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

The fundamental building units of Ba8.35Pb0.65(B3O6)6 are isolated planar B3O6 anionic groups, which are distributed layer upon layer perpendicular to [001], with (Pb/Ba) and Ba sites alternately located between the B3O6 sheets.


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, -BaB 2 O 4 (Chen et al., 1985), LiB 3 O 5 (Chen et al., 1989), CsB 3 O 5 (Sasaki et al., 2000), Sr 2 Be 2 B 2 O 7 (Chen et al., 1995), K 5 Ba 10 (BO 3 ) 8 F (Liu et al., 2016), PbB 4 O 7 (Bartwal et al., 2001), Pb 2 B 5 O 9 X (X = Cl, Br, I) (Huang et al., 2010) or Ba 3 Sr 4 (BO 3 ) 3 F 5 (Zhang et al., 2009) have been studied because of their second-order The principal building units in the crystal structure of the title compound. Displacement ellipsoids are drawn at the 50% probability level.
In this communication, we report on the synthesis and crystal structure of the solid solution Ba 8.35 Pb 0.65 (B 3 O 6 ) 6 .

Structural commentary
The crystal structure of Ba 8.35 Pb 0.65 (B 3 O 6 ) 6 is based on a Ba2O 9 polyhedron, a (Pb/Ba1)O 6 polyhedron and a condensed B 3 O 6 anion, as shown in Fig. 1. The planar B 3 O 6 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 B 3 O 6 sheets in (Pb/Ba)1 and Ba2 layers, as shown in Fig. 2a. The B atom is bound to one O1 atom and two O2 atoms to from a BO 3 triangle. Three BO 3 triangles are condensed through vertex-sharing to build a planar and cyclic  1.406 (5) Å (Table 1), and the O-B-O angles are between 116.8 (4) and 122.6 (4) .

Figure 3
The formation of a corrugated layer of Ba2O 9 polyhedra in the crystal structure of Ba 8.35 Pb 0.65 (B 3 O 6 ) 6 viewed down [001].

Figure 4
The 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.

Comparison with the structures of related solid solutions
It is interesting to compare the structure of Ba 8.35 Pb 0.65 (B 3 O 6 ) 6 with those of the related solid solutions Ba 7.87 Pb 1.13 (B 3 O 6 ) 6 (Wu et al., 2012) and Ba 2 Pb(B 3 O 6 ) 2 (Li et al., 2014;Tang et al., 2015). Whereas the title compound Ba 8.35 Pb 0.65 (B 3 O 6 ) 6 crystallizes in space group R3, Ba 7.87 Pb 1.13 (B 3 O 6 ) 6 was solved and refined in space group R32 on the basis of single crystal X-ray diffraction data (Wu et al., 2012); the lattice parameters of both compounds are very similar. Ba 2 Pb(B 3 O 6 ) 2 on the other hand was reported to crystallize either in space group R3 with lattice parameters in the same range as the previous two structures (single crystal X-ray diffraction data; Li et al., 2014) or in space group R3c with a doubled c axis in comparison with the other structures (powder X-ray diffraction data using the Rietveld method; Tang et al., 2015). All four crystal structures are characterized by an alternating stacking of cationic and anionic (001)  The arrangement of the planar B 3 O 6 rings in the crystal structures is a determining factor in whether a non-centrosymmetric or a centrosymmetric structure is obtained. In Ba 7.87 Pb 1.13 (B 3 O 6 ) 6 (Wu et al., 2012), the rings are aligned in a chiral arrangement (Fig. 4b), responsible for the SHG effect. In Ba 2 Pb(B 3 O 6 ) 2 (Li et al., 2014), the B 3 O 6 rings are parallel to each other, distributed layer upon layer along [001], and the B 3 O 6 rings in neighbouring layers point in exactly opposite directions (Fig. 4c), just like in the title compound (Fig. 4a). In the Ba 2 Pb(B 3 O 6 ) 2 structure with doubled volume (Tang et al., 2015), all of the B 3 O 6 rings are parallel to (001), and the B 3 O 6 rings in two neighbouring layers are rotated slightly relative to each other (Fig. 4d).

Synthesis and crystallization
Suitable crystals of the solid solution Ba 8.35 Pb 0.65 (B 3 O 6 ) 6 were obtained by spontaneous nucleation from a high-temperature melt mixture originating from PbO, H 3 BO 3 and BaF 2 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 À1 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 À1 , was applied, followed by cooling to room temperature at 20 K h À1 . Colorless crystals in the millimetre range were obtained.

Refinement
Crystal data, data collection and structure refinement details are summarized in Table 2. 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) 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.  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)
Crystal data where P = (F o 2 + 2F c 2 )/3 (Δ/σ) max < 0.001 Δρ max = 0.64 e Å −3 Δρ min = −0.74 e Å −3 Extinction correction: SHELXL97 (Sheldrick, 2008), Fc * =kFc[1+0.001xFc 2 λ 3 /sin(2θ)] -1/4 Extinction coefficient: 0.00125 (17) sup-2 . E73, 349-353 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. Refinement of F 2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F 2 , conventional R-factors R are based on F, with F set to zero for negative F 2 . The threshold expression of F 2 > 2sigma(F 2 ) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F 2 are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.