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ISSN: 2056-9890

Crystal structure of the solid solution Ba8.35Pb0.65(B3O6)6

aDepartment of Environmental and Chemical Engineering, Tangshan College, 38 North HuaYan Road, Tangshan 063000, Hebei, People's Republic of China
*Correspondence e-mail: zww995@163.com

Edited by M. Weil, Vienna University of Technology, Austria (Received 5 December 2016; accepted 2 February 2017; online 14 February 2017)

Single crystals of lead barium borate, Ba8.35Pb0.65(B3O6)6, octabarium lead(II) hexa­kis­(triborate), have been obtained by spontaneous nucleation from a high-temperature melt. Its three-dimensional structure is constructed on the basis of a BaO9 polyhedron, a (Pb/Ba)O6 octa­hedron (occupancy ratio Pb:Ba = 0.216:0.784) and a condensed B3O6 ring anion. In the crystal, the planar B3O6 anions are stacked in an alternating fashion with Ba and (Pb/Ba) atoms along [001]. A comparison is made with the structures of related solid solutions in the system Ba/Pb/B/O.

1. Chemical context

The study of inorganic borates is motivated by their possible non-linear optical properties, transparency in a wide range of wavelengths, high laser-damage tolerance, piezoelectricity and luminescent and other useful properties for technical applications of the respective compounds. For example, β-BaB2O4 (Chen et al., 1985[Chen, C., Wu, B., Jiang, A. & You, G. (1985). Sci. Sin. B28, 235-241.]), LiB3O5 (Chen et al., 1989[Chen, C., Wu, Y., Jiang, A., Wu, B., You, G., Li, R. & Lin, S. (1989). J. Opt. Soc. Am. B, 6, 616-621.]), CsB3O5 (Sasaki et al., 2000[Sasaki, T., Mori, Y., Yoshimura, M., Yap, Y. K. & Kamimura, T. (2000). Mater. Sci. Eng. Rep. 30, 1-54.]), Sr2Be2B2O7 (Chen et al., 1995[Chen, C., Wang, Y., Wu, B., Wu, K., Zeng, W. & Yu, L. (1995). Nature, 373, 322-324.]), K5Ba10(BO3)8F (Liu et al., 2016[Liu, L. L., Yang, Y., Jing, Q., Dong, X. Y., Yang, Z. H., Pan, S. L. & Wu, K. (2016). J. Phys. Chem. C, 120, 18763-18770.]), PbB4O7 (Bartwal et al., 2001[Bartwal, K. S., Bhatt, R., Kar, S. & Wadhawan, V. K. (2001). Mater. Sci. Eng. B, 85, 76-79.]), Pb2B5O9X (X = Cl, Br, I) (Huang et al., 2010[Huang, Y., Wu, L., Wu, X., Li, L., Chen, L. & Zhang, Y. (2010). J. Am. Chem. Soc. 132, 12788-12789.]) or Ba3Sr4(BO3)3F5 (Zhang et al., 2009[Zhang, G., Liu, Z., Zhang, J., Fan, F., Liu, Y. & Fu, P. (2009). Cryst. Growth Des. 9, 3137-3141.]) have been studied because of their second-order non-linear optical behavior. Among inorganic borates synthesized and characterized over the past decades, some lead(II) borates show comprehensive applications. These features are associated with the highly asymmetric stereochemistry typical for a lead(II) atom due to the stereoactivity of the 6s2 lone pair (Zhang et al., 2016[Zhang, F. F., Zhang, F. Y., Lei, B. H., Yang, Z. H. & Pan, S. L. (2016). J. Phys. Chem. C, 120, 12757-12764.]; Mutailipu et al., 2016[Mutailipu, M., Hou, D. W., Zhang, M., Yang, Z. H. & Pan, S. L. (2016). New J. Chem. 40, 6120-6126.]). Accordingly, numerous studies have been devoted to this family of compounds. Some lead borates are particularly attractive because of their high second-harmonic generation (SHG) response (Wu et al., 2012[Wu, H. P., Pan, S. L., Jia, D. Z., Chen, Z. H. & Yu, H. W. (2012). Chem. Lett. 41, 812-813.]; Dong et al., 2015[Dong, X. Y., Jing, Q., Shi, Y. J., Yang, Z. H., Pan, S. L., Poeppelmeier, K. R., Young, J. & Rondinelli, J. M. (2015). J. Am. Chem. Soc. 137, 9417-9422.]; Jing et al., 2015[Jing, Q., Dong, X. Y., Yang, Z. H. & Pan, S. L. (2015). Dalton Trans. 44, 16818-16823.]) or large birefringence (Liu et al., 2015[Liu, L., Zhang, B. B., Zhang, F. F., Pan, S. L., Zhang, F. Y., Zhang, X. W., Dong, X. Y. & Yang, Z. H. (2015). Dalton Trans. 44, 7041-7047.]).

In this communication, we report on the synthesis and crystal structure of the solid solution Ba8.35Pb0.65(B3O6)6.

2. Structural commentary

The crystal structure of Ba8.35Pb0.65(B3O6)6 is based on a Ba2O9 polyhedron, a (Pb/Ba1)O6 polyhedron and a condensed B3O6 anion, as shown in Fig. 1[link]. The planar B3O6 anions (point group symmetry 3.) are isolated from each other and distributed layer upon layer perpendicular to [001]. The occupationally disordered (Pb/Ba)1 site (occupancy ratio Pb:Ba = 0.216:0.784) and the Ba2 site are located alternately between the B3O6 sheets in (Pb/Ba)1 and Ba2 layers, as shown in Fig. 2[link]a. The B atom is bound to one O1 atom and two O2 atoms to from a BO3 triangle. Three BO3 triangles are condensed through vertex-sharing to build a planar and cyclic B3O6 unit. The B—O bond lengths vary from 1.318 (5) to 1.406 (5) Å (Table 1[link]), and the O—B—O angles are between 116.8 (4) and 122.6 (4)°.

Table 1
Selected geometric parameters (Å, °)

(Pb/Ba)1—O1 2.537 (3) B—O1 1.318 (5)
Ba2—O1 2.766 (3) B—O2 1.397 (5)
Ba2—O1i 2.810 (3) B—O2ii 1.406 (5)
Ba2—O2 3.030 (3)    
       
O1—B—O2 120.6 (4) O2—B—O2ii 116.8 (4)
O1—B—O2ii 122.6 (4)    
Symmetry codes: (i) [-x+{\script{2\over 3}}, -y+{\script{1\over 3}}, -z+{\script{1\over 3}}]; (ii) -y, x-y-1, z.
[Figure 1]
Figure 1
The principal building units in the crystal structure of the title compound. Displacement ellipsoids are drawn at the 50% probability level. [Symmetry codes: (i) −x, −y, −z; (ii) −y, x − y, z; (iii) y, −x + y, −z; (iv) x − y, x, −z; (v) −x + y, −x, z; (vi) −y + 1, x − y, z; (vii) −x + y + 1, −x + 1, z; (viii) y + [{2\over 3}], −x + y + [{1\over 3}], −z + [{1\over 3}]; (ix) x − y + [{2\over 3}], x + [{1\over 3}], −z + [{1\over 3}]; (x) −x + [{2\over 3}], −y + [{1\over 3}], −z + [{1\over 3}]; (xiii) −y, x − y − 1, z; (xiv) −x + y + 1, −x, z.]
[Figure 2]
Figure 2
The crystal structures of related solid solutions in the system Ba/Pb/B/O viewed down [010]: (a) Ba8.35Pb0.65(B3O6)6; (b) Ba7.87Pb1.13(B3O6)6 (Wu et al., 2012[Wu, H. P., Pan, S. L., Jia, D. Z., Chen, Z. H. & Yu, H. W. (2012). Chem. Lett. 41, 812-813.]); (c) Ba2Pb(B3O6)2 (Li et al., 2014[Li, H. Y., Dong, L., Lu, Y., Pan, S. L., Lu, X., Yu, H. W., Wu, H. P., Su, X. & Yang, Z. H. (2014). J. Alloys Compd. 615, 561-565.]); (d) Ba2Pb(B3O6)2 (Tang et al., 2015[Tang, X. L., Feng, D. X., Wan, S. M., Kang, L., Zhang, B. & Lin, Z. S. (2015). Mater. Chem. Phys. 163, 501-506.]). The numbers indicate the bond lengths (Å) of the PbO6 or (Ba/Pb)O6 octa­hedra.

The Ba2 atom (site symmetry 3.) is coordinated by nine O atoms. The Ba—O bond lengths of the Ba2O9 polyhedron range from 2.766 (3) to 3.030 (3) Å, with a mean distance of 2.869 Å (Table 1[link]). A similar environment for Ba is observed in the crystal structures of Na3Ba2(B3O6)2F (Zhang et al., 2015[Zhang, H., Zhang, M., Pan, S. L., Yang, Z., Wang, Z., Bian, Q., Hou, X., Yu, H., Zhang, F., Wu, K., Yang, F., Peng, Q., Xu, Z., Chang, K. B. & Poeppelmeier, K. R. (2015). Cryst. Growth Des. 15, 523-529.]), PbBa2(B3O6)2 (Li et al., 2014[Li, H. Y., Dong, L., Lu, Y., Pan, S. L., Lu, X., Yu, H. W., Wu, H. P., Su, X. & Yang, Z. H. (2014). J. Alloys Compd. 615, 561-565.]) and α-BBO (Wu et al., 2002[Wu, S., Wang, G., Xie, J., Wu, X., Zhang, Y. & Lin, X. (2002). J. Cryst. Growth, 245, 84-86.]). Each of the Ba2O9 polyhedra shares edges with adjacent Ba2O9 polyhedra to form six-membered rings that are arranged in corrugated layers extending parallel to (001) (Fig. 3[link]). The (Pb/Ba)1 site (site symmetry [\overline{3}].) is surrounded by six O atoms; the corresponding (Pb/Ba)1O6 octa­hedra are isolated from each other. The six (Pb/Ba1)—O bonds have an identical length of 2.537 (3) Å (Table 1[link], Fig. 2[link]a). In comparison with the M2 site, the M1 site has a more narrow coordin­ation environment which seems to be the reason why Pb atoms exclusively substitute Ba atoms at the latter position due to their smaller ionic radius.

[Figure 3]
Figure 3
The formation of a corrugated layer of Ba2O9 polyhedra in the crystal structure of Ba8.35Pb0.65(B3O6)6 viewed down [001].

3. Comparison with the structures of related solid solutions

It is inter­esting to compare the structure of Ba8.35Pb0.65(B3O6)6 with those of the related solid solutions Ba7.87Pb1.13(B3O6)6 (Wu et al., 2012[Wu, H. P., Pan, S. L., Jia, D. Z., Chen, Z. H. & Yu, H. W. (2012). Chem. Lett. 41, 812-813.]) and Ba2Pb(B3O6)2 (Li et al., 2014[Li, H. Y., Dong, L., Lu, Y., Pan, S. L., Lu, X., Yu, H. W., Wu, H. P., Su, X. & Yang, Z. H. (2014). J. Alloys Compd. 615, 561-565.]; Tang et al., 2015[Tang, X. L., Feng, D. X., Wan, S. M., Kang, L., Zhang, B. & Lin, Z. S. (2015). Mater. Chem. Phys. 163, 501-506.]). Whereas the title compound Ba8.35Pb0.65(B3O6)6 crystallizes in space group R[\overline{3}], Ba7.87Pb1.13(B3O6)6 was solved and refined in space group R32 on the basis of single crystal X-ray diffraction data (Wu et al., 2012[Wu, H. P., Pan, S. L., Jia, D. Z., Chen, Z. H. & Yu, H. W. (2012). Chem. Lett. 41, 812-813.]); the lattice parameters of both compounds are very similar. Ba2Pb(B3O6)2 on the other hand was reported to crystallize either in space group R[\overline{3}] with lattice parameters in the same range as the previous two structures (single crystal X-ray diffraction data; Li et al., 2014[Li, H. Y., Dong, L., Lu, Y., Pan, S. L., Lu, X., Yu, H. W., Wu, H. P., Su, X. & Yang, Z. H. (2014). J. Alloys Compd. 615, 561-565.]) or in space group R[\overline{3}]c with a doubled c axis in comparison with the other structures (powder X-ray diffraction data using the Rietveld method; Tang et al., 2015[Tang, X. L., Feng, D. X., Wan, S. M., Kang, L., Zhang, B. & Lin, Z. S. (2015). Mater. Chem. Phys. 163, 501-506.]). All four crystal structures are characterized by an alternating stacking of cationic and anionic (001) layers along [001], as shown in Fig. 2[link]. In each case, the Ba site is coordinated by nine O atoms to form BaO9 polyhedra, and the Pb or the (Pb/Ba) site is coordinated by six O atoms to form distorted PbO6 octa­hedra [in Ba2Pb(B3O6)2] or (Pb/Ba)O6 octa­hedra [in Ba8.35Pb0.65(B3O6)6 and Ba7.87Pb1.13(B3O6)6].

The arrangement of the planar B3O6 rings in the crystal structures is a determining factor in whether a non-centrosymmetric or a centrosymmetric structure is obtained. In Ba7.87Pb1.13(B3O6)6 (Wu et al., 2012[Wu, H. P., Pan, S. L., Jia, D. Z., Chen, Z. H. & Yu, H. W. (2012). Chem. Lett. 41, 812-813.]), the rings are aligned in a chiral arrangement (Fig. 4[link]b), responsible for the SHG effect. In Ba2Pb(B3O6)2 (Li et al., 2014[Li, H. Y., Dong, L., Lu, Y., Pan, S. L., Lu, X., Yu, H. W., Wu, H. P., Su, X. & Yang, Z. H. (2014). J. Alloys Compd. 615, 561-565.]), the B3O6 rings are parallel to each other, distributed layer upon layer along [001], and the B3O6 rings in neighbouring layers point in exactly opposite directions (Fig. 4[link]c), just like in the title compound (Fig. 4[link]a). In the Ba2Pb(B3O6)2 structure with doubled volume (Tang et al., 2015[Tang, X. L., Feng, D. X., Wan, S. M., Kang, L., Zhang, B. & Lin, Z. S. (2015). Mater. Chem. Phys. 163, 501-506.]), all of the B3O6 rings are parallel to (001), and the B3O6 rings in two neighbouring layers are rotated slightly relative to each other (Fig. 4[link]d).

[Figure 4]
Figure 4
The arrangement of B3O6 groups along the [001] direction in the different solid solutions: (a) Ba8.35Pb0.65(B3O6)6; (b) Ba7.87Pb1.13(B3O6)6 (Wu et al., 2012[Wu, H. P., Pan, S. L., Jia, D. Z., Chen, Z. H. & Yu, H. W. (2012). Chem. Lett. 41, 812-813.]); (c) Ba2Pb(B3O6)2 (Li et al., 2014[Li, H. Y., Dong, L., Lu, Y., Pan, S. L., Lu, X., Yu, H. W., Wu, H. P., Su, X. & Yang, Z. H. (2014). J. Alloys Compd. 615, 561-565.]); (d) Ba2Pb(B3O6)2 (Tang et al., 2015[Tang, X. L., Feng, D. X., Wan, S. M., Kang, L., Zhang, B. & Lin, Z. S. (2015). Mater. Chem. Phys. 163, 501-506.]).

4. Synthesis and crystallization

Suitable crystals of the solid solution Ba8.35Pb0.65(B3O6)6 were obtained by spontaneous nucleation from a high-temperature melt mixture originating from PbO, H3BO3 and BaF2 in molar ratios of 4:5:1. The starting materials were weighed and melted in a platinum crucible in several batches. The crucible position was fixed at the centre of a resistance-heated furnace. The temperature of the furnace was controlled within 0.1–1 K by an Al-708P controller and a Pt/Pt–Rh thermocouple. The temperature was raised by about 50 K h−1 to 50 K above the melting point and held for 15 h to ensure a homogenous mixture of the solution. After cooling down the furnace to 1073 K, a slow cooling rate of 5 K d−1, was applied, followed by cooling to room temperature at 20 K h−1. Colorless crystals in the millimetre range were obtained.

5. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 2[link]. From the two large cation positions in the structure (Wyckoff positions 3a and 6c), only those of M1 at 3a are occupationally disordered by Ba and Pb atoms. Refinement of the occupancy of Ba:Pb at this site under consideration of EXYZ and EADP commands (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]) resulted in a 21.6 (7)% occupancy of Pb. The highest peak and the deepest hole are located 0.98 and 2.06 Å from the Ba2 and B atoms, respectively.

Table 2
Experimental details

Crystal data
Chemical formula Ba8.35Pb0.65(B3O6)6
Mr 2051.83
Crystal system, space group Trigonal, R[\overline{3}]
Temperature (K) 296
a, c (Å) 7.206 (2), 18.653 (11)
V3) 838.7 (6)
Z 1
Radiation type Mo Kα
μ (mm−1) 13.00
Crystal size (mm) 0.16 × 0.08 × 0.02
 
Data collection
Diffractometer Bruker APEXII CCD
Absorption correction Numerical (face-indexed using SADABS; Bruker, 2000[Bruker (2000). APEX2, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.])
Tmin, Tmax 0.141, 0.547
No. of measured, independent and observed [I > 2σ(I)] reflections 1745, 441, 430
Rint 0.024
(sin θ/λ)max−1) 0.652
 
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.019, 0.048, 1.23
No. of reflections 441
No. of parameters 35
Δρmax, Δρmin (e Å−3) 0.64, −0.74
Computer programs: APEX2 and SAINT (Bruker, 2000[Bruker (2000). APEX2, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]), SHELXS97, SHELXL97 and SHELXTL (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]) and DIAMOND (Brandenburg, 2006[Brandenburg, K. (2006). DIAMOND. Crystal Impact GbR, Bonn, Germany.]).

Supporting information


Computing details top

Data collection: APEX2 (Bruker, 2000); cell refinement: SAINT (Bruker, 2000); data reduction: SAINT (Bruker, 2000); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 2006); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).

Octabarium lead(II) hexakis(triborate) top
Crystal data top
Ba8.35Pb0.65(B3O6)6Dx = 4.062 Mg m3
Mr = 2051.83Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3Cell parameters from 1161 reflections
Hall symbol: -R 3θ = 3.3–27.6°
a = 7.206 (2) ŵ = 13.00 mm1
c = 18.653 (11) ÅT = 296 K
V = 838.7 (6) Å3Plate, colourless
Z = 10.16 × 0.08 × 0.02 mm
F(000) = 899
Data collection top
Bruker APEXII CCD
diffractometer
441 independent reflections
Radiation source: fine-focus sealed tube430 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.024
phi and ω scansθmax = 27.6°, θmin = 3.3°
Absorption correction: numerical
(face-indexed using SADABS; Bruker, 2000)
h = 89
Tmin = 0.141, Tmax = 0.547k = 99
1745 measured reflectionsl = 1423
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.019 w = 1/[σ2(Fo2) + (0.0178P)2 + 5.852P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.048(Δ/σ)max < 0.001
S = 1.23Δρmax = 0.64 e Å3
441 reflectionsΔρmin = 0.74 e Å3
35 parametersExtinction correction: SHELXL97 (Sheldrick, 2008), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
0 restraintsExtinction coefficient: 0.00125 (17)
Special details top

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. 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 > 2sigma(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 (Å2) top
xyzUiso*/UeqOcc. (<1)
Pb10.00000.00000.00000.0147 (2)0.216 (7)
Ba10.00000.00000.00000.0147 (2)0.784 (7)
Ba20.66670.33330.12947 (2)0.01537 (18)
B0.2953 (7)0.1579 (7)0.0864 (3)0.0175 (9)
O10.2633 (5)0.0063 (4)0.09165 (18)0.0218 (6)
O20.5029 (5)0.1261 (5)0.08345 (18)0.0234 (7)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Pb10.0136 (2)0.0136 (2)0.0169 (3)0.00680 (12)0.0000.000
Ba10.0136 (2)0.0136 (2)0.0169 (3)0.00680 (12)0.0000.000
Ba20.01176 (19)0.01176 (19)0.0226 (3)0.00588 (9)0.0000.000
B0.019 (2)0.017 (2)0.018 (2)0.0103 (18)0.0009 (18)0.0002 (17)
O10.0185 (14)0.0159 (13)0.0320 (17)0.0093 (12)0.0011 (12)0.0022 (12)
O20.0162 (14)0.0142 (13)0.0384 (18)0.0066 (11)0.0012 (13)0.0017 (13)
Geometric parameters (Å, º) top
(Pb/Ba)1—O1i2.537 (3)Ba2—O1vii2.810 (3)
(Pb/Ba)1—O1ii2.537 (3)Ba2—O23.030 (3)
(Pb/Ba)1—O12.537 (3)Ba2—O2viii3.030 (3)
(Pb/Ba)1—O1iii2.537 (3)Ba2—O2ix3.030 (3)
(Pb/Ba)1—O1iv2.537 (3)Ba2—Bviii3.296 (5)
(Pb/Ba)1—O1v2.537 (3)Ba2—Bix3.296 (5)
Pb1—Ba2vi3.803 (2)Ba2—Pb1xii3.803 (2)
Pb1—Ba2vii3.803 (2)B—O11.318 (5)
Ba2—O1viii2.766 (3)B—O21.397 (5)
Ba2—O12.766 (3)B—O2xiii1.406 (5)
Ba2—O1ix2.766 (3)O1—Ba2vii2.810 (3)
Ba2—O1x2.810 (3)O2—Bxiv1.406 (5)
Ba2—O1xi2.810 (3)
O1i—Pb1—O1ii100.43 (11)O1xi—Ba2—O2viii67.48 (9)
O1i—Pb1—O1180.00 (17)O1vii—Ba2—O2viii135.55 (8)
O1ii—Pb1—O179.57 (11)O2—Ba2—O2viii112.31 (6)
O1i—Pb1—O1iii79.57 (11)O1viii—Ba2—O2ix147.14 (9)
O1ii—Pb1—O1iii180.00 (11)O1—Ba2—O2ix67.39 (8)
O1—Pb1—O1iii100.43 (11)O1ix—Ba2—O2ix47.75 (8)
O1i—Pb1—O1iv79.57 (11)O1x—Ba2—O2ix135.55 (8)
O1ii—Pb1—O1iv100.43 (11)O1xi—Ba2—O2ix107.59 (8)
O1—Pb1—O1iv100.43 (11)O1vii—Ba2—O2ix67.48 (9)
O1iii—Pb1—O1iv79.57 (11)O2—Ba2—O2ix112.31 (6)
O1i—Pb1—O1v100.43 (11)O2viii—Ba2—O2ix112.31 (6)
O1ii—Pb1—O1v79.57 (11)O1viii—Ba2—Bviii23.05 (10)
O1—Pb1—O1v79.57 (11)O1—Ba2—Bviii134.00 (10)
O1iii—Pb1—O1v100.43 (11)O1ix—Ba2—Bviii92.24 (10)
O1iv—Pb1—O1v180.00 (17)O1x—Ba2—Bviii89.14 (10)
O1i—Pb1—Ba2vi47.64 (7)O1xi—Ba2—Bviii75.27 (10)
O1ii—Pb1—Ba2vi132.36 (7)O1vii—Ba2—Bviii144.45 (11)
O1—Pb1—Ba2vi132.36 (7)O2—Ba2—Bviii89.88 (9)
O1iii—Pb1—Ba2vi47.64 (7)O2viii—Ba2—Bviii25.06 (9)
O1iv—Pb1—Ba2vi47.64 (7)O2ix—Ba2—Bviii134.51 (10)
O1v—Pb1—Ba2vi132.36 (7)O1viii—Ba2—Bix134.00 (10)
O1i—Pb1—Ba2vii132.36 (7)O1—Ba2—Bix92.24 (10)
O1ii—Pb1—Ba2vii47.64 (7)O1ix—Ba2—Bix23.05 (10)
O1—Pb1—Ba2vii47.64 (7)O1x—Ba2—Bix144.45 (11)
O1iii—Pb1—Ba2vii132.36 (7)O1xi—Ba2—Bix89.14 (10)
O1iv—Pb1—Ba2vii132.36 (7)O1vii—Ba2—Bix75.27 (10)
O1v—Pb1—Ba2vii47.64 (7)O2—Ba2—Bix134.51 (10)
Ba2vi—Pb1—Ba2vii180.0O2viii—Ba2—Bix89.88 (10)
O1viii—Ba2—O1113.73 (6)O2ix—Ba2—Bix25.06 (9)
O1viii—Ba2—O1ix113.73 (6)Bviii—Ba2—Bix114.27 (7)
O1—Ba2—O1ix113.73 (6)O1viii—Ba2—Pb1xii104.78 (7)
O1viii—Ba2—O1x76.27 (10)O1—Ba2—Pb1xii104.78 (7)
O1—Ba2—O1x89.15 (12)O1ix—Ba2—Pb1xii104.78 (7)
O1ix—Ba2—O1x145.30 (7)O1x—Ba2—Pb1xii41.85 (7)
O1viii—Ba2—O1xi89.15 (12)O1xi—Ba2—Pb1xii41.85 (7)
O1—Ba2—O1xi145.30 (7)O1vii—Ba2—Pb1xii41.85 (7)
O1ix—Ba2—O1xi76.27 (10)O2—Ba2—Pb1xii106.46 (7)
O1x—Ba2—O1xi70.59 (10)O2viii—Ba2—Pb1xii106.46 (7)
O1viii—Ba2—O1vii145.31 (7)O2ix—Ba2—Pb1xii106.46 (7)
O1—Ba2—O1vii76.27 (10)Bviii—Ba2—Pb1xii104.10 (8)
O1ix—Ba2—O1vii89.15 (12)Bix—Ba2—Pb1xii104.10 (8)
O1x—Ba2—O1vii70.59 (10)O1—B—O2120.6 (4)
O1xi—Ba2—O1vii70.59 (10)O1—B—O2xiii122.6 (4)
O1viii—Ba2—O267.39 (8)O2—B—O2xiii116.8 (4)
O1—Ba2—O247.75 (8)B—O1—Pb1113.5 (3)
O1ix—Ba2—O2147.14 (9)B—O1—Ba2101.7 (3)
O1x—Ba2—O267.48 (9)Pb1—O1—Ba2130.17 (12)
O1xi—Ba2—O2135.55 (8)B—O1—Ba2vii117.4 (3)
O1vii—Ba2—O2107.59 (8)Pb1—O1—Ba2vii90.51 (10)
O1viii—Ba2—O2viii47.75 (8)Ba2—O1—Ba2vii103.73 (10)
O1—Ba2—O2viii147.14 (9)B—O2—Bxiv122.9 (4)
O1ix—Ba2—O2viii67.39 (8)B—O2—Ba288.2 (2)
O1x—Ba2—O2viii107.59 (8)Bxiv—O2—Ba2143.4 (3)
Symmetry codes: (i) x, y, z; (ii) y, xy, z; (iii) y, x+y, z; (iv) xy, x, z; (v) x+y, x, z; (vi) x2/3, y1/3, z1/3; (vii) x+2/3, y+1/3, z+1/3; (viii) y+1, xy, z; (ix) x+y+1, x+1, z; (x) y+2/3, x+y+1/3, z+1/3; (xi) xy+2/3, x+1/3, z+1/3; (xii) x+2/3, y+1/3, z+1/3; (xiii) y, xy1, z; (xiv) x+y+1, x, z.
 

Funding information

Funding for this research was provided by: Discipline Construction Foundation of Tangshan College (award No. tsbc2013003).

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