of the tetrahedra triclusters. The strong tendencey for disorder in mullite may be understood from considerations of hypothetical superstructures which would have to be n-fivefold with respect to the three-dimensional average unit cell of 2:1 mullite and n-fourfold in case of 3:2 mullite. In any of these the possible arrangements of the vacancies and of the tetrahedral units would inevitably be unfavorable. Three directions of incommensurate modulations were determined: q1 = [0.3137 (2) 0 ½], q2 = [0 0.4021 (5) 0.1834 (2)] and q3 = [0 0.4009 (5) −0.1834 (2)]. The one-dimensional incommensurately modulated crystal structure associated with q1 was refined for the first time using the superspace approach. The modulation is dominated by harmonic occupational modulations of the atoms in the di- and the triclusters of the tetrahedral units in mullite. The modulation amplitudes are small and the harmonic character implies that the modulated structure still represents an average structure in the overall disordered arrangement of the vacancies and of the tetrahedral structural units. In other words, when projecting the local assemblies at the scale of a few tens of average mullite cells into cells determined by either one of the modulation vectors q1, q2 or q3 a weak average modulation results with slightly varying average occupation factors for the tetrahedral units. As a result, the real structure of mullite is locally ordered (as previously known), but on the long-range its average is not completely disordered, the modulated structure of mullite may be denoted the true `average structure of mullite'.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S205252061500757X/wf5116sup1.cif
Contains datablocks global, I, II

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S205252061500757X/wf5116Isup2.hkl
Contains datablock I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S205252061500757X/wf5116IIsup3.hkl
Contains datablock II

pdf

Portable Document Format (PDF) file https://doi.org/10.1107/S205252061500757X/wf5116sup4.pdf
Supplementary material

B-IncStrDB reference: 11262E9iecH

CCDC reference: 1060127

Computing details top

(I) top
Crystal data top
Al4.8O9.6Si1.2Z = 1
Mr = 316.8F(000) = 156
Orthorhombic, Pbam(α01/2)0ssDx = 3.117 Mg m3
q = 0.313700a* + 0.500000c*Mo Kα radiation, λ = 0.71073 Å
a = 7.5911 ŵ = 1.06 mm1
b = 7.6924 ÅT = 293 K
c = 2.8899 ÅStump wedge, colorless
V = 168.75 Å30.36 × 0.28 × 0.21 mm
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, −x2, x3, x3x4+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, x3x4.

Data collection top
Bruker CCD
diffractometer
1234 independent reflections
Radiation source: X-ray tube772 reflections with I > 3σ(I)
Graphite monochromatorRint = 0.028
integration technique scansθmax = 36.6°, θmin = 4.0°
Absorption correction: empirical (using intensity measurements)h = 1212
Tmin = 0.741, Tmax = 0.831k = 1212
8049 measured reflectionsl = 55
Refinement top
Refinement on F48 constraints
R[F2 > 2σ(F2)] = 0.028Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2)
wR(F2) = 0.057(Δ/σ)max = 0.032
S = 3.01Δρmax = 0.39 e Å3
1234 reflectionsΔρmin = 0.50 e Å3
106 parametersExtinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
0 restraintsExtinction coefficient: 2000 (200)
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Al10000.00670 (13)
Al20.14887 (5)0.34028 (4)0.50.00720 (13)0.5
Si20.14887 (5)0.34028 (4)0.50.00720 (13)0.2963
Al30.2626 (2)0.2055 (2)0.50.0087 (4)0.2037
Si30.2626 (2)0.2055 (2)0.50.0087 (4)0
O10.35820 (9)0.42264 (10)0.50.0132 (2)
O20.12772 (10)0.21868 (11)00.0134 (2)
O300.50.50.0198 (16)0.3889
O40.4523 (8)0.0457 (11)0.50.0119 (17)0.2037
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Al10.0079 (2)0.0068 (2)0.0054 (2)0.00073 (11)00
Al20.0065 (2)0.0081 (2)0.0070 (2)0.00052 (10)00
Si20.0065 (2)0.0081 (2)0.0070 (2)0.00052 (10)00
Al30.0088 (7)0.0090 (6)0.0082 (6)0.0015 (5)00
Si30.0088 (7)0.0090 (6)0.0082 (6)0.0015 (5)00
O10.0141 (4)0.0188 (4)0.0066 (3)0.0079 (3)00
O20.0156 (3)0.0136 (4)0.0109 (3)0.0063 (2)00
O30.007 (3)0.024 (4)0.0283 (17)0.0002 (16)00
O40.005 (3)0.017 (4)0.0138 (18)0.003 (2)00
Bond lengths (Å) top
AverageMinimumMaximum
Al1—O1i1.8977 (7)1.8907 (8)1.9047 (8)
Al1—O1ii1.8977 (7)1.8907 (8)1.9047 (8)
Al1—O1iii1.8977 (7)1.8907 (8)1.9047 (8)
Al1—O1iv1.8977 (7)1.8907 (8)1.9047 (8)
Al1—O21.9416 (8)1.9415 (8)1.9416 (8)
Al1—O2v1.9416 (8)1.9415 (8)1.9416 (8)
Al2—O11.7109 (12)1.7033 (12)1.7182 (12)
Al2—O21.7289 (8)1.7186 (8)1.7391 (8)
Al2—O2vi1.7289 (8)1.7186 (8)1.7391 (8)
Al2—O31.670 (3)1.650 (6)1.689 (6)
Al2—O4vii1.757 (12)1.692 (15)1.822 (15)
Al2—O4iv1.731 (11)1.688 (12)1.774 (12)
Si2—O11.7109 (12)1.7033 (12)1.7182 (12)
Si2—O21.7289 (8)1.7186 (8)1.7391 (8)
Si2—O2vi1.7289 (8)1.7186 (8)1.7391 (8)
Si2—O31.670 (3)1.650 (6)1.689 (6)
Si2—O4vii1.757 (12)1.692 (15)1.822 (15)
Si2—O4iv1.731 (11)1.688 (12)1.774 (12)
Al3—O11.822 (3)1.806 (3)1.838 (3)
Al3—O21.7739 (16)1.7611 (16)1.7865 (16)
Al3—O2vi1.7739 (16)1.7611 (16)1.7865 (16)
Al3—O41.894 (11)1.847 (13)1.940 (13)
Si3—O11.812 (3)1.806 (3)1.825 (3)
Si3—O21.7722 (16)1.7611 (16)1.7862 (16)
Si3—O2vi1.7722 (16)1.7611 (16)1.7862 (16)
Si3—O41.865 (11)1.847 (13)1.898 (13)
Symmetry codes: (i) x1+1/2, x21/2, x3, x4+1/2; (ii) x1+1/2, x21/2, x3+1, x4+1/2; (iii) x11/2, x2+1/2, x3, x3+x4; (iv) x11/2, x2+1/2, x3+1, x3+x4; (v) x1, x2, x3, x3x4+1/2; (vi) x1, x2, x3+1, x4; (vii) x1+1/2, x2+1/2, x3+1, x4+1/2.
(II) top
Crystal data top
Al4.78O9.61Si1.22Z = 1
Mr = 317F(000) = 156
Orthorhombic, PbamDx = 3.141 Mg m3
Hall symbol: -P -2xab;-2yab;-2zX-ray radiation, λ = 1.0408 Å
a = 7.5757 ŵ = 0.00044 mm1
b = 7.6651 ÅT = 293 K
c = 2.885 ÅAlmost a cube, colorless
V = 167.53 Å34 × 4 × 4 mm
Data collection top
Eulerian cradle
diffractometer
θmax = 58.5°, θmin = 5.5°
Graphite monochromatorh = 129
1545 measured reflectionsk = 812
1534 independent reflectionsl = 44
1516 reflections with I > 3σ(I)
Refinement top
Refinement on F16 constraints
R[F2 > 2σ(F2)] = 0.050Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0004F2)
wR(F2) = 0.067(Δ/σ)max = 0.007
S = 2.68Δρmax = 1.12 e Å3
1534 reflectionsΔρmin = 0.69 e Å3
47 parametersExtinction correction: B-C type 1 Lorentzian anisotropic (Becker & Coppens, 1975)
0 restraintsExtinction coefficient: -0.014(5), -0.026(2), -0.0078(8), -0.008(2), -0.001(1), -0.0009(7)
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Al10000.0045 (3)
Al20.14897 (9)0.34022 (13)0.50.0049 (3)0.56 (5)
Si20.14897 (9)0.34022 (13)0.50.0049 (3)0.24 (5)
Al30.2619 (4)0.2066 (4)0.50.0054 (9)0.13 (5)
Si30.2619 (4)0.2066 (4)0.50.0054 (9)0.06 (5)
O10.35845 (5)0.42238 (8)0.50.0111 (2)
O20.12734 (5)0.21852 (7)00.0116 (2)
O30.500.50.0194 (16)0.42 (2)
O40.4496 (11)0.0518 (9)0.50.0072 (9)0.195 (8)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Al10.0056 (4)0.0065 (4)0.0013 (5)0.0011 (3)00
Al20.0038 (4)0.0081 (5)0.0029 (5)0.0013 (2)00
Si20.0038 (4)0.0081 (5)0.0029 (5)0.0013 (2)00
Al30.0016 (14)0.0091 (13)0.0055 (19)0.0014 (10)00
Si30.0016 (14)0.0091 (13)0.0055 (19)0.0014 (10)00
O10.0116 (4)0.0199 (4)0.0018 (4)0.00831 (17)00
O20.0131 (3)0.0138 (4)0.0078 (4)0.00698 (15)00
O30.018 (3)0.018 (4)0.0224 (13)0.006 (3)00
O40.0094 (18)0.0047 (15)0.0073 (12)0.0002 (11)00
Bond lengths (Å) top
Al1—O1i1.8933 (3)Si2—O3vi1.790 (3)
Al1—O1ii1.8933 (3)Si2—O3iv1.705 (3)
Al1—O1iii1.8933 (3)Si2—O41.7243 (6)
Al1—O1iv1.8933 (3)Si2—O4vii1.7243 (6)
Al1—O41.9331 (5)Al3—O11.808 (4)
Al1—O4v1.9331 (5)Al3—O1ii2.362 (4)
Al2—Al31.334 (3)Al3—O22.398 (3)
Al2—Si31.334 (3)Al3—O31.879 (4)
Al2—O11.7078 (9)Al3—O41.7699 (17)
Al2—O2vi1.6680 (9)Al3—O4vii1.7699 (17)
Al2—O3vi1.790 (3)Si3—O11.808 (4)
Al2—O3iv1.705 (3)Si3—O1ii2.362 (4)
Al2—O41.7243 (6)Si3—O22.398 (3)
Al2—O4vii1.7243 (6)Si3—O31.879 (4)
Si2—Al31.334 (3)Si3—O41.7699 (17)
Si2—Si31.334 (3)Si3—O4vii1.7699 (17)
Si2—O11.7078 (9)O1—O1viii2.4525 (7)
Si2—O2vi1.6680 (9)O3—O3ix1.045 (4)
Symmetry codes: (i) x+1/2, y1/2, z; (ii) x+1/2, y1/2, z+1; (iii) x1/2, y+1/2, z; (iv) x1/2, y+1/2, z+1; (v) x, y, z; (vi) x+1/2, y+1/2, z+1; (vii) x, y, z+1; (viii) x+1, y+1, z; (ix) x+1, y, z.
 

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