Ba₄YZr₃F₂₃ and Ba₄LnZr₃F₂₃: a new noncentrosymmetric potential host structure type for optical devices

The first ternary BaF₂–Ln(Y)F₃–ZrF₄ phases crystallizing near the com­position range of fluoride glasses, namely Ba₄YZr₃F₂₃ (barium yttrium fluorido­zirconate) and isotypic Ba₄LnZr₃F₂₃ (Ln = Yb, Er and Nd), have been synthesized. The crystal structure of Ba₄YZr₃F₂₃ cannot be correctly determined in the centrosymmetric space group Pnma (R1 = 0.09); it is preferably described in the noncentrosymmetric space group Pn2₁a (R1 = 0.028). All cations are located at y = 0.25–0.29 and 0.75–0.79. This new structure type is formed by infinite {[YZr₃F₂₃]⁸⁻}_n columns associating, along [001], YF₉ tricapped trigonal prisms, ZrF₈ dodeca­hedra and ZrF₇ polyhedra. These columns are inter­connected via BaF₁₀₊₁ and BaF₁₂ irregular polyhedra.

Computing details

Data collection: COLLECT (Bruker–Nonius, 2004); cell refinement: DIRAX/LSQ (Duisenberg, 1992); data reduction: EVALCCD (Duisenberg et al., 2003); program(s) used to solve structure: SHELXS96 (Sheldrick, 2008); program(s) used to refine structure: SHELXL2018 (Sheldrick, 2015); molecular graphics: DIAMOND (Brandenburg, 1999); software used to prepare material for publication: WinGX (Farrugia, 2012).

Barium yttrium fluoridozirconate

Crystal data

Ba4YZr3F23	F(000) = 2360
Mr = 1348.93	Dx = 4.945 Mg m^−3
Orthorhombic, Pn21a	Mo Kα radiation, λ = 0.7107 Å
Hall symbol: P -2ac -2n	Cell parameters from 23945 reflections
a = 19.564 (8) Å	θ = 4.9–27.5°
b = 5.397 (2) Å	µ = 13.58 mm^−1
c = 17.161 (7) Å	T = 293 K
V = 1812.0 (12) Å^3	Prismatic, colourless
Z = 4	0.04 × 0.03 × 0.02 mm

Data collection

KappaCCD diffractometer	4111 independent reflections
Horizontally mounted graphite crystal monochromator	3530 reflections with I > 2σ(I)
Detector resolution: 9 pixels mm^-1	Rint = 0.049
CCD scans	θmax = 27.5°, θmin = 4.9°
Absorption correction: multi-scan (SADABS; Bruker, 2004)	h = −25→25
Tmin = 0.647, Tmax = 0.746	k = −7→7
23945 measured reflections	l = −22→22

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)] = 0.028	w = 1/[σ^2(Fo^2) + (0.0101P)^2 + 4.1573P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.041	(Δ/σ)max < 0.001
S = 1.03	Δρmax = 0.93 e Å^−3
4111 reflections	Δρmin = −0.89 e Å^−3
281 parameters	Absolute structure: Refined as an inversion twin.
1 restraint	Absolute structure parameter: 0.573 (13)

Special details

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 inversion twin.

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

	x	y	z	Uiso*/Ueq
Ba1	0.23441 (2)	0.25009 (16)	0.21956 (3)	0.01424 (13)
Ba2	−0.02884 (3)	0.24657 (16)	0.10428 (3)	0.01530 (13)
Ba3	0.42698 (3)	0.28326 (14)	0.06632 (3)	0.01350 (13)
Ba4	0.21400 (2)	0.25730 (17)	−0.04902 (3)	0.01424 (12)
Y	−0.07103 (4)	0.2860 (2)	0.71796 (5)	0.0104 (2)
Zr1	0.12902 (4)	0.2856 (2)	0.41414 (5)	0.0092 (2)
Zr2	0.11525 (4)	0.2449 (2)	0.74857 (5)	0.00930 (18)
Zr3	0.37125 (4)	0.2491 (2)	0.59028 (4)	0.00955 (18)
F1	0.0573 (2)	0.2660 (16)	0.5076 (3)	0.0191 (11)
F2	0.2946 (4)	−0.0022 (13)	0.5842 (5)	0.018 (2)
F3	0.1693 (4)	0.0204 (13)	0.4816 (5)	0.0165 (19)
F4	0.1698 (4)	0.5196 (14)	0.4953 (5)	0.0168 (19)
F5	0.2994 (4)	0.5145 (13)	0.5890 (5)	0.019 (2)
F6	0.3308 (3)	0.2123 (14)	0.7045 (3)	0.0226 (17)
F7	0.3435 (3)	0.2771 (19)	0.4718 (3)	0.0259 (14)
F8	0.1592 (4)	0.0392 (13)	0.6639 (5)	0.0213 (19)
F9	0.0954 (3)	0.3063 (15)	0.8651 (3)	0.0307 (18)
F10	0.1419 (4)	0.5182 (12)	0.6739 (5)	0.022 (2)
F11	0.0421 (3)	0.0824 (11)	0.3754 (3)	0.0176 (14)
F12	0.1598 (3)	−0.0175 (11)	0.3359 (3)	0.0186 (14)
F13	0.0303 (3)	0.4801 (11)	0.7528 (4)	0.0189 (15)
F14	0.4509 (4)	0.4257 (13)	0.5380 (4)	0.0306 (17)
F15	0.0689 (3)	0.6130 (12)	0.4079 (3)	0.0240 (15)
F16	0.2079 (3)	0.3373 (12)	0.7902 (3)	0.0286 (18)
F17	0.1134 (3)	0.4026 (11)	0.2973 (3)	0.0204 (14)
F18	0.0311 (3)	0.0651 (12)	0.6993 (4)	0.0236 (16)
F19	0.4505 (3)	0.1041 (11)	0.6657 (3)	0.0194 (14)
F20	0.1312 (3)	−0.0892 (12)	0.8013 (4)	0.0287 (16)
F21	0.4176 (4)	−0.0447 (12)	0.5312 (4)	0.0276 (17)
F22	0.2235 (3)	0.3816 (12)	0.3724 (4)	0.0277 (17)
F23	0.4081 (3)	0.5416 (11)	0.6753 (4)	0.0203 (15)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1	0.0139 (3)	0.0175 (3)	0.0113 (2)	0.0025 (4)	0.0011 (2)	0.0004 (4)
Ba2	0.0145 (3)	0.0174 (3)	0.0140 (3)	−0.0013 (4)	−0.0005 (2)	0.0007 (4)
Ba3	0.0120 (2)	0.0167 (3)	0.0119 (2)	0.0012 (4)	−0.0010 (2)	0.0002 (3)
Ba4	0.0138 (3)	0.0169 (3)	0.0121 (3)	0.0011 (5)	−0.0018 (2)	−0.0012 (4)
Y	0.0092 (4)	0.0131 (6)	0.0088 (4)	−0.0007 (5)	0.0000 (3)	−0.0008 (6)
Zr1	0.0079 (4)	0.0108 (5)	0.0090 (4)	0.0002 (5)	0.0009 (3)	0.0005 (5)
Zr2	0.0082 (4)	0.0116 (5)	0.0080 (4)	0.0007 (6)	−0.0004 (3)	−0.0003 (6)
Zr3	0.0113 (4)	0.0101 (5)	0.0073 (4)	0.0003 (6)	0.0005 (3)	−0.0007 (6)
F1	0.018 (3)	0.023 (3)	0.016 (2)	0.003 (5)	0.005 (2)	0.001 (4)
F2	0.024 (5)	0.021 (4)	0.008 (5)	−0.008 (3)	0.005 (4)	−0.005 (3)
F3	0.013 (4)	0.014 (4)	0.022 (5)	0.006 (3)	0.005 (3)	0.004 (3)
F4	0.020 (5)	0.013 (4)	0.017 (4)	0.001 (3)	0.003 (3)	−0.007 (3)
F5	0.020 (5)	0.017 (4)	0.020 (5)	0.005 (3)	−0.001 (4)	−0.002 (3)
F6	0.018 (3)	0.039 (5)	0.011 (3)	−0.007 (3)	0.000 (2)	0.000 (3)
F7	0.027 (3)	0.040 (4)	0.010 (3)	0.007 (5)	−0.003 (2)	0.001 (5)
F8	0.025 (4)	0.021 (4)	0.018 (4)	0.005 (3)	−0.001 (3)	−0.003 (3)
F9	0.026 (3)	0.053 (5)	0.013 (3)	0.018 (4)	0.001 (2)	0.000 (4)
F10	0.029 (5)	0.019 (4)	0.019 (5)	−0.004 (3)	0.001 (4)	0.010 (3)
F11	0.008 (3)	0.022 (3)	0.022 (4)	0.001 (3)	0.003 (3)	−0.008 (3)
F12	0.013 (3)	0.019 (3)	0.023 (4)	0.001 (3)	0.003 (3)	−0.006 (3)
F13	0.010 (3)	0.017 (3)	0.030 (4)	−0.001 (3)	−0.005 (3)	−0.002 (3)
F14	0.035 (4)	0.037 (4)	0.020 (4)	−0.020 (3)	0.008 (3)	−0.003 (3)
F15	0.031 (4)	0.029 (4)	0.013 (3)	0.012 (3)	−0.001 (3)	0.004 (3)
F16	0.015 (3)	0.047 (5)	0.024 (3)	−0.013 (3)	−0.013 (3)	0.011 (3)
F17	0.030 (4)	0.018 (3)	0.013 (3)	0.009 (3)	0.004 (3)	−0.002 (3)
F18	0.015 (3)	0.023 (4)	0.032 (4)	0.004 (3)	−0.003 (3)	−0.012 (3)
F19	0.025 (4)	0.018 (3)	0.015 (3)	0.009 (3)	0.002 (3)	−0.001 (3)
F20	0.043 (4)	0.020 (4)	0.024 (4)	0.000 (3)	−0.002 (3)	0.008 (3)
F21	0.032 (4)	0.033 (4)	0.018 (4)	0.019 (3)	−0.006 (3)	−0.008 (3)
F22	0.019 (3)	0.043 (4)	0.021 (3)	−0.012 (3)	0.007 (3)	−0.012 (3)
F23	0.023 (4)	0.016 (4)	0.022 (4)	−0.003 (3)	0.000 (3)	−0.002 (3)

Geometric parameters (Å, º)

Ba1—F5^i	2.660 (8)	Ba4—F16^vii	2.795 (6)
Ba1—F22	2.726 (6)	Ba4—F7^i	2.848 (9)
Ba1—F2^ii	2.740 (8)	Ba4—F7^ii	3.043 (10)
Ba1—F8^ii	2.772 (8)	Ba4—F21^ii	3.108 (7)
Ba1—F16^i	2.776 (6)	Ba4—Zr3^ii	3.9423 (16)
Ba1—F6^ii	2.814 (7)	Ba4—Zr2^vii	3.9753 (16)
Ba1—F10^i	2.836 (8)	Y—F17^v	2.245 (6)
Ba1—F17	2.839 (6)	Y—F12^iv	2.234 (6)
Ba1—F12	2.864 (6)	Y—F19^viii	2.264 (6)
Ba1—F20^ii	3.104 (7)	Y—F13	2.320 (6)
Ba1—F23^i	3.102 (6)	Y—F23^viii	2.328 (6)
Ba1—F6^i	3.181 (7)	Y—F11^iv	2.334 (6)
Ba2—F14^i	2.572 (7)	Y—F18	2.349 (6)
Ba2—F14^iii	2.656 (7)	Y—F15^v	2.354 (6)
Ba2—F19^ii	2.680 (6)	Y—F6^viii	2.370 (5)
Ba2—F20^iv	2.724 (6)	Y—Zr3^viii	3.4848 (17)
Ba2—F21^ii	2.753 (6)	Y—Zr2	3.6889 (19)
Ba2—F9^v	2.761 (7)	Y—Zr1^v	3.7043 (18)
Ba2—F7^iii	2.823 (5)	Zr1—F3	2.002 (8)
Ba2—F13^v	2.843 (6)	Zr1—F4	2.042 (8)
Ba2—F23^i	2.879 (6)	Zr1—F22	2.048 (6)
Ba2—F21^iii	2.996 (7)	Zr1—F15	2.126 (6)
Ba2—Zr3^iii	3.8689 (15)	Zr1—F17	2.125 (6)
Ba2—Zr2^iv	4.0580 (16)	Zr1—F11	2.130 (6)
Ba3—F4^i	2.664 (8)	Zr1—F1	2.134 (4)
Ba3—F11^vi	2.692 (6)	Zr1—F12	2.201 (6)
Ba3—F10^i	2.696 (8)	Zr2—F16	2.012 (5)
Ba3—F3^ii	2.703 (8)	Zr2—F8	2.020 (8)
Ba3—F8^ii	2.748 (8)	Zr2—F10	2.022 (7)
Ba3—F1^ii	2.810 (8)	Zr2—F20	2.041 (6)
Ba3—F1^vi	2.850 (5)	Zr2—F9	2.063 (5)
Ba3—F18^ii	2.862 (6)	Zr2—F18	2.089 (6)
Ba3—F15^i	2.871 (6)	Zr2—F13	2.093 (6)
Ba3—F1^i	2.984 (8)	Zr3—F5	2.007 (7)
Ba3—Zr1^i	3.9031 (16)	Zr3—F2	2.025 (7)
Ba3—Zr1^ii	3.9206 (16)	Zr3—F14	2.035 (6)
Ba4—F2^ii	2.634 (8)	Zr3—F21	2.089 (6)
Ba4—F4^i	2.719 (8)	Zr3—F7	2.110 (5)
Ba4—F5^i	2.720 (9)	Zr3—F6	2.123 (5)
Ba4—F22^i	2.725 (6)	Zr3—F19	2.166 (6)
Ba4—F3^ii	2.739 (8)	Zr3—F23	2.268 (6)
Ba4—F9^vii	2.761 (5)
F5^i—Ba1—F22	156.3 (2)	F18—Y—Zr3^viii	112.04 (17)
F5^i—Ba1—F2^ii	57.83 (15)	F15^v—Y—Zr3^viii	148.19 (15)
F22—Ba1—F2^ii	132.3 (2)	F6^viii—Y—Zr3^viii	36.64 (12)
F5^i—Ba1—F8^ii	99.5 (2)	F17^v—Y—Zr2	109.02 (16)
F22—Ba1—F8^ii	104.1 (2)	F12^iv—Y—Zr2	148.78 (15)
F2^ii—Ba1—F8^ii	65.7 (2)	F19^viii—Y—Zr2	70.40 (16)
F5^i—Ba1—F16^i	94.9 (2)	F13—Y—Zr2	31.41 (15)
F22—Ba1—F16^i	79.67 (19)	F23^viii—Y—Zr2	95.54 (16)
F2^ii—Ba1—F16^i	147.79 (19)	F11^iv—Y—Zr2	84.23 (14)
F8^ii—Ba1—F16^i	107.3 (2)	F18—Y—Zr2	31.61 (15)
F5^i—Ba1—F6^ii	103.51 (19)	F15^v—Y—Zr2	95.10 (15)
F22—Ba1—F6^ii	79.75 (18)	F6^viii—Y—Zr2	135.27 (13)
F2^ii—Ba1—F6^ii	52.81 (18)	Zr3^viii—Y—Zr2	100.50 (3)
F8^ii—Ba1—F6^ii	79.03 (19)	F17^v—Y—Zr1^v	31.06 (15)
F16^i—Ba1—F6^ii	159.38 (16)	F12^iv—Y—Zr1^v	81.66 (16)
F5^i—Ba1—F10^i	76.6 (2)	F19^viii—Y—Zr1^v	106.28 (17)
F22—Ba1—F10^i	116.6 (2)	F13—Y—Zr1^v	138.48 (16)
F2^ii—Ba1—F10^i	99.1 (2)	F23^viii—Y—Zr1^v	149.27 (16)
F8^ii—Ba1—F10^i	60.79 (18)	F11^iv—Y—Zr1^v	98.84 (16)
F16^i—Ba1—F10^i	54.52 (19)	F18—Y—Zr1^v	78.87 (15)
F6^ii—Ba1—F10^i	138.85 (18)	F15^v—Y—Zr1^v	32.28 (15)
F5^i—Ba1—F17	109.1 (2)	F6^viii—Y—Zr1^v	88.45 (16)
F22—Ba1—F17	53.63 (17)	Zr3^viii—Y—Zr1^v	115.91 (4)
F2^ii—Ba1—F17	94.8 (2)	Zr2—Y—Zr1^v	110.23 (4)
F8^ii—Ba1—F17	128.7 (2)	F3—Zr1—F4	83.9 (2)
F16^i—Ba1—F17	111.49 (16)	F3—Zr1—F22	91.6 (3)
F6^ii—Ba1—F17	53.71 (16)	F4—Zr1—F22	74.3 (3)
F10^i—Ba1—F17	165.85 (19)	F3—Zr1—F15	147.3 (3)
F5^i—Ba1—F12	102.7 (2)	F4—Zr1—F15	74.7 (3)
F22—Ba1—F12	54.59 (18)	F22—Zr1—F15	105.8 (3)
F2^ii—Ba1—F12	137.0 (2)	F3—Zr1—F17	144.5 (3)
F8^ii—Ba1—F12	155.1 (2)	F4—Zr1—F17	121.1 (3)
F16^i—Ba1—F12	59.87 (16)	F22—Zr1—F17	74.0 (2)
F6^ii—Ba1—F12	106.26 (16)	F15—Zr1—F17	68.0 (2)
F10^i—Ba1—F12	113.91 (19)	F3—Zr1—F11	97.3 (3)
F17—Ba1—F12	52.68 (17)	F4—Zr1—F11	147.5 (3)
F5^i—Ba1—F20^ii	136.5 (2)	F22—Zr1—F11	137.9 (2)
F22—Ba1—F20^ii	63.82 (17)	F15—Zr1—F11	88.3 (3)
F2^ii—Ba1—F20^ii	115.0 (2)	F17—Zr1—F11	75.1 (2)
F8^ii—Ba1—F20^ii	50.4 (2)	F3—Zr1—F1	77.8 (3)
F16^i—Ba1—F20^ii	71.49 (18)	F4—Zr1—F1	77.0 (3)
F6^ii—Ba1—F20^ii	100.25 (16)	F22—Zr1—F1	150.3 (2)
F10^i—Ba1—F20^ii	61.7 (2)	F15—Zr1—F1	73.5 (3)
F17—Ba1—F20^ii	114.40 (17)	F17—Zr1—F1	129.1 (2)
F12—Ba1—F20^ii	104.94 (17)	F11—Zr1—F1	71.6 (2)
F5^i—Ba1—F23^i	52.9 (2)	F3—Zr1—F12	73.4 (3)
F22—Ba1—F23^i	105.03 (16)	F4—Zr1—F12	140.3 (3)
F2^ii—Ba1—F23^i	77.5 (2)	F22—Zr1—F12	74.2 (2)
F8^ii—Ba1—F23^i	142.7 (2)	F15—Zr1—F12	137.6 (2)
F16^i—Ba1—F23^i	100.43 (17)	F17—Zr1—F12	71.6 (2)
F6^ii—Ba1—F23^i	83.77 (16)	F11—Zr1—F12	69.2 (2)
F10^i—Ba1—F23^i	122.66 (19)	F1—Zr1—F12	127.0 (3)
F17—Ba1—F23^i	58.02 (17)	F3—Zr1—Y^iv	174.6 (2)
F12—Ba1—F23^i	61.91 (17)	F4—Zr1—Y^iv	94.9 (2)
F20^ii—Ba1—F23^i	166.83 (16)	F22—Zr1—Y^iv	82.99 (19)
F5^i—Ba1—F6^i	52.81 (19)	F15—Zr1—Y^iv	36.25 (16)
F22—Ba1—F6^i	106.52 (16)	F17—Zr1—Y^iv	33.03 (16)
F2^ii—Ba1—F6^i	107.05 (18)	F11—Zr1—Y^iv	86.55 (17)
F8^ii—Ba1—F6^i	141.90 (18)	F1—Zr1—Y^iv	107.2 (2)
F16^i—Ba1—F6^i	57.74 (17)	F12—Zr1—Y^iv	104.60 (17)
F6^ii—Ba1—F6^i	128.29 (18)	F3—Zr1—Y^v	87.4 (2)
F10^i—Ba1—F6^i	85.24 (17)	F4—Zr1—Y^v	171.1 (2)
F17—Ba1—F6^i	88.18 (16)	F22—Zr1—Y^v	104.29 (17)
F12—Ba1—F6^i	52.56 (15)	F15—Zr1—Y^v	113.88 (17)
F20^ii—Ba1—F6^i	129.16 (15)	F17—Zr1—Y^v	66.05 (17)
F23^i—Ba1—F6^i	44.64 (14)	F11—Zr1—Y^v	35.80 (15)
F14^i—Ba2—F14^iii	85.81 (15)	F1—Zr1—Y^v	102.9 (2)
F14^i—Ba2—F19^ii	108.6 (2)	F12—Zr1—Y^v	33.73 (15)
F14^iii—Ba2—F19^ii	100.65 (19)	Y^iv—Zr1—Y^v	93.58 (4)
F14^i—Ba2—F20^iv	156.6 (2)	F3—Zr1—Ba3^ix	102.5 (2)
F14^iii—Ba2—F20^iv	108.6 (2)	F4—Zr1—Ba3^ix	39.5 (2)
F19^ii—Ba2—F20^iv	87.25 (19)	F22—Zr1—Ba3^ix	108.24 (18)
F14^i—Ba2—F21^ii	66.8 (3)	F15—Zr1—Ba3^ix	46.08 (16)
F14^iii—Ba2—F21^ii	63.3 (2)	F17—Zr1—Ba3^ix	112.76 (16)
F19^ii—Ba2—F21^ii	55.42 (18)	F11—Zr1—Ba3^ix	109.81 (15)
F20^iv—Ba2—F21^ii	136.0 (2)	F1—Zr1—Ba3^ix	49.2 (2)
F14^i—Ba2—F9^v	77.6 (2)	F12—Zr1—Ba3^ix	175.37 (17)
F14^iii—Ba2—F9^v	114.72 (18)	Y^iv—Zr1—Ba3^ix	79.73 (4)
F19^ii—Ba2—F9^v	144.55 (17)	Y^v—Zr1—Ba3^ix	145.60 (3)
F20^iv—Ba2—F9^v	79.61 (19)	F3—Zr1—Ba3^x	39.7 (2)
F21^ii—Ba2—F9^v	144.3 (2)	F4—Zr1—Ba3^x	94.7 (2)
F14^i—Ba2—F7^iii	111.1 (2)	F22—Zr1—Ba3^x	131.29 (19)
F14^iii—Ba2—F7^iii	54.68 (19)	F15—Zr1—Ba3^x	116.98 (17)
F19^ii—Ba2—F7^iii	130.2 (2)	F17—Zr1—Ba3^x	142.57 (17)
F20^iv—Ba2—F7^iii	66.77 (18)	F11—Zr1—Ba3^x	68.20 (17)
F21^ii—Ba2—F7^iii	117.7 (2)	F1—Zr1—Ba3^x	44.0 (2)
F9^v—Ba2—F7^iii	73.8 (2)	F12—Zr1—Ba3^x	88.23 (17)
F14^i—Ba2—F13^v	92.7 (2)	Y^iv—Zr1—Ba3^x	145.72 (3)
F14^iii—Ba2—F13^v	167.35 (18)	Y^v—Zr1—Ba3^x	79.55 (4)
F19^ii—Ba2—F13^v	91.75 (18)	Ba3^ix—Zr1—Ba3^x	87.23 (4)
F20^iv—Ba2—F13^v	69.17 (18)	F16—Zr2—F8	90.5 (3)
F21^ii—Ba2—F13^v	127.41 (18)	F16—Zr2—F10	79.2 (3)
F9^v—Ba2—F13^v	52.81 (16)	F8—Zr2—F10	80.5 (3)
F7^iii—Ba2—F13^v	114.81 (18)	F16—Zr2—F20	85.6 (3)
F14^i—Ba2—F23^i	56.11 (18)	F8—Zr2—F20	76.6 (3)
F14^iii—Ba2—F23^i	130.7 (2)	F10—Zr2—F20	152.4 (3)
F19^ii—Ba2—F23^i	68.97 (19)	F16—Zr2—F9	77.6 (2)
F20^iv—Ba2—F23^i	118.43 (19)	F8—Zr2—F9	149.9 (3)
F21^ii—Ba2—F23^i	72.6 (2)	F10—Zr2—F9	123.1 (3)
F9^v—Ba2—F23^i	88.60 (18)	F20—Zr2—F9	75.0 (3)
F7^iii—Ba2—F23^i	160.7 (2)	F16—Zr2—F18	165.7 (3)
F13^v—Ba2—F23^i	56.51 (17)	F8—Zr2—F18	77.8 (3)
F14^i—Ba2—F21^iii	60.7 (2)	F10—Zr2—F18	106.6 (3)
F14^iii—Ba2—F21^iii	54.92 (19)	F20—Zr2—F18	83.7 (3)
F19^ii—Ba2—F21^iii	152.02 (18)	F9—Zr2—F18	108.6 (3)
F20^iv—Ba2—F21^iii	112.02 (19)	F16—Zr2—F13	123.6 (3)
F21^ii—Ba2—F21^iii	97.93 (14)	F8—Zr2—F13	134.1 (3)
F9^v—Ba2—F21^iii	62.04 (17)	F10—Zr2—F13	77.5 (3)
F7^iii—Ba2—F21^iii	50.4 (2)	F20—Zr2—F13	129.9 (3)
F13^v—Ba2—F21^iii	113.61 (18)	F9—Zr2—F13	73.7 (3)
F23^i—Ba2—F21^iii	114.47 (17)	F18—Zr2—F13	70.7 (2)
F14^i—Ba2—Zr3^iii	85.43 (14)	F16—Zr2—Y	157.8 (2)
F14^iii—Ba2—Zr3^iii	29.54 (14)	F8—Zr2—Y	110.5 (2)
F19^ii—Ba2—Zr3^iii	128.74 (13)	F10—Zr2—Y	96.9 (2)
F20^iv—Ba2—Zr3^iii	98.09 (14)	F20—Zr2—Y	105.49 (19)
F21^ii—Ba2—Zr3^iii	90.29 (14)	F9—Zr2—Y	86.71 (15)
F9^v—Ba2—Zr3^iii	85.93 (11)	F18—Zr2—Y	36.11 (17)
F7^iii—Ba2—Zr3^iii	32.20 (10)	F13—Zr2—Y	35.28 (16)
F13^v—Ba2—Zr3^iii	137.83 (12)	F16—Zr2—Ba4^xi	41.19 (17)
F23^i—Ba2—Zr3^iii	141.38 (12)	F8—Zr2—Ba4^xi	115.5 (2)
F21^iii—Ba2—Zr3^iii	32.36 (12)	F10—Zr2—Ba4^xi	114.6 (2)
F14^i—Ba2—Zr2^iv	165.51 (15)	F20—Zr2—Ba4^xi	63.47 (18)
F14^iii—Ba2—Zr2^iv	105.59 (17)	F9—Zr2—Ba4^xi	40.70 (15)
F19^ii—Ba2—Zr2^iv	61.07 (14)	F18—Zr2—Ba4^xi	138.1 (2)
F20^iv—Ba2—Zr2^iv	26.87 (13)	F13—Zr2—Ba4^xi	110.19 (18)
F21^ii—Ba2—Zr2^iv	109.98 (14)	Y—Zr2—Ba4^xi	127.12 (3)
F9^v—Ba2—Zr2^iv	104.78 (13)	F16—Zr2—Ba1^x	63.09 (19)
F7^iii—Ba2—Zr2^iv	83.13 (15)	F8—Zr2—Ba1^x	39.8 (2)
F13^v—Ba2—Zr2^iv	78.14 (13)	F10—Zr2—Ba1^x	102.6 (2)
F23^i—Ba2—Zr2^iv	109.44 (12)	F20—Zr2—Ba1^x	49.76 (19)
F21^iii—Ba2—Zr2^iv	133.22 (13)	F9—Zr2—Ba1^x	111.45 (18)
Zr3^iii—Ba2—Zr2^iv	108.92 (3)	F18—Zr2—Ba1^x	102.63 (18)
F4^i—Ba3—F11^vi	123.3 (2)	F13—Zr2—Ba1^x	172.93 (17)
F4^i—Ba3—F10^i	71.0 (3)	Y—Zr2—Ba1^x	138.44 (4)
F11^vi—Ba3—F10^i	87.1 (2)	Ba4^xi—Zr2—Ba1^x	76.28 (3)
F4^i—Ba3—F3^ii	60.74 (15)	F16—Zr2—Ba1^ix	38.78 (18)
F11^vi—Ba3—F3^ii	166.9 (2)	F8—Zr2—Ba1^ix	88.4 (2)
F10^i—Ba3—F3^ii	105.7 (2)	F10—Zr2—Ba1^ix	40.8 (2)
F4^i—Ba3—F8^ii	96.4 (2)	F20—Zr2—Ba1^ix	122.65 (19)
F11^vi—Ba3—F8^ii	119.3 (2)	F9—Zr2—Ba1^ix	98.5 (2)
F10^i—Ba3—F8^ii	62.82 (17)	F18—Zr2—Ba1^ix	146.8 (2)
F3^ii—Ba3—F8^ii	70.3 (3)	F13—Zr2—Ba1^ix	99.97 (17)
F4^i—Ba3—F1^ii	114.1 (2)	Y—Zr2—Ba1^ix	131.36 (4)
F11^vi—Ba3—F1^ii	114.52 (15)	Ba4^xi—Zr2—Ba1^ix	75.08 (3)
F10^i—Ba3—F1^ii	142.38 (19)	Ba1^x—Zr2—Ba1^ix	84.27 (4)
F3^ii—Ba3—F1^ii	56.23 (18)	F16—Zr2—Ba2^v	108.59 (17)
F8^ii—Ba3—F1^ii	79.59 (19)	F8—Zr2—Ba2^v	105.1 (2)
F4^i—Ba3—F1^vi	114.5 (2)	F10—Zr2—Ba2^v	170.1 (2)
F11^vi—Ba3—F1^vi	53.39 (17)	F20—Zr2—Ba2^v	37.09 (19)
F10^i—Ba3—F1^vi	137.3 (2)	F9—Zr2—Ba2^v	54.9 (2)
F3^ii—Ba3—F1^vi	113.6 (2)	F18—Zr2—Ba2^v	67.4 (2)
F8^ii—Ba3—F1^vi	146.8 (2)	F13—Zr2—Ba2^v	92.82 (18)
F1^ii—Ba3—F1^vi	76.88 (16)	Y—Zr2—Ba2^v	73.56 (3)
F4^i—Ba3—F18^ii	148.5 (2)	Ba4^xi—Zr2—Ba2^v	70.73 (3)
F11^vi—Ba3—F18^ii	71.23 (19)	Ba1^x—Zr2—Ba2^v	86.64 (4)
F10^i—Ba3—F18^ii	83.1 (2)	Ba1^ix—Zr2—Ba2^v	145.79 (2)
F3^ii—Ba3—F18^ii	112.2 (2)	F5—Zr3—F2	87.6 (2)
F8^ii—Ba3—F18^ii	54.7 (2)	F5—Zr3—F14	101.4 (3)
F1^ii—Ba3—F18^ii	76.22 (17)	F2—Zr3—F14	149.1 (3)
F1^vi—Ba3—F18^ii	96.67 (17)	F5—Zr3—F21	147.2 (3)
F4^i—Ba3—F15^i	54.3 (2)	F2—Zr3—F21	77.7 (3)
F11^vi—Ba3—F15^i	101.48 (17)	F14—Zr3—F21	79.0 (3)
F10^i—Ba3—F15^i	119.5 (2)	F5—Zr3—F7	76.0 (4)
F3^ii—Ba3—F15^i	70.2 (2)	F2—Zr3—F7	78.9 (3)
F8^ii—Ba3—F15^i	139.0 (2)	F14—Zr3—F7	74.9 (3)
F1^ii—Ba3—F15^i	87.38 (16)	F21—Zr3—F7	72.4 (3)
F1^vi—Ba3—F15^i	62.77 (16)	F5—Zr3—F6	79.4 (3)
F18^ii—Ba3—F15^i	156.48 (17)	F2—Zr3—F6	73.1 (3)
F4^i—Ba3—F1^i	54.47 (18)	F14—Zr3—F6	137.4 (3)
F11^vi—Ba3—F1^i	70.28 (16)	F21—Zr3—F6	122.6 (3)
F10^i—Ba3—F1^i	77.64 (19)	F7—Zr3—F6	143.2 (2)
F3^ii—Ba3—F1^i	109.46 (18)	F5—Zr3—F19	140.0 (3)
F8^ii—Ba3—F1^i	137.65 (18)	F2—Zr3—F19	108.6 (3)
F1^ii—Ba3—F1^i	137.33 (17)	F14—Zr3—F19	83.4 (3)
F1^vi—Ba3—F1^i	74.16 (16)	F21—Zr3—F19	72.9 (2)
F18^ii—Ba3—F1^i	137.46 (17)	F7—Zr3—F19	141.8 (2)
F15^i—Ba3—F1^i	51.53 (16)	F6—Zr3—F19	71.4 (2)
F4^i—Ba3—Zr1^i	29.15 (17)	F5—Zr3—F23	74.5 (3)
F11^vi—Ba3—Zr1^i	101.91 (14)	F2—Zr3—F23	137.3 (3)
F10^i—Ba3—Zr1^i	87.28 (17)	F14—Zr3—F23	73.4 (2)
F3^ii—Ba3—Zr1^i	76.71 (17)	F21—Zr3—F23	134.6 (2)
F8^ii—Ba3—Zr1^i	125.55 (16)	F7—Zr3—F23	130.7 (3)
F1^ii—Ba3—Zr1^i	115.39 (11)	F6—Zr3—F23	65.8 (2)
F1^vi—Ba3—Zr1^i	86.03 (14)	F19—Zr3—F23	68.8 (2)
F18^ii—Ba3—Zr1^i	168.37 (14)	F5—Zr3—Y^xii	101.3 (3)
F15^i—Ba3—Zr1^i	32.23 (12)	F2—Zr3—Y^xii	109.1 (2)
F1^i—Ba3—Zr1^i	32.77 (9)	F14—Zr3—Y^xii	98.11 (19)
F4^i—Ba3—Zr1^ii	82.30 (18)	F21—Zr3—Y^xii	111.17 (18)
F11^vi—Ba3—Zr1^ii	139.43 (12)	F7—Zr3—Y^xii	171.6 (3)
F10^i—Ba3—Zr1^ii	133.11 (16)	F6—Zr3—Y^xii	41.79 (14)
F3^ii—Ba3—Zr1^ii	28.26 (16)	F19—Zr3—Y^xii	39.14 (15)
F8^ii—Ba3—Zr1^ii	83.50 (17)	F23—Zr3—Y^xii	41.34 (16)
F1^ii—Ba3—Zr1^ii	31.86 (9)	F5—Zr3—Ba2^vi	110.3 (3)
F1^vi—Ba3—Zr1^ii	88.63 (14)	F2—Zr3—Ba2^vi	109.1 (2)
F18^ii—Ba3—Zr1^ii	104.10 (14)	F14—Zr3—Ba2^vi	40.06 (19)
F15^i—Ba3—Zr1^ii	66.33 (13)	F21—Zr3—Ba2^vi	50.17 (19)
F1^i—Ba3—Zr1^ii	116.80 (10)	F7—Zr3—Ba2^vi	45.47 (14)
Zr1^i—Ba3—Zr1^ii	87.23 (4)	F6—Zr3—Ba2^vi	169.97 (17)
F2^ii—Ba4—F4^i	92.5 (2)	F19—Zr3—Ba2^vi	98.79 (16)
F2^ii—Ba4—F5^i	58.36 (15)	F23—Zr3—Ba2^vi	113.40 (16)
F4^i—Ba4—F5^i	67.0 (3)	Y^xii—Zr3—Ba2^vi	130.65 (4)
F2^ii—Ba4—F22^i	145.5 (2)	F5—Zr3—Ba4^x	100.2 (2)
F4^i—Ba4—F22^i	54.0 (2)	F2—Zr3—Ba4^x	37.3 (2)
F5^i—Ba4—F22^i	96.6 (2)	F14—Zr3—Ba4^x	111.86 (19)
F2^ii—Ba4—F3^ii	68.4 (3)	F21—Zr3—Ba4^x	51.55 (19)
F4^i—Ba4—F3^ii	59.63 (15)	F7—Zr3—Ba4^x	49.8 (3)
F5^i—Ba4—F3^ii	99.4 (2)	F6—Zr3—Ba4^x	109.81 (18)
F22^i—Ba4—F3^ii	96.1 (2)	F19—Zr3—Ba4^x	114.96 (17)
F2^ii—Ba4—F9^vii	111.3 (2)	F23—Zr3—Ba4^x	173.49 (16)
F4^i—Ba4—F9^vii	153.7 (2)	Y^xii—Zr3—Ba4^x	138.44 (4)
F5^i—Ba4—F9^vii	115.5 (2)	Ba2^vi—Zr3—Ba4^x	71.82 (3)
F22^i—Ba4—F9^vii	100.61 (19)	F5—Zr3—Ba4^ix	38.1 (3)
F3^ii—Ba4—F9^vii	138.8 (2)	F2—Zr3—Ba4^ix	96.9 (2)
F2^ii—Ba4—F16^vii	141.1 (2)	F14—Zr3—Ba4^ix	74.6 (2)
F4^i—Ba4—F16^vii	112.6 (2)	F21—Zr3—Ba4^ix	114.28 (18)
F5^i—Ba4—F16^vii	158.4 (2)	F7—Zr3—Ba4^ix	43.0 (3)
F22^i—Ba4—F16^vii	69.25 (19)	F6—Zr3—Ba4^ix	117.40 (18)
F3^ii—Ba4—F16^vii	98.3 (2)	F19—Zr3—Ba4^ix	154.53 (17)
F9^vii—Ba4—F16^vii	54.72 (16)	F23—Zr3—Ba4^ix	92.30 (16)
F2^ii—Ba4—F7^i	108.3 (2)	Y^xii—Zr3—Ba4^ix	131.29 (4)
F4^i—Ba4—F7^i	82.3 (2)	Ba2^vi—Zr3—Ba4^ix	72.39 (3)
F5^i—Ba4—F7^i	54.14 (19)	Ba4^x—Zr3—Ba4^ix	85.58 (3)
F22^i—Ba4—F7^i	64.03 (19)	Zr1—F1—Ba3^x	104.1 (3)
F3^ii—Ba4—F7^i	141.0 (2)	Zr1—F1—Ba3^iii	104.58 (17)
F9^vii—Ba4—F7^i	79.8 (2)	Ba3^x—F1—Ba3^iii	106.7 (2)
F16^vii—Ba4—F7^i	104.33 (16)	Zr1—F1—Ba3^ix	98.0 (3)
F2^ii—Ba4—F7^ii	54.58 (19)	Ba3^x—F1—Ba3^ix	137.33 (17)
F4^i—Ba4—F7^ii	135.34 (19)	Ba3^iii—F1—Ba3^ix	102.2 (2)
F5^i—Ba4—F7^ii	107.85 (19)	Zr3—F2—Ba4^x	115.0 (3)
F22^i—Ba4—F7^ii	155.48 (17)	Zr3—F2—Ba1^x	115.9 (4)
F3^ii—Ba4—F7^ii	78.9 (2)	Ba4^x—F2—Ba1^x	118.8 (3)
F9^vii—Ba4—F7^ii	70.4 (2)	Zr1—F3—Ba3^x	112.0 (3)
F16^vii—Ba4—F7^ii	87.57 (16)	Zr1—F3—Ba4^x	126.0 (4)
F7^i—Ba4—F7^ii	132.71 (18)	Ba3^x—F3—Ba4^x	116.0 (3)
F2^ii—Ba4—F21^ii	52.7 (2)	Zr1—F4—Ba3^ix	111.4 (3)
F4^i—Ba4—F21^ii	136.9 (2)	Zr1—F4—Ba4^ix	115.3 (3)
F5^i—Ba4—F21^ii	72.5 (2)	Ba3^ix—F4—Ba4^ix	118.0 (3)
F22^i—Ba4—F21^ii	147.85 (18)	Zr3—F5—Ba1^ix	120.4 (4)
F3^ii—Ba4—F21^ii	115.3 (2)	Zr3—F5—Ba4^ix	114.9 (4)
F9^vii—Ba4—F21^ii	60.53 (17)	Ba1^ix—F5—Ba4^ix	118.6 (3)
F16^vii—Ba4—F21^ii	110.43 (17)	Zr3—F6—Y^xii	101.6 (2)
F7^i—Ba4—F21^ii	86.01 (17)	Zr3—F6—Ba1^x	109.7 (3)
F7^ii—Ba4—F21^ii	47.56 (16)	Y^xii—F6—Ba1^x	117.7 (3)
F2^ii—Ba4—Zr3^ii	27.76 (16)	Zr3—F6—Ba1^ix	98.0 (2)
F4^i—Ba4—Zr3^ii	120.13 (17)	Y^xii—F6—Ba1^ix	97.2 (2)
F5^i—Ba4—Zr3^ii	75.85 (16)	Ba1^x—F6—Ba1^ix	128.29 (18)
F22^i—Ba4—Zr3^ii	172.28 (14)	Zr3—F7—Ba2^vi	102.33 (19)
F3^ii—Ba4—Zr3^ii	83.53 (17)	Zr3—F7—Ba4^ix	106.7 (3)
F9^vii—Ba4—Zr3^ii	84.49 (14)	Ba2^vi—F7—Ba4^ix	110.2 (3)
F16^vii—Ba4—Zr3^ii	118.46 (14)	Zr3—F7—Ba4^x	98.2 (3)
F7^i—Ba4—Zr3^ii	111.70 (12)	Ba2^vi—F7—Ba4^x	102.6 (3)
F7^ii—Ba4—Zr3^ii	32.00 (9)	Ba4^ix—F7—Ba4^x	132.72 (18)
F21^ii—Ba4—Zr3^ii	31.75 (11)	Zr2—F8—Ba3^x	117.0 (3)
F2^ii—Ba4—Zr2^vii	137.36 (16)	Zr2—F8—Ba1^x	112.4 (3)
F4^i—Ba4—Zr2^vii	129.99 (17)	Ba3^x—F8—Ba1^x	112.8 (2)
F5^i—Ba4—Zr2^vii	134.91 (16)	Zr2—F9—Ba4^xi	110.1 (2)
F22^i—Ba4—Zr2^vii	76.90 (12)	Zr2—F9—Ba2^iv	114.3 (3)
F3^ii—Ba4—Zr2^vii	125.54 (18)	Ba4^xi—F9—Ba2^iv	112.2 (2)
F9^vii—Ba4—Zr2^vii	29.16 (11)	Zr2—F10—Ba3^ix	133.8 (4)
F16^vii—Ba4—Zr2^vii	28.29 (11)	Zr2—F10—Ba1^ix	111.5 (3)
F7^i—Ba4—Zr2^vii	84.39 (10)	Ba3^ix—F10—Ba1^ix	112.4 (2)
F7^ii—Ba4—Zr2^vii	86.47 (9)	Zr1—F11—Y^v	111.9 (2)
F21^ii—Ba4—Zr2^vii	89.45 (12)	Zr1—F11—Ba3^iii	110.2 (2)
Zr3^ii—Ba4—Zr2^vii	109.61 (3)	Y^v—F11—Ba3^iii	137.2 (2)
F17^v—Y—F12^iv	95.9 (2)	Zr1—F12—Y^v	113.1 (2)
F17^v—Y—F19^viii	76.8 (2)	Zr1—F12—Ba1	101.0 (2)
F12^iv—Y—F19^viii	135.6 (2)	Y^v—F12—Ba1	110.3 (2)
F17^v—Y—F13	139.6 (2)	Zr2—F13—Y	113.3 (3)
F12^iv—Y—F13	123.8 (2)	Zr2—F13—Ba2^iv	110.2 (2)
F19^viii—Y—F13	79.0 (2)	Y—F13—Ba2^iv	116.3 (2)
F17^v—Y—F23^viii	125.0 (2)	Zr3—F14—Ba2^ix	125.1 (3)
F12^iv—Y—F23^viii	84.7 (2)	Zr3—F14—Ba2^vi	110.4 (3)
F19^viii—Y—F23^viii	66.2 (2)	Ba2^ix—F14—Ba2^vi	124.3 (2)
F13—Y—F23^viii	71.3 (2)	Zr1—F15—Y^iv	111.5 (2)
F17^v—Y—F11^iv	129.9 (2)	Zr1—F15—Ba3^ix	101.7 (2)
F12^iv—Y—F11^iv	65.1 (2)	Y^iv—F15—Ba3^ix	137.9 (3)
F19^viii—Y—F11^iv	149.0 (2)	Zr2—F16—Ba1^ix	114.2 (2)
F13—Y—F11^iv	70.2 (2)	Zr2—F16—Ba4^xi	110.5 (2)
F23^viii—Y—F11^iv	100.2 (2)	Ba1^ix—F16—Ba4^xi	122.5 (2)
F17^v—Y—F18	80.2 (2)	Zr1—F17—Y^iv	115.9 (3)
F12^iv—Y—F18	147.7 (2)	Zr1—F17—Ba1	103.7 (2)
F19^viii—Y—F18	75.0 (2)	Y^iv—F17—Ba1	121.4 (2)
F13—Y—F18	62.5 (2)	Zr2—F18—Y	112.3 (3)
F23^viii—Y—F18	123.8 (2)	Zr2—F18—Ba3^x	110.1 (3)
F11^iv—Y—F18	92.8 (2)	Y—F18—Ba3^x	128.5 (3)
F17^v—Y—F15^v	62.2 (2)	Zr3—F19—Y^xii	103.7 (2)
F12^iv—Y—F15^v	79.8 (2)	Zr3—F19—Ba2^x	115.7 (2)
F19^viii—Y—F15^v	129.3 (2)	Y^xii—F19—Ba2^x	139.9 (3)
F13—Y—F15^v	113.6 (2)	Zr2—F20—Ba2^v	116.0 (3)
F23^viii—Y—F15^v	163.7 (2)	Zr2—F20—Ba1^x	100.1 (2)
F11^iv—Y—F15^v	68.7 (2)	Ba2^v—F20—Ba1^x	143.2 (2)
F18—Y—F15^v	70.0 (2)	Zr3—F21—Ba2^x	115.6 (3)
F17^v—Y—F6^viii	67.1 (2)	Zr3—F21—Ba2^vi	97.5 (2)
F12^iv—Y—F6^viii	71.5 (2)	Ba2^x—F21—Ba2^vi	106.9 (2)
F19^viii—Y—F6^viii	65.3 (2)	Zr3—F21—Ba4^x	96.7 (2)
F13—Y—F6^viii	128.5 (2)	Ba2^x—F21—Ba4^x	135.7 (2)
F23^viii—Y—F6^viii	61.1 (2)	Ba2^vi—F21—Ba4^x	97.26 (18)
F11^iv—Y—F6^viii	134.2 (2)	Zr1—F22—Ba4^ix	114.9 (2)
F18—Y—F6^viii	132.9 (3)	Zr1—F22—Ba1	110.0 (2)
F15^v—Y—F6^viii	117.6 (2)	Ba4^ix—F22—Ba1	129.4 (2)
F17^v—Y—Zr3^viii	86.42 (15)	Zr3—F23—Y^xii	98.6 (2)
F12^iv—Y—Zr3^viii	99.54 (15)	Zr3—F23—Ba2^ix	104.8 (2)
F19^viii—Y—Zr3^viii	37.15 (15)	Y^xii—F23—Ba2^ix	114.7 (2)
F13—Y—Zr3^viii	93.38 (17)	Zr3—F23—Ba1^ix	97.1 (2)
F23^viii—Y—Zr3^viii	40.05 (15)	Y^xii—F23—Ba1^ix	100.4 (2)
F11^iv—Y—Zr3^viii	140.01 (16)	Ba2^ix—F23—Ba1^ix	134.6 (2)

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