Crystal structure of Cr-bearing Mg3BeAl8O16, a new polytype of magnesiotaaffeite-2N′2S

Malcherek, T.; Schlüter, J.

doi:10.1107/S2056989016010215

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Volume 72| Part 7| July 2016| Pages 1060-1063

https://doi.org/10.1107/S2056989016010215

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Crystal structure of Cr-bearing Mg₃BeAl₈O₁₆, a new polytype of magnesiotaaffeite-2N′2S

Thomas Malcherek ^a ^* and Jochen Schlüter ^b

^aMineralogisch-Petrographisches Institut, Universität Hamburg, Grindelallee 48, 20146 Hamburg, Germany, and ^bCentrum für Naturkunde (CeNak), Mineralogisches Museum, Universität Hamburg, Grindelallee 48, 20146 Hamburg, Germany
^*Correspondence e-mail: thomas.malcherek@uni-hamburg.de

Edited by M. Weil, Vienna University of Technology, Austria (Received 25 May 2016; accepted 22 June 2016; online 28 June 2016)

The crystal structure of a new polytype of magnesiotaaffeite-2N′2S, ideally Mg₃BeAl₈O₁₆ (trimagnesium beryllium octaaluminium hexadecaoxide), is described in space-group symmetry P-3m1. It has been identified in a fragment of a mineral sample from Burma (Myanmar). The new polytype is composed of two Mg₂Al₄O₈ (S)- and two BeMgAl₄O₈ (N′)-modules in a stacking sequence N′SSN′′ which differs from the N′SN′S-stacking sequence of the known magnesiotaaffeite-2N′2S polytype. The crystal structure can be derived from a close-packed arrangement of O atoms and is discussed with regard to its polytypism and its Cr³⁺ chromophore content.

Keywords: crystal structure; magnesiotaaffeite; gemstones; polytypism; polysomatism; modular structure.

CCDC reference: 1487140

1. Mineralogical and crystal-chemical context

The minerals of the taaffeite group form a polysomatic series, composed of spinel (S) and nolanite (N′) modules (Armbruster, 2002 ). The nolanite modules in the taaffeites are modified with respect to the nolanite, (V,Fe)₅O₇(OH), crystal structure (Gatehouse et al., 1983 ), such that Be nominally substitutes for the hydrogen atoms of the nolanite OH group, while Mg and Al replace V and Fe, respectively. Variable numbers of the S-modules, Mg₂Al₄O₈, and of the N′-modules, BeMgAl₄O₈, combine to yield different compositions of taaffeite minerals, i.e. different polysomes. Magnesiotaaffeite-2N′2S is composed of two modified nolanite modules N′ and two spinel modules S, yielding an idealized composition of Mg₃BeAl₈O₁₆. Be-doping of MgAl₂O₄ has been shown to cause growth of twinned spinel crystals as a precursor to the formation of magnesiotaaffeite polytypes (Drev et al., 2013 ).

Here we report the crystal structure of a new polytype of magnesiotaaffeite, magnesiotaaffeite-2N′2S₂ which differs from the known magnesiotaaffeite-2N′2S (Nuber & Schmetzer, 1983 ) by the module stacking sequence. The resulting space group symmetry is P-3m1, as opposed to the P6₃mc symmetry of the previously known polytype.

2. Structural commentary

The crystal structure of the title compound is shown in Fig. 1. It can be described by the stacking of close-packed oxygen layers along [001], with layers of cations filling the interstices. Following the layer nomenclature of Nuber & Schmetzer (1983), the ^[6]Al1, ^[6]Al3 and ^[6]Al4 cations can be attributed to O-layers, the ^[6]Al5, ^[4]Mg1 and ^[4]Mg2 cations to T₂-layers and the ^[4]Be,^[4]Al2 and ^[6]Mg3 cations to T₁-layers. The cation stacking sequence is then T₁-O-T₂-O-T₂-O-T₁′-⋯ while the anion stacking sequence is BACBACBC⋯. The orientation of T₁′ is upside down with respect to T₁. In the polytype described by Nuber & Schmetzer (1983), the stacking sequence is T₁-O-T₂-O-T₁-O-T₂-O-⋯ and BCABCBAC⋯ by comparison. In terms of polysomatism, the N′ layer is composed of one T₁ and one O-layer. The second nolanite layer, N′′, is also composed of these layer types, but its T₁ layer is inverted with respect to the stacking direction. The S-layer is composed of one O-layer and one T₂-layer. Stacking these modules in the order N′-S-S-N′′-N′-⋯ generates the new polytype structure (Fig. 1). The stacking sequence of the known magnesiotaaffeite-2N′2S polytype is N′-S-N′-S- ⋯.

Figure 1
Polyhedral plot of magnesiotaaffeite-2N′2S₂ viewed down [010] with cation site nomenclature and coordination numbers given to the right. Module sequence is N′–S–S–N′′–N′ from bottom to top, with boundaries indicated by horizontal lines. Displacement ellipsoids are drawn at the 99% probability level. Mg atoms are shown in yellow, Al in blue, Be in green and O in red.

The composition obtained by structure refinement is in good agreement with the composition obtained by electron microprobe analysis (EMPA). The calculated bond-valence sums agree reasonably well with the formal charges (Table 1), and on average they support the assumption that Cr is trivalent. Significant amounts of Cr³⁺ are found at the octahedrally coordinated Al3 and Al4-sites, where Cr³⁺ is overbonded, as well as at the tetrahedrally coordinated Mg1 and Mg2 sites, where Cr³⁺ is underbonded. Cr³⁺ in tetrahedral coordination is unusual, but has recently been reported for the brownmillerite-type compound Ca₂Cr₂O₅ (Arevalo-Lopez & Attfield, 2015 ) and for Cr-doped BaAl₂O₄ (Vrankić et al., 2015 ). However, without further confirmation by other methods, the appearance of tetrahedrally coordinated Cr³⁺ in the title compound should be treated with caution. The tetrahedral Mg1 coordination, with one Mg1—O6 distance of 1.9537 (12) Å and three Mg1—O4 distances of 1.9296 (7) Å is more distorted than the Mg2 coordination environment, where the longer Mg2—O1 distance [1.9361 (13) Å] hardly differs from the three 1.9300 (7) Å Mg2—O5 distances. The average bond lengths at the tetrahedral sites, nominally occupied by Mg (Mg1 1.936 Å, Mg2 1.932 Å), and at the octahedral sites, nominally occupied by Al (Al1 1.909 Å, Al3 1.916 Å, Al4 1.913 Å, Al5 1.909 Å), are similar to the T-O (1.936 Å) and M-O (1.923 Å) distances reported for a natural Cr and V-bearing spinel from Burma with a small inversion parameter (Widmer et al., 2015 ). This indicates that the degree of Mg, Al disorder is equally low in the title compound. The Al2 site is at the center of a nearly regular oxygen tetrahedron with an average Al—O distance of 1.785 Å. Al³⁺ is slightly underbonded at this site (Table 1), which might indicate admixture of Mg atoms. The slightly overbonded Mg2 site might accommodate the resulting Al-excess. The Be²⁺ cation forms one short bond with O7 [1.602 (2) Å] and three longer bonds [1.6615 (13) Å] with the O3-anions, while the tetrahedral angles are either 97.89 (9)° (O3—Be1—O3) or 119.45 (7)° (O7—Be1—O3). The Mg atom in the Mg3O₆-octahedron exhibits a strong out-of-centre distortion, away from the Al3-cation, to which it has a distance of only 3.0580 (7) Å.

Table 1
Bond-valence sums (BVS)

Calculated using JANA2006 (Petřìček et al., 2014 ) with bond-valence parameters taken from Brese & O'Keeffe (1991 ). Angular brackets indicate site-occupancy weighted averages for the corresponding Mab sites.

Site	BVS
Be1	1.956 (5)
Al1	3.007 (2)
Al2	2.788 (3)
Al3a	2.932 (2)
Cr3b	3.571 (3)
<M3ab>	2.943
Al4a	2.955 (2)
Cr4b	3.599 (3)
<M4ab>	2.966
Al5	2.991 (2)
Mg1a	2.077 (2)
Cr1b	2.259 (2)
<M1ab>	2.082
Mg2a	2.099 (3)
Cr2b	2.283 (3)
<M2ab>	2.108
Mg3	1.974 (2)
O1	2.006 (2)
O2	1.991 (3)
O3	1.962 (2)
O4	2.009 (2)
O5	2.008 (2)
O6	2.045 (2)
O7	1.993 (4)
O8	1.906 (2)

Rotation of the refined crystal structure by 60° about [001] brings the bottom O-layer (Fig. 1) into the same orientation as the third O-layer of the unrotated structure. Thus a correspondingly rotated twin domain of the polytype structure can form a strain free boundary after the first S-layer of the module sequence as shown in Fig. 1. At the twin boundary this results in a module sequence N′-S-N′-S, corresponding to the previously described polytype.

3. Sample details and EMPA

The studied natural sample of magnesiotaaffeite (m = 0.95 g) originates from Chaung-gyi, Mogok, Pyin-Oo-Lwin district, Burma (Myanmar). It has a red colour and a layered appearance (Fig. 2). A small fragment of the original sample was examined using single crystal X-ray diffraction. The same crystal fragment was subsequently prepared for electron microprobe analysis (EMPA) using a Cameca SX100 electron microprobe, operating in wavelength-dispersion mode at 15 kV and 20 nA. Standards were MgO, Al₂O₃ and Cr₂O₃. Based on 16 anions and the Be concentration from single-crystal X-ray structure refinement (1 Be), the empirical chemical formula was determined as Al_7.86Be_1.0Cr_0.19Mg_2.93O₁₆. The corresponding oxide composition (in wt%) is MgO 20.82, Cr₂O₃ 2.50, Al₂O₃ 70.72, BeO 4.41, yielding a total of 98.45%.

Figure 2
Magnesiotaaffeite sample, approximate size 1.0 × 0.9 × 0.8 cm. (Photograph courtesy of Daniela Braith, Munich.)

4. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 2. The results of the EMPA indicate that the magnesiotaaffeite crystal contains significant amounts of Cr. In order to accurately refine small Cr-site populations against the major constituent elements Al and Mg, intensities at small scattering angles were systematically weighted down by a factor of 1−exp[−5(sin θ/λ)²] in order to emphasize core electron contributions to the X-ray scattering. For that purpose, Cr and Mg or Al were constrained to have the same coordinates and displacement parameters under consideration of full occupancy for the corresponding site. Scattering factors for neutral atoms were used and all atoms were refined with anisotropic displacement parameters. No evidence for mixed occupancy was found at the Be site; small Cr amounts were found for the Al3, Al4, Mg1 and Mg2 sites with occupation factors for Cr of 0.017 (3), 0.017 (5), 0.028 (5) and 0.048 (5), respectively. Two twin domains (twinning by merohedry) with volume fractions of 0.64 and 0.36 contribute to the total scattering intensity, related by reflection parallel to [1 $[\overline{1}]$ 0] or, equivalently, by 60° rotation about [001].

Table 2
Experimental details

Crystal data
Chemical formula	Mg₃BeAl₈O₁₆
M_r	557.75
Crystal system, space group	Trigonal, P $[\overline{3}]$ m1
Temperature (K)	295
a, c (Å)	5.6788 (3), 18.3368 (14)
V (Å³)	512.11 (7)
Z	2
Radiation type	Mo Kα
μ (mm⁻¹)	1.25
Crystal size (mm)	0.23 × 0.22 × 0.10

Data collection
Diffractometer	Nonius KappaCCD
Absorption correction	Multi-scan (SADABS; Bruker, 2008 )
T_min, T_max	0.614, 0.747
No. of measured, independent and observed [I > 2σ(I)] reflections	10618, 940, 912
R_int	0.040
(sin θ/λ)_max (Å⁻¹)	0.807

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.018, 0.040, 0.83
No. of reflections	940
No. of parameters	75
Δρ_max, Δρ_min (e Å⁻³)	0.41, −1.01
Computer programs: COLLECT (Nonius, 1998 ), EVAL15/Peakref and EVAL15 (Schreurs et al., 2010 ), SUPERFLIP (Palatinus & Chapuis, 2007 ), SHELXL2014 (Sheldrick, 2015 ), VESTA (Momma & Izumi, 2011 ) and publCIF (Westrip, 2010 ).

Supporting information

CCDC reference: 1487140

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2056989016010215/wm5296sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989016010215/wm5296Isup2.hkl

checkCIF report

Computing details top

Data collection: COLLECT (Nonius, 1998); cell refinement: EVAL15/Peakref (Schreurs et al., 2010); data reduction: EVAL15 (Schreurs et al., 2010); program(s) used to solve structure: SUPERFLIP (Palatinus & Chapuis, 2007); program(s) used to refine structure: SHELXL2014 (Sheldrick, 2015); molecular graphics: VESTA (Momma & Izumi, 2011); software used to prepare material for publication: publCIF (Westrip, 2010).

Trimagnesium beryllium octaaluminium hexadecaoxide top

Crystal data top

Mg₃BeAl₈O₁₆	D_x = 3.617 Mg m⁻³
M_r = 557.75	Mo Kα radiation, λ = 0.71069 Å
Trigonal, P3m1	Cell parameters from 9717 reflections
a = 5.6788 (3) Å	θ = 2.2–35°
c = 18.3368 (14) Å	µ = 1.25 mm⁻¹
V = 512.11 (7) Å³	T = 295 K
Z = 2	Tabular, red
F(000) = 547	0.23 × 0.22 × 0.10 mm

Data collection top

Nonius KappaCCD diffractometer	940 independent reflections
Radiation source: fine-focus sealed X-ray tube	912 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.040
Detector resolution: 9 pixels mm^-1	θ_max = 35.0°, θ_min = 2.2°
φ scans, and ω scans with κ offsets	h = −8→9
Absorption correction: multi-scan (SADABS; Bruker, 2008)	k = −9→8
T_min = 0.614, T_max = 0.747	l = −29→29
10618 measured reflections

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	w = {1-exp[-5(sinθ/λ)²)]}/[σ²(F_o²) + (0.0296P)² + 0.031P] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.018	(Δ/σ)_max < 0.001
wR(F²) = 0.040	Δρ_max = 0.41 e Å⁻³
S = 0.83	Δρ_min = −1.01 e Å⁻³
940 reflections	Extinction correction: SHELXL2014 (Sheldrick, 2015), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
75 parameters	Extinction coefficient: 0.046 (3)

Special details top

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

Refinement. Refined as a 2-component twin

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Be1	0.3333	0.6667	0.10240 (12)	0.0054 (3)
Al1	0.5000	0.0000	0.0000	0.00335 (9)
Al2	0.6667	0.3333	0.15613 (3)	0.00344 (9)
Al3A	−0.33348 (5)	−0.16674 (3)	0.24468 (2)	0.00340 (11)	0.983 (3)
Cr3B	−0.33348 (5)	−0.16674 (3)	0.24468 (2)	0.00340 (11)	0.017 (3)
Al4A	0.5000	0.0000	0.5000	0.00331 (15)	0.983 (5)
Cr4B	0.5000	0.0000	0.5000	0.00331 (15)	0.017 (5)
Al5	0.3333	0.6667	0.37276 (3)	0.00293 (9)
Mg1A	0.0000	0.0000	0.40321 (3)	0.0040 (2)	0.972 (5)
Cr1B	0.0000	0.0000	0.40321 (3)	0.0040 (2)	0.028 (5)
Mg2A	0.6667	0.3333	0.34070 (3)	0.0041 (2)	0.952 (5)
Cr2B	0.6667	0.3333	0.34070 (3)	0.0041 (2)	0.048 (5)
Mg3	0.0000	0.0000	0.10393 (4)	0.00473 (11)
O1	0.6667	0.3333	0.44628 (7)	0.00471 (17)
O2	0.6667	0.3333	0.05925 (6)	0.00435 (18)
O3	−0.81376 (7)	−0.18624 (7)	0.05785 (4)	0.00439 (12)
O4	−0.81598 (7)	−0.18402 (7)	0.43966 (4)	0.00449 (12)
O5	−0.51854 (7)	−0.03709 (14)	0.30594 (3)	0.00497 (12)
O6	0.0000	0.0000	0.29666 (6)	0.00458 (18)
O7	0.3333	0.6667	0.18977 (6)	0.00459 (18)
O8	−0.16175 (6)	−0.83825 (6)	0.18822 (4)	0.00461 (11)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Be1	0.0056 (5)	0.0056 (5)	0.0050 (7)	0.0028 (2)	0.000	0.000
Al1	0.00339 (12)	0.00316 (15)	0.00343 (15)	0.00158 (7)	0.00049 (6)	0.00098 (11)
Al2	0.00375 (12)	0.00375 (12)	0.00281 (18)	0.00188 (6)	0.000	0.000
Al3A	0.00313 (13)	0.00356 (12)	0.00337 (14)	0.00157 (7)	0.00005 (8)	0.00003 (4)
Cr3B	0.00313 (13)	0.00356 (12)	0.00337 (14)	0.00157 (7)	0.00005 (8)	0.00003 (4)
Al4A	0.00349 (17)	0.00302 (19)	0.00326 (19)	0.00151 (10)	0.00000 (5)	0.00000 (11)
Cr4B	0.00349 (17)	0.00302 (19)	0.00326 (19)	0.00151 (10)	0.00000 (5)	0.00000 (11)
Al5	0.00329 (12)	0.00329 (12)	0.00220 (16)	0.00165 (6)	0.000	0.000
Mg1A	0.0041 (2)	0.0041 (2)	0.0039 (3)	0.00204 (12)	0.000	0.000
Cr1B	0.0041 (2)	0.0041 (2)	0.0039 (3)	0.00204 (12)	0.000	0.000
Mg2A	0.0043 (2)	0.0043 (2)	0.0038 (3)	0.00215 (11)	0.000	0.000
Cr2B	0.0043 (2)	0.0043 (2)	0.0038 (3)	0.00215 (11)	0.000	0.000
Mg3	0.00494 (15)	0.00494 (15)	0.0043 (2)	0.00247 (8)	0.000	0.000
O1	0.0045 (2)	0.0045 (2)	0.0051 (4)	0.00226 (12)	0.000	0.000
O2	0.0048 (2)	0.0048 (2)	0.0034 (4)	0.00241 (12)	0.000	0.000
O3	0.00421 (19)	0.00421 (19)	0.0045 (3)	0.0019 (2)	0.00005 (9)	−0.00005 (9)
O4	0.00431 (19)	0.00431 (19)	0.0049 (3)	0.0022 (2)	−0.00011 (9)	0.00011 (9)
O5	0.00519 (19)	0.0047 (2)	0.0049 (3)	0.00234 (12)	0.00010 (9)	0.00020 (18)
O6	0.0049 (3)	0.0049 (3)	0.0039 (4)	0.00247 (13)	0.000	0.000
O7	0.0053 (3)	0.0053 (3)	0.0031 (4)	0.00267 (13)	0.000	0.000
O8	0.00479 (18)	0.00479 (18)	0.0048 (2)	0.0028 (2)	−0.00033 (10)	0.00033 (10)

Geometric parameters (Å, º) top

Be1—O7	1.602 (2)	Mg1A—Al5^xiii	3.3259 (2)
Be1—O3ⁱ	1.6615 (13)	Mg1A—Al3A^iv	3.3376 (6)
Be1—O3ⁱⁱ	1.6615 (13)	Mg1A—Cr3B^iv	3.3376 (6)
Be1—O3ⁱⁱⁱ	1.6615 (13)	Mg1A—Al3Aⁱⁱⁱ	3.3376 (6)
Be1—Al1^iv	2.4926 (17)	Mg1A—Cr3Bⁱⁱⁱ	3.3376 (6)
Be1—Al1^v	2.4926 (17)	Mg2A—O5^viii	1.9300 (7)
Be1—Al1^vi	2.4926 (17)	Mg2A—O5^xxiv	1.9300 (7)
Al1—O3^vii	1.8799 (5)	Mg2A—O5ⁱⁱⁱ	1.9300 (7)
Al1—O3^viii	1.8799 (5)	Mg2A—O1	1.9361 (13)
Al1—O3^ix	1.8799 (5)	Mg2A—Al5^viii	3.3310 (2)
Al1—O3^x	1.8799 (5)	Mg2A—Al5^xiii	3.3310 (2)
Al1—O2	1.9666 (6)	Mg2A—Al3A^iv	3.3410 (3)
Al1—O2^xi	1.9667 (6)	Mg2A—Al3A^viii	3.3410 (3)
Al1—Be1^xii	2.4926 (17)	Mg2A—Al3A^xvi	3.3410 (3)
Al1—Be1^xiii	2.4926 (17)	Mg2A—Al3A^xxiv	3.3410 (3)
Al1—Al1^xiv	2.8394 (2)	Mg2A—Al3Aⁱⁱⁱ	3.3410 (3)
Al1—Al1^xv	2.8394 (1)	Mg3—O3^xvii	2.0173 (7)
Al1—Al1^vi	2.8394 (2)	Mg3—O3ⁱⁱ	2.0173 (7)
Al1—Al1^xvi	2.8394 (1)	Mg3—O3^viii	2.0173 (7)
Al2—O2	1.7765 (12)	Mg3—O8^xvi	2.2181 (8)
Al2—O8ⁱ	1.7874 (7)	Mg3—O8^v	2.2181 (8)
Al2—O8^iv	1.7874 (7)	Mg3—O8^xviii	2.2181 (8)
Al2—O8^xvi	1.7874 (7)	Mg3—Al3Aⁱⁱⁱ	3.0580 (7)
Al3A—O6	1.8969 (6)	Mg3—Cr3Bⁱⁱⁱ	3.0580 (7)
Al3A—O5^xvii	1.9189 (5)	Mg3—Al3A^iv	3.0580 (7)
Al3A—O5	1.9189 (5)	Mg3—Cr3B^iv	3.0580 (7)
Al3A—O8^v	1.9193 (5)	O1—Cr4B^xv	1.9125 (6)
Al3A—O8^xviii	1.9193 (5)	O1—Al4A^xv	1.9125 (6)
Al3A—O7^xix	1.9232 (6)	O1—Cr4B^vi	1.9125 (6)
Al3A—Cr3B^xvii	2.8381 (5)	O1—Al4A^vi	1.9125 (6)
Al3A—Al3A^xvii	2.8381 (5)	O2—Al1^xv	1.9666 (6)
Al3A—Al3A^xx	2.8381 (5)	O2—Al1^vi	1.9666 (6)
Al3A—Cr3B^xx	2.8381 (5)	O3—Be1^xix	1.6616 (13)
Al3A—Cr3Bⁱⁱⁱ	2.8407 (5)	O3—Al1^xviii	1.8799 (5)
Al3A—Al3Aⁱⁱⁱ	2.8407 (5)	O3—Al1^xxv	1.8799 (5)
Al4A—O1^xxi	1.9124 (6)	O3—Mg3^xxv	2.0173 (7)
Al4A—O1	1.9125 (6)	O4—Cr4B^xxv	1.9133 (5)
Al4A—O4^xxii	1.9133 (5)	O4—Al4A^xxv	1.9133 (5)
Al4A—O4^x	1.9133 (5)	O4—Cr4B^xviii	1.9133 (5)
Al4A—O4^xxiii	1.9133 (5)	O4—Al4A^xviii	1.9133 (5)
Al4A—O4^viii	1.9133 (5)	O4—Al5^xix	1.9136 (8)
Al4A—Al4A^xiv	2.8394 (1)	O4—Cr1B^xxv	1.9295 (7)
Al4A—Al4A^xv	2.8394 (1)	O4—Mg1A^xxv	1.9295 (7)
Al4A—Cr4B^xiv	2.8394 (1)	O5—Al5^xix	1.9036 (7)
Al4A—Cr4B^xv	2.8394 (1)	O5—Cr3B^xx	1.9188 (5)
Al4A—Al4A^vi	2.8394 (1)	O5—Al3A^xx	1.9188 (5)
Al4A—Cr4B^vi	2.8394 (1)	O5—Cr2B^xxv	1.9300 (7)
Al5—O5ⁱⁱⁱ	1.9037 (7)	O5—Mg2A^xxv	1.9300 (7)
Al5—O5ⁱⁱ	1.9037 (7)	O6—Cr3Bⁱⁱⁱ	1.8969 (6)
Al5—O5ⁱ	1.9037 (7)	O6—Al3Aⁱⁱⁱ	1.8969 (6)
Al5—O4ⁱⁱⁱ	1.9136 (8)	O6—Cr3B^iv	1.8969 (6)
Al5—O4ⁱⁱ	1.9136 (8)	O6—Al3A^iv	1.8969 (6)
Al5—O4ⁱ	1.9136 (8)	O7—Cr3Bⁱⁱ	1.9232 (6)
Al5—Cr4B^v	2.8515 (4)	O7—Al3Aⁱⁱ	1.9232 (6)
Al5—Al4A^v	2.8515 (4)	O7—Al3Aⁱ	1.9232 (6)
Al5—Cr4B^iv	2.8515 (4)	O7—Cr3Bⁱ	1.9232 (6)
Al5—Al4A^iv	2.8515 (4)	O7—Cr3Bⁱⁱⁱ	1.9232 (6)
Al5—Cr4B^vi	2.8515 (4)	O7—Al3Aⁱⁱⁱ	1.9232 (6)
Al5—Al4A^vi	2.8515 (4)	O8—Al2^xix	1.7874 (7)
Mg1A—O4^viii	1.9295 (7)	O8—Cr3B^x	1.9193 (5)
Mg1A—O4ⁱⁱ	1.9296 (7)	O8—Al3A^x	1.9193 (5)
Mg1A—O4^xvii	1.9296 (7)	O8—Al3A^xiii	1.9193 (5)
Mg1A—O6	1.9537 (12)	O8—Cr3B^xiii	1.9193 (5)
Mg1A—Al5^xix	3.3259 (2)	O8—Mg3^xiii	2.2181 (8)

O7—Be1—O3ⁱ	119.45 (7)	O4^viii—Mg1A—O4ⁱⁱ	108.66 (2)
O7—Be1—O3ⁱⁱ	119.45 (7)	O4^viii—Mg1A—O4^xvii	108.66 (2)
O3ⁱ—Be1—O3ⁱⁱ	97.89 (9)	O4ⁱⁱ—Mg1A—O4^xvii	108.66 (2)
O7—Be1—O3ⁱⁱⁱ	119.45 (7)	O4^viii—Mg1A—O6	110.27 (2)
O3ⁱ—Be1—O3ⁱⁱⁱ	97.89 (9)	O4ⁱⁱ—Mg1A—O6	110.27 (2)
O3ⁱⁱ—Be1—O3ⁱⁱⁱ	97.89 (9)	O4^xvii—Mg1A—O6	110.27 (2)
O7—Be1—Al1^iv	138.88 (3)	O4^viii—Mg1A—Al5^xix	121.368 (4)
O3ⁱ—Be1—Al1^iv	48.95 (5)	O4ⁱⁱ—Mg1A—Al5^xix	121.369 (4)
O3ⁱⁱ—Be1—Al1^iv	48.95 (5)	O4^xvii—Mg1A—Al5^xix	29.94 (2)
O3ⁱⁱⁱ—Be1—Al1^iv	101.67 (10)	O6—Mg1A—Al5^xix	80.334 (11)
O7—Be1—Al1^v	138.88 (3)	O4^viii—Mg1A—Al5	121.368 (4)
O3ⁱ—Be1—Al1^v	48.95 (5)	O4ⁱⁱ—Mg1A—Al5	29.94 (2)
O3ⁱⁱ—Be1—Al1^v	101.67 (10)	O4^xvii—Mg1A—Al5	121.368 (4)
O3ⁱⁱⁱ—Be1—Al1^v	48.95 (5)	O6—Mg1A—Al5	80.336 (11)
Al1^iv—Be1—Al1^v	69.44 (5)	Al5^xix—Mg1A—Al5	117.240 (6)
O7—Be1—Al1^vi	138.88 (3)	O4^viii—Mg1A—Al5^xiii	29.94 (2)
O3ⁱ—Be1—Al1^vi	101.67 (10)	O4ⁱⁱ—Mg1A—Al5^xiii	121.369 (4)
O3ⁱⁱ—Be1—Al1^vi	48.95 (5)	O4^xvii—Mg1A—Al5^xiii	121.369 (4)
O3ⁱⁱⁱ—Be1—Al1^vi	48.95 (5)	O6—Mg1A—Al5^xiii	80.334 (11)
Al1^iv—Be1—Al1^vi	69.44 (5)	Al5^xix—Mg1A—Al5^xiii	117.239 (6)
Al1^v—Be1—Al1^vi	69.44 (5)	Al5—Mg1A—Al5^xiii	117.240 (6)
O3^vii—Al1—O3^viii	180.00 (4)	O4^viii—Mg1A—Al3A^iv	80.84 (2)
O3^vii—Al1—O3^ix	83.60 (4)	O4ⁱⁱ—Mg1A—Al3A^iv	122.16 (2)
O3^viii—Al1—O3^ix	96.40 (4)	O4^xvii—Mg1A—Al3A^iv	122.16 (2)
O3^vii—Al1—O3^x	96.40 (4)	O6—Mg1A—Al3A^iv	29.432 (6)
O3^viii—Al1—O3^x	83.60 (4)	Al5^xix—Mg1A—Al3A^iv	95.507 (12)
O3^ix—Al1—O3^x	180.00 (4)	Al5—Mg1A—Al3A^iv	95.508 (12)
O3^vii—Al1—O2	84.58 (3)	Al5^xiii—Mg1A—Al3A^iv	50.903 (10)
O3^viii—Al1—O2	95.42 (3)	O4^viii—Mg1A—Cr3B^iv	80.84 (2)
O3^ix—Al1—O2	84.58 (3)	O4ⁱⁱ—Mg1A—Cr3B^iv	122.16 (2)
O3^x—Al1—O2	95.42 (3)	O4^xvii—Mg1A—Cr3B^iv	122.16 (2)
O3^vii—Al1—O2^xi	95.42 (3)	O6—Mg1A—Cr3B^iv	29.432 (6)
O3^viii—Al1—O2^xi	84.58 (3)	Al5^xix—Mg1A—Cr3B^iv	95.507 (12)
O3^ix—Al1—O2^xi	95.42 (3)	Al5—Mg1A—Cr3B^iv	95.508 (12)
O3^x—Al1—O2^xi	84.58 (3)	Al5^xiii—Mg1A—Cr3B^iv	50.903 (10)
O2—Al1—O2^xi	180.0	Al3A^iv—Mg1A—Cr3B^iv	0.000 (5)
O3^vii—Al1—Be1^xii	41.80 (2)	O4^viii—Mg1A—Al3Aⁱⁱⁱ	122.16 (2)
O3^viii—Al1—Be1^xii	138.20 (2)	O4ⁱⁱ—Mg1A—Al3Aⁱⁱⁱ	80.84 (2)
O3^ix—Al1—Be1^xii	41.80 (2)	O4^xvii—Mg1A—Al3Aⁱⁱⁱ	122.16 (2)
O3^x—Al1—Be1^xii	138.20 (2)	O6—Mg1A—Al3Aⁱⁱⁱ	29.432 (6)
O2—Al1—Be1^xii	82.41 (4)	Al5^xix—Mg1A—Al3Aⁱⁱⁱ	95.508 (12)
O2^xi—Al1—Be1^xii	97.59 (4)	Al5—Mg1A—Al3Aⁱⁱⁱ	50.904 (10)
O3^vii—Al1—Be1^xiii	138.20 (2)	Al5^xiii—Mg1A—Al3Aⁱⁱⁱ	95.508 (12)
O3^viii—Al1—Be1^xiii	41.80 (2)	Al3A^iv—Mg1A—Al3Aⁱⁱⁱ	50.371 (11)
O3^ix—Al1—Be1^xiii	138.20 (2)	Cr3B^iv—Mg1A—Al3Aⁱⁱⁱ	50.4
O3^x—Al1—Be1^xiii	41.80 (2)	O4^viii—Mg1A—Cr3Bⁱⁱⁱ	122.16 (2)
O2—Al1—Be1^xiii	97.59 (4)	O4ⁱⁱ—Mg1A—Cr3Bⁱⁱⁱ	80.84 (2)
O2^xi—Al1—Be1^xiii	82.41 (4)	O4^xvii—Mg1A—Cr3Bⁱⁱⁱ	122.16 (2)
Be1^xii—Al1—Be1^xiii	180.00 (7)	O6—Mg1A—Cr3Bⁱⁱⁱ	29.432 (6)
O3^vii—Al1—Al1^xiv	139.043 (16)	Al5^xix—Mg1A—Cr3Bⁱⁱⁱ	95.508 (12)
O3^viii—Al1—Al1^xiv	40.957 (16)	Al5—Mg1A—Cr3Bⁱⁱⁱ	50.904 (10)
O3^ix—Al1—Al1^xiv	95.088 (18)	Al5^xiii—Mg1A—Cr3Bⁱⁱⁱ	95.508 (12)
O3^x—Al1—Al1^xiv	84.912 (18)	Al3A^iv—Mg1A—Cr3Bⁱⁱⁱ	50.371 (11)
O2—Al1—Al1^xiv	136.211 (19)	Cr3B^iv—Mg1A—Cr3Bⁱⁱⁱ	50.371 (11)
O2^xi—Al1—Al1^xiv	43.790 (19)	Al3Aⁱⁱⁱ—Mg1A—Cr3Bⁱⁱⁱ	0.000 (15)
Be1^xii—Al1—Al1^xiv	124.72 (3)	O5^viii—Mg2A—O5^xxiv	109.66 (2)
Be1^xiii—Al1—Al1^xiv	55.28 (3)	O5^viii—Mg2A—O5ⁱⁱⁱ	109.66 (2)
O3^vii—Al1—Al1^xv	40.957 (16)	O5^xxiv—Mg2A—O5ⁱⁱⁱ	109.66 (2)
O3^viii—Al1—Al1^xv	139.043 (16)	O5^viii—Mg2A—O1	109.28 (2)
O3^ix—Al1—Al1^xv	84.912 (18)	O5^xxiv—Mg2A—O1	109.28 (2)
O3^x—Al1—Al1^xv	95.088 (18)	O5ⁱⁱⁱ—Mg2A—O1	109.28 (2)
O2—Al1—Al1^xv	43.789 (19)	O5^viii—Mg2A—Al5^viii	121.522 (3)
O2^xi—Al1—Al1^xv	136.210 (19)	O5^xxiv—Mg2A—Al5^viii	29.45 (2)
Be1^xii—Al1—Al1^xv	55.28 (3)	O5ⁱⁱⁱ—Mg2A—Al5^viii	121.522 (3)
Be1^xiii—Al1—Al1^xv	124.72 (3)	O1—Mg2A—Al5^viii	79.835 (12)
Al1^xiv—Al1—Al1^xv	180.0	O5^viii—Mg2A—Al5^xiii	29.45 (2)
O3^vii—Al1—Al1^vi	84.912 (18)	O5^xxiv—Mg2A—Al5^xiii	121.522 (3)
O3^viii—Al1—Al1^vi	95.088 (18)	O5ⁱⁱⁱ—Mg2A—Al5^xiii	121.522 (3)
O3^ix—Al1—Al1^vi	40.957 (16)	O1—Mg2A—Al5^xiii	79.835 (12)
O3^x—Al1—Al1^vi	139.043 (16)	Al5^viii—Mg2A—Al5^xiii	116.954 (7)
O2—Al1—Al1^vi	43.789 (19)	O5^viii—Mg2A—Al5	121.521 (4)
O2^xi—Al1—Al1^vi	136.211 (19)	O5^xxiv—Mg2A—Al5	121.521 (3)
Be1^xii—Al1—Al1^vi	55.28 (3)	O5ⁱⁱⁱ—Mg2A—Al5	29.45 (2)
Be1^xiii—Al1—Al1^vi	124.72 (3)	O1—Mg2A—Al5	79.834 (12)
Al1^xiv—Al1—Al1^vi	120.0	Al5^viii—Mg2A—Al5	116.954 (7)
Al1^xv—Al1—Al1^vi	60.0	Al5^xiii—Mg2A—Al5	116.954 (7)
O3^vii—Al1—Al1^xvi	95.088 (18)	O5^viii—Mg2A—Al3A^iv	29.673 (12)
O3^viii—Al1—Al1^xvi	84.912 (18)	O5^xxiv—Mg2A—Al3A^iv	121.37 (3)
O3^ix—Al1—Al1^xvi	139.043 (16)	O5ⁱⁱⁱ—Mg2A—Al3A^iv	79.990 (15)
O3^x—Al1—Al1^xvi	40.957 (16)	O1—Mg2A—Al3A^iv	121.802 (9)
O2—Al1—Al1^xvi	136.211 (19)	Al5^viii—Mg2A—Al3A^iv	144.821 (12)
O2^xi—Al1—Al1^xvi	43.789 (19)	Al5^xiii—Mg2A—Al3A^iv	50.834 (9)
Be1^xii—Al1—Al1^xvi	124.72 (3)	Al5—Mg2A—Al3A^iv	95.349 (7)
Be1^xiii—Al1—Al1^xvi	55.28 (3)	O5^viii—Mg2A—Al3A^viii	29.674 (12)
Al1^xiv—Al1—Al1^xvi	60.0	O5^xxiv—Mg2A—Al3A^viii	79.990 (15)
Al1^xv—Al1—Al1^xvi	120.0	O5ⁱⁱⁱ—Mg2A—Al3A^viii	121.37 (3)
Al1^vi—Al1—Al1^xvi	180.0	O1—Mg2A—Al3A^viii	121.802 (9)
O2—Al2—O8ⁱ	109.22 (3)	Al5^viii—Mg2A—Al3A^viii	95.348 (7)
O2—Al2—O8^iv	109.22 (3)	Al5^xiii—Mg2A—Al3A^viii	50.834 (8)
O8ⁱ—Al2—O8^iv	109.72 (3)	Al5—Mg2A—Al3A^viii	144.822 (12)
O2—Al2—O8^xvi	109.22 (3)	Al3A^iv—Mg2A—Al3A^viii	50.270 (9)
O8ⁱ—Al2—O8^xvi	109.72 (3)	O5^viii—Mg2A—Al3A^xvi	79.990 (15)
O8^iv—Al2—O8^xvi	109.72 (3)	O5^xxiv—Mg2A—Al3A^xvi	29.674 (12)
O6—Al3A—O5^xvii	96.66 (3)	O5ⁱⁱⁱ—Mg2A—Al3A^xvi	121.37 (3)
O6—Al3A—O5	96.66 (3)	O1—Mg2A—Al3A^xvi	121.802 (9)
O5^xvii—Al3A—O5	82.22 (4)	Al5^viii—Mg2A—Al3A^xvi	50.834 (9)
O6—Al3A—O8^v	83.72 (3)	Al5^xiii—Mg2A—Al3A^xvi	95.348 (7)
O5^xvii—Al3A—O8^v	175.23 (3)	Al5—Mg2A—Al3A^xvi	144.822 (12)
O5—Al3A—O8^v	93.01 (3)	Al3A^iv—Mg2A—Al3A^xvi	94.786 (12)
O6—Al3A—O8^xviii	83.72 (3)	Al3A^viii—Mg2A—Al3A^xvi	50.318 (10)
O5^xvii—Al3A—O8^xviii	93.01 (3)	O5^viii—Mg2A—Al3A^xxiv	121.37 (3)
O5—Al3A—O8^xviii	175.23 (3)	O5^xxiv—Mg2A—Al3A^xxiv	29.673 (12)
O8^v—Al3A—O8^xviii	91.76 (4)	O5ⁱⁱⁱ—Mg2A—Al3A^xxiv	79.990 (15)
O6—Al3A—O7^xix	178.60 (4)	O1—Mg2A—Al3A^xxiv	121.802 (9)
O5^xvii—Al3A—O7^xix	84.39 (3)	Al5^viii—Mg2A—Al3A^xxiv	50.834 (8)
O5—Al3A—O7^xix	84.40 (3)	Al5^xiii—Mg2A—Al3A^xxiv	144.821 (12)
O8^v—Al3A—O7^xix	95.31 (3)	Al5—Mg2A—Al3A^xxiv	95.349 (7)
O8^xviii—Al3A—O7^xix	95.31 (3)	Al3A^iv—Mg2A—Al3A^xxiv	116.397 (17)
O6—Al3A—Cr3B^xvii	138.48 (2)	Al3A^viii—Mg2A—Al3A^xxiv	94.786 (12)
O5^xvii—Al3A—Cr3B^xvii	42.307 (16)	Al3A^xvi—Mg2A—Al3A^xxiv	50.270 (9)
O5—Al3A—Cr3B^xvii	85.296 (19)	O5^viii—Mg2A—Al3Aⁱⁱⁱ	79.989 (15)
O8^v—Al3A—Cr3B^xvii	137.735 (18)	O5^xxiv—Mg2A—Al3Aⁱⁱⁱ	121.37 (3)
O8^xviii—Al3A—Cr3B^xvii	91.271 (18)	O5ⁱⁱⁱ—Mg2A—Al3Aⁱⁱⁱ	29.674 (12)
O7^xix—Al3A—Cr3B^xvii	42.450 (19)	O1—Mg2A—Al3Aⁱⁱⁱ	121.802 (9)
O6—Al3A—Al3A^xvii	138.48 (2)	Al5^viii—Mg2A—Al3Aⁱⁱⁱ	144.822 (12)
O5^xvii—Al3A—Al3A^xvii	42.307 (16)	Al5^xiii—Mg2A—Al3Aⁱⁱⁱ	95.349 (7)
O5—Al3A—Al3A^xvii	85.296 (19)	Al5—Mg2A—Al3Aⁱⁱⁱ	50.835 (9)
O8^v—Al3A—Al3A^xvii	137.735 (18)	Al3A^iv—Mg2A—Al3Aⁱⁱⁱ	50.317 (10)
O8^xviii—Al3A—Al3A^xvii	91.271 (18)	Al3A^viii—Mg2A—Al3Aⁱⁱⁱ	94.786 (12)
O7^xix—Al3A—Al3A^xvii	42.450 (19)	Al3A^xvi—Mg2A—Al3Aⁱⁱⁱ	116.397 (17)
Cr3B^xvii—Al3A—Al3A^xvii	0.0	Al3A^xxiv—Mg2A—Al3Aⁱⁱⁱ	94.786 (12)
O6—Al3A—Al3A^xx	138.48 (2)	O3^xvii—Mg3—O3ⁱⁱ	103.70 (3)
O5^xvii—Al3A—Al3A^xx	85.296 (19)	O3^xvii—Mg3—O3^viii	103.70 (3)
O5—Al3A—Al3A^xx	42.308 (16)	O3ⁱⁱ—Mg3—O3^viii	103.70 (3)
O8^v—Al3A—Al3A^xx	91.271 (18)	O3^xvii—Mg3—O8^xvi	160.59 (4)
O8^xviii—Al3A—Al3A^xx	137.735 (18)	O3ⁱⁱ—Mg3—O8^xvi	88.06 (2)
O7^xix—Al3A—Al3A^xx	42.451 (19)	O3^viii—Mg3—O8^xvi	88.06 (2)
Cr3B^xvii—Al3A—Al3A^xx	60.0	O3^xvii—Mg3—O8^v	88.06 (2)
Al3A^xvii—Al3A—Al3A^xx	60.0	O3ⁱⁱ—Mg3—O8^v	88.06 (2)
O6—Al3A—Cr3B^xx	138.48 (2)	O3^viii—Mg3—O8^v	160.59 (4)
O5^xvii—Al3A—Cr3B^xx	85.296 (19)	O8^xvi—Mg3—O8^v	76.80 (3)
O5—Al3A—Cr3B^xx	42.308 (16)	O3^xvii—Mg3—O8^xviii	88.064 (19)
O8^v—Al3A—Cr3B^xx	91.271 (18)	O3ⁱⁱ—Mg3—O8^xviii	160.59 (4)
O8^xviii—Al3A—Cr3B^xx	137.735 (18)	O3^viii—Mg3—O8^xviii	88.06 (2)
O7^xix—Al3A—Cr3B^xx	42.451 (19)	O8^xvi—Mg3—O8^xviii	76.80 (3)
Cr3B^xvii—Al3A—Cr3B^xx	60.0	O8^v—Mg3—O8^xviii	76.80 (3)
Al3A^xvii—Al3A—Cr3B^xx	60.0	O3^xvii—Mg3—Al3A	82.33 (2)
Al3A^xx—Al3A—Cr3B^xx	0.000 (14)	O3ⁱⁱ—Mg3—Al3A	126.66 (2)
O6—Al3A—Cr3Bⁱⁱⁱ	41.52 (2)	O3^viii—Mg3—Al3A	126.66 (2)
O5^xvii—Al3A—Cr3Bⁱⁱⁱ	137.691 (16)	O8^xvi—Mg3—Al3A	78.26 (3)
O5—Al3A—Cr3Bⁱⁱⁱ	94.703 (19)	O8^v—Mg3—Al3A	38.697 (14)
O8^v—Al3A—Cr3Bⁱⁱⁱ	42.266 (18)	O8^xviii—Mg3—Al3A	38.697 (14)
O8^xviii—Al3A—Cr3Bⁱⁱⁱ	88.730 (18)	O3^xvii—Mg3—Al3Aⁱⁱⁱ	126.66 (2)
O7^xix—Al3A—Cr3Bⁱⁱⁱ	137.552 (19)	O3ⁱⁱ—Mg3—Al3Aⁱⁱⁱ	82.33 (2)
Cr3B^xvii—Al3A—Cr3Bⁱⁱⁱ	180.0	O3^viii—Mg3—Al3Aⁱⁱⁱ	126.66 (2)
Al3A^xvii—Al3A—Cr3Bⁱⁱⁱ	180.0	O8^xvi—Mg3—Al3Aⁱⁱⁱ	38.697 (14)
Al3A^xx—Al3A—Cr3Bⁱⁱⁱ	120.0	O8^v—Mg3—Al3Aⁱⁱⁱ	38.697 (14)
Cr3B^xx—Al3A—Cr3Bⁱⁱⁱ	120.0	O8^xviii—Mg3—Al3Aⁱⁱⁱ	78.26 (3)
O6—Al3A—Al3Aⁱⁱⁱ	41.52 (2)	Al3A—Mg3—Al3Aⁱⁱⁱ	55.352 (15)
O5^xvii—Al3A—Al3Aⁱⁱⁱ	137.691 (16)	O3^xvii—Mg3—Cr3Bⁱⁱⁱ	126.66 (2)
O5—Al3A—Al3Aⁱⁱⁱ	94.703 (19)	O3ⁱⁱ—Mg3—Cr3Bⁱⁱⁱ	82.33 (2)
O8^v—Al3A—Al3Aⁱⁱⁱ	42.266 (18)	O3^viii—Mg3—Cr3Bⁱⁱⁱ	126.66 (2)
O8^xviii—Al3A—Al3Aⁱⁱⁱ	88.730 (18)	O8^xvi—Mg3—Cr3Bⁱⁱⁱ	38.697 (14)
O7^xix—Al3A—Al3Aⁱⁱⁱ	137.552 (19)	O8^v—Mg3—Cr3Bⁱⁱⁱ	38.697 (14)
Cr3B^xvii—Al3A—Al3Aⁱⁱⁱ	180.0	O8^xviii—Mg3—Cr3Bⁱⁱⁱ	78.26 (3)
Al3A^xvii—Al3A—Al3Aⁱⁱⁱ	180.0	Al3A—Mg3—Cr3Bⁱⁱⁱ	55.4
Al3A^xx—Al3A—Al3Aⁱⁱⁱ	120.0	Al3Aⁱⁱⁱ—Mg3—Cr3Bⁱⁱⁱ	0.000 (16)
Cr3B^xx—Al3A—Al3Aⁱⁱⁱ	120.0	O3^xvii—Mg3—Al3A^iv	126.66 (2)
Cr3Bⁱⁱⁱ—Al3A—Al3Aⁱⁱⁱ	0.0	O3ⁱⁱ—Mg3—Al3A^iv	126.66 (2)
O1^xxi—Al4A—O1	180.0	O3^viii—Mg3—Al3A^iv	82.33 (2)
O1^xxi—Al4A—O4^xxii	96.18 (3)	O8^xvi—Mg3—Al3A^iv	38.697 (14)
O1—Al4A—O4^xxii	83.82 (3)	O8^v—Mg3—Al3A^iv	78.26 (3)
O1^xxi—Al4A—O4^x	83.82 (3)	O8^xviii—Mg3—Al3A^iv	38.697 (14)
O1—Al4A—O4^x	96.18 (3)	Al3A—Mg3—Al3A^iv	55.352 (15)
O4^xxii—Al4A—O4^x	180.00 (3)	Al3Aⁱⁱⁱ—Mg3—Al3A^iv	55.351 (15)
O1^xxi—Al4A—O4^xxiii	96.18 (3)	Cr3Bⁱⁱⁱ—Mg3—Al3A^iv	55.4
O1—Al4A—O4^xxiii	83.82 (3)	O3^xvii—Mg3—Cr3B^iv	126.66 (2)
O4^xxii—Al4A—O4^xxiii	83.33 (4)	O3ⁱⁱ—Mg3—Cr3B^iv	126.66 (2)
O4^x—Al4A—O4^xxiii	96.67 (4)	O3^viii—Mg3—Cr3B^iv	82.33 (2)
O1^xxi—Al4A—O4^viii	83.82 (3)	O8^xvi—Mg3—Cr3B^iv	38.697 (14)
O1—Al4A—O4^viii	96.18 (3)	O8^v—Mg3—Cr3B^iv	78.26 (3)
O4^xxii—Al4A—O4^viii	96.67 (4)	O8^xviii—Mg3—Cr3B^iv	38.697 (14)
O4^x—Al4A—O4^viii	83.33 (4)	Al3A—Mg3—Cr3B^iv	55.4
O4^xxiii—Al4A—O4^viii	180.0	Al3Aⁱⁱⁱ—Mg3—Cr3B^iv	55.351 (15)
O1^xxi—Al4A—Al4A^xiv	42.07 (2)	Cr3Bⁱⁱⁱ—Mg3—Cr3B^iv	55.351 (15)
O1—Al4A—Al4A^xiv	137.93 (2)	Al3A^iv—Mg3—Cr3B^iv	0.000 (6)
O4^xxii—Al4A—Al4A^xiv	94.432 (19)	Cr4B^xv—O1—Al4A^xv	0.0
O4^x—Al4A—Al4A^xiv	85.568 (19)	Cr4B^xv—O1—Al4A	95.9
O4^xxiii—Al4A—Al4A^xiv	137.904 (15)	Al4A^xv—O1—Al4A	95.86 (4)
O4^viii—Al4A—Al4A^xiv	42.096 (15)	Cr4B^xv—O1—Cr4B^vi	95.86 (4)
O1^xxi—Al4A—Al4A^xv	137.93 (2)	Al4A^xv—O1—Cr4B^vi	95.86 (4)
O1—Al4A—Al4A^xv	42.07 (2)	Al4A—O1—Cr4B^vi	95.9
O4^xxii—Al4A—Al4A^xv	85.568 (19)	Cr4B^xv—O1—Al4A^vi	95.9
O4^x—Al4A—Al4A^xv	94.432 (19)	Al4A^xv—O1—Al4A^vi	95.86 (4)
O4^xxiii—Al4A—Al4A^xv	42.096 (15)	Al4A—O1—Al4A^vi	95.86 (4)
O4^viii—Al4A—Al4A^xv	137.904 (15)	Cr4B^vi—O1—Al4A^vi	0.0
Al4A^xiv—Al4A—Al4A^xv	180.0	Cr4B^xv—O1—Mg2A	121.00 (3)
O1^xxi—Al4A—Cr4B^xiv	42.07 (2)	Al4A^xv—O1—Mg2A	121.00 (3)
O1—Al4A—Cr4B^xiv	137.93 (2)	Al4A—O1—Mg2A	121.00 (3)
O4^xxii—Al4A—Cr4B^xiv	94.432 (19)	Cr4B^vi—O1—Mg2A	121.00 (3)
O4^x—Al4A—Cr4B^xiv	85.568 (19)	Al4A^vi—O1—Mg2A	121.00 (3)
O4^xxiii—Al4A—Cr4B^xiv	137.904 (15)	Al2—O2—Al1	123.53 (3)
O4^viii—Al4A—Cr4B^xiv	42.096 (15)	Al2—O2—Al1^xv	123.53 (3)
Al4A^xiv—Al4A—Cr4B^xiv	0.0	Al1—O2—Al1^xv	92.42 (4)
Al4A^xv—Al4A—Cr4B^xiv	180.0	Al2—O2—Al1^vi	123.53 (3)
O1^xxi—Al4A—Cr4B^xv	137.93 (2)	Al1—O2—Al1^vi	92.42 (4)
O1—Al4A—Cr4B^xv	42.07 (2)	Al1^xv—O2—Al1^vi	92.42 (4)
O4^xxii—Al4A—Cr4B^xv	85.568 (19)	Be1^xix—O3—Al1^xviii	89.25 (5)
O4^x—Al4A—Cr4B^xv	94.432 (19)	Be1^xix—O3—Al1^xxv	89.25 (5)
O4^xxiii—Al4A—Cr4B^xv	42.096 (15)	Al1^xviii—O3—Al1^xxv	98.09 (3)
O4^viii—Al4A—Cr4B^xv	137.904 (15)	Be1^xix—O3—Mg3^xxv	125.79 (8)
Al4A^xiv—Al4A—Cr4B^xv	180.0	Al1^xviii—O3—Mg3^xxv	122.63 (2)
Al4A^xv—Al4A—Cr4B^xv	0.0	Al1^xxv—O3—Mg3^xxv	122.63 (2)
Cr4B^xiv—Al4A—Cr4B^xv	180.0	Cr4B^xxv—O4—Al4A^xxv	0.0
O1^xxi—Al4A—Al4A^vi	137.93 (2)	Cr4B^xxv—O4—Cr4B^xviii	95.81 (3)
O1—Al4A—Al4A^vi	42.07 (2)	Al4A^xxv—O4—Cr4B^xviii	95.81 (3)
O4^xxii—Al4A—Al4A^vi	42.096 (15)	Cr4B^xxv—O4—Al4A^xviii	95.8
O4^x—Al4A—Al4A^vi	137.904 (15)	Al4A^xxv—O4—Al4A^xviii	95.81 (3)
O4^xxiii—Al4A—Al4A^vi	85.569 (18)	Cr4B^xviii—O4—Al4A^xviii	0.0
O4^viii—Al4A—Al4A^vi	94.431 (18)	Cr4B^xxv—O4—Al5^xix	96.34 (3)
Al4A^xiv—Al4A—Al4A^vi	120.0	Al4A^xxv—O4—Al5^xix	96.34 (3)
Al4A^xv—Al4A—Al4A^vi	60.0	Cr4B^xviii—O4—Al5^xix	96.34 (3)
Cr4B^xiv—Al4A—Al4A^vi	120.0	Al4A^xviii—O4—Al5^xix	96.34 (3)
Cr4B^xv—Al4A—Al4A^vi	60.0	Cr4B^xxv—O4—Cr1B^xxv	121.23 (2)
O1^xxi—Al4A—Cr4B^vi	137.93 (2)	Al4A^xxv—O4—Cr1B^xxv	121.23 (2)
O1—Al4A—Cr4B^vi	42.07 (2)	Cr4B^xviii—O4—Cr1B^xxv	121.23 (2)
O4^xxii—Al4A—Cr4B^vi	42.096 (15)	Al4A^xviii—O4—Cr1B^xxv	121.23 (2)
O4^x—Al4A—Cr4B^vi	137.904 (15)	Al5^xix—O4—Cr1B^xxv	119.86 (4)
O4^xxiii—Al4A—Cr4B^vi	85.569 (18)	Cr4B^xxv—O4—Mg1A^xxv	121.23 (2)
O4^viii—Al4A—Cr4B^vi	94.431 (18)	Al4A^xxv—O4—Mg1A^xxv	121.23 (2)
Al4A^xiv—Al4A—Cr4B^vi	120.0	Cr4B^xviii—O4—Mg1A^xxv	121.23 (2)
Al4A^xv—Al4A—Cr4B^vi	60.0	Al4A^xviii—O4—Mg1A^xxv	121.23 (2)
Cr4B^xiv—Al4A—Cr4B^vi	120.0	Al5^xix—O4—Mg1A^xxv	119.86 (4)
Cr4B^xv—Al4A—Cr4B^vi	60.0	Cr1B^xxv—O4—Mg1A^xxv	0.0
Al4A^vi—Al4A—Cr4B^vi	0.0	Al5^xix—O5—Cr3B^xx	97.03 (3)
O5ⁱⁱⁱ—Al5—O5ⁱⁱ	83.03 (3)	Al5^xix—O5—Al3A^xx	97.03 (3)
O5ⁱⁱⁱ—Al5—O5ⁱ	83.03 (3)	Cr3B^xx—O5—Al3A^xx	0.0
O5ⁱⁱ—Al5—O5ⁱ	83.02 (3)	Al5^xix—O5—Al3A	97.03 (3)
O5ⁱⁱⁱ—Al5—O4ⁱⁱⁱ	96.83 (2)	Cr3B^xx—O5—Al3A	95.4
O5ⁱⁱ—Al5—O4ⁱⁱⁱ	179.81 (3)	Al3A^xx—O5—Al3A	95.38 (3)
O5ⁱ—Al5—O4ⁱⁱⁱ	96.83 (2)	Al5^xix—O5—Cr2B^xxv	120.65 (4)
O5ⁱⁱⁱ—Al5—O4ⁱⁱ	96.83 (2)	Cr3B^xx—O5—Cr2B^xxv	120.46 (2)
O5ⁱⁱ—Al5—O4ⁱⁱ	96.83 (2)	Al3A^xx—O5—Cr2B^xxv	120.46 (2)
O5ⁱ—Al5—O4ⁱⁱ	179.81 (3)	Al3A—O5—Cr2B^xxv	120.46 (2)
O4ⁱⁱⁱ—Al5—O4ⁱⁱ	83.31 (3)	Al5^xix—O5—Mg2A^xxv	120.65 (4)
O5ⁱⁱⁱ—Al5—O4ⁱ	179.81 (3)	Cr3B^xx—O5—Mg2A^xxv	120.46 (2)
O5ⁱⁱ—Al5—O4ⁱ	96.83 (2)	Al3A^xx—O5—Mg2A^xxv	120.46 (2)
O5ⁱ—Al5—O4ⁱ	96.83 (2)	Al3A—O5—Mg2A^xxv	120.46 (2)
O4ⁱⁱⁱ—Al5—O4ⁱ	83.31 (3)	Cr2B^xxv—O5—Mg2A^xxv	0.0
O4ⁱⁱ—Al5—O4ⁱ	83.31 (3)	Cr3Bⁱⁱⁱ—O6—Al3Aⁱⁱⁱ	0.0
O5ⁱⁱⁱ—Al5—Cr4B^v	138.301 (15)	Cr3Bⁱⁱⁱ—O6—Cr3B^iv	96.97 (4)
O5ⁱⁱ—Al5—Cr4B^v	138.300 (15)	Al3Aⁱⁱⁱ—O6—Cr3B^iv	96.97 (4)
O5ⁱ—Al5—Cr4B^v	94.97 (2)	Cr3Bⁱⁱⁱ—O6—Al3A^iv	97.0
O4ⁱⁱⁱ—Al5—Cr4B^v	41.825 (15)	Al3Aⁱⁱⁱ—O6—Al3A^iv	96.97 (4)
O4ⁱⁱ—Al5—Cr4B^v	85.22 (2)	Cr3B^iv—O6—Al3A^iv	0.0
O4ⁱ—Al5—Cr4B^v	41.826 (15)	Cr3Bⁱⁱⁱ—O6—Al3A	97.0
O5ⁱⁱⁱ—Al5—Al4A^v	138.301 (15)	Al3Aⁱⁱⁱ—O6—Al3A	96.97 (4)
O5ⁱⁱ—Al5—Al4A^v	138.300 (15)	Cr3B^iv—O6—Al3A	97.0
O5ⁱ—Al5—Al4A^v	94.97 (2)	Al3A^iv—O6—Al3A	96.97 (4)
O4ⁱⁱⁱ—Al5—Al4A^v	41.825 (15)	Cr3Bⁱⁱⁱ—O6—Mg1A	120.16 (3)
O4ⁱⁱ—Al5—Al4A^v	85.22 (2)	Al3Aⁱⁱⁱ—O6—Mg1A	120.16 (3)
O4ⁱ—Al5—Al4A^v	41.826 (15)	Cr3B^iv—O6—Mg1A	120.16 (3)
Cr4B^v—Al5—Al4A^v	0.0	Al3A^iv—O6—Mg1A	120.16 (3)
O5ⁱⁱⁱ—Al5—Cr4B^iv	138.301 (15)	Al3A—O6—Mg1A	120.16 (3)
O5ⁱⁱ—Al5—Cr4B^iv	94.97 (2)	Be1—O7—Cr3Bⁱⁱ	121.57 (3)
O5ⁱ—Al5—Cr4B^iv	138.300 (15)	Be1—O7—Al3Aⁱⁱ	121.57 (3)
O4ⁱⁱⁱ—Al5—Cr4B^iv	85.22 (2)	Cr3Bⁱⁱ—O7—Al3Aⁱⁱ	0.0
O4ⁱⁱ—Al5—Cr4B^iv	41.825 (15)	Be1—O7—Al3Aⁱ	121.57 (3)
O4ⁱ—Al5—Cr4B^iv	41.826 (15)	Cr3Bⁱⁱ—O7—Al3Aⁱ	95.1
Cr4B^v—Al5—Cr4B^iv	59.719 (10)	Al3Aⁱⁱ—O7—Al3Aⁱ	95.10 (4)
Al4A^v—Al5—Cr4B^iv	59.719 (10)	Be1—O7—Cr3Bⁱ	121.57 (3)
O5ⁱⁱⁱ—Al5—Al4A^iv	138.301 (15)	Cr3Bⁱⁱ—O7—Cr3Bⁱ	95.10 (4)
O5ⁱⁱ—Al5—Al4A^iv	94.97 (2)	Al3Aⁱⁱ—O7—Cr3Bⁱ	95.10 (4)
O5ⁱ—Al5—Al4A^iv	138.300 (15)	Al3Aⁱ—O7—Cr3Bⁱ	0.000 (18)
O4ⁱⁱⁱ—Al5—Al4A^iv	85.22 (2)	Be1—O7—Cr3Bⁱⁱⁱ	121.57 (3)
O4ⁱⁱ—Al5—Al4A^iv	41.825 (15)	Cr3Bⁱⁱ—O7—Cr3Bⁱⁱⁱ	95.10 (4)
O4ⁱ—Al5—Al4A^iv	41.826 (15)	Al3Aⁱⁱ—O7—Cr3Bⁱⁱⁱ	95.10 (4)
Cr4B^v—Al5—Al4A^iv	59.7	Al3Aⁱ—O7—Cr3Bⁱⁱⁱ	95.10 (4)
Al4A^v—Al5—Al4A^iv	59.719 (10)	Cr3Bⁱ—O7—Cr3Bⁱⁱⁱ	95.10 (4)
Cr4B^iv—Al5—Al4A^iv	0.0	Be1—O7—Al3Aⁱⁱⁱ	121.57 (3)
O5ⁱⁱⁱ—Al5—Cr4B^vi	94.97 (2)	Cr3Bⁱⁱ—O7—Al3Aⁱⁱⁱ	95.1
O5ⁱⁱ—Al5—Cr4B^vi	138.301 (15)	Al3Aⁱⁱ—O7—Al3Aⁱⁱⁱ	95.10 (4)
O5ⁱ—Al5—Cr4B^vi	138.301 (15)	Al3Aⁱ—O7—Al3Aⁱⁱⁱ	95.10 (4)
O4ⁱⁱⁱ—Al5—Cr4B^vi	41.826 (15)	Cr3Bⁱ—O7—Al3Aⁱⁱⁱ	95.1
O4ⁱⁱ—Al5—Cr4B^vi	41.826 (15)	Cr3Bⁱⁱⁱ—O7—Al3Aⁱⁱⁱ	0.0
O4ⁱ—Al5—Cr4B^vi	85.22 (2)	Al2^xix—O8—Cr3B^x	123.84 (2)
Cr4B^v—Al5—Cr4B^vi	59.719 (10)	Al2^xix—O8—Al3A^x	123.84 (2)
Al4A^v—Al5—Cr4B^vi	59.719 (10)	Cr3B^x—O8—Al3A^x	0.0
Cr4B^iv—Al5—Cr4B^vi	59.719 (10)	Al2^xix—O8—Al3A^xiii	123.84 (2)
Al4A^iv—Al5—Cr4B^vi	59.719 (10)	Cr3B^x—O8—Al3A^xiii	95.5
O5ⁱⁱⁱ—Al5—Al4A^vi	94.97 (2)	Al3A^x—O8—Al3A^xiii	95.47 (4)
O5ⁱⁱ—Al5—Al4A^vi	138.301 (15)	Al2^xix—O8—Cr3B^xiii	123.84 (2)
O5ⁱ—Al5—Al4A^vi	138.301 (15)	Cr3B^x—O8—Cr3B^xiii	95.47 (4)
O4ⁱⁱⁱ—Al5—Al4A^vi	41.826 (15)	Al3A^x—O8—Cr3B^xiii	95.47 (4)
O4ⁱⁱ—Al5—Al4A^vi	41.826 (15)	Al3A^xiii—O8—Cr3B^xiii	0.000 (17)
O4ⁱ—Al5—Al4A^vi	85.22 (2)	Al2^xix—O8—Mg3^xiii	116.60 (4)
Cr4B^v—Al5—Al4A^vi	59.7	Cr3B^x—O8—Mg3^xiii	95.04 (3)
Al4A^v—Al5—Al4A^vi	59.719 (10)	Al3A^x—O8—Mg3^xiii	95.04 (3)
Cr4B^iv—Al5—Al4A^vi	59.7	Al3A^xiii—O8—Mg3^xiii	95.04 (3)
Al4A^iv—Al5—Al4A^vi	59.719 (10)	Cr3B^xiii—O8—Mg3^xiii	95.04 (3)
Cr4B^vi—Al5—Al4A^vi	0.0

Symmetry codes: (i) x+1, y+1, z; (ii) −y, x−y+1, z; (iii) −x+y, −x, z; (iv) −y, x−y, z; (v) x, y+1, z; (vi) −x+y+1, −x+1, z; (vii) −x, −y, −z; (viii) x+1, y, z; (ix) x−y+1, x+1, −z; (x) −x+y, −x−1, z; (xi) −x+1, −y, −z; (xii) −x+1, −y+1, −z; (xiii) x, y−1, z; (xiv) −y, x−y−1, z; (xv) −y+1, x−y, z; (xvi) −x+y+1, −x, z; (xvii) −x+y−1, −x−1, z; (xviii) −y−1, x−y−1, z; (xix) x−1, y−1, z; (xx) −y−1, x−y, z; (xxi) −x+1, −y, −z+1; (xxii) x−y+1, x+1, −z+1; (xxiii) −x, −y, −z+1; (xxiv) −y+1, x−y+1, z; (xxv) x−1, y, z.

Bond-valence sums (BVS) top

Calculated using Jana2006 (Petřìček et al., 2014) with bond-valence parameters taken from Brese & O'Keeffe (1991). Angular brackets indicate site-occupancy weighted averages for the corresponding Mab sites.

Site	BVS
Be1	1.956 (5)
Al1	3.007 (2)
Al2	2.788 (3)
Al3a	2.932 (2)
Cr3b	3.571 (3)
<M3ab>	2.943
Al4a	2.955 (2)
Cr4b	3.599 (3)
<M4ab>	2.966
Al5	2.991 (2)
Mg1a	2.077 (2)
Cr1b	2.259 (2)
<M1ab>	2.082
Mg2a	2.099 (3)
Cr2b	2.283 (3)
<M2ab>	2.108
Mg3	1.974 (2)
O1	2.006 (2)
O2	1.991 (3)
O3	1.962 (2)
O4	2.009 (2)
O5	2.008 (2)
O6	2.045 (2)
O7	1.993 (4)
O8	1.906 (2)

Acknowledgements

The sample material was kindly provided by D. Braith. The authors would like to thank S. Heidrich for providing the electron microprobe analysis and P. Stutz for sample preparation.

References

Arevalo-Lopez, A. & Attfield, J. P. (2015). Dalton Trans. 44, 10661–10664. CAS PubMed Google Scholar
Armbruster, T. (2002). Eur. j. Miner. 14, 389–395. CrossRef CAS Google Scholar
Brese, N. E. & O'Keeffe, M. (1991). Acta Cryst. B47, 192–197. CrossRef CAS Web of Science IUCr Journals Google Scholar
Bruker (2008). SADABS. Bruker AXS Inc., Madison, Wisconsin, USA. Google Scholar
Drev, S., Rečnik, A. & Daneu, N. (2013). CrystEngComm, 15, 2640–2647. CrossRef CAS Google Scholar
Gatehouse, B. M., Grey, I. E. & Nickel, E. H. (1983). Am. Mineral. 68, 833–839. CAS Google Scholar
Momma, K. & Izumi, F. (2011). J. Appl. Cryst. 44, 1272–1276. Web of Science CrossRef CAS IUCr Journals Google Scholar
Nonius (1998). COLLECT. Nonius BV, Delft, The Netherlands. Google Scholar
Nuber, B. & Schmetzer, K. (1983). Neues Jb. Miner. Monat. 393–402. Google Scholar
Palatinus, L. & Chapuis, G. (2007). J. Appl. Cryst. 40, 786–790. Web of Science CrossRef CAS IUCr Journals Google Scholar
Petřìček, V., Dušek, M. & Palatinus, L. (2014). Z. Kristallogr. 229, 345–352. Google Scholar
Schreurs, A. M. M., Xian, X. & Kroon-Batenburg, L. M. J. (2010). J. Appl. Cryst. 43, 70–82. Web of Science CrossRef CAS IUCr Journals Google Scholar
Sheldrick, G. M. (2015). Acta Cryst. C71, 3–8. Web of Science CrossRef IUCr Journals Google Scholar
Vrankić, M., Gržeta, B., Lützenkirchen-Hecht, D., Bosnar, S. & Šarić, A. (2015). Inorg. Chem. 54, 11127–11135. PubMed Google Scholar
Westrip, S. P. (2010). J. Appl. Cryst. 43, 920–925. Web of Science CrossRef CAS IUCr Journals Google Scholar
Widmer, R., Malsy, A.-K. & Armbruster, T. (2015). Phys. Chem. Miner. 42, 251–260. CrossRef CAS Google Scholar

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