Magnesium aluminium chromite

The cation distribution in a natural magnesium aluminium chromite spinel (cubic, space group Fdm), Al_0.41Cr_1.42Fe_0.65Mg_0.4O₄, was determined by electron-microprobe analysis, Mössbauer spectroscopy and single-crystal X-ray analysis. Several structural models of the octahedral and tetrahedral cation distributions were tested; the most probable is (Mg,Al,Fe)[Al,Cr,Fe,Φ_0.19]O, where (…) and […] represent the tetrahedral and octahedral sites, respectively, and Φ represents a vacancy.

S1. Comment

Chromite, (Fe²⁺)[Cr³⁺]₂O₄, which belongs to the spinel group of minerals, is an important material widely used in the metallurgical and chemical industries (Rollinson, 1973). The first structural studies concerning spinels were performed by Bragg (1915) and Nishikawa (1915). Spinels are mixed-valence compounds, AB₂X₄, and for most compounds, X is oxygen, A is a divalent cation and B is a trivalent cation. The spinels may be classified as normal spinel, (A)[B₂]O₄, and inverse spinel, (B)[A,B]O₄, where (···) and [···] represent the tetrahedral and octahedral sites, respectively. In general, (A_1-i, Bi)[Ai, B_2-i]O₄²⁻ represents a partially inverse spinel, where i is the degree of inversion. Chromite is a normal spinel with cubic Fd3m symmetry. Several overviews of spinels and their properties are available in the literature (O'Neill & Navrotsky, 1983; Valenzuela, 1994, and references therein).

In natural chromites, chromium and iron may be replaced by other metallic cations with similar charges and/or ionic radii. Therefore, because a wide variety of solid solutions may form in natural spinels, it can be helpful to use complementary experimental techniques in order to establish their structures. This strategy can be seen in several studies concerning chromites, e.g. powder and single-crystal X-ray diffraction (Salviulo et al., 2000), and Mössbauer spectroscopy and single-crystal X-ray diffraction (Lenaz et al., 2004; Figueiras & Waerenborgh, 1997).

This work forms part of a project involving the structural studies of natural spinels from Brazil. In particular, attention is focused on the cation distribution in this class of compounds. The structure of a magnesium- and aluminium-rich natural chromite has been analysed by single-crystal X-ray diffraction combined with Mössbauer spectroscopy and electron microprobe analysis. Single crystals were collected in a geological site near Piumhi town (20° 22' 00" S and 45° 56' 00" W), Minas Gerais, Brazil. A typically well shaped chromite single-crystal was mounted on a diffractometer to perform the X-ray data collection. This same crystal was later characterized by electron microprobe analysis as (Mg_0.45 (8) Al_0.41 (5) Cr_1.49 (4) Fe_0.65 (6))O_4.00 (s.u. values calculated from measurements on four differents points using MgO, Al₂O₃, Cr₂O₃ and Fe₂O₃ as standards. Mössbauer spectra of a powder sample showed that around 70% of the total Fe content is tetrahedral Fe²⁺ and 30% is octahedral Fe³⁺. The refined chemical formula and cation distribution is (Mg²⁺_0.40 (11), Al³⁺_0.28 (5), Fe²⁺_0.39 (4))[Al³⁺_0.13 (5), Cr³⁺_1.42 (6), Fe³⁺_0.26 (4), Φ_0.19]O₄, where Φ represents the vacancy. This composition is in agreement with the microprobe analysis and the Mössbauer data. Moreover, the tetrahedral site occupancy is 1.1 (1) and the crystal electroneutrality is maintained with a total cation charge of +7.9 (3). Fig. 1 shows the structure of the Mg,Al-rich chromite. As can be seen, it has a trigonal distortion in the [111] direction. Table 1 gives selected geometrical parameters.

S2. Experimental

Single crystals were extracted from rocks by mechanical separation, followed by a bath in deionized water. The aluminosilicate minerals were dissolved by repeated treatment with hot HCl and HF solutions. The residue was rinsed with distilled water and the purity of crystals was checked by powder X-ray diffraction.

S3. Refinement

The microprobe analysis result (Mg_0.45 (8) Al_0.41 (5) Cr_1.49 (4) Fe_0.65 (6))O_4.00 was used as a first approximation for cation substitution. In all refinements, different atoms on the same site were constrained to share the same anisotropic displacement parameter. Models with an inverse distribution or a partial degree of inversion were rejected for chemical reasons and on the basis of the refinement results. Four normal spinel models have been tested:

(1) Model 1: (Mg²⁺_0.52 (1), Fe²⁺_0.48 (1))[Cr³⁺_1.57 (3), Al³⁺_0.43 (3))O₄²⁻, with R(F_o) = 0.0163, wR(F_o²) = 0.0456, S(F_o²) = 1.477 and NP = 12.

(2) Model 2: on the basis of the Mössbauer data, Fe³⁺ was added to the octahedral site, keeping the total amount of iron given by the electron microprobe analysis. The refined formula is (Mg²⁺_0.51 (1), Fe²⁺_0.49 (1))[Al³⁺_0.47 (3), Cr³⁺_1.37 (3), Fe³⁺_0.16 (1)]O₄, R(F_o) = 0.0167, wR(F_o²) = 0.0470, S(F_o²) = 1.478 and NP = 13. From a statistical point of view, this model is not better than model 1.

(3) Model 3: according to O'Neill & Navrotsky (1983, 1984), Al³⁺ in spinels can be found on both octahedral and tetrahedral sites. A refinement with an additional constraint on the total Al content yielded the formula (Mg²⁺_0.26 (5), Al³⁺_0.30 (5), Fe²⁺_0.44 (1))[Al³⁺_0.11 (5), Cr³⁺_1.49 (3), Fe³⁺_0.21 (1), Φ_0.19]O₄. with R(F_o) = 0.0155, wR(F_o²) = 0.0409, S(F_o²) = 1.406 and NP = 14. This refinement clearly indicates that Al³⁺ is present at both sites, but the Mg²⁺ content disagrees with the chemical analysis.

(4) Model 4: the total tetrahedral site occupancy is relaxed, which yields the formula (Mg²⁺_0.40 (11), Al³⁺_0.28 (5), Fe²⁺_0.39 (4))[Al³⁺_0.13 (5), Cr³⁺_1.42 (6), Fe³⁺_0.26 (4), Φ_0.19]O₄, with R(F_o) = 0.0155, wR(F_o²) = 0.0408, S(F_o²) = 1.402 and NP = 14. Although it does not seem to be statistically different from model 3, this is the preferred model since electroneutrality is reached with a total positive charge of +7.9 (3), against +7.7 (2) for model 3.

Computing details

Data collection: XSCANS (Siemens, 1991); cell refinement: XSCANS; data reduction: XSCANS; program(s) used to solve structure: SHELXTL-PC (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEP-3 (Farrugia, 1997); software used to prepare material for publication: PLATON (Spek, 2003).

Figures

Fig. 1. An ORTEP-3 (Farrugia, 1997) plot of the chromite structure from Piumhi. T (large ellipsoid) represents the tetrahedral site containing the Fe^2+, Mg^2+ and Al^3+ions. M (large circle) represents the octahedral site containing the Cr^3+, Fe^3+ and Al^3+ions. The ellipsoids are drawn at the 50% probability level [symmetry code: (i) x, y − 1/4, z − 1/4].

(I)

Crystal data

Al0.41Cr1.42Fe0.65Mg0.40O4.00	Dx = 4.512 Mg m^−3
Mr = 194.94	Mo Kα radiation, λ = 0.71073 Å
Cubic, Fd3m	Cell parameters from 98 reflections
Hall symbol: -F 4vw 2vw 3	θ = 20.0–32.8°
a = 8.31058 (5) Å	µ = 8.67 mm^−1
V = 573.98 (1) Å^3	T = 298 K
Z = 8	Octahedron, black
F(000) = 746	0.07 × 0.07 × 0.07 mm

Data collection

Siemens P4 diffractometer	219 reflections with I > 2σ(I)
Radiation source: Fine-focus sealed X-ray tube	Rint = 0.049
Graphite monochromator	θmax = 56.4°, θmin = 4.3°
θ/2θ scans	h = −1→19
Absorption correction: analytical (Lundgren, 1982)	k = −19→19
Tmin = 0.385, Tmax = 0.445	l = −19→19
5083 measured reflections	3 standard reflections every 297 reflections
220 independent reflections	intensity decay: 0.5%

Refinement

Refinement on F^2	Primary atom site location: heavy-atom method
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.015	w = 1/[σ^2(Fo^2) + (0.0138P)^2 + 0.6778P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.041	(Δ/σ)max < 0.001
S = 1.40	Δρmax = 0.96 e Å^−3
220 reflections	Δρmin = −0.69 e Å^−3
14 parameters	Extinction correction: SHELXL97, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
2 restraints	Extinction coefficient: 0.0152 (10)

Special details

Experimental. ? #Insert any special details here.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
O	0.26254 (5)	0.26254 (5)	0.26254 (5)	0.00650 (14)
CrM	0.5000	0.5000	0.5000	0.00477 (9)	0.71 (3)
AlM	0.5000	0.5000	0.5000	0.00477 (9)	0.063 (27)
Fe3M	0.5000	0.5000	0.5000	0.00477 (9)	0.13 (2)
Fe2T	0.1250	0.1250	0.1250	0.0062 (3)	0.39 (4)
MgT	0.1250	0.1250	0.1250	0.0062 (3)	0.40 (11)
AlT	0.1250	0.1250	0.1250	0.0062 (3)	0.28 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O	0.00650 (14)	0.00650 (14)	0.00650 (14)	−0.00079 (9)	−0.00079 (9)	−0.00079 (9)
CrM	0.00477 (9)	0.00477 (9)	0.00477 (9)	−0.00037 (2)	−0.00037 (2)	−0.00037 (2)
AlM	0.00477 (9)	0.00477 (9)	0.00477 (9)	−0.00037 (2)	−0.00037 (2)	−0.00037 (2)
Fe3M	0.00477 (9)	0.00477 (9)	0.00477 (9)	−0.00037 (2)	−0.00037 (2)	−0.00037 (2)
Fe2T	0.0062 (3)	0.0062 (3)	0.0062 (3)	0.000	0.000	0.000
MgT	0.0062 (3)	0.0062 (3)	0.0062 (3)	0.000	0.000	0.000
AlT	0.0062 (3)	0.0062 (3)	0.0062 (3)	0.000	0.000	0.000

Geometric parameters (Å, º)

O—Fe3M^i	1.9790 (4)	AlM—CrM^viii	2.9382
O—Fe3M^ii	1.9790 (4)	AlM—CrM^iii	2.9382
O—Fe3M^iii	1.9790 (4)	AlM—CrM^ii	2.9382
O—AlM^i	1.9790 (4)	AlM—CrM^ix	2.9382
O—M^iii	1.9790 (4)	AlM—CrM^i	2.9382
O—CrM^ii	1.9790 (4)	Fe3M—O^iv	1.9789 (4)
O—CrM^i	1.9790 (4)	Fe3M—O^v	1.9789 (4)
O—AlM^iii	1.9790 (4)	Fe3M—O^ii	1.9790 (4)
O—AlM^ii	1.9790 (4)	Fe3M—O^iii	1.9790 (4)
O—T	1.9797 (8)	Fe3M—O^i	1.9790 (4)
O—AlT	1.9797 (8)	Fe3M—O^vi	1.9790 (4)
O—MgT	1.9797 (8)	Fe3M—Fe3M^vii	2.9382
CrM—O^iv	1.9789 (4)	Fe3M—CrM^viii	2.9382
CrM—O^v	1.9789 (4)	Fe3M—CrM^iii	2.9382
CrM—O^ii	1.9790 (4)	Fe3M—CrM^ii	2.9382
CrM—O^iii	1.9790 (4)	Fe3M—CrM^ix	2.9382
CrM—O^i	1.9790 (4)	Fe3M—CrM^i	2.9382
CrM—O^vi	1.9790 (4)	Fe2T—O^x	1.9798 (8)
CrM—Fe3M^vii	2.9382	Fe2T—O^xi	1.9798 (8)
CrM—CrM^viii	2.9382	Fe2T—O^xii	1.9798 (8)
CrM—CrM^iii	2.9382	MgT—O^x	1.9798 (8)
CrM—CrM^ii	2.9382	MgT—O^xi	1.9798 (8)
CrM—CrM^ix	2.9382	MgT—O^xii	1.9798 (8)
CrM—CrM^i	2.9382	MgT—MgT^xiii	3.5986
AlM—O^iv	1.9789 (4)	MgT—MgT^xiv	3.5986
AlM—O^v	1.9789 (4)	MgT—MgT^xv	3.5986
AlM—O^ii	1.9790 (4)	MgT—MgT^xvi	3.5987
AlM—O^iii	1.9790 (4)	AlT—O^x	1.9798 (8)
AlM—O^i	1.9790 (4)	AlT—O^xi	1.9798 (8)
AlM—O^vi	1.9790 (4)	AlT—O^xii	1.9798 (8)
AlM—Fe3M^vii	2.9382
Fe3M^i—O—Fe3M^ii	95.87 (3)	O^vi—AlM—CrM^viii	42.066 (13)
Fe3M^i—O—Fe3M^iii	95.87 (3)	Fe3M^vii—AlM—CrM^viii	60.0
Fe3M^ii—O—Fe3M^iii	95.87 (3)	O^iv—AlM—CrM^iii	137.934 (13)
Fe3M^ii—O—AlM^i	95.87 (3)	O^v—AlM—CrM^iii	94.27 (2)
Fe3M^iii—O—AlM^i	95.87 (3)	O^ii—AlM—CrM^iii	42.066 (13)
Fe3M^i—O—CrM^iii	95.87 (3)	O^iii—AlM—CrM^iii	85.73 (2)
Fe3M^ii—O—CrM^iii	95.87 (3)	O^i—AlM—CrM^iii	42.066 (13)
AlM^i—O—CrM^iii	95.87 (3)	O^vi—AlM—CrM^iii	137.934 (13)
Fe3M^i—O—CrM^ii	95.87 (3)	Fe3M^vii—AlM—CrM^iii	120.0
Fe3M^iii—O—CrM^ii	95.87 (3)	CrM^viii—AlM—CrM^iii	180.0
AlM^i—O—CrM^ii	95.87 (3)	O^iv—AlM—CrM^ii	137.934 (13)
CrM^iii—O—CrM^ii	95.87 (3)	O^v—AlM—CrM^ii	137.934 (13)
Fe3M^ii—O—CrM^i	95.87 (3)	O^ii—AlM—CrM^ii	85.73 (2)
Fe3M^iii—O—CrM^i	95.87 (3)	O^iii—AlM—CrM^ii	42.066 (13)
CrM^iii—O—CrM^i	95.87 (3)	O^i—AlM—CrM^ii	42.066 (13)
CrM^ii—O—CrM^i	95.87 (3)	O^vi—AlM—CrM^ii	94.27 (2)
Fe3M^i—O—AlM^iii	95.87 (3)	Fe3M^vii—AlM—CrM^ii	120.0
Fe3M^ii—O—AlM^iii	95.87 (3)	CrM^viii—AlM—CrM^ii	120.0
AlM^i—O—AlM^iii	95.87 (3)	CrM^iii—AlM—CrM^ii	60.0
CrM^ii—O—AlM^iii	95.87 (3)	O^iv—AlM—CrM^ix	42.066 (13)
CrM^i—O—AlM^iii	95.87 (3)	O^v—AlM—CrM^ix	42.066 (13)
Fe3M^i—O—AlM^ii	95.87 (3)	O^ii—AlM—CrM^ix	94.27 (2)
Fe3M^iii—O—AlM^ii	95.87 (3)	O^iii—AlM—CrM^ix	137.934 (13)
AlM^i—O—AlM^ii	95.87 (3)	O^i—AlM—CrM^ix	137.934 (13)
CrM^iii—O—AlM^ii	95.87 (3)	O^vi—AlM—CrM^ix	85.73 (2)
CrM^i—O—AlM^ii	95.87 (3)	Fe3M^vii—AlM—CrM^ix	60.0
AlM^iii—O—AlM^ii	95.87 (3)	CrM^viii—AlM—CrM^ix	60.0
Fe3M^i—O—Fe2T	120.99 (2)	CrM^iii—AlM—CrM^ix	120.0
Fe3M^ii—O—Fe2T	120.99 (2)	CrM^ii—AlM—CrM^ix	180.0
Fe3M^iii—O—Fe2T	120.99 (2)	O^iv—AlM—CrM^i	94.27 (2)
AlM^i—O—Fe2T	120.99 (2)	O^v—AlM—CrM^i	137.934 (13)
CrM^iii—O—Fe2T	120.99 (2)	O^ii—AlM—CrM^i	42.066 (13)
CrM^ii—O—Fe2T	120.99 (2)	O^iii—AlM—CrM^i	42.066 (13)
CrM^i—O—Fe2T	120.99 (2)	O^i—AlM—CrM^i	85.73 (2)
AlM^iii—O—Fe2T	120.99 (2)	O^vi—AlM—CrM^i	137.934 (13)
AlM^ii—O—Fe2T	120.99 (2)	Fe3M^vii—AlM—CrM^i	180.0
Fe3M^i—O—AlT	120.99 (2)	CrM^viii—AlM—CrM^i	120.0
Fe3M^ii—O—AlT	120.99 (2)	CrM^iii—AlM—CrM^i	60.0
Fe3M^iii—O—AlT	120.99 (2)	CrM^ii—AlM—CrM^i	60.0
AlM^i—O—AlT	120.99 (2)	CrM^ix—AlM—CrM^i	120.0
CrM^iii—O—AlT	120.99 (2)	O^iv—Fe3M—O^v	83.81 (3)
CrM^ii—O—AlT	120.99 (2)	O^iv—Fe3M—O^ii	96.19 (3)
CrM^i—O—AlT	120.99 (2)	O^v—Fe3M—O^ii	96.19 (3)
AlM^iii—O—AlT	120.99 (2)	O^iv—Fe3M—O^iii	96.19 (3)
AlM^ii—O—AlT	120.99 (2)	O^v—Fe3M—O^iii	180.0
Fe3M^i—O—MgT	120.99 (2)	O^ii—Fe3M—O^iii	83.81 (3)
Fe3M^ii—O—MgT	120.99 (2)	O^iv—Fe3M—O^i	180.0
Fe3M^iii—O—MgT	120.99 (2)	O^v—Fe3M—O^i	96.19 (3)
AlM^i—O—MgT	120.99 (2)	O^ii—Fe3M—O^i	83.81 (3)
CrM^iii—O—MgT	120.99 (2)	O^iii—Fe3M—O^i	83.81 (3)
CrM^ii—O—MgT	120.99 (2)	O^iv—Fe3M—O^vi	83.81 (3)
CrM^i—O—MgT	120.99 (2)	O^v—Fe3M—O^vi	83.81 (3)
AlM^iii—O—MgT	120.99 (2)	O^ii—Fe3M—O^vi	180.0
AlM^ii—O—MgT	120.99 (2)	O^iii—Fe3M—O^vi	96.19 (3)
O^iv—M—O^v	83.81 (3)	O^i—Fe3M—O^vi	96.19 (3)
O^iv—M—O^ii	96.19 (3)	O^iv—Fe3M—Fe3M^vii	85.73 (2)
O^v—CrM—O^ii	96.19 (3)	O^v—Fe3M—Fe3M^vii	42.066 (13)
O^iv—CrM—O^iii	96.19 (3)	O^ii—Fe3M—Fe3M^vii	137.934 (13)
O^v—CrM—O^iii	180.0	O^iii—Fe3M—Fe3M^vii	137.934 (13)
O^ii—CrM—O^iii	83.81 (3)	O^i—Fe3M—Fe3M^vii	94.27 (2)
O^iv—M—O^i	180.0	O^vi—Fe3M—Fe3M^vii	42.066 (13)
O^v—CrM—O^i	96.19 (3)	O^iv—Fe3M—CrM^viii	42.066 (13)
O^ii—CrM—O^i	83.81 (3)	O^v—Fe3M—CrM^viii	85.73 (2)
O^iii—CrM—O^i	83.81 (3)	O^ii—Fe3M—CrM^viii	137.934 (13)
O^iv—CrM—O^vi	83.81 (3)	O^iii—Fe3M—CrM^viii	94.27 (2)
O^v—CrM—O^vi	83.81 (3)	O^i—Fe3M—CrM^viii	137.934 (13)
O^ii—CrM—O^vi	180.0	O^vi—Fe3M—CrM^viii	42.066 (13)
O^iii—CrM—O^vi	96.19 (3)	Fe3M^vii—Fe3M—CrM^viii	60.0
O^i—CrM—O^vi	96.19 (3)	O^iv—Fe3M—CrM^iii	137.934 (13)
O^iv—CrM—Fe3M^vii	85.73 (2)	O^v—Fe3M—CrM^iii	94.27 (2)
O^v—CrM—Fe3M^vii	42.066 (13)	O^ii—Fe3M—CrM^iii	42.066 (13)
O^ii—CrM—Fe3M^vii	137.934 (13)	O^iii—Fe3M—CrM^iii	85.73 (2)
O^iii—CrM—Fe3M^vii	137.934 (13)	O^i—Fe3M—CrM^iii	42.066 (13)
O^i—CrM—Fe3M^vii	94.27 (2)	O^vi—Fe3M—CrM^iii	137.934 (13)
O^vi—CrM—Fe3M^vii	42.066 (13)	Fe3M^vii—Fe3M—CrM^iii	120.0
O^iv—CrM—CrM^viii	42.066 (13)	CrM^viii—Fe3M—CrM^iii	180.0
O^v—CrM—CrM^viii	85.73 (2)	O^iv—Fe3M—CrM^ii	137.934 (13)
O^ii—CrM—CrM^viii	137.934 (13)	O^v—Fe3M—CrM^ii	137.934 (13)
O^iii—CrM—CrM^viii	94.27 (2)	O^ii—Fe3M—CrM^ii	85.73 (2)
O^i—CrM—CrM^viii	137.934 (13)	O^iii—Fe3M—CrM^ii	42.066 (13)
O^vi—CrM—CrM^viii	42.066 (13)	O^i—Fe3M—CrM^ii	42.066 (13)
Fe3M^vii—CrM—CrM^viii	60.0	O^vi—Fe3M—CrM^ii	94.27 (2)
O^iv—CrM—CrM^iii	137.934 (13)	Fe3M^vii—Fe3M—CrM^ii	120.0
O^v—CrM—CrM^iii	94.27 (2)	CrM^viii—Fe3M—CrM^ii	120.0
O^ii—CrM—CrM^iii	42.066 (13)	CrM^iii—Fe3M—CrM^ii	60.0
O^iii—CrM—CrM^iii	85.73 (2)	O^iv—Fe3M—CrM^ix	42.066 (13)
O^i—CrM—CrM^iii	42.066 (13)	O^v—Fe3M—CrM^ix	42.066 (13)
O^vi—CrM—CrM^iii	137.934 (13)	O^ii—Fe3M—CrM^ix	94.27 (2)
Fe3M^vii—CrM—CrM^iii	120.0	O^iii—Fe3M—CrM^ix	137.934 (13)
CrM^viii—CrM—CrM^iii	180.0	O^i—Fe3M—CrM^ix	137.934 (13)
O^iv—CrM—CrM^ii	137.934 (13)	O^vi—Fe3M—CrM^ix	85.73 (2)
O^v—CrM—CrM^ii	137.934 (13)	Fe3M^vii—Fe3M—CrM^ix	60.0
O^ii—CrM—CrM^ii	85.73 (2)	CrM^viii—Fe3M—CrM^ix	60.0
O^iii—CrM—CrM^ii	42.066 (13)	CrM^iii—Fe3M—CrM^ix	120.0
O^i—CrM—CrM^ii	42.066 (13)	CrM^ii—Fe3M—CrM^ix	180.0
O^vi—CrM—CrM^ii	94.27 (2)	O^iv—Fe3M—CrM^i	94.27 (2)
Fe3M^vii—CrM—CrM^ii	120.0	O^v—Fe3M—CrM^i	137.934 (13)
CrM^viii—CrM—CrM^ii	120.0	O^ii—Fe3M—CrM^i	42.066 (13)
CrM^iii—CrM—CrM^ii	60.0	O^iii—Fe3M—CrM^i	42.066 (13)
O^iv—CrM—CrM^ix	42.066 (13)	O^i—Fe3M—CrM^i	85.73 (2)
O^v—CrM—CrM^ix	42.066 (13)	O^vi—Fe3M—CrM^i	137.934 (13)
O^ii—CrM—CrM^ix	94.27 (2)	Fe3M^vii—Fe3M—CrM^i	180.0
O^iii—CrM—CrM^ix	137.934 (13)	CrM^viii—Fe3M—CrM^i	120.0
O^i—CrM—CrM^ix	137.934 (13)	CrM^iii—Fe3M—CrM^i	60.0
O^vi—CrM—CrM^ix	85.73 (2)	CrM^ii—Fe3M—CrM^i	60.0
Fe3M^vii—CrM—CrM^ix	60.0	CrM^ix—Fe3M—CrM^i	120.0
CrM^viii—CrM—CrM^ix	60.0	O—Fe2T—O^x	109.5
CrM^iii—CrM—CrM^ix	120.0	O—T—O^xi	109.5
CrM^ii—CrM—CrM^ix	180.0	O^x—Fe2T—O^xi	109.5
O^iv—CrM—CrM^i	94.27 (2)	O—Fe2T—O^xii	109.5
O^v—CrM—CrM^i	137.934 (13)	O^x—Fe2T—O^xii	109.5
O^ii—CrM—CrM^i	42.066 (13)	O^xi—Fe2T—O^xii	109.5
O^iii—CrM—CrM^i	42.066 (13)	O—MgT—O^x	109.5
O^i—CrM—CrM^i	85.73 (2)	O—MgT—O^xi	109.5
O^vi—CrM—CrM^i	137.934 (13)	O^x—MgT—O^xi	109.5
Fe3M^vii—CrM—CrM^i	180.0	O—MgT—O^xii	109.5
CrM^viii—CrM—CrM^i	120.0	O^x—MgT—O^xii	109.5
CrM^iii—CrM—CrM^i	60.0	O^xi—MgT—O^xii	109.5
CrM^ii—CrM—CrM^i	60.0	O—MgT—MgT^xiii	70.5
CrM^ix—CrM—CrM^i	120.0	O^x—MgT—MgT^xiii	70.5
O^iv—AlM—O^v	83.81 (3)	O^xi—MgT—MgT^xiii	70.5
O^iv—AlM—O^ii	96.19 (3)	O^xii—MgT—MgT^xiii	179.998 (10)
O^v—AlM—O^ii	96.19 (3)	O—MgT—MgT^xiv	70.5
O^iv—AlM—O^iii	96.19 (3)	O^x—MgT—MgT^xiv	179.998 (10)
O^v—AlM—O^iii	180.0	O^xi—MgT—MgT^xiv	70.5
O^ii—AlM—O^iii	83.81 (3)	O^xii—MgT—MgT^xiv	70.5
O^iv—AlM—O^i	180.0	MgT^xiii—MgT—MgT^xiv	109.5
O^v—AlM—O^i	96.19 (3)	O—MgT—MgT^xv	70.5
O^ii—AlM—O^i	83.81 (3)	O^x—MgT—MgT^xv	70.5
O^iii—AlM—O^i	83.81 (3)	O^xi—MgT—MgT^xv	179.998 (10)
O^iv—AlM—O^vi	83.81 (3)	O^xii—MgT—MgT^xv	70.5
O^v—AlM—O^vi	83.81 (3)	MgT^xiii—MgT—MgT^xv	109.5
O^ii—AlM—O^vi	180.0	MgT^xiv—MgT—MgT^xv	109.5
O^iii—AlM—O^vi	96.19 (3)	O—MgT—MgT^xvi	180.000 (11)
O^i—AlM—O^vi	96.19 (3)	O^x—MgT—MgT^xvi	70.5
O^iv—AlM—Fe3M^vii	85.73 (2)	O^xi—MgT—MgT^xvi	70.5
O^v—AlM—Fe3M^vii	42.066 (13)	O^xii—MgT—MgT^xvi	70.5
O^ii—AlM—Fe3M^vii	137.934 (13)	MgT^xiii—MgT—MgT^xvi	109.5
O^iii—AlM—Fe3M^vii	137.934 (13)	MgT^xiv—MgT—MgT^xvi	109.5
O^i—AlM—Fe3M^vii	94.27 (2)	MgT^xv—MgT—MgT^xvi	109.5
O^vi—AlM—Fe3M^vii	42.066 (13)	O—AlT—O^x	109.5
O^iv—AlM—CrM^viii	42.066 (13)	O—AlT—O^xi	109.5
O^v—AlM—CrM^viii	85.73 (2)	O^x—AlT—O^xi	109.5
O^ii—AlM—CrM^viii	137.934 (13)	O—AlT—O^xii	109.5
O^iii—AlM—CrM^viii	94.27 (2)	O^x—AlT—O^xii	109.5
O^i—AlM—CrM^viii	137.934 (13)	O^xi—AlT—O^xii	109.5

Symmetry codes: (i) −x+3/4, y, −z+3/4; (ii) −x+3/4, −y+3/4, z; (iii) x, −y+3/4, −z+3/4; (iv) x+1/4, −y+1, z+1/4; (v) −x+1, y+1/4, z+1/4; (vi) x+1/4, y+1/4, −z+1; (vii) −x+5/4, y, −z+5/4; (viii) x, −y+5/4, −z+5/4; (ix) −x+5/4, −y+5/4, z; (x) −x+1/4, y, −z+1/4; (xi) x, −y+1/4, −z+1/4; (xii) −x+1/4, −y+1/4, z; (xiii) −x+1/2, −y+1/2, −z; (xiv) −x+1/2, −y, −z+1/2; (xv) −x, −y+1/2, −z+1/2; (xvi) −x, −y, −z.