Meta-barium borate, II-BaB₂O₄, at 163 and 293 K

The single-crystal X-ray diffraction structure analysis of an excellent non-linear optical material, viz. II-BaB₂O₄ or Ba₃(B₃O₆)₂, has been carried out at 163 and 293 K. The two sets of structural data are compared and indicate a significant shortening of the c axial length in the unit cell at 163 K, whereas the a and b axial lengths essentially do not change.

S1. Comment

In 1982, the low-temperature form of meta-barium borate, II-BaB₂O₄ (abbreviated BBO hereinafter), was first reported by us to crystallize in the trigonal crystal system (Lu et al., 1982), instead of in the monoclinic system (space group C2/c) as was determined by Hübner's early work (Hübner, 1969). Using matrix transformation, we also demonstrated that the unit-cell parameters of BBO obtained both in our structure analysis and in Hübner's actually reflect the same crystal lattice. However, regrettably, on account of some limitations in our experimental conditions at that time, we were not sufficiently confident to eliminate several relatively weak reflections which violated the systematic extinction by the c-glide plane, and thus we assigned the space group of BBO as simply R3, although we pointed out that it is, at the same time, very close to R3c. In addition, the coordination number of the Ba cation was erroneously stated as 7, rather than 8 as shown in our present work. Nevertheless, the results of our crystal structure analysis of BBO still provided a reasonable structural foundation for the development of BBO as an excellent UV second-harmonic generation (UV-SHG) material in our institute (Chen et al., 1985). Following our work, some papers on the crystal structure of BBO were published, such as articles reported by Liebertz et al. (1983), Fröhlich (1984) and Ito et al. (1990). They all showed the space group of BBO to be R3c. It is noteworthy that, in the more than 20 years since our first work was published, the optical nonlinearity of BBO has been studied extensively (Chen et al., 1989; Xue et al., 1998; Banks et al., 1999), and it has become one of the most common UV-SHG crystals in the field. In a recent review paper, Abrahams (2006) made a suggestion regarding a further measurement of the crystal structure of BBO from the point of view of the prediction of new ferroelectrics. We now respond to this proposal, and in this paper the crystal structures of BBO at 163 and 293 K are reported once again, in the hope that they are helpful for research into the properties of BBO.

Figs. 1–4 show the [B₃O₆]^3- anion group and the coordination environment of the Ba cation at the two different temperatures, 163 and 293 K. A view of the packing structure at 163 K is depicted in Fig. 5. It is apparent from a comparison of the main structural parameters at low temperature (163 K) with those at room temperature (293 K) that the equivalent isotropic displacement U_eq values of all atoms at 163 K (U_eq = 0.005–0.010 Ų) are about half those at 293 K (U_eq = 0.010–0.018 Ų). In particular, with the change in temperature from 293 to 163 K the c axial length is noticeably shortened, by about 0.064 Å, while the volume of the unit cell is reduced accordingly by about 9 ų [c = 12.721 (4) Å and V = 1729.9 (7) ų at 293 K, and c = 12.659 (4) Å and V = 1721.0 (7) ų at 163 K]. On the other hand, the a and b axial lengths do not change, approximately within the error range [a = b = 12.531 (3) Å at 293 K and a = b = 12.530 (3) Å at 163 K].

Details of the bonding data are presented in Tables 1 and 2. In the B–O [B₃O₆] ring, which is located exactly in the [ab] layer, the average intra-ring and extra-ring B—O bond lengths are 1.404 (5) and 1.314 (5) Å, respectively, at 293 K, and 1.404 (5) and 1.316 (5) Å, respectively, at 163 K. This means that the size of the rigid [B₃O₆] group is almost unchanged from room temperature down to low temperature. This may be why no noticeable reduction has been found in the a and b axial lengths at 163 K. It is interesting to note that the difference between the maximum and minimum intra-ring B—O bond lengths in the structure at 163 K is slightly smaller than the difference at 293 K (1.409 - 1.394 = 0.015 Å at 163 K, and 1.411 - 1.392 = 0.019 Å at 293 K), i.e. the B—O bond lengths of the six-membered [B₃O₃] ring are more averaged, indicating the conjugated π-bonding character of this ring at 163 K.

With regard to the coordination environment of the Ba cation, although no change is observed between the room- and low-temperature structures, most of the Ba—O bond lengths are shortened at 163 K, except for two [Ba—O3 and Ba—O3ⁱⁱ; symmetry code: (ii) Please provide], owing to the small displacement parameter of the O atom in the direction of the Ba—O bond. In particular for those linking the [B₃O₆] ring layers to the Ba layers, i.e. those located on the two sides of the [B₃O₆] ring layer, for instance Ba—O3^iv, Ba—O1ⁱ, Ba—O1ⁱⁱⁱ etc. [symmetry codes: (i) Please provide; (iii) Please provide; (iv) Please provide], the Ba—O bond lengths are shortened more markedly, with the maximum shortening reaching a value of 0.023 Å (3.049 - 3.026 = 0.023 Å for Ba—O3^iv). Therefore, it is reasonable to believe that it is the variation of the Ba—O bond lengths that results in the shrinkage of the c axial length mentioned above. Incidentally, on account of the unusually small atomic displacement parameters of some O atoms in the [B₃O₆] ring (e.g. O2 and O3) along the lines of B—O and Ba—O at 163 K, a prolate displacement ellipsoid may be observed.

If a comparison is made between the unit-cell parameters measured by Ito and Fröhlich with our present values at 293 K, the result are as follows. Ito: a = b = 12.5316 (3) Å and c = 12.7285 (9) Å; Fröhlich: a = b = 12.519 Å and c = 12.723 Å; this work: a = b = 12.531 (3) Å and c = 12.721 (4) Å. It can be seen that the values obtained by us are quite close to those of Ito, whereas there is a large difference from those found by Fröhlich, especially for the a and b axes (difference of about 0.012 Å). Considering the description by Abrahams of the comparison of the r.m.s. thermal displacement Δx for these three data sets, "It is notable that no atom in a unit cell with R3c symmetry, derived from Lu et al.'s (1982) determination, ······ has Δx ≥ 1.1 Å with respect to R3c, as is the case with the more accurate coordinates of Ito et al. (1990)", it can be said that the very close aggreement in unit-cell parameters between Ito's work and ours is consistent with Abrahams's assessment.

S2. Experimental

Transparent crystals of the title compound were obtained using the TSSG (Please give technique name in full) method in a BaB₂O₄–Na₂B₂O₄ flux system and were provided by the laboratory of Professor Zhuang Jian and Mr Zeng Wen-Rong.

Computing details

For both compounds, data collection: CrystalClear (Rigaku/MSC, 2001); cell refinement: CrystalClear; data reduction: CrystalStructure (Rigaku/MSC, 2004); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: SHELXL97; software used to prepare material for publication: SHELXL97.

Figures

	Fig. 1. A diagram of the anion group at 163 K. Displacement ellipsoids are drawn at the 80% probability level. [Symmetry codes: (v) -x + y, 1 - x, z; (vi) -x + y, -x, z; (vii) 1 - y,1 + x-y, z; (viii) -y, x-y, z.]
	Fig. 2. A view of the coordination enviroment of the Ba cation at 163 K. Displacement ellipsoids are drawn at the 80% probability level. [Symmetry codes: (i) 1/3 + x, 2/3 + x-y, 1/6 + z; (ii) 2/3 - x + y, 1/3 + y, z - 1/6; (iii) 2/3 - y, 1/3 - x, z - 1/6; (iv) 1/3 - y, 2/3 - x, z + 1/6.]
	Fig. 3. A diagram of the anion group at 293 K. Displacement ellipsoids are drawn at the 80% probability level·[Symmetry codes: (v) -x + y, 1 - x, z; (vi) -x + y, -x, z; (vii) 1 - y,1 + x-y, z; (viii) -y, x-y, z.]
	Fig. 4. A view of the coordination enviroment of the Ba cation at 293 K. Displacement ellipsoids are drawn at the 80% probability level. [Symmetry codes: (i) 1/3 + x, 2/3 + x-y, 1/6 + z; (ii) 2/3 - x + y, 1/3 + y, z - 1/6; (iii) 2/3 - y, 1/3 - x, z - 1/6; (iv) 1/3 - y, 2/3 - x, z + 1/6.]
	Fig. 5. A view of the packing structure measured at 163 K.

(BBO_293K) meta-barium borate

Crystal data

Ba3(B3O6)2	Dx = 3.852 Mg m^−3
Mr = 668.85	Mo Kα radiation, λ = 0.71073 Å
TrigonalR3c	Cell parameters from 1770 reflections
a = 12.531 (3) Å	θ = 2.5–27.5°
c = 12.721 (4) Å	µ = 10.19 mm^−1
V = 1729.9 (7) Å^3	T = 293 K
Z = 6	Block, colourless
F(000) = 1764	0.16 × 0.14 × 0.11 mm

Data collection

Rigaku Saturn70 CCD area-detector diffractometer	628 independent reflections
Radiation source: Rotating Anode	621 reflections with I > 2σ(I)
Confocal monochromator	Rint = 0.021
φ and ω scans	θmax = 27.5°, θmin = 3.7°
Absorption correction: multi-scan (ABSCOR; Jacobson, 1998)	h = −15→13
Tmin = 0.213, Tmax = 0.326	k = −16→15
1799 measured reflections	l = −11→16

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)] = 0.013	w = 1/[σ^2(Fo^2) + (0.0142P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.030	(Δ/σ)max < 0.001
S = 1.06	Δρmax = 0.68 e Å^−3
628 reflections	Δρmin = −0.61 e Å^−3
64 parameters	Absolute structure: Flack (1983), with how many Friedel pairs
1 restraint	Absolute structure parameter: 0.02 (3)

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
Ba	0.30592 (2)	0.33041 (3)	0.45106 (6)	0.01043 (8)
B1	0.2318 (4)	0.5437 (5)	0.4221 (4)	0.0116 (10)
B2	0.1305 (5)	0.0438 (5)	0.4938 (4)	0.0112 (10)
O1	0.1408 (3)	0.4291 (3)	0.4297 (3)	0.0143 (6)
O2	0.3548 (3)	0.5695 (3)	0.4206 (3)	0.0175 (8)
O3	0.2494 (3)	0.0860 (3)	0.4890 (3)	0.0164 (7)
O4	0.0827 (3)	0.1239 (3)	0.4961 (3)	0.0183 (8)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba	0.00664 (15)	0.00716 (11)	0.01712 (13)	0.00318 (13)	−0.00076 (17)	−0.00056 (7)
B1	0.007 (2)	0.013 (2)	0.011 (2)	0.003 (2)	−0.001 (2)	−0.0024 (19)
B2	0.010 (2)	0.007 (2)	0.015 (3)	0.0035 (19)	0.0002 (19)	0.002 (2)
O1	0.0125 (14)	0.0079 (14)	0.0202 (17)	0.0034 (12)	−0.0018 (13)	0.0007 (13)
O2	0.0055 (16)	0.0066 (16)	0.038 (2)	0.0012 (13)	0.0005 (16)	−0.0003 (15)
O3	0.0095 (15)	0.0131 (14)	0.0257 (19)	0.0049 (12)	−0.0036 (13)	0.0024 (13)
O4	0.0089 (16)	0.0072 (15)	0.039 (2)	0.0043 (14)	−0.0041 (15)	−0.0002 (13)

Geometric parameters (Å, º)

Ba—O1^i	2.638 (3)	B1—O1	1.317 (6)
Ba—O3^ii	2.699 (3)	B1—O2^vii	1.392 (6)
Ba—O4	2.758 (3)	B1—O2	1.409 (5)
Ba—O2	2.769 (3)	B2—O3	1.310 (6)
Ba—O3	2.819 (3)	B2—O4	1.403 (6)
Ba—O1^iii	2.821 (3)	B2—O4^viii	1.411 (6)
Ba—O1	2.906 (3)	O1—Ba^ix	2.638 (3)
Ba—O3^iv	3.049 (4)	O1—Ba^iv	2.821 (3)
Ba—B2	3.183 (5)	O2—B1^x	1.392 (6)
Ba—B1	3.260 (6)	O3—Ba^xi	2.699 (3)
Ba—Ba^v	4.2780 (12)	O3—Ba^iii	3.049 (4)
Ba—Ba^vi	4.2780 (13)	O4—B2^xii	1.411 (6)
O1^i—Ba—O3^ii	82.43 (10)	O2—Ba—Ba^v	103.20 (8)
O1^i—Ba—O4	112.85 (10)	O3—Ba—Ba^v	75.15 (8)
O3^ii—Ba—O4	143.44 (10)	O1^iii—Ba—Ba^v	144.19 (6)
O1^i—Ba—O2	97.59 (10)	O1—Ba—Ba^v	102.95 (7)
O3^ii—Ba—O2	78.87 (9)	O3^iv—Ba—Ba^v	38.86 (6)
O4—Ba—O2	128.04 (11)	B2—Ba—Ba^v	78.01 (10)
O1^i—Ba—O3	82.28 (9)	B1—Ba—Ba^v	103.57 (9)
O3^ii—Ba—O3	103.48 (7)	O1^i—Ba—Ba^vi	127.30 (7)
O4—Ba—O3	50.14 (9)	O3^ii—Ba—Ba^vi	45.14 (8)
O2—Ba—O3	177.59 (10)	O4—Ba—Ba^vi	109.08 (8)
O1^i—Ba—O1^iii	134.20 (5)	O2—Ba—Ba^vi	79.84 (8)
O3^ii—Ba—O1^iii	70.94 (10)	O3—Ba—Ba^vi	102.17 (8)
O4—Ba—O1^iii	75.31 (10)	O1^iii—Ba—Ba^vi	36.90 (6)
O2—Ba—O1^iii	112.29 (10)	O1—Ba—Ba^vi	88.78 (7)
O3—Ba—O1^iii	69.22 (10)	O3^iv—Ba—Ba^vi	150.16 (6)
O1^i—Ba—O1	128.79 (9)	B2—Ba—Ba^vi	104.97 (10)
O3^ii—Ba—O1	117.92 (9)	B1—Ba—Ba^vi	84.72 (10)
O4—Ba—O1	79.33 (9)	Ba^v—Ba—Ba^vi	166.844 (9)
O2—Ba—O1	49.15 (9)	O1—B1—O2^vii	123.5 (4)
O3—Ba—O1	129.26 (8)	O1—B1—O2	120.2 (5)
O1^iii—Ba—O1	96.82 (9)	O2^vii—B1—O2	116.2 (4)
O1^i—Ba—O3^iv	68.15 (9)	O1—B1—Ba	62.9 (2)
O3^ii—Ba—O3^iv	134.83 (6)	O2^vii—B1—Ba	171.2 (3)
O4—Ba—O3^iv	81.12 (10)	O2—B1—Ba	57.4 (3)
O2—Ba—O3^iv	72.28 (10)	O3—B2—O4	121.2 (4)
O3—Ba—O3^iv	105.49 (10)	O3—B2—O4^viii	123.9 (4)
O1^iii—Ba—O3^iv	152.71 (8)	O4—B2—O4^viii	114.9 (4)
O1—Ba—O3^iv	65.04 (9)	O3—B2—Ba	62.1 (2)
O1^i—Ba—B2	99.19 (12)	O4—B2—Ba	59.8 (2)
O3^ii—Ba—B2	122.88 (11)	O4^viii—B2—Ba	169.5 (4)
O4—Ba—B2	26.07 (11)	B1—O1—Ba^ix	125.4 (3)
O2—Ba—B2	154.05 (12)	B1—O1—Ba^iv	117.3 (3)
O3—Ba—B2	24.24 (11)	Ba^ix—O1—Ba^iv	103.15 (10)
O1^iii—Ba—B2	68.10 (11)	B1—O1—Ba	93.4 (3)
O1—Ba—B2	105.02 (11)	Ba^ix—O1—Ba	110.98 (10)
O3^iv—Ba—B2	95.92 (11)	Ba^iv—O1—Ba	104.48 (10)
O1^i—Ba—B1	114.54 (11)	B1^x—O2—B1	123.8 (4)
O3^ii—Ba—B1	99.84 (11)	B1^x—O2—Ba	138.0 (3)
O4—Ba—B1	102.81 (12)	B1—O2—Ba	97.2 (3)
O2—Ba—B1	25.39 (10)	B2—O3—Ba^xi	120.7 (3)
O3—Ba—B1	152.93 (11)	B2—O3—Ba	93.7 (3)
O1^iii—Ba—B1	106.42 (11)	Ba^xi—O3—Ba	130.36 (12)
O1—Ba—B1	23.78 (10)	B2—O3—Ba^iii	114.4 (3)
O3^iv—Ba—B1	65.52 (11)	Ba^xi—O3—Ba^iii	96.00 (10)
B2—Ba—B1	128.70 (13)	Ba—O3—Ba^iii	100.91 (10)
O1^i—Ba—Ba^v	39.95 (7)	B2—O4—B2^xii	125.0 (4)
O3^ii—Ba—Ba^v	122.38 (8)	B2—O4—Ba	94.1 (3)
O4—Ba—Ba^v	79.37 (8)	B2^xii—O4—Ba	138.6 (3)

Symmetry codes: (i) x+1/3, x−y+2/3, z+1/6; (ii) −x+y+2/3, y+1/3, z−1/6; (iii) −y+2/3, −x+1/3, z−1/6; (iv) −y+1/3, −x+2/3, z+1/6; (v) −y+2/3, x−y+1/3, z+1/3; (vi) −x+y+1/3, −x+2/3, z−1/3; (vii) −x+y, −x+1, z; (viii) −x+y, −x, z; (ix) x−1/3, x−y+1/3, z−1/6; (x) −y+1, x−y+1, z; (xi) −x+y+1/3, y−1/3, z+1/6; (xii) −y, x−y, z.

(BBO_163K) meta-barium borate

Crystal data

Ba3(B3O6)2	Dx = 3.872 Mg m^−3
Mr = 668.85	Mo Kα radiation, λ = 0.71073 Å
TrigonalR3c	Cell parameters from 1761 reflections
a = 12.530 (3) Å	θ = 2.5–27.4°
c = 12.657 (4) Å	µ = 10.24 mm^−1
V = 1721.0 (7) Å^3	T = 163 K
Z = 6	Block, colourless
F(000) = 1764	0.16 × 0.14 × 0.11 mm

Data collection

Rigaku Saturn70 CCD area-detector diffractometer	625 independent reflections
Radiation source: Rotating Anode	623 reflections with I > 2σ(I)
Confocal monochromator	Rint = 0.021
φ and ω scans	θmax = 27.4°, θmin = 3.7°
Absorption correction: multi-scan (ABSCOR; Jacobson, 1998)	h = −16→15
Tmin = 0.212, Tmax = 0.324	k = −8→16
1778 measured reflections	l = −11→16

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)] = 0.011	w = 1/[σ^2(Fo^2) + (0.0095P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.027	(Δ/σ)max = 0.001
S = 1.08	Δρmax = 0.53 e Å^−3
625 reflections	Δρmin = −0.45 e Å^−3
64 parameters	Absolute structure: Flack (1983), with how many Friedel pairs
1 restraint	Absolute structure parameter: 0.05 (3)

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
Ba	0.305461 (19)	0.33040 (3)	0.45117 (6)	0.00547 (7)
B1	0.2314 (4)	0.5436 (4)	0.4216 (4)	0.0067 (9)
B2	0.1301 (4)	0.0433 (5)	0.4934 (4)	0.0078 (9)
O1	0.1406 (2)	0.4287 (2)	0.4295 (2)	0.0078 (6)
O2	0.3545 (3)	0.5692 (3)	0.4201 (3)	0.0096 (6)
O3	0.2495 (2)	0.0858 (2)	0.4884 (2)	0.0091 (6)
O4	0.0829 (3)	0.1239 (3)	0.4958 (2)	0.0102 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba	0.00351 (13)	0.00372 (10)	0.00912 (11)	0.00177 (12)	−0.00031 (15)	−0.00033 (6)
B1	0.004 (2)	0.009 (2)	0.005 (2)	0.0027 (19)	−0.0011 (18)	−0.0012 (17)
B2	0.007 (2)	0.005 (2)	0.010 (2)	0.0021 (19)	0.0003 (17)	0.002 (2)
O1	0.0079 (13)	0.0042 (13)	0.0089 (14)	0.0013 (11)	−0.0031 (11)	−0.0009 (11)
O2	0.0020 (15)	0.0040 (15)	0.0212 (18)	0.0004 (13)	−0.0012 (14)	−0.0014 (13)
O3	0.0052 (13)	0.0095 (13)	0.0122 (15)	0.0033 (11)	−0.0018 (11)	0.0003 (11)
O4	0.0046 (14)	0.0035 (14)	0.0216 (18)	0.0013 (12)	0.0000 (13)	0.0009 (11)

Geometric parameters (Å, º)

Ba—O1^i	2.630 (3)	B1—O1	1.318 (5)
Ba—O3^ii	2.701 (3)	B1—O2^vii	1.394 (5)
Ba—O4	2.752 (3)	B1—O2	1.409 (5)
Ba—O2	2.765 (3)	B2—O3	1.315 (5)
Ba—O1^iii	2.813 (3)	B2—O4	1.402 (6)
Ba—O3	2.821 (3)	B2—O4^viii	1.409 (6)
Ba—O1	2.900 (3)	O1—Ba^ix	2.630 (3)
Ba—O3^iv	3.026 (3)	O1—Ba^iv	2.813 (3)
Ba—B2	3.186 (5)	O2—B1^x	1.394 (5)
Ba—B1	3.258 (5)	O3—Ba^xi	2.701 (3)
Ba—Ba^v	4.2583 (12)	O3—Ba^iii	3.026 (3)
Ba—Ba^vi	4.2583 (12)	O4—B2^xii	1.409 (6)
O1^i—Ba—O3^ii	82.18 (9)	O2—Ba—Ba^v	103.45 (7)
O1^i—Ba—O4	113.07 (9)	O1^iii—Ba—Ba^v	144.01 (6)
O3^ii—Ba—O4	143.19 (9)	O3—Ba—Ba^v	75.26 (6)
O1^i—Ba—O2	97.62 (9)	O1—Ba—Ba^v	103.18 (6)
O3^ii—Ba—O2	78.84 (8)	O3^iv—Ba—Ba^v	39.12 (6)
O4—Ba—O2	128.24 (10)	B2—Ba—Ba^v	78.12 (9)
O1^i—Ba—O1^iii	133.87 (4)	B1—Ba—Ba^v	103.82 (9)
O3^ii—Ba—O1^iii	70.80 (9)	O1^i—Ba—Ba^vi	126.90 (6)
O4—Ba—O1^iii	75.21 (8)	O3^ii—Ba—Ba^vi	44.98 (6)
O2—Ba—O1^iii	112.27 (9)	O4—Ba—Ba^vi	109.09 (7)
O1^i—Ba—O3	82.39 (8)	O2—Ba—Ba^vi	79.68 (7)
O3^ii—Ba—O3	103.15 (6)	O1^iii—Ba—Ba^vi	37.01 (6)
O4—Ba—O3	50.17 (8)	O3—Ba—Ba^vi	101.94 (6)
O2—Ba—O3	177.99 (9)	O1—Ba—Ba^vi	88.82 (6)
O1^iii—Ba—O3	68.91 (8)	O3^iv—Ba—Ba^vi	150.07 (5)
O1^i—Ba—O1	128.99 (8)	B2—Ba—Ba^vi	104.89 (9)
O3^ii—Ba—O1	117.95 (8)	B1—Ba—Ba^vi	84.67 (9)
O4—Ba—O1	79.44 (8)	Ba^v—Ba—Ba^vi	166.553 (8)
O2—Ba—O1	49.21 (8)	O1—B1—O2^vii	123.9 (4)
O1^iii—Ba—O1	96.93 (8)	O1—B1—O2	119.9 (4)
O3—Ba—O1	129.38 (8)	O2^vii—B1—O2	116.0 (4)
O1^i—Ba—O3^iv	68.38 (8)	O1—B1—Ba	62.7 (2)
O3^ii—Ba—O3^iv	134.79 (5)	O2^vii—B1—Ba	171.0 (3)
O4—Ba—O3^iv	81.40 (9)	O2—B1—Ba	57.4 (2)
O2—Ba—O3^iv	72.28 (9)	O3—B2—O4	120.9 (4)
O1^iii—Ba—O3^iv	152.90 (8)	O3—B2—O4^viii	123.9 (4)
O3—Ba—O3^iv	105.91 (9)	O4—B2—O4^viii	115.1 (4)
O1—Ba—O3^iv	65.03 (8)	O3—B2—Ba	62.1 (2)
O1^i—Ba—B2	99.38 (11)	O4—B2—Ba	59.5 (2)
O3^ii—Ba—B2	122.65 (11)	O4^viii—B2—Ba	169.6 (3)
O4—Ba—B2	26.02 (10)	B1—O1—Ba^ix	125.5 (3)
O2—Ba—B2	154.18 (12)	B1—O1—Ba^iv	117.2 (3)
O1^iii—Ba—B2	67.91 (11)	Ba^ix—O1—Ba^iv	102.92 (9)
O3—Ba—B2	24.33 (10)	B1—O1—Ba	93.5 (3)
O1—Ba—B2	105.06 (10)	Ba^ix—O1—Ba	111.13 (9)
O3^iv—Ba—B2	96.23 (10)	Ba^iv—O1—Ba	104.60 (9)
O1^i—Ba—B1	114.66 (10)	B1^x—O2—B1	123.9 (4)
O3^ii—Ba—B1	99.84 (10)	B1^x—O2—Ba	137.8 (3)
O4—Ba—B1	102.97 (11)	B1—O2—Ba	97.2 (3)
O2—Ba—B1	25.41 (10)	B2—O3—Ba^xi	120.7 (3)
O1^iii—Ba—B1	106.48 (10)	B2—O3—Ba	93.6 (3)
O3—Ba—B1	153.11 (10)	Ba^xi—O3—Ba	130.24 (10)
O1—Ba—B1	23.82 (10)	B2—O3—Ba^iii	114.7 (3)
O3^iv—Ba—B1	65.50 (10)	Ba^xi—O3—Ba^iii	95.89 (9)
B2—Ba—B1	128.79 (12)	Ba—O3—Ba^iii	101.20 (9)
O1^i—Ba—Ba^v	40.08 (6)	B2—O4—B2^xii	124.8 (4)
O3^ii—Ba—Ba^v	122.26 (7)	B2—O4—Ba	94.5 (3)
O4—Ba—Ba^v	79.50 (7)	B2^xii—O4—Ba	138.5 (3)

Symmetry codes: (i) x+1/3, x−y+2/3, z+1/6; (ii) −x+y+2/3, y+1/3, z−1/6; (iii) −y+2/3, −x+1/3, z−1/6; (iv) −y+1/3, −x+2/3, z+1/6; (v) −y+2/3, x−y+1/3, z+1/3; (vi) −x+y+1/3, −x+2/3, z−1/3; (vii) −x+y, −x+1, z; (viii) −x+y, −x, z; (ix) x−1/3, x−y+1/3, z−1/6; (x) −y+1, x−y+1, z; (xi) −x+y+1/3, y−1/3, z+1/6; (xii) −y, x−y, z.