Ag_3.5Bi_7.5S₁₃, a new member (N = 8) of the homologous series [Bi₂S₃]₂·[AgBiS₂]_(N-1)/2

The silver bismuth trideca­sulfide Ag_3.5Bi_7.5S₁₃ crystallizes in the monoclinic space group C2/m. Its structure is built up of two alternating kinds of layered modules parallel to (001). In the module denoted A, octa­hedra around the metal positions (M = Ag/Bi, M2 and an S atom on 2/m, other atoms on m) alternate with paired monocapped trigonal prisms around Bi. The NaCl-type module B is composed of parallel eight-membered chains of edge-sharing octa­hedra running dia­gonally across it. Ag_3.5Bi_7.5S₁₃ is the member with N = 8 of the pavonite homologous series ^NP of ternary compounds with the general formula [Bi₂S₃]₂·[AgBiS₂]_(N-1)/2.

S1. Comment

Current knowledge of ternary sulfides with silver and bismuth is somewhat incomplete. Only the existence of AgBiS₂ (Geller & Wernick, 1959), `AgBi₆S₉' (N = 4; Mumme, 1990), Ag₂Bi₆S₁₀ (N = 5; Makovicky et al., 1977) and Ag₃Bi₇S₁₂ (N = 7; Herbert & Mumme, 1981) have been reported to date. All these phases lie on the Ag₂S–Bi₂S₃ pseudo-binary section in the ternary Ag–Bi–S system. The three latter compounds crystallize in the monoclinic space group C2/m and adopt structures that are closely related to each other. Their structures are built up of two alternating kinds of layered modules, denoted A and B. Module A is composed of double chains of monocapped trigonal prisms around Bi atoms, which alternate in the [100] direction with octahedrally coordinated metal atoms (M = Ag or Bi). Module B represents NaCl-like fragments of varying thickness defined by the parameter N, which corresponds to the number of octahedra within the chain of edge-sharing octahedra that runs diagonally across the module (Fig. 1). The structures of the above-mentioned phases with N = 4, 5 and 7 belong to the homologous series [Bi₂S₃]₂·[AgBiS₂]_(N-1)/2 (pavonite series), denoted by ^NP (Makovicky et al., 1977). Known and hypothetical members of the series can be derived from the first member, Ag_0.5Bi_4.5S₇ (N = 2), by successive additions of (AgBiS₂)_0.5 equivalents to the NaCl-like module B, AgBiS₂ being the end member with N = ∞.

The title compound, Ag_3.5Bi_7.5S₁₃, represents the member with N = 8 of the homologous series [Bi₂S₃]₂·[AgBiS₂]_(N-1)/2. It crystallizes in the monoclinic space group C2/m and is isotypic with Cu_1.34Ag_2.38Pb_1.44Bi_6.28S₁₃ (Mumme, 1990). Its structure is built up according to the principle described above. The NaCl-type module B is, in this case, eight octahedra thick (Fig. 2). Therefore, Ag_3.5Bi_7.5S₁₃ can be denoted by the symbol ⁸P, according to the nomenclature of pavonite homologues.

Atom Bi1 displays a slightly distorted monocapped trigonal prismatic coordination of S atoms (Table 1). The cations M2 to M6 exhibit octahedral environments with varying degrees of distortion. The `octahedron' around M2 is the most distorted, with two short bonds [2.564 (3) Å] in trans positions and four elongated bonds [2.870 (8) Å] in the equatorial plane. This type of distortion towards a linear coordination ([2 + 4] geometry) is commonly observed for Ag atoms in the structures of multinary silver-containing bismuth chalcogenides. Typical examples are various members of the pavonite homologous series. The octahedra around the M3 and M4 positions are distorted towards [1 + 2+2 + 1] geometry, with short bonds trans to long bonds. Similar coordination environments are usually observed for Bi atoms in many multinary bismuth sulphosalts. The M5 and M6 positions display more regular octahedral environments, with bond distances ranging between 2.754 (2) and 2.899 (2) Å.

All octahedral metal positions show mixed occupancy between Ag and Bi. The composition of each position obtained from the refinement is consistent with the above analysis of the distortion of their coordination polyhedra. The M2 position shows a preference for Ag atoms (79%), while the M3 and M4 positions are predominantly occupied by Bi atoms (78% for M3 and 84% for M4). In the M5 position, Ag dominates. while in M6 more Bi is found. The Ag/Bi disorder generally observed in octahedrally coordinated metal positions in the structures of pavonite homologues can be related to their general formula. For odd members (N = 5 and 7), an ordered distribution of Ag and Bi between the metal positions may be envisaged, while for even members (N = 4 and 8), some octahedral positions will be necessarily of mixed occupancy or a superstructure must be established.

S2. Experimental

Single crystals of Ag_3.5Bi_7.5S₁₃ were obtained as a by-product of a solid-state reaction involving AgI and Bi₂S₃ in the molar ratio 1:1. The mixture of the starting materials was thoroughly ground and loaded into a silica tube, which was flame-sealed under a pressure of 10 ⁻² Torr (1 Torr = 133.322 Pa). The tube was placed in a tubular oven, heated at 850 K for 7 d and then rapidly cooled to room temperature. The product consisted of a mixture of black plate crystals of AgBiS₂ (Geller & Wernick, 1959), Ag₂Bi₆S₁₀ (Makovicky et al., 1977) and Ag_3.5Bi_7.5S₁₃ (about 30% of the product), together with grey needle-like crystals of (Bi₂S₃)₉BiI₃ (Miehe & Kup~cik, 1971). Qualitative energy-dispersive X-ray analysis performed on the single-crystal of Ag_3.5Bi_7.5S₁₃ used for this study revealed an average composition Ag_3.43 (2)Bi_7.48 (2)S₁₃. No indication of iodine in the crystal was detected.

S3. Refinement

In the first stage of the refinement, the Bi positions M3, M4 and M6 showed temperature factors larger than that of M1 = Bi1. This suggested that, in addition to bismuth, these positions are partly occupied by the lighter element Ag. On the other hand, the thermal parameters of the Ag positions M2 and M5 were smaller than that of Bi1 and mixed occupancy with the heavier element Bi was also considered for these positions. The SUMP restraint was used to ensure the electroneutrality of the compound. The final occupancies of these positions obtained from the refinement were: M2 = 79% Ag + 21% Bi, M3 = 22% Ag + 78% Bi, M4 = 16% Ag + 84% Bi, M5 = 64% Ag + 36% Bi and M6 = 33% Ag + 67% Bi.

Computing details

Data collection: EXPOSE (Stoe & Cie, 2000); cell refinement: CELL (Stoe & Cie, 2000); data reduction: INTEGRATE (Stoe & Cie, 2000); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: DIAMOND (Brandenburg, 1999); software used to prepare material for publication: SHELXL97 and DIAMOND.

Figures

	Fig. 1. Comparison of the structures of three [Bi2S3]2·[AgBiS2](N-1)/2 homologues. (a) `AgBiS9' (N = 4). (b) Ag2Bi6S10 (N = 5, pavonite). (c) Ag3Bi7S12 (N = 7). Bi atoms are denoted by black spheres, Ag/Bi by medium-grey spheres and S atoms by light-grey spheres.
	Fig. 2. The crystal structure of Ag3.5Bi7.5S13. Displacement ellipsoids are drawn at the 95% probability level for all atoms. M denotes Ag/Bi.

Silver bismuth sulfide (3.5/7.5/13)

Crystal data

Ag3.5Bi7.5S13	F(000) = 1990
Mr = 2361.81	Dx = 6.782 Mg m^−3
Monoclinic, C2/m	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -C2y	Cell parameters from 1295 reflections
a = 13.3237 (2) Å	θ = 2.9–26.0°
b = 4.0455 (4) Å	µ = 60.9 mm^−1
c = 21.484 (3) Å	T = 297 K
β = 92.90 (1)°	Plate, black
V = 1156.5 (2) Å^3	0.14 × 0.04 × 0.02 mm
Z = 2

Data collection

Stoe IPDS I diffractometer	1295 independent reflections
Radiation source: fine-focus sealed tube	980 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.040
ϕ oscillation scans	θmax = 26.0°, θmin = 2.9°
Absorption correction: numerical [X-RED32 (Stoe & Cie, 2001); crystal description using FACEIT (Stoe & Cie, 1999), optimization using equivalent reflections (X-SHAPE; Stoe & Cie, 1999)]	h = −16→16
Tmin = 0.067, Tmax = 0.343	k = −4→4
3944 measured reflections	l = −26→26

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)] = 0.044	w = 1/[σ^2(Fo^2) + (0.041P)^2 + 88.7342P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.104	(Δ/σ)max = 0.009
S = 1.07	Δρmax = 1.90 e Å^−3
1295 reflections	Δρmin = −1.47 e Å^−3
81 parameters	Extinction correction: SHELXL97, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
1 restraint	Extinction coefficient: 0.00038 (6)

Special details

Experimental. collection of intensity data: phi movement mode (oscillation), crystal to detector distance (70 mm), lattice parameters from Stoe IPDS-I diffraction data using Mo Kα radiation

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. A disorder model M = Bi, Ag was applied for the atomic sites M2, M3, M4, M5 and M6 that were constrained to full occupation. In each mixed position both types of atoms were forced to have the same coordinates and thermal parameters. The mixed occupation in cation positions were restrained to keep the electroneutrality of the compound. 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	Occ. (<1)
Bi1	0.23594 (6)	0.0000	0.08464 (4)	0.0322 (3)
Bi2	0.5000	0.0000	0.0000	0.0458 (7)	0.2022 (10)
Ag2	0.5000	0.0000	0.0000	0.0458 (7)	0.80
Bi3	0.01767 (7)	0.5000	0.21444 (5)	0.0313 (4)	0.777 (4)
Ag3	0.01767 (7)	0.5000	0.21444 (5)	0.0313 (4)	0.22
Bi4	0.30067 (6)	0.5000	0.29459 (5)	0.0292 (4)	0.844 (4)
Ag4	0.30067 (6)	0.5000	0.29459 (5)	0.0292 (4)	0.16
Bi5	0.08218 (9)	0.0000	0.37761 (7)	0.0374 (6)	0.358 (4)
Ag5	0.08218 (9)	0.0000	0.37761 (7)	0.0374 (6)	0.64
Bi6	0.36005 (7)	0.0000	0.46000 (5)	0.0323 (4)	0.670 (4)
Ag6	0.36005 (7)	0.0000	0.46000 (5)	0.0323 (4)	0.33
S1	0.3550 (4)	0.5000	0.0257 (3)	0.0227 (11)
S2	0.0975 (4)	0.5000	0.1060 (3)	0.0301 (13)
S3	0.3801 (4)	0.5000	0.1850 (3)	0.0241 (12)
S4	0.1612 (4)	0.0000	0.2616 (3)	0.0323 (14)
S5	0.4389 (4)	0.0000	0.3418 (3)	0.0298 (13)
S6	0.2184 (4)	0.5000	0.4222 (3)	0.0332 (14)
S7	0.5000	0.5000	0.5000	0.039 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Bi1	0.0322 (5)	0.0330 (6)	0.0311 (6)	0.000	−0.0018 (3)	0.000
Bi2	0.0356 (11)	0.0460 (16)	0.0551 (16)	0.000	−0.0037 (10)	0.000
Ag2	0.0356 (11)	0.0460 (16)	0.0551 (16)	0.000	−0.0037 (10)	0.000
Bi3	0.0331 (6)	0.0303 (7)	0.0310 (7)	0.000	0.0051 (4)	0.000
Ag3	0.0331 (6)	0.0303 (7)	0.0310 (7)	0.000	0.0051 (4)	0.000
Bi4	0.0273 (5)	0.0275 (6)	0.0331 (6)	0.000	0.0048 (4)	0.000
Ag4	0.0273 (5)	0.0275 (6)	0.0331 (6)	0.000	0.0048 (4)	0.000
Bi5	0.0331 (8)	0.0346 (10)	0.0444 (10)	0.000	−0.0005 (6)	0.000
Ag5	0.0331 (8)	0.0346 (10)	0.0444 (10)	0.000	−0.0005 (6)	0.000
Bi6	0.0328 (7)	0.0309 (7)	0.0334 (7)	0.000	0.0047 (5)	0.000
Ag6	0.0328 (7)	0.0309 (7)	0.0334 (7)	0.000	0.0047 (5)	0.000
S1	0.019 (2)	0.021 (3)	0.029 (3)	0.000	0.0056 (19)	0.000
S2	0.031 (3)	0.023 (3)	0.037 (3)	0.000	0.008 (2)	0.000
S3	0.020 (2)	0.024 (3)	0.028 (3)	0.000	−0.001 (2)	0.000
S4	0.026 (3)	0.023 (3)	0.046 (4)	0.000	−0.008 (3)	0.000
S5	0.030 (3)	0.028 (3)	0.032 (3)	0.000	0.005 (2)	0.000
S6	0.029 (3)	0.033 (4)	0.037 (4)	0.000	0.000 (2)	0.000
S7	0.030 (4)	0.029 (5)	0.056 (6)	0.000	−0.016 (4)	0.000

Geometric parameters (Å, º)

Bi1—S1^i	2.608 (6)	Bi6—S5	2.797 (6)
Bi1—S2^ii	2.791 (4)	Bi6—S7	2.8539 (7)
Bi1—S2	2.791 (4)	Bi6—S7^ii	2.8539 (7)
Bi1—S1	2.900 (4)	Bi6—S6^ii	2.856 (4)
Bi1—S1^ii	2.900 (4)	Bi6—S6	2.856 (4)
Bi1—S3	3.465 (4)	S1—Bi1^i	2.608 (6)
Bi1—S3^ii	3.465 (4)	S1—Bi2^viii	2.871 (3)
Bi2—S2^iii	2.565 (6)	S1—Bi1^viii	2.900 (4)
Bi2—S2^i	2.565 (6)	S1—S3	3.420 (8)
Bi2—S1^ii	2.871 (3)	S1—S2^i	3.562 (7)
Bi2—S1	2.871 (3)	S1—S2^x	3.562 (7)
Bi2—S1^iv	2.871 (3)	S2—Bi2^vii	2.565 (6)
Bi2—S1^v	2.871 (3)	S2—Bi1^viii	2.791 (4)
Bi3—S2	2.609 (6)	S2—S1^i	3.562 (7)
Bi3—S3^vi	2.781 (3)	S2—S1^x	3.562 (7)
Bi3—S3^vii	2.781 (3)	S3—Bi3^xi	2.781 (3)
Bi3—S4^viii	2.929 (4)	S3—Bi3^iii	2.781 (3)
Bi3—S4	2.929 (4)	S3—Bi1^viii	3.465 (4)
Bi3—S5^vii	2.979 (6)	S4—Bi4^ii	2.813 (4)
Bi4—S3	2.630 (6)	S4—Bi3^ii	2.929 (4)
Bi4—S4	2.813 (4)	S5—Bi5^xi	2.860 (4)
Bi4—S4^viii	2.813 (4)	S5—Bi5^iii	2.860 (4)
Bi4—S5^viii	2.885 (4)	S5—Bi4^ii	2.885 (4)
Bi4—S5	2.885 (4)	S5—Bi3^iii	2.979 (6)
Bi4—S6	3.002 (6)	S6—Bi6^ix	2.788 (6)
Bi5—S4	2.753 (7)	S6—Bi5^viii	2.851 (4)
Bi5—S6	2.851 (4)	S6—Bi6^viii	2.856 (4)
Bi5—S6^ii	2.851 (4)	S7—Bi6^xii	2.8539 (8)
Bi5—S5^vi	2.860 (4)	S7—Bi6^xiii	2.8539 (7)
Bi5—S5^vii	2.860 (4)	S7—Bi6^viii	2.8539 (7)
Bi5—S7^vi	2.8990 (16)	S7—Bi5^ix	2.8990 (16)
Bi6—S6^ix	2.788 (6)	S7—Bi5^xi	2.8990 (16)
S1^i—Bi1—S2^ii	82.50 (15)	Bi1^viii—S1—Bi1	88.46 (14)
S1^i—Bi1—S2	82.50 (15)	Bi1^i—S1—S3	157.97 (19)
S2^ii—Bi1—S2	92.88 (16)	Bi2^viii—S1—S3	99.20 (14)
S1^i—Bi1—S1	80.93 (13)	Bi2—S1—S3	99.20 (14)
S2^ii—Bi1—S1	163.30 (17)	Bi1^viii—S1—S3	65.90 (11)
S2—Bi1—S1	86.96 (11)	Bi1—S1—S3	65.90 (11)
S1^i—Bi1—S1^ii	80.93 (13)	Bi1^i—S1—S2^i	50.97 (12)
S2^ii—Bi1—S1^ii	86.96 (11)	Bi2^viii—S1—S2^i	95.65 (15)
S2—Bi1—S1^ii	163.30 (17)	Bi2—S1—S2^i	45.43 (10)
S1—Bi1—S1^ii	88.46 (14)	Bi1^viii—S1—S2^i	150.0 (2)
S1^i—Bi1—S3	141.53 (7)	Bi1—S1—S2^i	94.23 (8)
S2^ii—Bi1—S3	132.12 (16)	S3—S1—S2^i	141.50 (11)
S2—Bi1—S3	79.90 (12)	Bi1^i—S1—S2^x	50.97 (12)
S1—Bi1—S3	64.28 (13)	Bi2^viii—S1—S2^x	45.43 (10)
S1^ii—Bi1—S3	112.36 (12)	Bi2—S1—S2^x	95.65 (15)
S1^i—Bi1—S3^ii	141.53 (7)	Bi1^viii—S1—S2^x	94.23 (8)
S2^ii—Bi1—S3^ii	79.90 (12)	Bi1—S1—S2^x	150.0 (2)
S2—Bi1—S3^ii	132.12 (16)	S3—S1—S2^x	141.50 (11)
S1—Bi1—S3^ii	112.36 (12)	S2^i—S1—S2^x	69.19 (15)
S1^ii—Bi1—S3^ii	64.28 (13)	Bi2^vii—S2—Bi3	125.6 (2)
S3—Bi1—S3^ii	71.44 (10)	Bi2^vii—S2—Bi1^viii	99.37 (17)
S2^iii—Bi2—S2^i	180.00 (14)	Bi3—S2—Bi1^viii	116.73 (17)
S2^iii—Bi2—S1^ii	98.31 (14)	Bi2^vii—S2—Bi1	99.37 (17)
S2^i—Bi2—S1^ii	81.69 (14)	Bi3—S2—Bi1	116.73 (17)
S2^iii—Bi2—S1	98.31 (14)	Bi1^viii—S2—Bi1	92.88 (16)
S2^i—Bi2—S1	81.69 (14)	Bi2^vii—S2—S1^i	52.88 (12)
S1^ii—Bi2—S1	89.60 (13)	Bi3—S2—S1^i	143.75 (9)
S2^iii—Bi2—S1^iv	81.69 (14)	Bi1^viii—S2—S1^i	97.75 (17)
S2^i—Bi2—S1^iv	98.31 (14)	Bi1—S2—S1^i	46.53 (10)
S1^ii—Bi2—S1^iv	180.0 (2)	Bi2^vii—S2—S1^x	52.88 (12)
S1—Bi2—S1^iv	90.40 (13)	Bi3—S2—S1^x	143.75 (9)
S2^iii—Bi2—S1^v	81.69 (14)	Bi1^viii—S2—S1^x	46.53 (10)
S2^i—Bi2—S1^v	98.31 (14)	Bi1—S2—S1^x	97.75 (17)
S1^ii—Bi2—S1^v	90.40 (13)	S1^i—S2—S1^x	69.19 (15)
S1—Bi2—S1^v	180.0 (2)	Bi4—S3—Bi3^xi	94.96 (15)
S1^iv—Bi2—S1^v	89.60 (13)	Bi4—S3—Bi3^iii	94.96 (15)
S2—Bi3—S3^vi	95.19 (15)	Bi3^xi—S3—Bi3^iii	93.31 (15)
S2—Bi3—S3^vii	95.19 (15)	Bi4—S3—S1	150.71 (19)
S3^vi—Bi3—S3^vii	93.31 (15)	Bi3^xi—S3—S1	104.94 (14)
S2—Bi3—S4^viii	91.17 (16)	Bi3^iii—S3—S1	104.94 (14)
S3^vi—Bi3—S4^viii	172.87 (18)	Bi4—S3—Bi1	108.76 (13)
S3^vii—Bi3—S4^viii	89.30 (10)	Bi3^xi—S3—Bi1	154.74 (19)
S2—Bi3—S4	91.17 (16)	Bi3^iii—S3—Bi1	93.17 (6)
S3^vi—Bi3—S4	89.30 (10)	S1—S3—Bi1	49.82 (9)
S3^vii—Bi3—S4	172.87 (18)	Bi4—S3—Bi1^viii	108.76 (13)
S4^viii—Bi3—S4	87.36 (15)	Bi3^xi—S3—Bi1^viii	93.17 (6)
S2—Bi3—S5^vii	176.57 (18)	Bi3^iii—S3—Bi1^viii	154.74 (19)
S3^vi—Bi3—S5^vii	87.16 (14)	S1—S3—Bi1^viii	49.82 (9)
S3^vii—Bi3—S5^vii	87.16 (14)	Bi1—S3—Bi1^viii	71.44 (10)
S4^viii—Bi3—S5^vii	86.34 (15)	Bi5—S4—Bi4	92.87 (16)
S4—Bi3—S5^vii	86.34 (15)	Bi5—S4—Bi4^ii	92.87 (16)
S3—Bi4—S4	93.73 (16)	Bi4—S4—Bi4^ii	91.94 (15)
S3—Bi4—S4^viii	93.73 (16)	Bi5—S4—Bi3^ii	92.32 (15)
S4—Bi4—S4^viii	91.94 (15)	Bi4—S4—Bi3^ii	174.3 (3)
S3—Bi4—S5^viii	92.07 (14)	Bi4^ii—S4—Bi3^ii	90.11 (2)
S4—Bi4—S5^viii	174.00 (19)	Bi5—S4—Bi3	92.32 (15)
S4^viii—Bi4—S5^viii	89.22 (10)	Bi4—S4—Bi3	90.11 (2)
S3—Bi4—S5	92.07 (14)	Bi4^ii—S4—Bi3	174.3 (3)
S4—Bi4—S5	89.22 (10)	Bi3^ii—S4—Bi3	87.36 (15)
S4^viii—Bi4—S5	174.00 (19)	Bi6—S5—Bi5^xi	91.83 (15)
S5^viii—Bi4—S5	89.03 (16)	Bi6—S5—Bi5^iii	91.83 (15)
S3—Bi4—S6	177.69 (16)	Bi5^xi—S5—Bi5^iii	90.03 (16)
S4—Bi4—S6	87.87 (16)	Bi6—S5—Bi4^ii	93.24 (14)
S4^viii—Bi4—S6	87.87 (16)	Bi5^xi—S5—Bi4^ii	174.9 (2)
S5^viii—Bi4—S6	86.29 (14)	Bi5^iii—S5—Bi4^ii	90.24 (3)
S5—Bi4—S6	86.29 (14)	Bi6—S5—Bi4	93.24 (14)
S4—Bi5—S6	92.16 (15)	Bi5^xi—S5—Bi4	90.24 (3)
S4—Bi5—S6^ii	92.16 (15)	Bi5^iii—S5—Bi4	174.9 (2)
S6—Bi5—S6^ii	90.39 (16)	Bi4^ii—S5—Bi4	89.03 (15)
S4—Bi5—S5^vi	92.11 (14)	Bi6—S5—Bi3^iii	178.6 (2)
S6—Bi5—S5^vi	175.72 (19)	Bi5^xi—S5—Bi3^iii	89.19 (14)
S6^ii—Bi5—S5^vi	89.63 (11)	Bi5^iii—S5—Bi3^iii	89.19 (14)
S4—Bi5—S5^vii	92.11 (14)	Bi4^ii—S5—Bi3^iii	85.73 (14)
S6—Bi5—S5^vii	89.63 (11)	Bi4—S5—Bi3^iii	85.73 (14)
S6^ii—Bi5—S5^vii	175.72 (19)	Bi6^ix—S6—Bi5	92.47 (15)
S5^vi—Bi5—S5^vii	90.03 (16)	Bi6^ix—S6—Bi5^viii	92.47 (15)
S4—Bi5—S7^vi	179.72 (12)	Bi5—S6—Bi5^viii	90.39 (16)
S6—Bi5—S7^vi	87.64 (13)	Bi6^ix—S6—Bi6^viii	90.82 (16)
S6^ii—Bi5—S7^vi	87.64 (13)	Bi5—S6—Bi6^viii	176.7 (3)
S5^vi—Bi5—S7^vi	88.08 (12)	Bi5^viii—S6—Bi6^viii	89.62 (3)
S5^vii—Bi5—S7^vi	88.08 (12)	Bi6^ix—S6—Bi6	90.82 (16)
S6^ix—Bi6—S5	179.97 (16)	Bi5—S6—Bi6	89.62 (3)
S6^ix—Bi6—S7	89.77 (8)	Bi5^viii—S6—Bi6	176.7 (3)
S5—Bi6—S7	90.21 (8)	Bi6^viii—S6—Bi6	90.18 (16)
S6^ix—Bi6—S7^ii	89.77 (8)	Bi6^ix—S6—Bi4	179.4 (2)
S5—Bi6—S7^ii	90.21 (8)	Bi5—S6—Bi4	87.09 (15)
S7—Bi6—S7^ii	90.27 (3)	Bi5^viii—S6—Bi4	87.09 (15)
S6^ix—Bi6—S6^ii	89.18 (16)	Bi6^viii—S6—Bi4	89.63 (14)
S5—Bi6—S6^ii	90.84 (15)	Bi6—S6—Bi4	89.63 (14)
S7—Bi6—S6^ii	178.95 (13)	Bi6^xii—S7—Bi6	180.0
S7^ii—Bi6—S6^ii	89.77 (8)	Bi6^xii—S7—Bi6^xiii	90.27 (3)
S6^ix—Bi6—S6	89.18 (16)	Bi6—S7—Bi6^xiii	89.73 (3)
S5—Bi6—S6	90.84 (15)	Bi6^xii—S7—Bi6^viii	89.73 (3)
S7—Bi6—S6	89.77 (8)	Bi6—S7—Bi6^viii	90.27 (3)
S7^ii—Bi6—S6	178.95 (13)	Bi6^xiii—S7—Bi6^viii	180.00 (4)
S6^ii—Bi6—S6	90.18 (16)	Bi6^xii—S7—Bi5^ix	89.88 (3)
Bi1^i—S1—Bi2^viii	96.37 (14)	Bi6—S7—Bi5^ix	90.12 (3)
Bi1^i—S1—Bi2	96.37 (14)	Bi6^xiii—S7—Bi5^ix	89.88 (3)
Bi2^viii—S1—Bi2	89.60 (13)	Bi6^viii—S7—Bi5^ix	90.12 (3)
Bi1^i—S1—Bi1^viii	99.07 (13)	Bi6^xii—S7—Bi5^xi	90.12 (3)
Bi2^viii—S1—Bi1^viii	88.90 (3)	Bi6—S7—Bi5^xi	89.88 (3)
Bi2—S1—Bi1^viii	164.6 (2)	Bi6^xiii—S7—Bi5^xi	90.12 (3)
Bi1^i—S1—Bi1	99.07 (13)	Bi6^viii—S7—Bi5^xi	89.88 (3)
Bi2^viii—S1—Bi1	164.6 (2)	Bi5^ix—S7—Bi5^xi	180.0
Bi2—S1—Bi1	88.90 (3)

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