Pb_5.0(1)In_8.4(1)Bi_1.6(1)S₂₀, a new quaternary lead indium bis­muth sulfide

The title phase, first detected in the early 1980s but hitherto unpublished, has been resynthesized and structurally characterized. Unambiguous determination of the chemical com­position was not possible by structure analysis alone, but required additional analytical methods. The complex structure shows a close similarity to the structures of two related compounds, one known by the formula Pb_1.6In₈Bi₄S₁₉ and the other being the ternary compound Pb₆In₁₀S₂₁. This is despite the fact that the three phases correspond to very different Pb:Bi ratios. A geometric mechanism is described by which the three structures can be transformed into each other, provided that the heavy atoms Pb and Bi are treated as equivalent.

S1. Comment

In the first half of the 1980s, six different quaternary lead indium bismuth sulfides were synthesized (Reis, 1984), of which only three have hitherto been fully characterized with respect to their structures (Krämer, 1983, 1986; Krämer & Reis, 1986). The other three were structurally characterized only by the determination of lattice constants and space groups (Reis, 1984). No other structures of quaternary lead indium bismuth sulfides have been published since then. The title phase is thus the fourth of the six phases to be structurally characterized. Determining the chemical identity of the obtained composition variant of this phase was not possible by structure analysis alone, but required additional analytical methods (see Experimental).

Like most of the structurally known phases in the quaternary Pb–In–Bi–S system and its three ternary sulfidic subsystems, Pb_5.0 (1)In_8.4 (1)Bi_1.6 (1)S₂₀ adopts a structure where one of the unit vectors (b) has a magnitude of only about 4 Å, while the other two are much longer. Fig. 1 shows a projection of the structure parallel to this short vector. Bond-length ranges for the different metal atoms (Table 1) agree with those from the known binary and ternary subsystem compounds and the other structurally known quaternary sulfides. The asymmetric unit of our structure model contains five positions with a mixed In_xBi_1-x occupancy (atom labels denoted with the suffix F; see Experimental). Such mixing of In and Bi at one position has previously been observed for Pb₄In₂Bi₄S₁₃ (Krämer, 1986) and Pb₄In₃Bi₇S₁₈ (Krämer & Reis, 1986). It is not really evident in the bond-length ranges and mean bond lengths (Table 1), except perhaps for site In9F, for which the largest Bi content (27%) is found. All Pb atoms show an eightfold coordination, with a coordination polyhedron that can be described as a trigonal prism with two rectangular faces capped. Such coordination has been observed, for example, for Pb in PbIn₂S₄ (Arriortua et al., 1983) and for Bi in Bi₃In₅S₁₂ (Krämer, 1980). If the Bi1—S6 distance of 3.650 (2) Å is interpreted as a Bi—S bond, then atom Bi1 in the title compound is also coordinated this way. Otherwise, its coordination polyhedron can be described as a mono-capped trigonal prism or a `tri/tetragonal antiprism'. The In atoms (and the Bi atoms replacing them statistically) are coordinated octahedrally with various degrees of distortion.

Fig. 1 illustrates a two-dimensional pattern composed of M₂S₂ quadrangles and M₃S₃ hexagons (M = Pb, Bi or In), which are the cross-sections of one-dimensionally infinite columnar aggregates (like rods and ribbons) oriented parallel to b. Fig. 2 shows another representation of the structure, in which quadrangles containing two Bi atoms are shaded grey (at the vertices of the unit-cell box [Please check added text]; blue in the electronic version of the paper), those with two Pb atoms shaded dark grey, those containing a Bi and a Pb atom medium grey and those containing two In (or In_xBi_1-x) atoms light grey (pink in the electronic version). These last form different motifs: finite chains set up by three corner-sharing quadrangles (A in Fig. 2), slightly distorted rectangles built from four edge-sharing quadrangles (B) and infinite chains (C) composed of five-membered A-like chains (C₁), which are concatenated via single rectangles (C₂) by edge-sharing.

In ternary subsystem compounds, motifs of type A are found in Bi₃In₅S₁₂ (Krämer, 1980), while those of types B and C are found in Pb₆In₁₀S₂₁ (Krämer & Berroth, 1980). The motif formed by the heavy atoms (Pb and Bi) in Fig. 2 can also be found in the latter phase (except for the Bi₂S₂ rhomb), and also in the structure of another quaternary compound, Pb_1.6In₈Bi₄S₁₉ (Krämer, 1983). Fig. 3 shows a representation of this latter structure, which contains motifs A and B. The published formula (derived solely from structure-analytical considerations) corresponds to a net positive charge of 1.2. Preliminary re-investigation of this phase by electron-microprobe analysis (Topa & Keller, 2011) shows that the formula is rather Pb₂In₈Bi_3.33S₁₉, with no net charge, meaning that the assignments of Pb and Bi to the corresponding heavy-atom positions should probably be modified. In Fig. 3, all heavy-atom positions are shown as Pb/Bi mixtures. All quadrangles containing two of these hybrids are shown with grey shading, with the exception of some rhombs for which another grey (blue in the electronic version) has been used for comparison with Fig. 2. It is clear that the heavy-atom motif of Fig. 2 also occurs in Fig. 3, albeit in a concatenated one-dimensionally infinite way (two-dimensionally infinite when considered in three dimensions).

In Figs. 2 and 3, we have defined a stripe running parallel to c by drawing its left and right borders (saw-tooth-like dashed dark-grey lines, green in the electronic version). The two lines are identical by lattice translation in Fig. 3 but not in Fig. 2. Nevertheless, the stripes in the two figures are almost identical if the differences in the assignment of Pb and Bi to the different heavy-atom sites and the In/Bi mixing in the title phase are neglected. In both structures, the next (vicinal) stripe is obtained from the original one by a shift t = a (with different a vectors in the two cases). In Pb_1.6In₈Bi₄S₁₉ (Fig. 3), the two vicinal stripes match perfectly. In the title compound, however, some gaps remain between the original and the copied stripe, the latter here visualized by its left-hand dashed border line, drawn in light grey [orange in the electronic version, not to be confused with the similar dotted (violet) lines around x = 0 and x = 1 which will be addressed below]. These gaps contain two S atoms (2 × S20) and two In atoms (2 × In4) per unit cell. If the copied stripe is shifted further by t' = -0.050a + 0.387c (arrow in Fig. 2), all gaps between the two stripes disappear, i.e. the `superfluous' atoms are `eliminated'. The complex of the two `united' stripes would then have to undergo another shift of t' to match with the next stripe on the left-hand side, and so on. Additional small `annealing' shifts for some atoms, the largest one affecting Pb5 (about 0.45 Å approximately parallel to a), generate the complete structure pattern of Pb_1.6In₈Bi₄S₁₉, which contains two fewer In and two fewer S positions per unit cell. In Fig. 2, two copies of Pb5 which will belong to one common quadrangle after the application of t' are indicated by asterisks (*). Finally, it should be mentioned that, while in Pb_1.6In₈Bi₄S₁₉ apparently one heavy-atom position is occupied by only 4/5 of a Pb atom (Krämer, 1983) or 2/3 of a Bi atom (Topa & Keller, 2011) (with no In), a corresponding partial occupancy is not observed in the title compound.

A very similar structural relationship (but inverted) exists between the title phase and the already mentioned ternary phase Pb₆In₁₀S₂₁ (Fig. 4). The more central stripe in Fig. 2, defined by the two lattice-translationally related dotted grey lines (dashed violet in the electronic version) is just a section of the Pb₆In₁₀S₂₁ structure, provided again that Pb and Bi are not distinguished from each other and In/Bi mixing in the title phase is neglected. In the latter structure (Fig. 4) the two border lines are not related by lattice translation. To transform the ternary structure into the quaternary one, each stripe in Fig. 4 must be shifted by the bold black (red in the electronic version) vector relative to its vicinal one along a. This shift vector is the same as that in Fig. 2, in both cases being the mean vector between an In atom in the C₁ motif (Fig. 2) and its second-nearest In neighbour in the same motif. That this shift operation actually generates the pattern of Fig. 2 becomes more obvious if the leftmost stripe in Fig. 4 is shifted (practically or mentally) in the inverse direction (medium-grey arrow; light blue in the electronic version). Again, the disappearance of the gaps eliminates two In atoms and two S atoms per unit cell, this time all gathered into one gap, instead of two gaps as in Fig. 2.

Finally, in comparing Figs. 2, 3 and 4, we can state that the geometry of the atomic arrangement in the title compound between x ≈ -0.45 and x ≈ 0.45 has grown `monoculturally' in the structure of Pb<sub>1.6</sub>In<sub>8</sub>Bi<sub>4</sub>S<sub>19</sub>, while the arrangement between x ≈ 0.05 and x ≈ 0.95 has grown monoculturally in the structure of Pb<sub>6</sub>In<sub>10</sub>S<sub>21</sub>. Thus, the former structure can be viewed as a genuine hybrid of the two latter ones. We also can formulate the following `structural transition scheme', in which each step involves the loss of two In and two S atoms per unit cell by the above-described shearing mechanisms. The aforementioned In/Bi mixing in the title compound is responsible for the fact that the second formula in the scheme contains In_8.4 instead of the expected In₉ (all In atoms eliminated in the two steps are nevertheless `pure' In atoms):

(Pb₆In₁₀S₂₁)₂ → (Pb_5.0In_8.4Bi_1.6S₂₀)₂ → (Pb_1.6In₈Bi₄S₁₉)₂ [(Pb₂In₈Bi_3.33S₁₉)₂]

Replacing Pb and Bi by a common atom type M, the scheme becomes:

(M₆In₁₀S₂₁)₂ → (M_6.6In_8.4S₂₀)₂ → (M_5.6In₈S₁₉)₂ [(M_5.33In₈S₁₉)₂]

Looking at all of these formulae, the strong similarity between the three structures suggests that the structural pattern in this type of compound is determined mainly by the M:S and In:S ratios, while the Pb:Bi ratio seems to be of much less importance.

Related literature

For related literature, see: Adams & St (2001); Arriortua et al. (1983); Berlepsch et al. (2001); Chapuis et al. (1972); Ginderow (1978); Krämer (1980, 1983, 1986); Krämer & Berroth (1980); Krämer & Reis (1986); Kupcik & Vesela-Novakova (1970); Reis (1984); Seiler (2009); Spek (2009); Topa & Keller (2011); Yin et al. (2010).

S2. Experimental

The binary sulfides PbS, In₂S₃ and Bi₂S₃ were synthesized from nearly stoichiometric amounts of the elements [5 N Pb (Strem Chemicals Inc.); 5 N In (Johnson Matthey GmbH); 5 N Bi (Chempur Feinchemikalien); 5 N S (Johnson Matthey GmbH)] in evacuated quartz ampoules. Before adding S (ca 1% more than calculated), the metals (except In) were purified by reaction with hydrogen at 770 K. The reaction mixtures were heated to 670 K (870 K for In₂S₃) for 4–5 d. The end of the ampoule holding the reaction mixture was then heated to 570 K for 1 d and the other end to 540 K, to remove excess S by sublimation. Powder diffractograms of the reaction products showed only the peak patterns of the corresponding pure sulfides.

A mixture of PbS (860 mg, 3.6 mmol), In₂S₃ (593 mg, 1.8 mmol), Bi₂S₃ (308 mg, 0.6 mmol) and I₂ (40 mg, as a transport agent) was placed into a quartz ampoule of length ~20 cm and internal diameter 1.3 cm. The ampoule was sealed under vacuum and placed in a two-zone tube furnace. The end containing the reaction mixture (zone A) was heated to 940 K and the other end (zone C) to 870 K. After eight weeks, a carpet of comparatively large black needle-like crystals of the title compound had grown on a bulk which had formed in zone A. In the centre of the ampoule (zone B), more of these crystals had been deposited. At the cool end of the ampoule (zone C) a conglomerate of crystals of a different phase had grown. Structural investigation and electron-microprobe analysis showed them to be Pb₄In_3.7Bi_2.3S₁₃, a composition variant of Pb₄In₂Bi₄S₁₃ (Krämer, 1986).

Two crystal needles grown in zone A were chemically analysed using a Jeol Superprobe JXA-8600 electron microprobe, controlled by the Probe for Windows system of programs (Reference?) and operated at 25 kV and 20 nA, with a beam diameter of 5 µm. Wavelength-dispersion data were collected using the following standards and emission lines: PbS (Pb L_α), InAs (In L_α), Bi₂S₃ (Bi L_α) and Sb₂S₃ (S K_α). The raw data were corrected using the online ZAF-4 procedure (Reference?). Averaged results for ten electron-probe analyses (five per crystal) are Pb 35.0 (3), In 31.7 (1), Bi 12.2 (1) and S 21.3 (1), total 100.2 (3) wt%. In good agreement with these results, an atomic absorption spectroscopy (AAS) analysis of a 20 mg sample of crystals taken from zone A yielded the following results: Pb 34.5, In 31.2 and Bi 11.5 wt%.

Crystals of the title phase were also obtained and identified by powder diffractometry in a number of other similar experiments, where mixtures of the three binary sulfides in slightly different molar ratios (e.g. 5:4:1) were exposed to different temperature gradients (e.g. 860 → 810 K) (Reis, 1984; Seiler, 2009). Indexing of these powder patterns resulted in lattice parameters covering the ranges a = 27.05–27.17, b = 3.88–3.96 and c = 15.67–15.71 Å, and β = 103.59–103.65°, which suggests that most of these crystals have a higher Bi (and/or Pb) content and a lower In content than the crystals described here. These observations additionally justify the use of standard deviations in the stoichiometric coefficients of the chemical formula (see Refinement).

S3. Refinement

After solving the structure with direct methods, refinement showed that the electron density at five of the 15 non-S positions was much too small for a heavy atom (Pb or Bi) but also much too large for an In atom, i.e. having site-occupancy factors (s.o.f.s) for In atoms refining to values significantly larger than 1. These positions were therefore modelled as In_xBi_1-x atom pairs, with the two atoms of each pair constrained to have the same coordinates and displacement parameters, and with x refining to values between 0.952 (4) and 0.723 (4). In Fig. 2, one of these positions is labelled as In(Bi). Free refinement of the s.o.f.s for all ten other non-S atoms (four In atoms and six heavy atoms) showed, by yielding values close to 1, that no significant heavy/light-metal atom mixing takes place. From the six heavy-atom positions, one with a coordination number (CN) of 7 [neglecting one long bond distance of 3.650 (2) Å] was assigned as a Bi atom, while the other five, with CN = 8, were assigned as Pb atoms. This was done because Pb has (with one exception where 1/3 Pb is mixed with 2/3 In; Ginderow, 1978) always been found with an eightfold coordination in ternary lead indium sulfides (Ginderow, 1978; Krämer & Berroth, 1980; Arriortua et al., 1983), while Bi can have a CN = 6 or 7 (the latter as in Bi₂S₃, e.g. Kupcik & Vesela-Novakova, 1970) as frequently as CN = 8 in ternary bismuth indium sulfides (Chapuis et al., 1972; Krämer, 1980; Yin et al., 2010; excluding lower-valent Bi atoms and `bonds' with lengths > 3.5 Å). The described assignments, together with the refined x values of the five In_xBi_1-x atom pairs, led to the electrically neutral chemical formula Pb₅In_8.38Bi_1.62S₂₀ (with Z = 2). This is in good agreement with the formula obtained from the electron-microprobe results (see Experimental) under the assumption that there are exactly 20 S atoms, i.e. Pb_5.09 (5)In_8.31 (4)Bi_1.75 (2)S₂₀ [with a net positive charge of 0.4 (3)]. Since the former formula is the electrically neutral one, it is used for the title compound, but with standard deviations of 0.1 for the stoichiometric coefficients of the non-S elements. For the final refinements, the reflections 101 and 101 were removed from the data set as they had been identified as outliers by checkCIF (Spek, 2009).

Bond-valence sum (BVS) calculations performed using SoftBV (Adams, 2001) yielded an acceptable global instability index of 0.139 and values differing by less than 0.08 valence units (v.u.) from the ideal ones for the non-S atoms with s.o.f.s of 1, except, however, for atoms Pb3 (0.28 v.u.) and Bi1 (-0.44 v.u.) [indicated by a hash sign (#) in Fig. 2 and Table 1]. Interchanging these two atoms again led to unsatisfactory values (-0.40 and 0.23 v.u.). There is therefore a question of whether Pb/Bi mixing (as observed in ternary Pb–Bi sulfides; e.g. Berlepsch et al., 2001) should be taken into account for the two positions. A check by structure refinement is not possible, because the two elements have almost the same number of electrons (82 versus 83). It should be noted that SoftBV also calculated large BVS deviations (-0.29 v.u.) for two S atoms, one of them coordinated to neither Bi1 nor Pb3. In judging all of the evidence, the original assignment of atom types according to the CN (see above) and s.o.f.s of 1 were retained for the two atoms in the structure model. However, some probability of Pb/Bi mixing at the two positions cannot be excluded.

Computing details

Data collection: SMART (Bruker, 2001); cell refinement: SAINT (Bruker, 2001); data reduction: SAINT (Bruker, 2001); program(s) used to solve structure: SHELXTL (Sheldrick, 2008); program(s) used to refine structure: SHELXTL (Sheldrick, 2008); molecular graphics: SCHAKAL99 (Keller, 2004); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).

Figures

	Fig. 1. The structure of Pb5.0 (1)In8.4 (1)Bi1.6 (1)S20, viewed along the b axis. Atoms and bonds in the layer more distant to the viewer have been drawn paler. Some long Bi—S bonds [3.650 (2) Å] are represented by dashed lines. Primed atoms are generated by the symmetry operator (-x + 1, y - 1/2, -z + 1).
	Fig. 2. The structure of Pb5.0 (1)In8.4 (1)Bi1.6 (1)S20. Two representatives of atom Pb1 are indicated by asterisks (*). One representative of atoms Bi1 and Pb3 is indicated by a hash symbol (#). For the meaning of these symbols, the arrow, the dashed lines and the shading scheme, see Comment.
	Fig. 3. The structure of Pb1.6In8Bi4S19 (Krämer, 1983). For the meaning of the arrow, the dashed lines and the shading scheme, see Comment.
	Fig. 4. The structure of Pb6In10S21 (Krämer & Berroth, 1980). For the meaning of the arrow, the dashed lines and the shading scheme, see Comment.

pentalead octaindium dibismuth icosasulfide

Crystal data

Pb5In8.38Bi1.62S20	F(000) = 2548.8
Mr = 2978.24	Dx = 6.175 Mg m^−3
Monoclinic, P21/m	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2yb	Cell parameters from 5431 reflections
a = 27.065 (4) Å	θ = 2.3–30.0°
b = 3.8825 (3) Å	µ = 42.66 mm^−1
c = 15.683 (2) Å	T = 293 K
β = 103.59 (1)°	Flat needle, black
V = 1601.8 (3) Å^3	0.16 × 0.05 × 0.01 mm
Z = 2

Data collection

Bruker SMART CCD diffractometer	5322 independent reflections
Radiation source: fine-focus sealed tube	4539 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.094
ϕ and ω scans	θmax = 30.0°, θmin = 1.6°
Absorption correction: integration SHELXTL (Sheldrick, 2008)	h = −38→38
Tmin = 0.12, Tmax = 0.55	k = −5→4
25700 measured reflections	l = −22→21

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.034	Secondary atom site location: difference Fourier map
wR(F^2) = 0.088	w = 1/[σ^2(Fo^2) + (0.0441P)^2] where P = (Fo^2 + 2Fc^2)/3
S = 1.07	(Δ/σ)max = 0.001
5322 reflections	Δρmax = 4.26 e Å^−3
216 parameters	Δρmin = −5.52 e Å^−3

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 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 (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Pb1	0.177521 (17)	0.7500	0.25146 (3)	0.03560 (12)
Pb2	0.150481 (19)	0.7500	0.50693 (3)	0.03198 (11)
Pb3	0.311256 (14)	0.7500	0.18519 (2)	0.01847 (9)
Pb4	0.287168 (18)	0.7500	0.45122 (3)	0.03283 (11)
Pb5	0.383240 (17)	0.7500	0.68965 (2)	0.02587 (10)
Bi1	0.076214 (15)	0.7500	0.00714 (2)	0.02188 (9)
In1	0.00204 (2)	0.7500	0.39888 (4)	0.01036 (12)
In2	0.25038 (2)	0.2500	0.72384 (4)	0.01196 (12)
In3	0.22225 (2)	0.2500	0.97350 (4)	0.01282 (12)
In4	0.48497 (2)	0.2500	0.09838 (4)	0.01346 (13)
In5F	0.03837 (2)	0.2500	0.21254 (4)	0.01129 (19)	0.952 (4)
Bi5F	0.03837 (2)	0.2500	0.21254 (4)	0.01129 (19)	0.048 (4)
In6F	0.135452 (19)	0.7500	0.77711 (3)	0.00950 (18)	0.947 (4)
Bi6F	0.135452 (19)	0.7500	0.77711 (3)	0.00950 (18)	0.053 (4)
In7F	0.46332 (2)	0.7500	0.28556 (4)	0.01204 (19)	0.932 (4)
Bi7F	0.46332 (2)	0.7500	0.28556 (4)	0.01204 (19)	0.068 (4)
In8F	0.433242 (19)	0.2500	0.47873 (3)	0.01132 (17)	0.824 (4)
Bi8F	0.433242 (19)	0.2500	0.47873 (3)	0.01132 (17)	0.176 (4)
In9F	0.341967 (17)	0.7500	0.92671 (3)	0.01150 (16)	0.723 (4)
Bi9F	0.341967 (17)	0.7500	0.92671 (3)	0.01150 (16)	0.277 (4)
S1	0.11514 (8)	0.2500	0.14060 (13)	0.0113 (4)
S2	0.07833 (7)	0.7500	0.31634 (12)	0.0097 (4)
S3	0.05515 (7)	0.2500	0.49438 (12)	0.0094 (4)
S4	0.03839 (7)	0.7500	0.70918 (13)	0.0100 (4)
S5	0.00120 (8)	0.2500	0.90261 (13)	0.0117 (4)
S6	0.21471 (8)	0.7500	0.07632 (13)	0.0114 (4)
S7	0.19698 (7)	0.2500	0.42125 (13)	0.0113 (4)
S8	0.15474 (7)	0.2500	0.67503 (12)	0.0106 (4)
S9	0.13068 (7)	0.2500	0.88861 (12)	0.0105 (4)
S10	0.31894 (8)	0.2500	0.02444 (14)	0.0149 (4)
S11	0.27430 (8)	0.2500	0.27436 (14)	0.0150 (4)
S12	0.26298 (8)	0.7500	0.62444 (14)	0.0149 (4)
S13	0.23760 (7)	0.7500	0.84843 (12)	0.0121 (4)
S14	0.41837 (7)	0.2500	0.19127 (13)	0.0109 (4)
S15	0.39492 (8)	0.7500	0.37610 (13)	0.0116 (4)
S16	0.35834 (8)	0.2500	0.55170 (13)	0.0114 (4)
S17	0.34328 (8)	0.2500	0.80880 (14)	0.0139 (4)
S18	0.55687 (8)	0.2500	0.00795 (13)	0.0133 (4)
S19	0.53304 (8)	0.7500	0.20373 (13)	0.0120 (4)
S20	0.51618 (9)	0.2500	0.40703 (15)	0.0238 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb1	0.0262 (2)	0.0252 (2)	0.0464 (3)	0.000	−0.00966 (18)	0.000
Pb2	0.0503 (3)	0.0170 (2)	0.0326 (2)	0.000	0.0175 (2)	0.000
Pb3	0.02711 (19)	0.01173 (18)	0.01732 (17)	0.000	0.00677 (14)	0.000
Pb4	0.0353 (2)	0.0281 (2)	0.0291 (2)	0.000	−0.00441 (18)	0.000
Pb5	0.0446 (2)	0.0154 (2)	0.01948 (18)	0.000	0.01130 (16)	0.000
Bi1	0.0313 (2)	0.01433 (19)	0.01913 (18)	0.000	0.00415 (15)	0.000
In1	0.0135 (3)	0.0089 (3)	0.0096 (3)	0.000	0.0046 (2)	0.000
In2	0.0078 (2)	0.0117 (3)	0.0159 (3)	0.000	0.0016 (2)	0.000
In3	0.0088 (3)	0.0126 (3)	0.0150 (3)	0.000	−0.0012 (2)	0.000
In4	0.0217 (3)	0.0090 (3)	0.0119 (3)	0.000	0.0084 (2)	0.000
In5F	0.0127 (3)	0.0106 (3)	0.0114 (3)	0.000	0.0047 (2)	0.000
Bi5F	0.0127 (3)	0.0106 (3)	0.0114 (3)	0.000	0.0047 (2)	0.000
In6F	0.0076 (3)	0.0092 (3)	0.0116 (3)	0.000	0.00200 (19)	0.000
Bi6F	0.0076 (3)	0.0092 (3)	0.0116 (3)	0.000	0.00200 (19)	0.000
In7F	0.0153 (3)	0.0111 (3)	0.0114 (3)	0.000	0.0067 (2)	0.000
Bi7F	0.0153 (3)	0.0111 (3)	0.0114 (3)	0.000	0.0067 (2)	0.000
In8F	0.0125 (3)	0.0102 (3)	0.0118 (3)	0.000	0.00397 (18)	0.000
Bi8F	0.0125 (3)	0.0102 (3)	0.0118 (3)	0.000	0.00397 (18)	0.000
In9F	0.0121 (2)	0.0108 (3)	0.0122 (2)	0.000	0.00406 (17)	0.000
Bi9F	0.0121 (2)	0.0108 (3)	0.0122 (2)	0.000	0.00406 (17)	0.000
S1	0.0111 (9)	0.0106 (10)	0.0127 (9)	0.000	0.0038 (7)	0.000
S2	0.0094 (8)	0.0116 (10)	0.0086 (8)	0.000	0.0031 (7)	0.000
S3	0.0079 (8)	0.0108 (10)	0.0094 (8)	0.000	0.0019 (7)	0.000
S4	0.0078 (8)	0.0107 (10)	0.0107 (9)	0.000	0.0010 (7)	0.000
S5	0.0100 (9)	0.0126 (11)	0.0125 (9)	0.000	0.0027 (7)	0.000
S6	0.0114 (9)	0.0131 (11)	0.0103 (9)	0.000	0.0038 (7)	0.000
S7	0.0106 (9)	0.0114 (10)	0.0123 (9)	0.000	0.0036 (7)	0.000
S8	0.0090 (8)	0.0132 (11)	0.0100 (9)	0.000	0.0028 (7)	0.000
S9	0.0087 (8)	0.0115 (10)	0.0115 (9)	0.000	0.0028 (7)	0.000
S10	0.0111 (9)	0.0169 (12)	0.0157 (10)	0.000	0.0013 (7)	0.000
S11	0.0141 (10)	0.0172 (12)	0.0144 (9)	0.000	0.0048 (8)	0.000
S12	0.0217 (11)	0.0113 (11)	0.0154 (9)	0.000	0.0117 (8)	0.000
S13	0.0087 (9)	0.0157 (12)	0.0115 (9)	0.000	0.0013 (7)	0.000
S14	0.0086 (8)	0.0115 (10)	0.0124 (9)	0.000	0.0023 (7)	0.000
S15	0.0130 (9)	0.0116 (11)	0.0103 (9)	0.000	0.0026 (7)	0.000
S16	0.0136 (9)	0.0093 (10)	0.0121 (9)	0.000	0.0049 (7)	0.000
S17	0.0100 (9)	0.0174 (12)	0.0150 (9)	0.000	0.0045 (7)	0.000
S18	0.0203 (10)	0.0100 (11)	0.0108 (9)	0.000	0.0061 (8)	0.000
S19	0.0094 (9)	0.0110 (10)	0.0159 (9)	0.000	0.0038 (7)	0.000
S20	0.0160 (11)	0.0376 (16)	0.0159 (11)	0.000	−0.0003 (8)	0.000

Bond lengths (Å)

Pb1—S1	2.8745 (15)	In7F—S19	2.519 (2)
Pb1—S1^i	2.8745 (15)	In7F—S14	2.5670 (13)
Pb1—S2	3.086 (2)	In7F—S14^i	2.5670 (13)
Pb1—S6	3.140 (2)	In7F—S15	2.584 (2)
Pb1—S11^i	3.2118 (17)	In7F—S20^i	2.8571 (17)
Pb1—S11	3.2119 (17)	In7F—S20	2.8572 (17)
Pb1—S7	3.2368 (16)	In8F—S16	2.551 (2)
Pb1—S7^i	3.2368 (16)	In8F—S15	2.5788 (13)
Pb2—S7^i	2.8200 (14)	In8F—S15^viii	2.5789 (13)
Pb2—S7	2.8201 (14)	In8F—S20	2.737 (2)
Pb2—S2	3.163 (2)	In8F—S20^iii	2.7749 (17)
Pb2—S12	3.167 (2)	In8F—S20^xiv	2.7749 (16)
Pb2—S3	3.1978 (16)	In9F—S10^xv	2.6372 (15)
Pb2—S3^i	3.1979 (16)	In9F—S10^ix	2.6372 (15)
Pb2—S8	3.2540 (16)	In9F—S17^i	2.6870 (15)
Pb2—S8^i	3.2541 (16)	In9F—S17	2.6870 (15)
Pb3—S11	2.7169 (15)	In9F—S18^iii	2.688 (2)
Pb3—S11^i	2.7170 (15)	In9F—S13	2.803 (2)
Pb3—S6	2.765 (2)	S1—Bi1^viii	2.8675 (15)
Pb3—S10^i	3.2271 (17)	S1—Pb1^viii	2.8744 (15)
Pb3—S10	3.2271 (17)	S2—Bi5F^i	2.6002 (13)
Pb3—S15	3.302 (2)	S2—In5F^i	2.6002 (13)
Pb3—S14^i	3.4716 (17)	S3—In1^iv	2.533 (2)
Pb3—S14	3.4717 (17)	S3—In1^viii	2.6581 (14)
Pb4—S16^i	2.9216 (16)	S3—Pb2^viii	3.1978 (16)
Pb4—S16	2.9216 (16)	S4—In1^iv	2.6395 (13)
Pb4—S12	2.940 (2)	S4—In1^vii	2.6395 (13)
Pb4—S7	3.0673 (16)	S4—Bi5F^iv	2.650 (2)
Pb4—S7^i	3.0673 (16)	S4—In5F^iv	2.650 (2)
Pb4—S11^i	3.3361 (17)	S5—Bi5F^xiii	2.6959 (14)
Pb4—S11	3.3361 (17)	S5—In5F^xiii	2.6959 (14)
Pb4—S15	3.392 (2)	S5—Bi5F^iv	2.6959 (14)
Pb5—S16^i	2.8667 (15)	S5—In5F^iv	2.6959 (14)
Pb5—S16	2.8667 (15)	S5—Bi1^iv	2.791 (2)
Pb5—S17	3.0626 (16)	S5—Bi1^ix	3.0023 (16)
Pb5—S17^i	3.0626 (16)	S5—Bi1^x	3.0023 (16)
Pb5—S19^ii	3.1492 (17)	S6—In3^v	2.5622 (13)
Pb5—S19^iii	3.1492 (17)	S6—In3^vi	2.5622 (13)
Pb5—S12	3.174 (2)	S7—Pb2^viii	2.8201 (14)
Pb5—S20^iii	3.413 (2)	S7—Pb4^viii	3.0673 (16)
Bi1—S5^iv	2.791 (2)	S7—Pb1^viii	3.2368 (16)
Bi1—S1	2.8675 (15)	S8—Bi6F^viii	2.6453 (13)
Bi1—S1^i	2.8675 (15)	S8—In6F^viii	2.6453 (13)
Bi1—S5^v	3.0023 (16)	S8—Pb2^viii	3.2540 (16)
Bi1—S5^vi	3.0023 (16)	S9—Bi6F^viii	2.6360 (13)
Bi1—S9^v	3.2686 (16)	S9—In6F^viii	2.6360 (13)
Bi1—S9^vi	3.2686 (16)	S9—Bi1^ix	3.2687 (16)
Bi1—S6	3.649 (2)	S9—Bi1^x	3.2687 (16)
In1—S3^iv	2.533 (2)	S10—In3^v	2.550 (2)
In1—S4^iv	2.6395 (13)	S10—Bi9F^xvi	2.6371 (15)
In1—S4^vii	2.6395 (13)	S10—In9F^xvi	2.6371 (15)
In1—S3^i	2.6581 (14)	S10—Bi9F^v	2.6371 (15)
In1—S3	2.6581 (14)	S10—In9F^v	2.6371 (15)
In1—S2	2.682 (2)	S10—Pb3^viii	3.2271 (17)
In2—S8	2.521 (2)	S11—Pb3^viii	2.7169 (15)
In2—S17	2.554 (2)	S11—Pb1^viii	3.2120 (17)
In2—S12^viii	2.5622 (14)	S11—Pb4^viii	3.3361 (17)
In2—S12	2.5622 (14)	S12—In2^i	2.5623 (14)
In2—S13	2.8326 (14)	S13—In2^i	2.8326 (14)
In2—S13^viii	2.8327 (14)	S13—In3^i	2.8585 (14)
In3—S9	2.523 (2)	S14—Bi7F^viii	2.5669 (13)
In3—S10^ix	2.550 (2)	S14—In7F^viii	2.5669 (13)
In3—S6^ix	2.5622 (13)	S14—Pb3^viii	3.4717 (17)
In3—S6^x	2.5622 (13)	S15—Bi8F^i	2.5788 (13)
In3—S13^viii	2.8584 (14)	S15—In8F^i	2.5788 (13)
In3—S13	2.8585 (15)	S16—Pb5^viii	2.8668 (15)
In4—S14	2.570 (2)	S16—Pb4^viii	2.9216 (16)
In4—S18^xi	2.6353 (15)	S17—Bi9F^viii	2.6871 (15)
In4—S18^xii	2.6353 (15)	S17—In9F^viii	2.6871 (15)
In4—S18	2.664 (2)	S17—Pb5^viii	3.0625 (16)
In4—S19	2.6796 (15)	S18—In4^xi	2.6352 (15)
In4—S19^viii	2.6796 (15)	S18—In4^xii	2.6352 (15)
In5F—S1	2.587 (2)	S18—Bi9F^iii	2.688 (2)
In5F—S2	2.6002 (13)	S18—In9F^iii	2.688 (2)
In5F—S2^viii	2.6002 (13)	S19—In4^i	2.6797 (15)
In5F—S4^iv	2.650 (2)	S19—Pb5^ii	3.1493 (17)
In5F—S5^xiii	2.6959 (14)	S19—Pb5^iii	3.1493 (17)
In5F—S5^iv	2.6959 (14)	S20—Bi8F^iii	2.7748 (16)
In6F—S4	2.592 (2)	S20—In8F^iii	2.7748 (16)
In6F—S9	2.6361 (13)	S20—Bi8F^xiv	2.7748 (16)
In6F—S9^i	2.6362 (13)	S20—In8F^xiv	2.7748 (16)
In6F—S8^i	2.6451 (13)	S20—Bi7F^viii	2.8572 (17)
In6F—S8	2.6452 (13)	S20—In7F^viii	2.8572 (17)
In6F—S13	2.728 (2)	S20—Pb5^iii	3.413 (2)

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