Investigation of thermal behavior of mixed-valent iron borates vonsenite and hulsite containing [OM₄]ⁿ⁺ and [OM₅]ⁿ⁺ oxocentred polyhedra by in situ high-temperature Mössbauer spectroscopy, X-ray diffraction and thermal analysis

The investigation of elemental composition, crystal structure and thermal behavior of vonsenite and hulsite from the Titovskoe boron deposit in Russia is reported. The structures of the borates are described in terms of cation-centered and oxocentred polyhedra. There are different sequences of double chains and layers consisting of oxocentred [OM₄]ⁿ⁺ tetrahedra and [OM₅]ⁿ⁺ tetragonal pyramids forming a framework. Elemental composition was determined by energy-dispersive X-ray spectroscopy (EDX). Oxidation states and coordination sites of iron and tin in the oxoborates are determined using Mössbauer spectroscopy and compared with EDX and X-ray diffraction data (XRD). According to results obtained from high-temperature Mössbauer spectroscopy, the Fe²⁺ to Fe³⁺ oxidation in vonsenite and hulsite occurs at approximately 500 and 600 K, respectively. According to the high-temperature XRD data, this process is accompanied by an assumed deformation of crystal structures and subsequent solid-phase decomposition to hematite and warwickite. It is seen as a monotonic decrease of volume thermal expansion coefficients with an increase in temperature. A partial magnetic ordering in hulsite is observed for the first time with T_c ≃ 383 K. Near this temperature, an unusual change of thermal expansion coefficients is revealed. Vonsenite starts to melt at 1571 K and hulsite melts at 1504 K. Eigenvalues of thermal expansion tensor are calculated for the oxoborates as well as anisotropy of the expansion is described in comparison with their crystal structures.

Computing details

(vonsenite_293K)

Crystal data

BFe2.654Mg0.346O5	F(000) = 473
Mr = 247.4	Dx = 4.634 Mg m^−3
Orthorhombic, Pbam	Mo Kα radiation, λ = 0.71069 Å
Hall symbol: -P 2 2ab	Cell parameters from 404 reflections
a = 9.3914 (10) Å	θ = 1.0–26.0°
b = 12.3034 (10) Å	µ = 10.70 mm^−1
c = 3.0697 (6) Å	T = 293 K
V = 354.69 (8) Å^3	Prizm, black
Z = 4	0.4 × 0.1 × 0.1 mm

Data collection

Bruker Smart APEX II diffractometer	329 reflections with I > 3σ(I)
Radiation source: X-ray tube	Rint = 0.037
Absorption correction: multi-scan (Krause et al., 2015)	θmax = 26.0°, θmin = 6.6°
Tmin = 0.820, Tmax = 0.870	h = −11→11
1886 measured reflections	k = −14→15
404 independent reflections	l = −3→3

Refinement

Refinement on F	1 restraint
R[F^2 > 2σ(F^2)] = 0.036	10 constraints
wR(F^2) = 0.039	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 1.66	(Δ/σ)max = 0.016
404 reflections	Δρmax = 1.02 e Å^−3
57 parameters	Δρmin = −0.81 e Å^−3

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Fe1	0	0	0	0.0086 (5)	0.76 (2)
Mg1'	0	0	0	0.0086 (5)	0.24 (2)
Fe2	0.5	0	0.5	0.0125 (5)
Fe3	0.00114 (14)	0.27499 (10)	0	0.0093 (4)	0.77 (2)
Mg3'	0.00114 (14)	0.27499 (10)	0	0.0093 (4)	0.23 (2)
Fe4	0.74397 (12)	0.38759 (9)	0.5	0.0095 (4)
B1	0.2706 (9)	0.3625 (6)	0.5	0.006 (2)
O1	0.8450 (5)	0.0425 (4)	0.5	0.0095 (16)
O2	0.3865 (5)	0.0780 (4)	0	0.0095 (16)
O3	0.6233 (5)	0.1398 (4)	0.5	0.0080 (16)
O4	0.1123 (5)	0.1409 (4)	0	0.0062 (15)
O5	0.3438 (6)	0.2640 (4)	0.5	0.0095 (16)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Fe1	0.0085 (10)	0.0067 (10)	0.0105 (9)	−0.0021 (8)	0	0
Mg1'	0.0085 (10)	0.0067 (10)	0.0105 (9)	−0.0021 (8)	0	0
Fe2	0.0215 (10)	0.0059 (9)	0.0101 (8)	−0.0031 (7)	0	0
Fe3	0.0107 (7)	0.0065 (7)	0.0108 (7)	0.0015 (6)	0	0
Mg3'	0.0107 (7)	0.0065 (7)	0.0108 (7)	0.0015 (6)	0	0
Fe4	0.0112 (6)	0.0080 (6)	0.0095 (6)	0.0017 (5)	0	0
B1	0.005 (4)	0.010 (4)	0.002 (4)	−0.002 (4)	0	0
O1	0.012 (3)	0.005 (3)	0.012 (3)	−0.002 (2)	0	0
O2	0.006 (3)	0.009 (3)	0.014 (3)	0.000 (2)	0	0
O3	0.009 (3)	0.003 (3)	0.012 (3)	0.002 (2)	0	0
O4	0.003 (3)	0.008 (3)	0.007 (3)	0.003 (2)	0	0
O5	0.012 (3)	0.002 (3)	0.014 (3)	−0.002 (2)	0	0

Geometric parameters (Å, º)

Fe1—Mg1'	0	Fe3—O3^ix	2.183 (4)
Fe1—O1^i	2.178 (4)	Fe3—O4	1.952 (5)
Fe1—O1^ii	2.178 (4)	Fe3—O5^viii	2.183 (4)
Fe1—O1^iii	2.178 (4)	Fe3—O5^ix	2.183 (4)
Fe1—O1^iv	2.178 (4)	Mg3'—O2^viii	2.106 (5)
Fe1—O4	2.031 (5)	Mg3'—O3^viii	2.183 (4)
Fe1—O4^v	2.031 (5)	Mg3'—O3^ix	2.183 (4)
Mg1'—O1^i	2.178 (4)	Mg3'—O4	1.952 (5)
Mg1'—O1^ii	2.178 (4)	Mg3'—O5^viii	2.183 (4)
Mg1'—O1^iii	2.178 (4)	Mg3'—O5^ix	2.183 (4)
Mg1'—O1^iv	2.178 (4)	Fe4—O1^x	2.083 (5)
Mg1'—O4	2.031 (5)	Fe4—O2^xi	2.081 (3)
Mg1'—O4^v	2.031 (5)	Fe4—O2^xii	2.081 (3)
Fe2—O2	2.100 (3)	Fe4—O4^xi	2.002 (3)
Fe2—O2^vi	2.100 (3)	Fe4—O4^xii	2.002 (3)
Fe2—O2^iv	2.100 (3)	Fe4—O5^xii	2.086 (5)
Fe2—O2^vii	2.100 (3)	B1—O1^ix	1.361 (9)
Fe2—O3	2.076 (5)	B1—O3^ix	1.385 (9)
Fe2—O3^iv	2.076 (5)	B1—O5	1.392 (9)
Fe3—Mg3'	0	O1—O3	2.403 (7)
Fe3—O2^viii	2.106 (5)	O1—O5^xii	2.381 (7)
Fe3—O3^viii	2.183 (4)	O3—O5^xii	2.384 (7)
Mg1'—Fe1—O1^i	0	O3^ix—B1—O5	118.2 (6)
Mg1'—Fe1—O1^ii	0	Fe1^xiii—O1—Fe1^xiv	89.59 (19)
Mg1'—Fe1—O1^iii	0	Fe1^xiii—O1—Mg1'^xiii	0.0 (5)
Mg1'—Fe1—O1^iv	0	Fe1^xiii—O1—Mg1'^xiv	89.59 (19)
Mg1'—Fe1—O4	0	Fe1^xiii—O1—Fe4^xv	92.75 (17)
Mg1'—Fe1—O4^v	0	Fe1^xiii—O1—B1^xii	123.3 (3)
O1^i—Fe1—O1^ii	89.59 (14)	Fe1^xiii—O1—O3	134.31 (10)
O1^i—Fe1—O1^iii	90.41 (14)	Fe1^xiii—O1—O5^xii	104.12 (19)
O1^i—Fe1—O1^iv	180.0 (5)	Fe1^xiv—O1—Mg1'^xiii	89.59 (19)
O1^i—Fe1—O4	98.13 (16)	Fe1^xiv—O1—Mg1'^xiv	0.0 (5)
O1^i—Fe1—O4^v	81.87 (16)	Fe1^xiv—O1—Fe4^xv	92.75 (17)
O1^ii—Fe1—O1^iii	180.0 (5)	Fe1^xiv—O1—B1^xii	123.3 (3)
O1^ii—Fe1—O1^iv	90.41 (14)	Fe1^xiv—O1—O3	134.31 (10)
O1^ii—Fe1—O4	98.13 (16)	Fe1^xiv—O1—O5^xii	104.12 (19)
O1^ii—Fe1—O4^v	81.87 (16)	Mg1'^xiii—O1—Mg1'^xiv	89.59 (19)
O1^iii—Fe1—O1^iv	89.59 (14)	Mg1'^xiii—O1—Fe4^xv	92.75 (17)
O1^iii—Fe1—O4	81.87 (16)	Mg1'^xiii—O1—B1^xii	123.3 (3)
O1^iii—Fe1—O4^v	98.13 (16)	Mg1'^xiii—O1—O3	134.31 (10)
O1^iv—Fe1—O4	81.87 (16)	Mg1'^xiii—O1—O5^xii	104.12 (19)
O1^iv—Fe1—O4^v	98.13 (16)	Mg1'^xiv—O1—Fe4^xv	92.75 (17)
O4—Fe1—O4^v	180.0 (5)	Mg1'^xiv—O1—B1^xii	123.3 (3)
Fe1—Mg1'—O1^i	0	Mg1'^xiv—O1—O3	134.31 (10)
Fe1—Mg1'—O1^ii	0	Mg1'^xiv—O1—O5^xii	104.12 (19)
Fe1—Mg1'—O1^iii	0	Fe4^xv—O1—B1^xii	125.5 (5)
Fe1—Mg1'—O1^iv	0	Fe4^xv—O1—O3	96.2 (2)
Fe1—Mg1'—O4	0	Fe4^xv—O1—O5^xii	156.0 (3)
Fe1—Mg1'—O4^v	0	B1^xii—O1—O3	29.2 (4)
O1^i—Mg1'—O1^ii	89.59 (14)	B1^xii—O1—O5^xii	30.5 (4)
O1^i—Mg1'—O1^iii	90.41 (14)	O3—O1—O5^xii	59.8 (2)
O1^i—Mg1'—O1^iv	180.0 (5)	Fe2^xvi—O2—Fe2	93.9 (2)
O1^i—Mg1'—O4	98.13 (16)	Fe2^xvi—O2—Fe3^xi	97.65 (17)
O1^i—Mg1'—O4^v	81.87 (16)	Fe2^xvi—O2—Mg3'^xi	97.65 (17)
O1^ii—Mg1'—O1^iii	180.0 (5)	Fe2^xvi—O2—Fe4^viii	83.14 (4)
O1^ii—Mg1'—O1^iv	90.41 (14)	Fe2^xvi—O2—Fe4^ix	163.5 (3)
O1^ii—Mg1'—O4	98.13 (16)	Fe2—O2—Fe3^xi	97.65 (17)
O1^ii—Mg1'—O4^v	81.87 (16)	Fe2—O2—Mg3'^xi	97.65 (17)
O1^iii—Mg1'—O1^iv	89.59 (14)	Fe2—O2—Fe4^viii	163.5 (3)
O1^iii—Mg1'—O4	81.87 (16)	Fe2—O2—Fe4^ix	83.14 (4)
O1^iii—Mg1'—O4^v	98.13 (16)	Fe3^xi—O2—Mg3'^xi	0.0 (5)
O1^iv—Mg1'—O4	81.87 (16)	Fe3^xi—O2—Fe4^viii	98.80 (18)
O1^iv—Mg1'—O4^v	98.13 (16)	Fe3^xi—O2—Fe4^ix	98.80 (18)
O4—Mg1'—O4^v	180.0 (5)	Mg3'^xi—O2—Fe4^viii	98.80 (18)
O2—Fe2—O2^vi	93.93 (14)	Mg3'^xi—O2—Fe4^ix	98.80 (18)
O2—Fe2—O2^iv	86.07 (14)	Fe4^viii—O2—Fe4^ix	95.1 (2)
O2—Fe2—O2^vii	180.0 (5)	Fe2—O3—Fe3^xi	95.96 (17)
O2—Fe2—O3	84.52 (17)	Fe2—O3—Fe3^xii	95.96 (17)
O2—Fe2—O3^iv	95.48 (17)	Fe2—O3—Mg3'^xi	95.96 (17)
O2^vi—Fe2—O2^iv	180.0 (5)	Fe2—O3—Mg3'^xii	95.96 (17)
O2^vi—Fe2—O2^vii	86.07 (14)	Fe2—O3—B1^xii	122.7 (4)
O2^vi—Fe2—O3	84.52 (17)	Fe2—O3—O1	94.0 (2)
O2^vi—Fe2—O3^iv	95.48 (17)	Fe2—O3—O5^xii	153.6 (3)
O2^iv—Fe2—O2^vii	93.93 (14)	Fe3^xi—O3—Fe3^xii	89.33 (19)
O2^iv—Fe2—O3	95.48 (17)	Fe3^xi—O3—Mg3'^xi	0.0 (5)
O2^iv—Fe2—O3^iv	84.52 (17)	Fe3^xi—O3—Mg3'^xii	89.33 (19)
O2^vii—Fe2—O3	95.48 (17)	Fe3^xi—O3—B1^xii	122.4 (2)
O2^vii—Fe2—O3^iv	84.52 (17)	Fe3^xi—O3—O1	134.00 (11)
O3—Fe2—O3^iv	180.0 (5)	Fe3^xi—O3—O5^xii	102.67 (18)
Mg3'—Fe3—O2^viii	0	Fe3^xii—O3—Mg3'^xi	89.33 (19)
Mg3'—Fe3—O3^viii	0	Fe3^xii—O3—Mg3'^xii	0.0 (5)
Mg3'—Fe3—O3^ix	0	Fe3^xii—O3—B1^xii	122.4 (2)
Mg3'—Fe3—O4	0	Fe3^xii—O3—O1	134.00 (11)
Mg3'—Fe3—O5^viii	0	Fe3^xii—O3—O5^xii	102.67 (18)
Mg3'—Fe3—O5^ix	0	Mg3'^xi—O3—Mg3'^xii	89.33 (19)
O2^viii—Fe3—O3^viii	81.78 (17)	Mg3'^xi—O3—B1^xii	122.4 (2)
O2^viii—Fe3—O3^ix	81.78 (17)	Mg3'^xi—O3—O1	134.00 (11)
O2^viii—Fe3—O4	178.3 (2)	Mg3'^xi—O3—O5^xii	102.67 (18)
O2^viii—Fe3—O5^viii	80.96 (16)	Mg3'^xii—O3—B1^xii	122.4 (2)
O2^viii—Fe3—O5^ix	80.96 (16)	Mg3'^xii—O3—O1	134.00 (11)
O3^viii—Fe3—O3^ix	89.33 (14)	Mg3'^xii—O3—O5^xii	102.67 (18)
O3^viii—Fe3—O4	97.05 (17)	B1^xii—O3—O1	28.7 (3)
O3^viii—Fe3—O5^viii	88.09 (14)	B1^xii—O3—O5^xii	31.0 (3)
O3^viii—Fe3—O5^ix	162.74 (19)	O1—O3—O5^xii	59.6 (2)
O3^ix—Fe3—O4	97.05 (17)	Fe1—O4—Mg1'	0.0 (5)
O3^ix—Fe3—O5^viii	162.74 (19)	Fe1—O4—Fe3	116.3 (2)
O3^ix—Fe3—O5^ix	88.09 (14)	Fe1—O4—Mg3'	116.3 (2)
O4—Fe3—O5^viii	100.20 (17)	Fe1—O4—Fe4^viii	99.82 (17)
O4—Fe3—O5^ix	100.20 (17)	Fe1—O4—Fe4^ix	99.82 (17)
O5^viii—Fe3—O5^ix	89.34 (15)	Mg1'—O4—Fe3	116.3 (2)
Fe3—Mg3'—O2^viii	0	Mg1'—O4—Mg3'	116.3 (2)
Fe3—Mg3'—O3^viii	0	Mg1'—O4—Fe4^viii	99.82 (17)
Fe3—Mg3'—O3^ix	0	Mg1'—O4—Fe4^ix	99.82 (17)
Fe3—Mg3'—O4	0	Fe3—O4—Mg3'	0.0 (5)
Fe3—Mg3'—O5^viii	0	Fe3—O4—Fe4^viii	118.63 (16)
Fe3—Mg3'—O5^ix	0	Fe3—O4—Fe4^ix	118.63 (16)
O2^viii—Mg3'—O3^viii	81.78 (17)	Mg3'—O4—Fe4^viii	118.63 (16)
O2^viii—Mg3'—O3^ix	81.78 (17)	Mg3'—O4—Fe4^ix	118.63 (16)
O2^viii—Mg3'—O4	178.3 (2)	Fe4^viii—O4—Fe4^ix	100.1 (2)
O2^viii—Mg3'—O5^viii	80.96 (16)	Fe3^xi—O5—Fe3^xii	89.3 (2)
O2^viii—Mg3'—O5^ix	80.96 (16)	Fe3^xi—O5—Mg3'^xi	0.0 (5)
O3^viii—Mg3'—O3^ix	89.33 (14)	Fe3^xi—O5—Mg3'^xii	89.3 (2)
O3^viii—Mg3'—O4	97.05 (17)	Fe3^xi—O5—Fe4^ix	96.21 (16)
O3^viii—Mg3'—O5^viii	88.09 (14)	Fe3^xi—O5—B1	121.6 (3)
O3^viii—Mg3'—O5^ix	162.74 (19)	Fe3^xi—O5—O1^ix	102.45 (19)
O3^ix—Mg3'—O4	97.05 (17)	Fe3^xi—O5—O3^ix	134.12 (11)
O3^ix—Mg3'—O5^viii	162.74 (19)	Fe3^xii—O5—Mg3'^xi	89.3 (2)
O3^ix—Mg3'—O5^ix	88.09 (14)	Fe3^xii—O5—Mg3'^xii	0.0 (5)
O4—Mg3'—O5^viii	100.20 (17)	Fe3^xii—O5—Fe4^ix	96.21 (16)
O4—Mg3'—O5^ix	100.20 (17)	Fe3^xii—O5—B1	121.6 (3)
O5^viii—Mg3'—O5^ix	89.34 (15)	Fe3^xii—O5—O1^ix	102.45 (19)
O1^x—Fe4—O2^xi	94.10 (18)	Fe3^xii—O5—O3^ix	134.12 (11)
O1^x—Fe4—O2^xii	94.10 (18)	Mg3'^xi—O5—Mg3'^xii	89.3 (2)
O1^x—Fe4—O4^xi	85.00 (17)	Mg3'^xi—O5—Fe4^ix	96.21 (16)
O1^x—Fe4—O4^xii	85.00 (17)	Mg3'^xi—O5—B1	121.6 (3)
O1^x—Fe4—O5^xii	177.0 (2)	Mg3'^xi—O5—O1^ix	102.45 (19)
O2^xi—Fe4—O2^xii	95.06 (15)	Mg3'^xi—O5—O3^ix	134.12 (11)
O2^xi—Fe4—O4^xi	82.40 (15)	Mg3'^xii—O5—Fe4^ix	96.21 (16)
O2^xi—Fe4—O4^xii	177.23 (17)	Mg3'^xii—O5—B1	121.6 (3)
O2^xi—Fe4—O5^xii	83.88 (18)	Mg3'^xii—O5—O1^ix	102.45 (19)
O2^xii—Fe4—O4^xi	177.23 (17)	Mg3'^xii—O5—O3^ix	134.12 (11)
O2^xii—Fe4—O4^xii	82.40 (15)	Fe4^ix—O5—B1	123.8 (5)
O2^xii—Fe4—O5^xii	83.88 (18)	Fe4^ix—O5—O1^ix	153.6 (3)
O4^xi—Fe4—O4^xii	100.11 (16)	Fe4^ix—O5—O3^ix	93.0 (2)
O4^xi—Fe4—O5^xii	96.92 (17)	B1—O5—O1^ix	29.8 (4)
O4^xii—Fe4—O5^xii	96.92 (17)	B1—O5—O3^ix	30.8 (4)
O1^ix—B1—O3^ix	122.1 (6)	O1^ix—O5—O3^ix	60.6 (2)
O1^ix—B1—O5	119.7 (6)

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

(vonsenite_400K)

Crystal data

BFe2.654Mg0.346O5	F(000) = 473
Mr = 247.4	Dx = 4.583 Mg m^−3
Orthorhombic, Pbam	Mo Kα radiation, λ = 0.71069 Å
Hall symbol: -P 2 2ab	Cell parameters from 404 reflections
a = 9.425 (1) Å	θ = 1.0–25.9°
b = 12.3528 (10) Å	µ = 10.59 mm^−1
c = 3.0799 (6) Å	T = 400 K
V = 358.58 (8) Å^3	Prizm, black
Z = 4	0.4 × 0.1 × 0.1 mm

Data collection

Bruker Smart APEX II diffractometer	337 reflections with I > 3σ(I)
Radiation source: X-ray tube	Rint = 0.086
Absorption correction: multi-scan (Krause et al., 2015)	θmax = 25.9°, θmin = 6.6°
Tmin = 0.820, Tmax = 0.870	h = −11→11
1882 measured reflections	k = −14→15
404 independent reflections	l = −3→3

Refinement

Refinement on F	1 restraint
R[F^2 > 2σ(F^2)] = 0.029	10 constraints
wR(F^2) = 0.032	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 1.48	(Δ/σ)max = 0.006
404 reflections	Δρmax = 0.54 e Å^−3
57 parameters	Δρmin = −0.58 e Å^−3

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Fe1	0	0	0	0.0087 (5)	0.7622
Mg1'	0	0	0	0.0087 (5)	0.2378
Fe2	0.5	0	0.5	0.0125 (4)
Fe3	0.00133 (11)	0.27511 (8)	0	0.0099 (3)	0.7733
Mg3'	0.00133 (11)	0.27511 (8)	0	0.0099 (3)	0.2267
Fe4	0.74361 (10)	0.38726 (7)	0.5	0.0095 (3)
B1	0.2705 (7)	0.3622 (5)	0.5	0.006 (2)
O1	0.8454 (4)	0.0431 (3)	0.5	0.0107 (13)
O2	0.3871 (4)	0.0788 (3)	0	0.0100 (14)
O3	0.6244 (4)	0.1399 (3)	0.5	0.0105 (14)
O4	0.1119 (4)	0.1412 (3)	0	0.0081 (13)
O5	0.3434 (5)	0.2638 (3)	0.5	0.0104 (14)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Fe1	0.0087 (8)	0.0086 (8)	0.0088 (8)	−0.0017 (6)	0	0
Mg1'	0.0087 (8)	0.0086 (8)	0.0088 (8)	−0.0017 (6)	0	0
Fe2	0.0206 (8)	0.0099 (7)	0.0069 (7)	−0.0027 (6)	0	0
Fe3	0.0109 (6)	0.0089 (6)	0.0099 (6)	0.0016 (5)	0	0
Mg3'	0.0109 (6)	0.0089 (6)	0.0099 (6)	0.0016 (5)	0	0
Fe4	0.0107 (5)	0.0104 (5)	0.0074 (5)	0.0012 (4)	0	0
B1	0.005 (4)	0.012 (4)	0.001 (3)	−0.002 (3)	0	0
O1	0.011 (2)	0.009 (2)	0.012 (2)	−0.0022 (19)	0	0
O2	0.007 (2)	0.010 (2)	0.013 (2)	−0.0002 (19)	0	0
O3	0.010 (3)	0.009 (2)	0.012 (2)	0.0005 (18)	0	0
O4	0.005 (2)	0.011 (2)	0.008 (2)	0.0018 (18)	0	0
O5	0.014 (2)	0.007 (2)	0.011 (2)	−0.0014 (19)	0	0

Geometric parameters (Å, º)

Fe1—Mg1'	0	Fe3—O4	1.955 (4)
Fe1—O4	2.038 (4)	Mg3'—Mg3'^ii	3.0799 (12)
Fe1—O4^i	2.038 (4)	Mg3'—Mg3'^iii	3.0799 (12)
Mg1'—Mg1'^ii	3.0799 (12)	Mg3'—O2^vi	2.102 (4)
Mg1'—Mg1'^iii	3.0799 (12)	Mg3'—O4	1.955 (4)
Mg1'—O4	2.038 (4)	Fe4—O1^vii	2.099 (4)
Mg1'—O4^i	2.038 (4)	Fe4—O2^viii	2.092 (3)
Fe2—O2	2.110 (3)	Fe4—O2^ix	2.092 (3)
Fe2—O2^iii	2.110 (3)	Fe4—O4^viii	2.009 (3)
Fe2—O2^iv	2.110 (3)	Fe4—O4^ix	2.009 (3)
Fe2—O2^v	2.110 (3)	Fe4—O5^ix	2.089 (4)
Fe2—O3	2.089 (4)	B1—O1^x	1.367 (8)
Fe2—O3^iv	2.089 (4)	B1—O3^x	1.377 (8)
Fe3—Mg3'	0	B1—O5	1.396 (7)
Fe3—O2^vi	2.102 (4)
Mg1'—Fe1—O4	0	O2^viii—Fe4—O2^ix	94.82 (12)
Mg1'—Fe1—O4^i	0	O2^viii—Fe4—O4^viii	82.54 (12)
O4—Fe1—O4^i	180.0 (5)	O2^viii—Fe4—O4^ix	177.20 (13)
Fe1—Mg1'—Mg1'^ii	0	O2^viii—Fe4—O5^ix	83.58 (14)
Fe1—Mg1'—Mg1'^iii	0	O2^ix—Fe4—O4^viii	177.20 (13)
Fe1—Mg1'—O4	0	O2^ix—Fe4—O4^ix	82.54 (12)
Fe1—Mg1'—O4^i	0	O2^ix—Fe4—O5^ix	83.58 (14)
Mg1'^ii—Mg1'—Mg1'^iii	180.0 (5)	O4^viii—Fe4—O4^ix	100.09 (13)
Mg1'^ii—Mg1'—O4	90	O4^viii—Fe4—O5^ix	97.00 (14)
Mg1'^ii—Mg1'—O4^i	90	O4^ix—Fe4—O5^ix	97.00 (14)
Mg1'^iii—Mg1'—O4	90	O1^x—B1—O3^x	122.2 (5)
Mg1'^iii—Mg1'—O4^i	90	O1^x—B1—O5	119.5 (5)
O4—Mg1'—O4^i	180.0 (5)	O3^x—B1—O5	118.4 (5)
O2—Fe2—O2^iii	93.75 (11)	Fe4^xi—O1—B1^ix	125.4 (4)
O2—Fe2—O2^iv	86.25 (11)	Fe2^ii—O2—Fe2	93.75 (16)
O2—Fe2—O2^v	180.0 (5)	Fe2^ii—O2—Fe3^viii	97.91 (14)
O2—Fe2—O3	84.35 (13)	Fe2^ii—O2—Mg3'^viii	97.91 (14)
O2—Fe2—O3^iv	95.65 (13)	Fe2^ii—O2—Fe4^vi	83.18 (4)
O2^iii—Fe2—O2^iv	180.0 (5)	Fe2^ii—O2—Fe4^x	162.9 (2)
O2^iii—Fe2—O2^v	86.25 (11)	Fe2—O2—Fe3^viii	97.91 (14)
O2^iii—Fe2—O3	84.35 (13)	Fe2—O2—Mg3'^viii	97.91 (14)
O2^iii—Fe2—O3^iv	95.65 (13)	Fe2—O2—Fe4^vi	162.9 (2)
O2^iv—Fe2—O2^v	93.75 (11)	Fe2—O2—Fe4^x	83.18 (4)
O2^iv—Fe2—O3	95.65 (13)	Fe3^viii—O2—Mg3'^viii	0.0 (5)
O2^iv—Fe2—O3^iv	84.35 (13)	Fe3^viii—O2—Fe4^vi	99.15 (15)
O2^v—Fe2—O3	95.65 (13)	Fe3^viii—O2—Fe4^x	99.15 (15)
O2^v—Fe2—O3^iv	84.35 (13)	Mg3'^viii—O2—Fe4^vi	99.15 (15)
O3—Fe2—O3^iv	180.0 (5)	Mg3'^viii—O2—Fe4^x	99.15 (15)
Mg3'—Fe3—O2^vi	0	Fe4^vi—O2—Fe4^x	94.82 (16)
Mg3'—Fe3—O4	0	Fe2—O3—B1^ix	123.1 (4)
O2^vi—Fe3—O4	178.62 (17)	Fe1—O4—Mg1'	0.0 (5)
Fe3—Mg3'—Mg3'^ii	0	Fe1—O4—Fe3	116.6 (2)
Fe3—Mg3'—Mg3'^iii	0	Fe1—O4—Mg3'	116.6 (2)
Fe3—Mg3'—O2^vi	0	Fe1—O4—Fe4^vi	99.79 (14)
Fe3—Mg3'—O4	0	Fe1—O4—Fe4^x	99.79 (14)
Mg3'^ii—Mg3'—Mg3'^iii	180.0 (5)	Mg1'—O4—Fe3	116.6 (2)
Mg3'^ii—Mg3'—O2^vi	90.00 (3)	Mg1'—O4—Mg3'	116.6 (2)
Mg3'^ii—Mg3'—O4	90.00 (3)	Mg1'—O4—Fe4^vi	99.79 (14)
Mg3'^iii—Mg3'—O2^vi	90.00 (3)	Mg1'—O4—Fe4^x	99.79 (14)
Mg3'^iii—Mg3'—O4	90.00 (3)	Fe3—O4—Mg3'	0.0 (5)
O2^vi—Mg3'—O4	178.62 (17)	Fe3—O4—Fe4^vi	118.51 (13)
O1^vii—Fe4—O2^viii	94.27 (14)	Fe3—O4—Fe4^x	118.51 (13)
O1^vii—Fe4—O2^ix	94.27 (14)	Mg3'—O4—Fe4^vi	118.51 (13)
O1^vii—Fe4—O4^viii	85.03 (14)	Mg3'—O4—Fe4^x	118.51 (13)
O1^vii—Fe4—O4^ix	85.03 (14)	Fe4^vi—O4—Fe4^x	100.09 (18)
O1^vii—Fe4—O5^ix	176.80 (17)	Fe4^x—O5—B1	123.8 (4)

Symmetry codes: (i) −x, −y, z; (ii) x, y, z−1; (iii) x, y, z+1; (iv) −x+1, −y, z; (v) −x+1, −y, z+1; (vi) x−1/2, −y+1/2, −z; (vii) −x+3/2, y+1/2, −z+1; (viii) x+1/2, −y+1/2, −z; (ix) x+1/2, −y+1/2, −z+1; (x) x−1/2, −y+1/2, −z+1; (xi) −x+3/2, y−1/2, −z+1.