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The structure of γ-alumina (Al21+1/32+2/3O32) crystals obtained as a product of a corrosion reaction between β-sialon and steel was refined in the space group Fd\overline{3}m. The oxygen sublattice is fully occupied. The refined occupancy parameters are 0.83 (3), 0.818 (13), 0.066 (14) and 0.044 (18) for Al ions in 8a, 16d, 16c and 48f positions, respectively. The Al ions are distributed over octa­hedral and tetra­hedral sites in a 63:37 ratio, with 6% of all Al ions occupying non-spinel positions.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270106026850/bc3006sup1.cif
Contains datablocks I, global

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108270106026850/bc3006Isup2.hkl
Contains datablock I

Comment top

Aluminium oxide, Al2O3, is a technologically important ceramic material with a large variety of applications. Its great usefulness rests especially on its high thermal stability, extreme hardness and low electrical conductivity. Al2O3 is known tO1 form several polymorphs, of which the best crystallographically defined is the α-form, i.e. corundum. Besides this well defined form, there exist several so-called `transition γ, κ, θ aluminas', whose structures are not yet well understood because they dO1 not yield single crystals suitable for a standard structure analysis (Lippens & de Boer, 1964; Olivier et al., 1997; Zhou & Snyder, 1991; Smrčok et al., 2001; Paglia et al., 2003). In as much as γ-alumina is widely used in catalysis, its structure and properties have been the subject of numerous studies. A review (Sohlberg et al., 2000) provides a good survey of experimental and computational approaches used tO1 study both bulk and surface structures of γ-alumina.

Since the early study of Verwey (1935), the structure of γ-alumina has been conventionally described as a defect spinel (Fd3m) with the idealized formula Al21 + 1/3□2 + 2/3O32, where □ denotes a vacancy. By accepting this formula, we implicitly assume that the oxygen sublattice (32e positions) is fully occupied, while Al ions and vacancies are distributed over octahedral (16d) and tetrahedral (8a) positions of the ideal spinel structure.

With the advent of more powerful computers, γ-alumina has soon become a subject of several computational studies. Among others, Gutiérrez et al. (2002) and Wolverton & Haas (2000) found that vacancies are preferably located in octahedral positions. Similarly, the lowest energy configuration found in a density functional theory (DFT) study of electronic and optic properties of γ-alumina (Ahuja et al., 2004) alsO1 contained vacancies on octahedral sites. Similar results, although obtained at a lower level of theory (empirical potentials), were reported by Watson & Willock (2001). Vacancies residing at octahedral sites were alsO1 found in a solid-state DFT study of γ-aluminium oxynitride (Fang et al., 2001). In contrast, Pecharromán et al. (1999) provided evidence of vacancies located in tetrahedral positions through NMR and IR experiments. In addition, they identified a small number of pentahedrally coordinated Al atoms appearing at the external surface of alumina. Enumerating all the approaches used tO1 study vacancy distribution in `transition' aluminas is beyond the scope of this paper and the reader is referred tO1 the critical review by Wolverton & Haas (2000).

A standard route tO1 γ-alumina is the thermal decomposition of boehmite, yielding a fine powder whose diffraction pattern is, as a rule, influenced by disorder, size/strain effects, etc. These factors normally preclude a reliable structure solution and/or refinement (Paglia, 2004; Paglia et al., 2003, 2005, and references therein). In our case, γ-alumina whiskers appeared as an unexpected product of a corrosion reaction between β-sialon and steel. Refined occupancy parameters indicate that, in addition tO1 the ideal spinel positions, the Al ions alsO1 occupy `non-spinel' 48f (tetrahedral) and 16c (octahedral) positions. Such a cation distribution is in accord with the results of a recent computational study (Paglia et al., 2005). The Al—O1 distances are 6 × 1.9326 (8) Å, 6 × 2.0394 (8) Å, 4 × 1.8112 (14) Å, and 2 × 1.700 (12) Å and 2 × 1.743 (10) Å for Al atoms in special positions 16d, 16c, 8a and 48f, respectively. These values are in reasonable agreement with the reference values of 1.785 Å for AlIV—O1 and 1.910 Å for AlVI—O (International Tables for Crystallography, 1962, Vol. III). An attempt was alsO1 made tO1 refine the occupancy parameter of the oxygen site but the final value was not statisticaly different from unity.

Of all Al ions, approximately 37% reside in tetrahedral positions. A review of the reported distributions of Al ions in tetrahedral positions (Sohlberg et al., 1999) shows that the closest is 30% found in an 27Al MAS NMR study (Lee et al., 1997). The difference can be probably attributed to the different methods of preparation. Approximately 6% of Al ions reside in non-spinel positions.

Experimental top

A mixture of β-sialon and steel was prepared by homogenization of β-sialon powder and 20 wt% of steel sawdust in a planetary ball mill. Heating tO1 1973 K initiated solid-state reactions leading tO1 the formation of several iron silicides and whiskers of γ-alumina (Křesťan et al., 2006).

Refinement top

An initial refinement with Al and O1 in ideal spinel positions converged smoothly with, however, residual electron density in octahedral 16d and `tetrahedral' 48f positions. An unconstrained refinement with Al atoms present in these positions gave a unit-cell content of 21.4 A l atoms per 32 O atoms, breaking electroneutrality. A final refinement with constrained total Al occupancies of 21.3 was then carried out.

Computing details top

Data collection: SMART (Bruker, 2003); cell refinement: SAINT (Bruker, 2003); data reduction: SAINT and SADABS (Sheldrick, 2003); program(s) used to solve structure: SHELXTL (Bruker, 2001); program(s) used to refine structure: SHELXTL; molecular graphics: none; software used to prepare material for publication: PLATON (Spek, 2003).

(I) top
Crystal data top
Al2.67O4Dx = 3.610 Mg m3
Mr = 135.94Mo Kα radiation, λ = 0.71073 Å
CubicFd3mCell parameters from 2395 reflections
Hall symbol: -F 4vw 2vw 3θ = 4.5–45.2°
a = 7.9382 (1) ŵ = 1.18 mm1
V = 500.23 (1) Å3T = 173 K
Z = 8Needle, colourless
F(000) = 5330.58 × 0.06 × 0.06 mm
Data collection top
Bruker SMART CCD area-detector
diffractometer
129 independent reflections
Radiation source: fine-focus sealed tube119 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.021
ω scansθmax = 45.2°, θmin = 4.5°
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)
h = 1514
Tmin = 0.547, Tmax = 0.932k = 1515
4211 measured reflectionsl = 1514
Refinement top
Refinement on F21 restraint
Least-squares matrix: fullPrimary atom site location: structure-invariant direct methods
R[F2 > 2σ(F2)] = 0.027Secondary atom site location: difference Fourier map
wR(F2) = 0.100 w = 1/[σ2(Fo2) + (0.0726P)2 + 1.4303P]
where P = (Fo2 + 2Fc2)/3
S = 0.98(Δ/σ)max = 0.012
129 reflectionsΔρmax = 0.42 e Å3
17 parametersΔρmin = 0.58 e Å3
Crystal data top
Al2.67O4Z = 8
Mr = 135.94Mo Kα radiation
CubicFd3mµ = 1.18 mm1
a = 7.9382 (1) ÅT = 173 K
V = 500.23 (1) Å30.58 × 0.06 × 0.06 mm
Data collection top
Bruker SMART CCD area-detector
diffractometer
129 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)
119 reflections with I > 2σ(I)
Tmin = 0.547, Tmax = 0.932Rint = 0.021
4211 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.02717 parameters
wR(F2) = 0.1001 restraint
S = 0.98Δρmax = 0.42 e Å3
129 reflectionsΔρmin = 0.58 e Å3
Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between twO1 l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken intO1 account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set tO1 zerO1 for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant tO1 the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Al10.12500.12500.12500.0062 (3)0.8633 (5)
Al20.50000.50000.50000.0092 (3)0.816 (5)
O10.25673 (10)0.25673 (10)0.25673 (10)0.0111 (3)
Al30.00000.00000.00000.009 (6)0.028 (5)
Al40.123 (3)0.12500.12500.006 (5)0.019 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Al10.0062 (3)0.0062 (3)0.0062 (3)0.0000.0000.000
Al20.0092 (3)0.0092 (3)0.0092 (3)0.00008 (12)0.00008 (12)0.00008 (12)
O10.0111 (3)0.0111 (3)0.0111 (3)0.00055 (16)0.00055 (16)0.00055 (16)
Al30.009 (6)0.009 (6)0.009 (6)0.001 (3)0.001 (3)0.001 (3)
Al40.005 (7)0.006 (6)0.006 (6)0.0000.0000.003 (5)
Geometric parameters (Å, º) top
Al1—Al3i1.7187O1—Al4iv1.743 (10)
Al1—Al3ii1.7187O1—Al4vi1.743 (10)
Al1—Al31.7187O1—Al2xviii1.9325 (8)
Al1—Al3iii1.7187O1—Al2xvi1.9326 (8)
Al1—O1iii1.8112 (14)O1—Al2xvii1.9326 (8)
Al1—O1ii1.8112 (14)O1—Al3ii2.0394 (8)
Al1—O1i1.8112 (14)O1—Al3i2.0394 (8)
Al1—O11.8113 (14)Al3—Al4v1.710 (12)
Al1—Al4ii1.97 (2)Al3—Al4xxii1.710 (12)
Al1—Al4iv1.97 (2)Al3—Al4xxiii1.710 (12)
Al1—Al4v1.97 (2)Al3—Al41.710 (12)
Al1—Al4vi1.97 (2)Al3—Al4xxiv1.710 (12)
Al2—Al4vii1.728 (12)Al3—Al4xxv1.710 (12)
Al2—Al4viii1.728 (12)Al3—Al1xxiii1.7187
Al2—Al4ix1.728 (12)Al3—O1iii2.0394 (8)
Al2—Al4x1.728 (12)Al3—O1xxvi2.0394 (8)
Al2—Al4xi1.728 (12)Al3—O1xxvii2.0394 (8)
Al2—Al4xii1.728 (12)Al3—O1ii2.0394 (8)
Al2—O1xiii1.9326 (8)Al4—Al3iii1.710 (12)
Al2—O1xiv1.9326 (8)Al4—O1xxviii1.700 (12)
Al2—O1xv1.9326 (8)Al4—O1xxi1.700 (12)
Al2—O1xvi1.9326 (8)Al4—Al2xxix1.728 (12)
Al2—O1xvii1.9326 (8)Al4—Al2xxx1.728 (12)
Al2—O1xviii1.9326 (8)Al4—O1i1.743 (10)
O1—Al4xix1.700 (12)Al4—O1ii1.743 (10)
O1—Al4xx1.700 (12)Al4—Al4xxxi1.9847 (3)
O1—Al4xxi1.700 (12)Al4—Al4xxiv1.9847 (3)
O1—Al4ii1.743 (10)Al4—Al4xxxii1.9847 (3)
Al3i—Al1—Al3ii109.5Al4vi—O1—Al2xvi126.7 (2)
Al3i—Al1—Al3109.5Al1—O1—Al2xvi123.02 (3)
Al3ii—Al1—Al3109.5Al2xviii—O1—Al2xvi93.13 (5)
Al3i—Al1—Al3iii109.5Al4xix—O1—Al2xvii56.4 (3)
Al3ii—Al1—Al3iii109.5Al4xx—O1—Al2xvii130.9 (6)
Al3—Al1—Al3iii109.5Al4xxi—O1—Al2xvii56.4 (3)
Al3i—Al1—O1iii70.5Al4ii—O1—Al2xvii126.7 (2)
Al3ii—Al1—O1iii70.5Al4iv—O1—Al2xvii126.7 (2)
Al3—Al1—O1iii70.5Al4vi—O1—Al2xvii55.8 (6)
Al3iii—Al1—O1iii180.00 (2)Al1—O1—Al2xvii123.02 (3)
Al3i—Al1—O1ii70.5Al2xviii—O1—Al2xvii93.13 (5)
Al3ii—Al1—O1ii180.00 (2)Al2xvi—O1—Al2xvii93.13 (5)
Al3—Al1—O1ii70.529 (1)Al4xix—O1—Al3ii53.5 (5)
Al3iii—Al1—O1ii70.5Al4xx—O1—Al3ii123.4 (3)
O1iii—Al1—O1ii109.5Al4xxi—O1—Al3ii123.4 (3)
Al3i—Al1—O1i180.00 (2)Al4ii—O1—Al3ii53.0 (3)
Al3ii—Al1—O1i70.5Al4iv—O1—Al3ii119.8 (6)
Al3—Al1—O1i70.5Al4vi—O1—Al3ii53.0 (3)
Al3iii—Al1—O1i70.5Al1—O1—Al3ii52.61 (3)
O1iii—Al1—O1i109.5Al2xviii—O1—Al3ii89.876 (4)
O1ii—Al1—O1i109.470 (1)Al2xvi—O1—Al3ii175.63 (7)
Al3i—Al1—O170.5Al2xvii—O1—Al3ii89.875 (4)
Al3ii—Al1—O170.5Al4xix—O1—Al3i123.4 (3)
Al3—Al1—O1180.00 (2)Al4xx—O1—Al3i53.5 (5)
Al3iii—Al1—O170.5Al4xxi—O1—Al3i123.4 (3)
O1iii—Al1—O1109.5Al4ii—O1—Al3i53.0 (3)
O1ii—Al1—O1109.471 (1)Al4iv—O1—Al3i53.0 (3)
O1i—Al1—O1109.471 (1)Al4vi—O1—Al3i119.8 (6)
Al3i—Al1—Al4ii54.736 (1)Al1—O1—Al3i52.61 (3)
Al3ii—Al1—Al4ii54.736 (1)Al2xviii—O1—Al3i89.876 (4)
Al3—Al1—Al4ii125.3Al2xvi—O1—Al3i89.875 (4)
Al3iii—Al1—Al4ii125.265 (1)Al2xvii—O1—Al3i175.63 (7)
O1iii—Al1—Al4ii54.7Al3ii—O1—Al3i86.96 (5)
O1ii—Al1—Al4ii125.3Al4v—Al3—Al4xxii109.0 (6)
O1i—Al1—Al4ii125.265 (1)Al4v—Al3—Al4xxiii71.0 (6)
O1—Al1—Al4ii54.736 (1)Al4xxii—Al3—Al4xxiii71.0 (6)
Al3i—Al1—Al4iv54.7Al4v—Al3—Al4109.0 (6)
Al3ii—Al1—Al4iv125.265 (1)Al4xxii—Al3—Al4109.0 (6)
Al3—Al1—Al4iv125.264 (1)Al4xxiii—Al3—Al4179.999 (1)
Al3iii—Al1—Al4iv54.7Al4v—Al3—Al4xxiv180.0
O1iii—Al1—Al4iv125.3Al4xxii—Al3—Al4xxiv71.0 (6)
O1ii—Al1—Al4iv54.7Al4xxiii—Al3—Al4xxiv109.0 (6)
O1i—Al1—Al4iv125.264 (1)Al4—Al3—Al4xxiv71.0 (6)
O1—Al1—Al4iv54.736 (1)Al4v—Al3—Al4xxv71.0 (6)
Al4ii—Al1—Al4iv90.0Al4xxii—Al3—Al4xxv179.999 (1)
Al3i—Al1—Al4v125.3Al4xxiii—Al3—Al4xxv109.0 (6)
Al3ii—Al1—Al4v54.736 (1)Al4—Al3—Al4xxv71.0 (6)
Al3—Al1—Al4v54.7Al4xxiv—Al3—Al4xxv109.0 (6)
Al3iii—Al1—Al4v125.264 (1)Al4v—Al3—Al170.1 (6)
O1iii—Al1—Al4v54.736 (1)Al4xxii—Al3—Al170.1 (6)
O1ii—Al1—Al4v125.264 (1)Al4xxiii—Al3—Al1109.9 (6)
O1i—Al1—Al4v54.7Al4—Al3—Al170.1 (6)
O1—Al1—Al4v125.265 (1)Al4xxiv—Al3—Al1109.9 (6)
Al4ii—Al1—Al4v90.0Al4xxv—Al3—Al1109.9 (6)
Al4iv—Al1—Al4v180.0Al4v—Al3—Al1xxiii109.9 (6)
Al3i—Al1—Al4vi125.265 (1)Al4xxii—Al3—Al1xxiii109.9 (6)
Al3ii—Al1—Al4vi54.7Al4xxiii—Al3—Al1xxiii70.1 (6)
Al3—Al1—Al4vi125.3Al4—Al3—Al1xxiii109.9 (6)
Al3iii—Al1—Al4vi54.7Al4xxiv—Al3—Al1xxiii70.1 (6)
O1iii—Al1—Al4vi125.265 (1)Al4xxv—Al3—Al1xxiii70.1 (6)
O1ii—Al1—Al4vi125.264 (1)Al1—Al3—Al1xxiii180.0
O1i—Al1—Al4vi54.7Al4v—Al3—O1iii54.6 (3)
O1—Al1—Al4vi54.736 (1)Al4xxii—Al3—O1iii54.6 (3)
Al4ii—Al1—Al4vi90.001 (1)Al4xxiii—Al3—O1iii53.0 (5)
Al4iv—Al1—Al4vi90.000 (1)Al4—Al3—O1iii127.0 (5)
Al4v—Al1—Al4vi90.0Al4xxiv—Al3—O1iii125.4 (3)
Al4vii—Al2—Al4viii70.1 (5)Al4xxv—Al3—O1iii125.4 (3)
Al4vii—Al2—Al4ix70.1 (5)Al1—Al3—O1iii56.86 (3)
Al4viii—Al2—Al4ix109.9 (5)Al1xxiii—Al3—O1iii123.14 (3)
Al4vii—Al2—Al4x109.9 (5)Al4v—Al3—O1xxvi125.4 (3)
Al4viii—Al2—Al4x179.999 (1)Al4xxii—Al3—O1xxvi53.0 (5)
Al4ix—Al2—Al4x70.1 (5)Al4xxiii—Al3—O1xxvi54.6 (3)
Al4vii—Al2—Al4xi109.9 (5)Al4—Al3—O1xxvi125.4 (3)
Al4viii—Al2—Al4xi70.1 (5)Al4xxiv—Al3—O1xxvi54.6 (3)
Al4ix—Al2—Al4xi179.999 (1)Al4xxv—Al3—O1xxvi127.0 (5)
Al4x—Al2—Al4xi109.9 (5)Al1—Al3—O1xxvi123.14 (3)
Al4vii—Al2—Al4xii179.999 (3)Al1xxiii—Al3—O1xxvi56.86 (3)
Al4viii—Al2—Al4xii109.9 (5)O1iii—Al3—O1xxvi87.04 (4)
Al4ix—Al2—Al4xii109.9 (5)Al4v—Al3—O1xxvii53.0 (5)
Al4x—Al2—Al4xii70.1 (5)Al4xxii—Al3—O1xxvii125.4 (3)
Al4xi—Al2—Al4xii70.1 (5)Al4xxiii—Al3—O1xxvii54.6 (3)
Al4vii—Al2—O1xiii56.6 (5)Al4—Al3—O1xxvii125.4 (3)
Al4viii—Al2—O1xiii55.0 (3)Al4xxiv—Al3—O1xxvii127.0 (5)
Al4ix—Al2—O1xiii55.0 (3)Al4xxv—Al3—O1xxvii54.6 (3)
Al4x—Al2—O1xiii125.0 (3)Al1—Al3—O1xxvii123.14 (3)
Al4xi—Al2—O1xiii125.0 (3)Al1xxiii—Al3—O1xxvii56.86 (3)
Al4xii—Al2—O1xiii123.4 (5)O1iii—Al3—O1xxvii87.04 (4)
Al4vii—Al2—O1xiv125.0 (3)O1xxvi—Al3—O1xxvii92.96 (4)
Al4viii—Al2—O1xiv55.0 (3)Al4v—Al3—O1ii127.0 (5)
Al4ix—Al2—O1xiv123.4 (5)Al4xxii—Al3—O1ii54.6 (3)
Al4x—Al2—O1xiv125.0 (3)Al4xxiii—Al3—O1ii125.4 (3)
Al4xi—Al2—O1xiv56.6 (5)Al4—Al3—O1ii54.6 (3)
Al4xii—Al2—O1xiv55.0 (3)Al4xxiv—Al3—O1ii53.0 (5)
O1xiii—Al2—O1xiv86.79 (5)Al4xxv—Al3—O1ii125.4 (3)
Al4vii—Al2—O1xv125.0 (3)Al1—Al3—O1ii56.86 (3)
Al4viii—Al2—O1xv123.4 (5)Al1xxiii—Al3—O1ii123.14 (3)
Al4ix—Al2—O1xv55.0 (3)O1iii—Al3—O1ii92.96 (4)
Al4x—Al2—O1xv56.6 (5)O1xxvi—Al3—O1ii87.04 (4)
Al4xi—Al2—O1xv125.0 (3)O1xxvii—Al3—O1ii180.00 (4)
Al4xii—Al2—O1xv55.0 (3)Al3iii—Al4—Al3110.3 (11)
O1xiii—Al2—O1xv86.79 (5)Al3iii—Al4—O1xxviii176.2 (11)
O1xiv—Al2—O1xv86.79 (5)Al3—Al4—O1xxviii73.48 (4)
Al4vii—Al2—O1xvi55.0 (3)Al3iii—Al4—O1xxi73.47 (4)
Al4viii—Al2—O1xvi56.6 (5)Al3—Al4—O1xxi176.2 (11)
Al4ix—Al2—O1xvi125.0 (3)O1xxviii—Al4—O1xxi102.7 (11)
Al4x—Al2—O1xvi123.4 (5)Al3iii—Al4—Al2xxix109.466 (15)
Al4xi—Al2—O1xvi55.0 (3)Al3—Al4—Al2xxix109.466 (16)
Al4xii—Al2—O1xvi125.0 (3)O1xxviii—Al4—Al2xxix68.6 (6)
O1xiii—Al2—O1xvi93.21 (5)O1xxi—Al4—Al2xxix68.6 (6)
O1xiv—Al2—O1xvi93.21 (5)Al3iii—Al4—Al2xxx109.466 (15)
O1xv—Al2—O1xvi180.0Al3—Al4—Al2xxx109.466 (16)
Al4vii—Al2—O1xvii55.0 (3)O1xxviii—Al4—Al2xxx68.6 (6)
Al4viii—Al2—O1xvii125.0 (3)O1xxi—Al4—Al2xxx68.6 (6)
Al4ix—Al2—O1xvii56.6 (5)Al2xxix—Al4—Al2xxx108.6 (11)
Al4x—Al2—O1xvii55.0 (3)Al3iii—Al4—O1i72.4 (5)
Al4xi—Al2—O1xvii123.4 (5)Al3—Al4—O1i72.4 (5)
Al4xii—Al2—O1xvii125.0 (3)O1xxviii—Al4—O1i109.31 (9)
O1xiii—Al2—O1xvii93.21 (5)O1xxi—Al4—O1i109.31 (9)
O1xiv—Al2—O1xvii180.0Al2xxix—Al4—O1i176.3 (11)
O1xv—Al2—O1xvii93.21 (5)Al2xxx—Al4—O1i67.66 (5)
O1xvi—Al2—O1xvii86.79 (5)Al3iii—Al4—O1ii72.4 (5)
Al4vii—Al2—O1xviii123.4 (5)Al3—Al4—O1ii72.4 (5)
Al4viii—Al2—O1xviii125.0 (3)O1xxviii—Al4—O1ii109.31 (9)
Al4ix—Al2—O1xviii125.0 (3)O1xxi—Al4—O1ii109.31 (9)
Al4x—Al2—O1xviii55.0 (3)Al2xxix—Al4—O1ii67.66 (5)
Al4xi—Al2—O1xviii55.0 (3)Al2xxx—Al4—O1ii176.3 (11)
Al4xii—Al2—O1xviii56.6 (5)O1i—Al4—O1ii116.1 (12)
O1xiii—Al2—O1xviii180.0Al3iii—Al4—Al155.2 (6)
O1xiv—Al2—O1xviii93.21 (5)Al3—Al4—Al155.2 (6)
O1xv—Al2—O1xviii93.21 (5)O1xxviii—Al4—Al1128.6 (6)
O1xvi—Al2—O1xviii86.79 (5)O1xxi—Al4—Al1128.6 (6)
O1xvii—Al2—O1xviii86.79 (5)Al2xxix—Al4—Al1125.7 (5)
Al4xix—O1—Al4xx112.6 (5)Al2xxx—Al4—Al1125.7 (5)
Al4xix—O1—Al4xxi112.6 (5)O1i—Al4—Al158.0 (6)
Al4xx—O1—Al4xxi112.6 (5)O1ii—Al4—Al158.0 (6)
Al4xix—O1—Al4ii70.38 (2)Al3iii—Al4—Al4xxxi54.5 (3)
Al4xx—O1—Al4ii70.38 (2)Al3—Al4—Al4xxxi126.1 (11)
Al4xxi—O1—Al4ii173.3 (11)O1xxviii—Al4—Al4xxxi123.5 (4)
Al4xix—O1—Al4iv173.3 (11)O1xxi—Al4—Al4xxxi55.8 (5)
Al4xx—O1—Al4iv70.38 (2)Al2xxix—Al4—Al4xxxi124.4 (11)
Al4xxi—O1—Al4iv70.38 (2)Al2xxx—Al4—Al4xxxi54.9 (3)
Al4ii—O1—Al4iv106.0 (6)O1i—Al4—Al4xxxi53.8 (6)
Al4xix—O1—Al4vi70.38 (2)O1ii—Al4—Al4xxxi126.8 (2)
Al4xx—O1—Al4vi173.3 (11)Al1—Al4—Al4xxxi90.5 (6)
Al4xxi—O1—Al4vi70.38 (2)Al3iii—Al4—Al4xxiv126.1 (11)
Al4ii—O1—Al4vi106.0 (6)Al3—Al4—Al4xxiv54.5 (3)
Al4iv—O1—Al4vi106.0 (6)O1xxviii—Al4—Al4xxiv55.8 (5)
Al4xix—O1—Al1106.1 (6)O1xxi—Al4—Al4xxiv123.5 (4)
Al4xx—O1—Al1106.1 (6)Al2xxix—Al4—Al4xxiv54.9 (3)
Al4xxi—O1—Al1106.1 (6)Al2xxx—Al4—Al4xxiv124.4 (11)
Al4ii—O1—Al167.2 (6)O1i—Al4—Al4xxiv126.8 (2)
Al4iv—O1—Al167.2 (6)O1ii—Al4—Al4xxiv53.8 (6)
Al4vi—O1—Al167.2 (6)Al1—Al4—Al4xxiv90.5 (6)
Al4xix—O1—Al2xviii56.4 (3)Al4xxxi—Al4—Al4xxiv179.1 (12)
Al4xx—O1—Al2xviii56.4 (3)Al3iii—Al4—Al4xxxii54.5 (3)
Al4xxi—O1—Al2xviii130.9 (6)Al3—Al4—Al4xxxii126.1 (11)
Al4ii—O1—Al2xviii55.8 (6)O1xxviii—Al4—Al4xxxii123.5 (4)
Al4iv—O1—Al2xviii126.7 (2)O1xxi—Al4—Al4xxxii55.8 (5)
Al4vi—O1—Al2xviii126.7 (2)Al2xxix—Al4—Al4xxxii54.9 (3)
Al1—O1—Al2xviii123.02 (3)Al2xxx—Al4—Al4xxxii124.4 (11)
Al4xix—O1—Al2xvi130.9 (6)O1i—Al4—Al4xxxii126.8 (2)
Al4xx—O1—Al2xvi56.4 (3)O1ii—Al4—Al4xxxii53.8 (6)
Al4xxi—O1—Al2xvi56.4 (3)Al1—Al4—Al4xxxii90.5 (6)
Al4ii—O1—Al2xvi126.7 (2)Al4xxxi—Al4—Al4xxxii89.1 (12)
Al4iv—O1—Al2xvi55.8 (6)Al4xxiv—Al4—Al4xxxii90.9 (12)
Symmetry codes: (i) x+1/4, y, z+1/4; (ii) x+1/4, y+1/4, z; (iii) x, y+1/4, z+1/4; (iv) y+1/4, z, x+1/4; (v) y, z, x; (vi) z, x+1/4, y+1/4; (vii) x+3/4, y+1/4, z+1/2; (viii) y+3/4, z+1/2, x+1/4; (ix) z+1/2, x+1/4, y+3/4; (x) y+1/4, z+1/2, x+3/4; (xi) z+1/2, x+3/4, y+1/4; (xii) x+1/4, y+3/4, z+1/2; (xiii) x+1, y+1/4, z+1/4; (xiv) x+1/4, y+1, z+1/4; (xv) x+1/4, y+1/4, z+1; (xvi) x+3/4, y+3/4, z; (xvii) x+3/4, y, z+3/4; (xviii) x, y+3/4, z+3/4; (xix) y+1/2, z+1/2, x; (xx) z+1/2, x, y+1/2; (xxi) x, y+1/2, z+1/2; (xxii) z, x, y; (xxiii) x, y, z; (xxiv) y, z, x; (xxv) z, x, y; (xxvi) x1/4, y, z1/4; (xxvii) x1/4, y1/4, z; (xxviii) x, y1/4, z1/4; (xxix) x+1/4, y1/2, z+3/4; (xxx) x+1/4, y+3/4, z1/2; (xxxi) y1/4, z+1/2, x+1/4; (xxxii) z, x+1/4, y+1/4.

Experimental details

Crystal data
Chemical formulaAl2.67O4
Mr135.94
Crystal system, space groupCubicFd3m
Temperature (K)173
a (Å)7.9382 (1)
V3)500.23 (1)
Z8
Radiation typeMo Kα
µ (mm1)1.18
Crystal size (mm)0.58 × 0.06 × 0.06
Data collection
DiffractometerBruker SMART CCD area-detector
diffractometer
Absorption correctionMulti-scan
(SADABS; Sheldrick, 2003)
Tmin, Tmax0.547, 0.932
No. of measured, independent and
observed [I > 2σ(I)] reflections
4211, 129, 119
Rint0.021
(sin θ/λ)max1)0.998
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.027, 0.100, 0.98
No. of reflections129
No. of parameters17
No. of restraints1
Δρmax, Δρmin (e Å3)0.42, 0.58

Computer programs: SMART (Bruker, 2003), SAINT (Bruker, 2003), SAINT and SADABS (Sheldrick, 2003), SHELXTL (Bruker, 2001), SHELXTL, none, PLATON (Spek, 2003).

 

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