A new mechanism of anionic substitution in fluoride borates

A comprehensive study of the BaF₂–Ba₃(BO₃)₂ phase diagram has revealed a significant difference between the two intermediate phases Ba₅(BO₃)₃F and Ba₇(BO₃)_4−yF_2+3y. The latter exhibited (BO₃)³⁻ ↔ 3F⁻ anionic substitution which, unusually, strongly influences the solidus temperature. A comparison of the Ba₅(BO₃)₃F and Ba₇(BO₃)_4−yF_2+3y crystal structures, along with consideration of other compounds demonstrating (BO₃)³⁻ ↔ 3F⁻ isomorphism, allows for the disclosure of the mechanism of (BO₃)³⁻ ↔ 3F⁻ heterovalent anionic substitution in fluoride borates via [(BO₃)F]⁴⁻ tetrahedral groups being replaced by four fluoride anions. No exception to this mechanism has been discovered among all known phases with (BO₃)³⁻ ↔ 3F⁻ substitution.

Computing details

Data collection: CrysAlis PRO, Oxford Diffraction Ltd., Version 1.171.34.40 (release 27-08-2010 CrysAlis171 .NET) (compiled Aug 27 2010,11:50:40); cell refinement: CrysAlis PRO, Oxford Diffraction Ltd., Version 1.171.34.40 (release 27-08-2010 CrysAlis171 .NET) (compiled Aug 27 2010,11:50:40); data reduction: CrysAlis PRO, Oxford Diffraction Ltd., Version 1.171.34.40 (release 27-08-2010 CrysAlis171 .NET) (compiled Aug 27 2010,11:50:40); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008) in WinGX v1.80.05 (Farrugia, 1999).

Barium Fluoride Borate

Crystal data

B3Ba5FO9	Dx = 5.049 Mg m^−3
Mr = 882.13	Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, Pnma	Cell parameters from 12561 reflections
a = 7.60788 (12) Å	θ = 2.0–31.8°
b = 14.8299 (2) Å	µ = 16.76 mm^−1
c = 10.28650 (16) Å	T = 293 K
V = 1160.57 (3) Å^3	Tabular, colourless
Z = 4	0.26 × 0.13 × 0.05 mm
F(000) = 1504

Data collection

Xcalibur, Ruby, Gemini ultra diffractometer	2020 independent reflections
Radiation source: Enhance (Mo) X-ray Source	1875 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.051
Detector resolution: 10.3457 pixels mm^-1	θmax = 31.9°, θmin = 2.4°
ω scans	h = −11→11
Absorption correction: multi-scan CrysAlis PRO, Oxford Diffraction Ltd., Version 1.171.34.40 (release 27-08-2010 CrysAlis171 .NET) (compiled Aug 27 2010,11:50:40) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.	k = −21→21
Tmin = 0.254, Tmax = 1.000	l = −15→14
22057 measured reflections

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.021	w = 1/[σ^2(Fo^2) + (0.0305P)^2 + 1.4282P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.056	(Δ/σ)max = 0.002
S = 1.11	Δρmax = 1.82 e Å^−3
2020 reflections	Δρmin = −1.76 e Å^−3
92 parameters	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.0347 (5)

Special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into 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 to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to 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 (Ų)

	x	y	z	Uiso*/Ueq
Ba1	0.21232 (4)	0.7500	0.02070 (3)	0.00983 (9)
Ba2	−0.02618 (3)	0.610112 (13)	−0.251686 (16)	0.00897 (8)
Ba3	−0.25591 (3)	0.619490 (14)	0.12631 (2)	0.01346 (8)
B1	0.1996 (5)	0.5407 (2)	0.0597 (3)	0.0110 (6)
O1	0.0919 (3)	0.58837 (17)	0.1428 (2)	0.0166 (5)
O2	0.2193 (3)	0.53729 (18)	−0.3948 (3)	0.0158 (5)
O3	0.2265 (3)	0.56854 (17)	−0.0664 (2)	0.0138 (5)
B2	0.2194 (7)	0.7500	−0.3853 (5)	0.0089 (9)
O4	0.2187 (4)	0.7500	−0.2506 (3)	0.0093 (6)
O5	0.5654 (5)	0.7500	−0.0461 (3)	0.0155 (7)
O6	−0.1206 (4)	0.7500	−0.0507 (3)	0.0136 (6)
F	0.3984 (5)	0.7500	0.2351 (3)	0.0249 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1	0.00910 (14)	0.01085 (14)	0.00955 (14)	0.000	−0.00146 (8)	0.000
Ba2	0.00593 (12)	0.01069 (12)	0.01028 (12)	−0.00003 (6)	0.00025 (6)	−0.00038 (5)
Ba3	0.01634 (13)	0.01413 (12)	0.00993 (12)	−0.00146 (7)	0.00123 (6)	0.00058 (6)
B1	0.0106 (15)	0.0120 (16)	0.0105 (15)	−0.0013 (12)	−0.0031 (12)	−0.0018 (12)
O1	0.0150 (12)	0.0203 (12)	0.0145 (11)	0.0019 (10)	0.0011 (9)	−0.0029 (9)
O2	0.0152 (12)	0.0154 (12)	0.0169 (12)	0.0034 (9)	0.0008 (9)	−0.0058 (10)
O3	0.0170 (12)	0.0144 (12)	0.0100 (11)	−0.0004 (9)	0.0006 (8)	0.0030 (9)
B2	0.008 (2)	0.009 (2)	0.009 (2)	0.000	0.0005 (15)	0.000
O4	0.0101 (16)	0.0096 (15)	0.0083 (15)	0.000	0.0012 (10)	0.000
O5	0.0095 (15)	0.0222 (17)	0.0148 (15)	0.000	0.0040 (12)	0.000
O6	0.0067 (15)	0.0199 (17)	0.0143 (15)	0.000	−0.0031 (12)	0.000
F	0.0316 (19)	0.0260 (17)	0.0169 (14)	0.000	−0.0036 (13)	0.000

Geometric parameters (Å, º)

Ba1—F	2.621 (3)	Ba3—Ba2^vi	3.9897 (3)
Ba1—O6	2.637 (3)	B1—O3	1.376 (4)
Ba1—O5	2.772 (3)	B1—O1	1.380 (4)
Ba1—O4	2.791 (3)	B1—O2^vii	1.392 (4)
Ba1—O3	2.838 (2)	B1—Ba3^iii	3.080 (4)
Ba1—O3^i	2.838 (2)	B1—Ba2^iii	3.263 (4)
Ba1—O1	2.857 (3)	B1—Ba3^viii	3.452 (4)
Ba1—O1^i	2.857 (3)	O1—Ba3^viii	2.682 (2)
Ba1—B1^i	3.131 (4)	O1—Ba2^iii	3.189 (3)
Ba1—B1	3.131 (4)	O2—B1^ix	1.392 (4)
Ba1—Ba2	3.9302 (3)	O2—Ba2^x	2.681 (3)
Ba1—Ba2^i	3.9302 (3)	O2—Ba3^x	2.682 (3)
Ba2—O2	2.612 (2)	O3—Ba2^x	2.725 (2)
Ba2—O2^ii	2.681 (3)	O3—Ba3^iii	2.865 (3)
Ba2—O3^ii	2.725 (2)	B2—O5^ii	1.368 (6)
Ba2—O3	2.777 (2)	B2—O6^x	1.384 (6)
Ba2—O4	2.788 (2)	B2—O4	1.386 (6)
Ba2—O4^ii	2.841 (2)	B2—Ba2^i	3.112 (4)
Ba2—O6	3.015 (2)	B2—Ba3^x	3.151 (4)
Ba2—O5^ii	3.019 (3)	B2—Ba3^xi	3.151 (4)
Ba2—B2	3.112 (4)	B2—Ba2^xi	3.168 (4)
Ba2—B2^ii	3.168 (4)	B2—Ba2^x	3.168 (4)
Ba2—O1^iii	3.189 (3)	O4—Ba2^i	2.788 (2)
Ba2—B1^iii	3.263 (4)	O4—Ba2^xi	2.841 (2)
Ba3—F^iv	2.675 (2)	O4—Ba2^x	2.841 (2)
Ba3—O2^ii	2.682 (3)	O5—B2^x	1.368 (6)
Ba3—O1^iv	2.682 (2)	O5—Ba3^xii	2.956 (3)
Ba3—O1	2.691 (3)	O5—Ba3^xiii	2.956 (3)
Ba3—O6	2.850 (2)	O5—Ba2^x	3.019 (3)
Ba3—O3^iii	2.865 (3)	O5—Ba2^xi	3.019 (3)
Ba3—O5^v	2.956 (3)	O6—B2^ii	1.384 (6)
Ba3—B1^iii	3.080 (4)	O6—Ba3^i	2.850 (2)
Ba3—B2^ii	3.151 (4)	O6—Ba2^i	3.015 (2)
Ba3—B1^iv	3.452 (4)	F—Ba3^xiv	2.675 (2)
Ba3—Ba3^i	3.8709 (4)	F—Ba3^viii	2.675 (2)
F—Ba1—O6	138.87 (11)	O3^iii—Ba3—B2^ii	115.67 (8)
F—Ba1—O5	71.65 (11)	O5^v—Ba3—B2^ii	25.64 (11)
O6—Ba1—O5	149.48 (11)	B1^iii—Ba3—B2^ii	89.62 (9)
F—Ba1—O4	146.32 (10)	F^iv—Ba3—B1^iv	77.83 (8)
O6—Ba1—O4	74.81 (10)	O2^ii—Ba3—B1^iv	132.09 (8)
O5—Ba1—O4	74.66 (10)	O1^iv—Ba3—B1^iv	21.69 (8)
F—Ba1—O3	104.18 (5)	O1—Ba3—B1^iv	88.81 (8)
O6—Ba1—O3	87.05 (5)	O6—Ba3—B1^iv	149.68 (8)
O5—Ba1—O3	83.40 (5)	O3^iii—Ba3—B1^iv	83.09 (8)
O4—Ba1—O3	71.57 (5)	O5^v—Ba3—B1^iv	137.55 (9)
F—Ba1—O3^i	104.18 (5)	B1^iii—Ba3—B1^iv	109.50 (4)
O6—Ba1—O3^i	87.05 (5)	B2^ii—Ba3—B1^iv	159.79 (9)
O5—Ba1—O3^i	83.40 (5)	F^iv—Ba3—Ba3^i	43.65 (5)
O4—Ba1—O3^i	71.57 (5)	O2^ii—Ba3—Ba3^i	117.04 (6)
O3—Ba1—O3^i	142.94 (10)	O1^iv—Ba3—Ba3^i	99.91 (6)
F—Ba1—O1	78.65 (6)	O1—Ba3—Ba3^i	99.87 (6)
O6—Ba1—O1	79.31 (6)	O6—Ba3—Ba3^i	47.23 (5)
O5—Ba1—O1	114.81 (6)	O3^iii—Ba3—Ba3^i	166.76 (5)
O4—Ba1—O1	116.44 (5)	O5^v—Ba3—Ba3^i	49.10 (5)
O3—Ba1—O1	49.88 (7)	B1^iii—Ba3—Ba3^i	140.48 (7)
O3^i—Ba1—O1	161.15 (7)	B2^ii—Ba3—Ba3^i	52.10 (6)
F—Ba1—O1^i	78.65 (6)	B1^iv—Ba3—Ba3^i	109.78 (6)
O6—Ba1—O1^i	79.31 (6)	F^iv—Ba3—Ba2^vi	129.21 (5)
O5—Ba1—O1^i	114.81 (6)	O2^ii—Ba3—Ba2^vi	82.08 (6)
O4—Ba1—O1^i	116.44 (5)	O1^iv—Ba3—Ba2^vi	52.79 (6)
O3—Ba1—O1^i	161.15 (7)	O1—Ba3—Ba2^vi	104.02 (5)
O3^i—Ba1—O1^i	49.88 (7)	O6—Ba3—Ba2^vi	158.54 (5)
O1—Ba1—O1^i	114.05 (10)	O3^iii—Ba3—Ba2^vi	43.06 (5)
F—Ba1—B1^i	84.78 (6)	O5^v—Ba3—Ba2^vi	123.80 (6)
O6—Ba1—B1^i	90.34 (7)	B1^iii—Ba3—Ba2^vi	66.10 (7)
O5—Ba1—B1^i	93.53 (7)	B2^ii—Ba3—Ba2^vi	138.33 (7)
O4—Ba1—B1^i	97.38 (7)	B1^iv—Ba3—Ba2^vi	51.40 (6)
O3—Ba1—B1^i	168.95 (8)	Ba3^i—Ba3—Ba2^vi	148.589 (4)
O3^i—Ba1—B1^i	26.06 (8)	O3—B1—O1	121.3 (3)
O1—Ba1—B1^i	139.94 (9)	O3—B1—O2^vii	120.0 (3)
O1^i—Ba1—B1^i	26.13 (8)	O1—B1—O2^vii	118.7 (3)
F—Ba1—B1	84.78 (6)	O3—B1—Ba3^iii	68.00 (18)
O6—Ba1—B1	90.34 (7)	O1—B1—Ba3^iii	149.6 (2)
O5—Ba1—B1	93.53 (7)	O2^vii—B1—Ba3^iii	60.41 (17)
O4—Ba1—B1	97.38 (7)	O3—B1—Ba1	65.01 (18)
O3—Ba1—B1	26.06 (8)	O1—B1—Ba1	65.80 (17)
O3^i—Ba1—B1	168.95 (8)	O2^vii—B1—Ba1	148.6 (2)
O1—Ba1—B1	26.13 (8)	Ba3^iii—B1—Ba1	132.91 (12)
O1^i—Ba1—B1	139.94 (9)	O3—B1—Ba2^iii	146.7 (2)
B1^i—Ba1—B1	164.87 (13)	O1—B1—Ba2^iii	74.66 (18)
F—Ba1—Ba2	148.139 (3)	O2^vii—B1—Ba2^iii	53.54 (16)
O6—Ba1—Ba2	50.06 (5)	Ba3^iii—B1—Ba2^iii	84.45 (9)
O5—Ba1—Ba2	105.70 (6)	Ba1—B1—Ba2^iii	140.32 (12)
O4—Ba1—Ba2	45.19 (4)	O3—B1—Ba3^viii	140.0 (2)
O3—Ba1—Ba2	44.94 (5)	O1—B1—Ba3^viii	45.93 (15)
O3^i—Ba1—Ba2	107.04 (5)	O2^vii—B1—Ba3^viii	85.59 (19)
O1—Ba1—Ba2	73.90 (5)	Ba3^iii—B1—Ba3^viii	145.95 (12)
O1^i—Ba1—Ba2	127.46 (5)	Ba1—B1—Ba3^viii	77.37 (8)
B1^i—Ba1—Ba2	126.89 (6)	Ba2^iii—B1—Ba3^viii	72.85 (7)
B1—Ba1—Ba2	63.50 (6)	B1—O1—Ba3^viii	112.4 (2)
F—Ba1—Ba2^i	148.140 (3)	B1—O1—Ba3	129.3 (2)
O6—Ba1—Ba2^i	50.06 (5)	Ba3^viii—O1—Ba3	116.81 (9)
O5—Ba1—Ba2^i	105.70 (6)	B1—O1—Ba1	88.07 (19)
O4—Ba1—Ba2^i	45.19 (4)	Ba3^viii—O1—Ba1	96.11 (8)
O3—Ba1—Ba2^i	107.04 (5)	Ba3—O1—Ba1	98.26 (8)
O3^i—Ba1—Ba2^i	44.94 (5)	B1—O1—Ba2^iii	80.69 (19)
O1—Ba1—Ba2^i	127.46 (5)	Ba3^viii—O1—Ba2^iii	85.16 (6)
O1^i—Ba1—Ba2^i	73.90 (5)	Ba3—O1—Ba2^iii	91.51 (7)
B1^i—Ba1—Ba2^i	63.50 (6)	Ba1—O1—Ba2^iii	168.26 (10)
B1—Ba1—Ba2^i	126.89 (6)	B1^ix—O2—Ba2	148.2 (2)
Ba2—Ba1—Ba2^i	63.719 (7)	B1^ix—O2—Ba2^x	101.77 (19)
O2—Ba2—O2^ii	131.82 (11)	Ba2—O2—Ba2^x	91.89 (8)
O2—Ba2—O3^ii	90.75 (8)	B1^ix—O2—Ba3^x	92.76 (19)
O2^ii—Ba2—O3^ii	78.24 (8)	Ba2—O2—Ba3^x	111.27 (9)
O2—Ba2—O3	78.47 (8)	Ba2^x—O2—Ba3^x	105.39 (9)
O2^ii—Ba2—O3	91.41 (7)	B1—O3—Ba2^x	144.9 (2)
O3^ii—Ba2—O3	154.09 (10)	B1—O3—Ba2	127.6 (2)
O2—Ba2—O4	80.34 (8)	Ba2^x—O3—Ba2	87.49 (7)
O2^ii—Ba2—O4	141.25 (9)	B1—O3—Ba1	88.92 (19)
O3^ii—Ba2—O4	129.24 (8)	Ba2^x—O3—Ba1	91.63 (7)
O3—Ba2—O4	72.53 (8)	Ba2—O3—Ba1	88.84 (7)
O2—Ba2—O4^ii	142.66 (9)	B1—O3—Ba3^iii	85.56 (19)
O2^ii—Ba2—O4^ii	78.24 (8)	Ba2^x—O3—Ba3^iii	91.06 (7)
O3^ii—Ba2—O4^ii	72.48 (8)	Ba2—O3—Ba3^iii	97.03 (7)
O3—Ba2—O4^ii	129.02 (8)	Ba1—O3—Ba3^iii	173.64 (10)
O4—Ba2—O4^ii	85.018 (6)	O5^ii—B2—O6^x	120.5 (4)
O2—Ba2—O6	147.26 (8)	O5^ii—B2—O4	120.8 (4)
O2^ii—Ba2—O6	73.72 (8)	O6^x—B2—O4	118.6 (4)
O3^ii—Ba2—O6	117.52 (8)	O5^ii—B2—Ba2	73.36 (19)
O3—Ba2—O6	81.20 (8)	O6^x—B2—Ba2	137.58 (8)
O4—Ba2—O6	69.17 (8)	O4—B2—Ba2	63.64 (16)
O4^ii—Ba2—O6	47.88 (8)	O5^ii—B2—Ba2^i	73.36 (19)
O2—Ba2—O5^ii	74.38 (8)	O6^x—B2—Ba2^i	137.58 (8)
O2^ii—Ba2—O5^ii	146.18 (8)	O4—B2—Ba2^i	63.64 (16)
O3^ii—Ba2—O5^ii	80.88 (8)	Ba2—B2—Ba2^i	83.62 (12)
O3—Ba2—O5^ii	117.77 (8)	O5^ii—B2—Ba3^x	69.20 (19)
O4—Ba2—O5^ii	48.51 (9)	O6^x—B2—Ba3^x	64.75 (18)
O4^ii—Ba2—O5^ii	70.22 (8)	O4—B2—Ba3^x	141.92 (6)
O6—Ba2—O5^ii	93.13 (7)	Ba2—B2—Ba3^x	88.50 (6)
O2—Ba2—B2	66.26 (9)	Ba2^i—B2—Ba3^x	142.45 (17)
O2^ii—Ba2—B2	161.90 (9)	O5^ii—B2—Ba3^xi	69.20 (19)
O3^ii—Ba2—B2	105.20 (11)	O6^x—B2—Ba3^xi	64.75 (18)
O3—Ba2—B2	92.04 (10)	O4—B2—Ba3^xi	141.92 (6)
O4—Ba2—B2	26.45 (11)	Ba2—B2—Ba3^xi	142.45 (17)
O4^ii—Ba2—B2	85.82 (8)	Ba2^i—B2—Ba3^xi	88.50 (6)
O6—Ba2—B2	89.26 (8)	Ba3^x—B2—Ba3^xi	75.79 (11)
O5^ii—Ba2—B2	25.73 (11)	O5^ii—B2—Ba2^xi	138.84 (7)
O2—Ba2—B2^ii	163.41 (9)	O6^x—B2—Ba2^xi	70.98 (19)
O2^ii—Ba2—B2^ii	64.69 (8)	O4—B2—Ba2^xi	63.75 (17)
O3^ii—Ba2—B2^ii	91.82 (10)	Ba2—B2—Ba2^xi	127.38 (17)
O3—Ba2—B2^ii	105.25 (10)	Ba2^i—B2—Ba2^xi	74.57 (6)
O4—Ba2—B2^ii	85.36 (8)	Ba3^x—B2—Ba2^xi	135.71 (17)
O4^ii—Ba2—B2^ii	25.94 (10)	Ba3^xi—B2—Ba2^xi	84.91 (6)
O6—Ba2—B2^ii	25.71 (10)	O5^ii—B2—Ba2^x	138.84 (7)
O5^ii—Ba2—B2^ii	89.85 (8)	O6^x—B2—Ba2^x	70.98 (19)
B2—Ba2—B2^ii	97.28 (7)	O4—B2—Ba2^x	63.75 (17)
O2—Ba2—O1^iii	85.89 (7)	Ba2—B2—Ba2^x	74.57 (6)
O2^ii—Ba2—O1^iii	46.96 (7)	Ba2^i—B2—Ba2^x	127.38 (17)
O3^ii—Ba2—O1^iii	85.65 (7)	Ba3^x—B2—Ba2^x	84.91 (6)
O3—Ba2—O1^iii	70.27 (7)	Ba3^xi—B2—Ba2^x	135.71 (17)
O4—Ba2—O1^iii	142.19 (7)	Ba2^xi—B2—Ba2^x	81.82 (12)
O4^ii—Ba2—O1^iii	124.34 (7)	B2—O4—Ba2	89.92 (18)
O6—Ba2—O1^iii	110.92 (6)	B2—O4—Ba2^i	89.92 (18)
O5^ii—Ba2—O1^iii	155.83 (6)	Ba2—O4—Ba2^i	96.16 (10)
B2—Ba2—O1^iii	149.84 (8)	B2—O4—Ba1	179.2 (3)
B2^ii—Ba2—O1^iii	110.65 (8)	Ba2—O4—Ba1	89.58 (8)
O2—Ba2—B1^iii	110.30 (9)	Ba2^i—O4—Ba1	89.58 (8)
O2^ii—Ba2—B1^iii	24.69 (8)	B2—O4—Ba2^xi	90.31 (18)
O3^ii—Ba2—B1^iii	88.94 (8)	Ba2—O4—Ba2^xi	178.80 (10)
O3—Ba2—B1^iii	73.27 (8)	Ba2^i—O4—Ba2^xi	85.022 (6)
O4—Ba2—B1^iii	141.05 (9)	Ba1—O4—Ba2^xi	90.21 (8)
O4^ii—Ba2—B1^iii	102.67 (9)	B2—O4—Ba2^x	90.31 (18)
O6—Ba2—B1^iii	87.73 (8)	Ba2—O4—Ba2^x	85.022 (6)
O5^ii—Ba2—B1^iii	168.94 (9)	Ba2^i—O4—Ba2^x	178.80 (10)
B2—Ba2—B1^iii	165.28 (11)	Ba1—O4—Ba2^x	90.21 (8)
B2^ii—Ba2—B1^iii	86.14 (9)	Ba2^xi—O4—Ba2^x	93.80 (9)
O1^iii—Ba2—B1^iii	24.66 (8)	B2^x—O5—Ba1	163.3 (3)
F^iv—Ba3—O2^ii	146.40 (9)	B2^x—O5—Ba3^xii	85.2 (2)
F^iv—Ba3—O1^iv	80.92 (8)	Ba1—O5—Ba3^xii	107.28 (9)
O2^ii—Ba3—O1^iv	132.66 (8)	B2^x—O5—Ba3^xiii	85.2 (2)
F^iv—Ba3—O1	70.06 (9)	Ba1—O5—Ba3^xiii	107.28 (9)
O2^ii—Ba3—O1	92.71 (7)	Ba3^xii—O5—Ba3^xiii	81.80 (9)
O1^iv—Ba3—O1	109.82 (6)	B2^x—O5—Ba2^x	80.91 (19)
F^iv—Ba3—O6	71.98 (8)	Ba1—O5—Ba2^x	86.97 (8)
O2^ii—Ba3—O6	76.51 (7)	Ba3^xii—O5—Ba2^x	165.75 (13)
O1^iv—Ba3—O6	146.99 (7)	Ba3^xiii—O5—Ba2^x	93.988 (18)
O1—Ba3—O6	78.56 (8)	B2^x—O5—Ba2^xi	80.91 (19)
F^iv—Ba3—O3^iii	141.70 (8)	Ba1—O5—Ba2^xi	86.97 (8)
O2^ii—Ba3—O3^iii	51.09 (8)	Ba3^xii—O5—Ba2^xi	93.988 (18)
O1^iv—Ba3—O3^iii	93.26 (7)	Ba3^xiii—O5—Ba2^xi	165.75 (13)
O1—Ba3—O3^iii	76.70 (7)	Ba2^x—O5—Ba2^xi	86.80 (9)
O6—Ba3—O3^iii	119.69 (7)	B2^ii—O6—Ba1	167.8 (3)
F^iv—Ba3—O5^v	92.74 (7)	B2^ii—O6—Ba3^i	89.2 (2)
O2^ii—Ba3—O5^v	74.50 (7)	Ba1—O6—Ba3^i	99.72 (9)
O1^iv—Ba3—O5^v	116.43 (9)	B2^ii—O6—Ba3	89.2 (2)
O1—Ba3—O5^v	127.04 (8)	Ba1—O6—Ba3	99.72 (9)
O6—Ba3—O5^v	48.57 (9)	Ba3^i—O6—Ba3	85.54 (9)
O3^iii—Ba3—O5^v	122.97 (7)	B2^ii—O6—Ba2	83.31 (19)
F^iv—Ba3—B1^iii	145.90 (10)	Ba1—O6—Ba2	87.84 (8)
O2^ii—Ba3—B1^iii	26.84 (8)	Ba3^i—O6—Ba2	172.44 (12)
O1^iv—Ba3—B1^iii	118.50 (9)	Ba3—O6—Ba2	93.261 (10)
O1—Ba3—B1^iii	76.72 (8)	B2^ii—O6—Ba2^i	83.31 (19)
O6—Ba3—B1^iii	94.40 (8)	Ba1—O6—Ba2^i	87.84 (8)
O3^iii—Ba3—B1^iii	26.44 (8)	Ba3^i—O6—Ba2^i	93.261 (10)
O5^v—Ba3—B1^iii	101.33 (8)	Ba3—O6—Ba2^i	172.44 (12)
F^iv—Ba3—B2^ii	90.06 (8)	Ba2—O6—Ba2^i	86.94 (9)
O2^ii—Ba3—B2^ii	64.93 (8)	Ba1—F—Ba3^xiv	102.21 (10)
O1^iv—Ba3—B2^ii	140.95 (10)	Ba1—F—Ba3^viii	102.21 (10)
O1—Ba3—B2^ii	102.33 (10)	Ba3^xiv—F—Ba3^viii	92.70 (10)
O6—Ba3—B2^ii	26.05 (11)

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