Substitution of indium for chromium in TlIn5−xCrxSe8: crystal structure of TlIn4.811(5)Cr0.189(5)Se8

Lefèvre, R.; Berthebaud, D.; Gascoin, F.

doi:10.1107/S2056989017003292

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ISSN: 2056-9890

Volume 73| Part 4| April 2017| Pages 500-502

https://doi.org/10.1107/S2056989017003292

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Substitution of indium for chromium in TlIn_5−xCr_xSe₈: crystal structure of TlIn_4.811(5)Cr_0.189(5)Se₈

Robin Lefèvre,^a ^* David Berthebaud ^a and Franck Gascoin ^a

^aLaboratoire CRISMAT UMR6508, 6 Blvd du Maréchal Juin, 14050 Caen Cedex 4, France
^*Correspondence e-mail: robin.lefevre@ensicaen.fr

Edited by M. Weil, Vienna University of Technology, Austria (Received 12 February 2017; accepted 28 February 2017; online 14 March 2017)

The new thallium penta(indium/chromium) octaselenide, TlIn_4.811(5)Cr_0.189(5)Se₈, has been synthesized by solid-state reaction. It crystallizes isotypically with TlIn₅Se₈ in the space group C2/m. Although the two Tl positions are disordered and only partially occupied, no Tl deficiency was observed. The insertion of chromium in the structure has been confirmed by EDS analysis. Chromium substitutes indium exclusively at one of three In sites, viz. at one of the positions with site symmetry 2/m (Wyckoff position 2a). In the crystal structure, edge-sharing InSe₆ octahedra, and (In,Cr)Se₆ octahedra and InSe₄ tetrahedra make up two types of columns that are linked into a framework in which two different types of channels parallel to [010] are present. The Tl atoms are located in the larger of the channels, whereas the other, smaller channel remains unoccupied.

Keywords: crystal structure; selenide; intermetallics; pseudo-hollandite; solid solution.

CCDC reference: 1535178

1. Chemical context

This study is part of an on-going project focused on low-dimensional chalcogenides with low thermal conductivity. Quasi one-dimensional networks are of great interest for thermoelectric applications. Such structures can combine structural disorder, responsible for scattering of phonons, to an electronically conductive network.

Recently, low thermal conductive compounds belonging to the family of pseudo-hollandites were studied. A thermoelectric figure of merit up to ZT = 0.5 at 800 K was found for TlCr₅Se₈ (Takahashi et al., 2013 ). This discovery inspired further studies on this class of materials. Pseudo-hollandites are compounds with general formula AM₅X₈, (A = alkali metal, alkaline earth metal, Tl; M = V, Ti, Cr; X = S, Se, Te), the structures of which are made up from CdI₂-type layers and double chains of MX₆ octahedra sharing edges and faces in such a way that channels are created along one axis in which the A cations are located. Monoclinic TlCr₅Se₈ and the related triclinic compound Ba_0.5Cr₅Se₈ have thermal conductivities well below 1 W m⁻¹ K⁻¹ from room temperature to 873 K (Lefèvre et al., 2015 , 2016 ). As part of our project, we successfully synthesized a solid solution of TlV_5–xCr_xSe₈ (x = 0, 1, 2, 3, 4, 5) and studied the magnetism and thermoelectric properties of TlV₅Se₈ (Maier et al., 2015 ).

Working on a similar compound, monoclinic TlIn₅Se₈, we attempted to synthesize a solid solution TlIn_5–xCr_xSe₈. Initially, the nominal composition TlIn₄CrSe₈ was chosen so that chromium fully substitutes indium at the octahedral site (Wyckoff position 2a) of TlIn₅Se₈. Here we present the structure of one compound of the solid solution series TlIn_5–xCr_xSe₈ (x = 0.189) with only a partial substitution of indium for chromium at this site.

2. Structural commentary

The composition of the crystals as determined from the refinement is in good agreement with the EDS analysis. The refined structure is represented in Fig. 1, both as individual atoms and in a polyhedral representation. All atoms in the asymmetric unit (two Tl, one mixed-occupied In/Cr, two In and four Se sites) are located on special positions. Except Tl2 and mixed-occupied (In1/Cr) on positions with site symmetry 2/m (Wyckoff positions 2d and 2a, respectively), all other atoms are located on a mirror plane (4i).

Figure 1
The crystal structure of TlIn_4.811(5)Cr_0.189(5)Se₈. (a) Representation by atoms displayed with displacement ellipsoids at the 50% probability level; (b) polyhedral representation.

Indium atoms are found in octahedral (In1, In2) and tetrahedral (In3) environments by selenium atoms. Only one of the indium atoms, In1, shares its position with chromium in an octahedral environment. The (In1,Cr)Se₆ and In2Se₆ octahedra form two types of columns. One column is made up only of edge-sharing In2Se₆ octahedra in a zigzag shape. The second column is made up of alternating (In1/Cr)Se₆ octahedra and In3Se₄ tetrahedra connected by edge-sharing, likewise in a zigzag shape. These two building units are linked together to form a framework in which two types of channels propagating parallel to [010] are present. One of the channels hosts the two partly occupied Tl atoms, while the other is smaller and thus empty. Compared to the pseudo-hollandite network, the infinite planes are broken into columns in the title structure, leaving a supplementary channel at the junction of the columns and the double chains.

The existence of the title solid solution is in agreement with the decrease or increase of unit-cell parameters of TlIn_5–xCr_xSe₈ from x = 0 (Walther & Deiseroth, 1998 ) to x = 5 (Klepp & Boller, 1983 ), as explicited in Fig. 2a. Further, the decrease in the determined metal-to-metal and metal-to-selenium distances shows a clear trend in agreement with the increase of the chromium content (Fig. 2b,c).

Figure 2
Evolution of (a) the unit-cell parameters, (b) M—M distances and (c) M—Se distances depending on x in the TlIn_5–xCr_xSe₈ solid solution series.

3. Synthesis and crystallization

To prevent oxidation of reactants and products, all manipulations were performed under inert gas or vacuum (glove box or sealed containers). The elements, Cr (powder, 325 mesh, 99%), In (teardrops, 4 mm, 99.9%) and Se (shots, 99.999%), all from Alfa Aesar, were used as received; Tl (granules, 99.99%), as well from Alfa Aesar, received in water, was first rinsed and dried before being stored in a glovebox. The elements Tl, In, Cr and Se in the molar ratio 1:4:1:8 were loaded directly in a fused silica tube that was subsequently evacuated and flame sealed. The mixture was first heated up to 723 K within 7 h for half a day, and then to 1073 K in 7 h for half a day. The mixture was then cooled down to room temperature in 48 h. An intermediate annealing process at 873 K for 15 h was performed. Single crystals were extracted from the bulk.

The bulk sample quality was checked by means of X-ray powder diffraction using a X-Pert Pro Panalytical diffractometer (Cu Kα_1,2 radiations) equipped with a PIXCEL detector. Phase identification was performed with X'Pert HighScore plus (Panalytical, 2009 ). Phase analysis using X-ray powder diffraction revealed at first sight TlCr₅Se₈ (Klepp & Boller, 1983) and TlIn₅Se₈ (Walther & Deiseroth, 1998). However, the Bragg positions of these reflections were clearly shifted, pointing to the presence of a TlIn_5–xCr_xSe₈ solid solution.

Energy Dispersive X-Ray Spectroscopy (EDS) analyses were also performed to check the composition using a scanning electron microscope (SEM; ZEISS Supra 55, 15 kV). Analysis on basis of nine measured crystallites confirmed the presence of four elements, with a determined average molar composition of Tl 1.05; In 4.54; Cr 0.46; Se 9.1.

4. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1.

Table 1
Experimental details

Crystal data
Chemical formula	TlIn_4.811Cr_0.189Se₈
M_r	1398.3
Crystal system, space group	Monoclinic, C2/m
Temperature (K)	293
a, b, c (Å)	19.8257 (18), 3.9754 (4), 9.5881 (9)
β (°)	101.645 (5)
V (Å³)	740.13 (12)
Z	2
Radiation type	Mo Kα
μ (mm⁻¹)	37.98
Crystal size (mm)	0.13 × 0.11 × 0.10

Data collection
Diffractometer	Bruker APEXII CCD area detector
Absorption correction	Numerical (SADABS; Bruker, 2004 )
T_min, T_max	0.405, 0.747
No. of measured, independent and observed [I > 3σ(I)] reflections	5647, 1537, 1181
R_int	0.028
(sin θ/λ)_max (Å⁻¹)	0.770

Refinement
R[F > 3σ(F)], wR(F), S	0.030, 0.031, 1.34
No. of reflections	1537
No. of parameters	50
Δρ_max, Δρ_min (e Å⁻³)	1.41, −1.69
Computer programs: APEX2 and SAINT (Bruker, 2004), SUPERFLIP (Palatinus & Chapuis, 2007), DIAMOND (Brandenburg & Putz, 2014 ), JANA2006 (Petříček et al., 2014 ) and publCIF (Westrip, 2010 ).

Structure solution using SUPERFLIP (Palatinus & Chapuis, 2007 ) led to one thallium site, three indium sites and four selenium sites. Refinement of Tl1 in position (0.5,0,0.5) resulted in large anisotropic displacement parameters. As previously reported, Tl1 usually is located at a partly occupied position around the center position with approximate coordinates of (0.46, 0, 0.52) (Walther & Deiseroth, 1998). Consideration of the split model (in addition, the In1 site occupancy refined to 0.81 while other indium sites were modelled as fully occupied) led to much more reasonable displacement parameters and improved reliability factors. At that step, the reliability factors were: GOF(all reflections) = 2.42 and wR (all reflections) = 0.056, while the maximum and minimum electron densities were +10.28 and −6.03 e⁻ Å⁻³.

The insertion of chromium in the structure has been confirmed by EDS analysis. Consideration of a mixed-occupied In/Cr site for the original In1 position (same coordinates and anisotropic displacement parameters for the two atoms and full occupation for this site) led to a further improvement of reliability factors [GOF (all) = 2.06 and wR(all) = 0.0476] and a decrease of the residual electron densities to +9.71 and −5.83 e⁻ Å⁻³. The maximum electron density was found on position (0, 0.5, 0.5). This position is between the partially occupied Tl1 atoms. Thus, a second partially occupied thallium atom, Tl2, was introduced. The two thallium sites are non-simultaneously occupied. The displacement parameter of Tl2 was modelled as isotropic due to its low occupancy compared to Tl1. Adding this second Tl site significantly reduced the residual electron density to final values of +1.41 and −1.69 e⁻ Å⁻³. These density peaks are found at 0.82 and 0.73 Å, respectively, from atoms Se2 and In3.

Supporting information

CCDC reference: 1535178

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2056989017003292/wm5368sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989017003292/wm5368Isup2.hkl

checkCIF report

Computing details top

Data collection: APEX2 (Bruker, 2004); cell refinement: SAINT (Bruker, 2004); data reduction: SAINT (Bruker, 2004); program(s) used to solve structure: SUPERFLIP (Palatinus & Chapuis, 2007); program(s) used to refine structure: JANA2006 (Petříček et al., 2014); molecular graphics: DIAMOND (Brandenburg & Putz, 2014); software used to prepare material for publication: JANA2006 (Petříček et al., 2014) and publCIF (Westrip, 2010).

Thallium penta(indium/chromium) octaselenide top

Crystal data top

TlIn_4.811Cr_0.189Se₈	F(000) = 1187
M_r = 1398.3	D_x = 6.274 Mg m⁻³
Monoclinic, C2/m	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -C 2y	Cell parameters from 2692 reflections
a = 19.8257 (18) Å	θ = 2.7–32.8°
b = 3.9754 (4) Å	µ = 37.98 mm⁻¹
c = 9.5881 (9) Å	T = 293 K
β = 101.645 (5)°	Irregular, black
V = 740.13 (12) Å³	0.13 × 0.11 × 0.10 mm
Z = 2

Data collection top

Bruker APEXII CCD area detector diffractometer	1537 independent reflections
Radiation source: X-ray tube	1181 reflections with I > 3σ(I)
Graphite monochromator	R_int = 0.028
Detector resolution: 8.3333 pixels mm^-1	θ_max = 33.2°, θ_min = 2.1°
ω and φ scans	h = −30→26
Absorption correction: numerical (SADABS; Bruker, 2004)	k = −5→6
T_min = 0.405, T_max = 0.747	l = −12→14
5647 measured reflections

Refinement top

Refinement on F	0 restraints
R[F > 3σ(F)] = 0.030	4 constraints
wR(F) = 0.031	Weighting scheme based on measured s.u.'s w = 1/(σ²(F) + 0.0001F²)
S = 1.34	(Δ/σ)_max = 0.003
1537 reflections	Δρ_max = 1.41 e Å⁻³
50 parameters	Δρ_min = −1.69 e Å⁻³

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Tl1	0.46491 (5)	0	0.52551 (8)	0.0407 (3)	0.4631 (16)
Tl2	0	0.5	0.5	0.032 (2)*	0.074 (3)
In1	0	0	0	0.0155 (2)	0.811 (5)
Cr	0	0	0	0.0155 (2)	0.189 (5)
In2	0.28034 (3)	0	0.66298 (5)	0.02131 (15)
In3	0.36250 (2)	0	0.10972 (5)	0.02052 (15)
Se1	0.24067 (3)	0	0.15323 (6)	0.01295 (17)
Se2	0.16279 (4)	0	0.47058 (7)	0.0197 (2)
Se3	0.58556 (3)	0	0.11945 (6)	0.01640 (19)
Se4	0.06189 (3)	0	0.76833 (7)	0.01829 (19)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Tl1	0.0434 (6)	0.0352 (4)	0.0376 (4)	0	−0.0058 (3)	0
In1	0.0110 (4)	0.0129 (4)	0.0240 (4)	0	0.0069 (3)	0
Cr	0.0110 (4)	0.0129 (4)	0.0240 (4)	0	0.0069 (3)	0
In2	0.0346 (3)	0.0138 (2)	0.01692 (19)	0	0.00868 (19)	0
In3	0.0158 (2)	0.0166 (2)	0.0327 (3)	0	0.01323 (19)	0
Se1	0.0129 (3)	0.0129 (3)	0.0142 (3)	0	0.0053 (2)	0
Se2	0.0256 (4)	0.0174 (3)	0.0183 (3)	0	0.0094 (2)	0
Se3	0.0121 (3)	0.0179 (3)	0.0187 (3)	0	0.0019 (2)	0
Se4	0.0189 (3)	0.0153 (3)	0.0204 (3)	0	0.0035 (2)	0

Geometric parameters (Å, º) top

Tl1—Tl1ⁱ	3.9754 (8)	Cr—Se3^xiii	2.7122 (5)
Tl1—Tl1ⁱⁱ	3.9754 (8)	Cr—Se4^xiv	2.7460 (8)
Tl1—Tl1ⁱⁱⁱ	1.5654 (15)	Cr—Se4^viii	2.7460 (8)
Tl1—Tl2^iv	0.7827 (11)	In2—In2ⁱ	3.9754 (8)
Tl1—Se2^v	3.2249 (11)	In2—In2ⁱⁱ	3.9754 (8)
Tl1—Se2^vi	3.2249 (11)	In2—In2^v	3.6944 (8)
Tl1—Se3ⁱⁱⁱ	3.7369 (13)	In2—In2^vi	3.6944 (8)
Tl1—Se4^iv	3.3558 (9)	In2—Se1^v	2.7433 (6)
Tl1—Se4^vii	3.3558 (9)	In2—Se1^vi	2.7433 (6)
Tl1—Se4^v	3.4010 (9)	In2—Se2	2.6644 (9)
Tl1—Se4^vi	3.4010 (9)	In2—Se2^v	2.7286 (7)
Tl2—Tl2ⁱ	3.9754 (8)	In2—Se2^vi	2.7286 (7)
Tl2—Tl2ⁱⁱ	3.9754 (8)	In2—Se3ⁱⁱⁱ	3.0300 (9)
Tl2—Se2	3.8489 (8)	In3—In3ⁱ	3.9754 (8)
Tl2—Se2ⁱⁱ	3.8489 (8)	In3—In3ⁱⁱ	3.9754 (8)
Tl2—Se2^viii	3.8489 (8)	In3—Se1	2.5328 (9)
Tl2—Se2^ix	3.8489 (8)	In3—Se1^xii	3.5227 (7)
Tl2—Se4	3.2865 (7)	In3—Se1^xiii	3.5227 (7)
Tl2—Se4ⁱⁱ	3.2865 (7)	In3—Se3^xv	2.6080 (9)
Tl2—Se4^viii	3.2865 (7)	In3—Se4^v	2.6186 (6)
Tl2—Se4^ix	3.2865 (7)	In3—Se4^vi	2.6186 (6)
In1—In1ⁱ	3.9754 (8)	Se1—Se1ⁱ	3.9754 (8)
In1—In1ⁱⁱ	3.9754 (8)	Se1—Se1ⁱⁱ	3.9754 (8)
In1—Crⁱ	3.9754 (8)	Se1—Se1^xii	3.6278 (9)
In1—Cr	0	Se1—Se1^xiii	3.6278 (9)
In1—Crⁱⁱ	3.9754 (8)	Se1—Se2	3.6795 (11)
In1—In3^x	3.6941 (6)	Se1—Se3^x	3.6207 (9)
In1—In3^xi	3.6941 (6)	Se1—Se3^xi	3.6207 (9)
In1—In3^xii	3.6941 (6)	Se2—Se2ⁱ	3.9754 (8)
In1—In3^xiii	3.6941 (6)	Se2—Se2ⁱⁱ	3.9754 (8)
In1—Se3^x	2.7122 (5)	Se2—Se2^v	3.9294 (10)
In1—Se3^xi	2.7122 (5)	Se2—Se2^vi	3.9294 (10)
In1—Se3^xii	2.7122 (5)	Se2—Se3^x	3.9432 (9)
In1—Se3^xiii	2.7122 (5)	Se2—Se3^xi	3.9432 (9)
In1—Se4^xiv	2.7460 (8)	Se2—Se4	3.8022 (11)
In1—Se4^viii	2.7460 (8)	Se3—Se3ⁱ	3.9754 (8)
Cr—Crⁱ	3.9754 (8)	Se3—Se3ⁱⁱ	3.9754 (8)
Cr—Crⁱⁱ	3.9754 (8)	Se3—Se3^xv	3.6905 (11)
Cr—In3^x	3.6941 (6)	Se3—Se4^xvi	3.8558 (10)
Cr—In3^xi	3.6941 (6)	Se3—Se4^xvii	3.8558 (10)
Cr—In3^xii	3.6941 (6)	Se3—Se4^v	3.8633 (10)
Cr—In3^xiii	3.6941 (6)	Se3—Se4^vi	3.8633 (10)
Cr—Se3^x	2.7122 (5)	Se4—Se4ⁱ	3.9754 (8)
Cr—Se3^xi	2.7122 (5)	Se4—Se4ⁱⁱ	3.9754 (8)
Cr—Se3^xii	2.7122 (5)

Tl1ⁱ—Tl1—Tl1ⁱⁱ	180.0 (5)	In3^xii—Se1—Se1^xiii	82.466 (16)
Tl1ⁱ—Tl1—Tl1ⁱⁱⁱ	90.00 (2)	In3^xii—Se1—Se2	108.174 (19)
Tl1ⁱ—Tl1—Tl2^iv	90.00 (2)	In3^xii—Se1—Se3^x	42.799 (14)
Tl1ⁱ—Tl1—Se2^v	51.949 (18)	In3^xii—Se1—Se3^xi	83.442 (16)
Tl1ⁱ—Tl1—Se2^vi	128.05 (3)	In3^xiii—Se1—Se1ⁱ	124.351 (15)
Tl1ⁱ—Tl1—Se3ⁱⁱⁱ	90.000 (18)	In3^xiii—Se1—Se1ⁱⁱ	55.649 (10)
Tl1ⁱ—Tl1—Se4^iv	53.678 (14)	In3^xiii—Se1—Se1^xii	82.466 (16)
Tl1ⁱ—Tl1—Se4^vii	126.32 (2)	In3^xiii—Se1—Se1^xiii	41.459 (14)
Tl1ⁱ—Tl1—Se4^v	54.236 (14)	In3^xiii—Se1—Se2	108.174 (19)
Tl1ⁱ—Tl1—Se4^vi	125.76 (2)	In3^xiii—Se1—Se3^x	83.442 (16)
Tl1ⁱⁱ—Tl1—Tl1ⁱⁱⁱ	90.00 (2)	In3^xiii—Se1—Se3^xi	42.799 (14)
Tl1ⁱⁱ—Tl1—Tl2^iv	90.00 (2)	Se1ⁱ—Se1—Se1^xii	56.776 (11)
Tl1ⁱⁱ—Tl1—Se2^v	128.05 (3)	Se1ⁱ—Se1—Se1^xiii	123.224 (17)
Tl1ⁱⁱ—Tl1—Se2^vi	51.949 (18)	Se1ⁱ—Se1—Se3^x	56.703 (11)
Tl1ⁱⁱ—Tl1—Se3ⁱⁱⁱ	90.000 (18)	Se1ⁱ—Se1—Se3^xi	123.297 (17)
Tl1ⁱⁱ—Tl1—Se4^iv	126.32 (2)	Se1ⁱⁱ—Se1—Se1^xii	123.224 (17)
Tl1ⁱⁱ—Tl1—Se4^vii	53.678 (14)	Se1ⁱⁱ—Se1—Se1^xiii	56.776 (11)
Tl1ⁱⁱ—Tl1—Se4^v	125.76 (2)	Se1ⁱⁱ—Se1—Se3^x	123.297 (17)
Tl1ⁱⁱ—Tl1—Se4^vi	54.236 (14)	Se1ⁱⁱ—Se1—Se3^xi	56.703 (11)
Tl1ⁱⁱⁱ—Tl1—Se2^v	138.86 (2)	Se1^xii—Se1—Se1^xiii	66.448 (14)
Tl1ⁱⁱⁱ—Tl1—Se2^vi	138.86 (2)	Se1^xii—Se1—Se2	142.961 (13)
Tl1ⁱⁱⁱ—Tl1—Se3ⁱⁱⁱ	134.67 (5)	Se1^xii—Se1—Se3^x	81.396 (15)
Tl1ⁱⁱⁱ—Tl1—Se4^iv	78.22 (4)	Se1^xii—Se1—Se3^xi	116.871 (19)
Tl1ⁱⁱⁱ—Tl1—Se4^vii	78.22 (4)	Se1^xiii—Se1—Se2	142.961 (13)
Tl1ⁱⁱⁱ—Tl1—Se4^v	75.00 (4)	Se1^xiii—Se1—Se3^x	116.871 (19)
Tl1ⁱⁱⁱ—Tl1—Se4^vi	75.00 (4)	Se1^xiii—Se1—Se3^xi	81.396 (15)
Tl2^iv—Tl1—Se2^v	138.86 (3)	Se2—Se1—Se3^x	65.381 (17)
Tl2^iv—Tl1—Se2^vi	138.86 (3)	Se2—Se1—Se3^xi	65.381 (17)
Tl2^iv—Tl1—Se3ⁱⁱⁱ	134.67 (7)	Se3^x—Se1—Se3^xi	66.594 (15)
Tl2^iv—Tl1—Se4^iv	78.22 (5)	Tl1^v—Se2—Tl1^vi	76.10 (2)
Tl2^iv—Tl1—Se4^vii	78.22 (5)	Tl1^v—Se2—Tl2ⁱ	7.689 (13)
Tl2^iv—Tl1—Se4^v	75.00 (5)	Tl1^v—Se2—Tl2	69.244 (19)
Tl2^iv—Tl1—Se4^vi	75.00 (5)	Tl1^v—Se2—In2	124.82 (2)
Se2^v—Tl1—Se2^vi	76.10 (3)	Tl1^v—Se2—In2^v	87.489 (18)
Se2^v—Tl1—Se3ⁱⁱⁱ	68.55 (2)	Tl1^v—Se2—In2^vi	148.67 (3)
Se2^v—Tl1—Se4^iv	88.171 (18)	Tl1^v—Se2—Se1	118.10 (2)
Se2^v—Tl1—Se4^vii	134.29 (3)	Tl1^v—Se2—Se2ⁱ	51.949 (16)
Se2^v—Tl1—Se4^v	69.98 (2)	Tl1^v—Se2—Se2ⁱⁱ	128.05 (2)
Se2^v—Tl1—Se4^vi	112.22 (3)	Tl1^v—Se2—Se2^v	110.899 (15)
Se2^vi—Tl1—Se3ⁱⁱⁱ	68.55 (2)	Tl1^v—Se2—Se2^vi	168.61 (2)
Se2^vi—Tl1—Se4^iv	134.29 (3)	Tl1^v—Se2—Se3^x	61.888 (19)
Se2^vi—Tl1—Se4^vii	88.171 (18)	Tl1^v—Se2—Se3^xi	98.64 (2)
Se2^vi—Tl1—Se4^v	112.22 (3)	Tl1^v—Se2—Se4	57.184 (19)
Se2^vi—Tl1—Se4^vi	69.98 (2)	Tl1^vi—Se2—Tl2ⁱ	69.244 (19)
Se3ⁱⁱⁱ—Tl1—Se4^iv	65.75 (2)	Tl1^vi—Se2—Tl2	7.689 (13)
Se3ⁱⁱⁱ—Tl1—Se4^vii	65.75 (2)	Tl1^vi—Se2—In2	124.82 (2)
Se3ⁱⁱⁱ—Tl1—Se4^v	136.79 (2)	Tl1^vi—Se2—In2^v	148.67 (3)
Se3ⁱⁱⁱ—Tl1—Se4^vi	136.79 (2)	Tl1^vi—Se2—In2^vi	87.489 (18)
Se4^iv—Tl1—Se4^vii	72.64 (2)	Tl1^vi—Se2—Se1	118.10 (2)
Se4^iv—Tl1—Se4^v	101.558 (16)	Tl1^vi—Se2—Se2ⁱ	128.05 (2)
Se4^iv—Tl1—Se4^vi	153.22 (4)	Tl1^vi—Se2—Se2ⁱⁱ	51.949 (16)
Se4^vii—Tl1—Se4^v	153.22 (4)	Tl1^vi—Se2—Se2^v	168.61 (2)
Se4^vii—Tl1—Se4^vi	101.558 (16)	Tl1^vi—Se2—Se2^vi	110.899 (15)
Se4^v—Tl1—Se4^vi	71.529 (19)	Tl1^vi—Se2—Se3^x	98.64 (2)
Tl1^xi—Tl2—Tl1^vi	180.0 (5)	Tl1^vi—Se2—Se3^xi	61.888 (19)
Tl1^xi—Tl2—Tl2ⁱ	90	Tl1^vi—Se2—Se4	57.184 (19)
Tl1^xi—Tl2—Tl2ⁱⁱ	90	Tl2ⁱ—Se2—Tl2	62.186 (13)
Tl1^xi—Tl2—Se2	146.55 (2)	Tl2ⁱ—Se2—In2	125.34 (2)
Tl1^xi—Tl2—Se2ⁱⁱ	146.55 (2)	Tl2ⁱ—Se2—In2^v	95.178 (13)
Tl1^xi—Tl2—Se2^viii	33.45 (2)	Tl2ⁱ—Se2—In2^vi	147.42 (2)
Tl1^xi—Tl2—Se2^ix	33.45 (2)	Tl2ⁱ—Se2—Se1	123.962 (15)
Tl1^xi—Tl2—Se4	88.30 (5)	Tl2ⁱ—Se2—Se2ⁱ	58.907 (12)
Tl1^xi—Tl2—Se4ⁱⁱ	88.30 (5)	Tl2ⁱ—Se2—Se2ⁱⁱ	121.093 (19)
Tl1^xi—Tl2—Se4^viii	91.70 (5)	Tl2ⁱ—Se2—Se2^v	117.058 (10)
Tl1^xi—Tl2—Se4^ix	91.70 (5)	Tl2ⁱ—Se2—Se2^vi	167.79 (2)
Tl1^vi—Tl2—Tl2ⁱ	90	Tl2ⁱ—Se2—Se3^x	67.384 (13)
Tl1^vi—Tl2—Tl2ⁱⁱ	90	Tl2ⁱ—Se2—Se3^xi	97.822 (17)
Tl1^vi—Tl2—Se2	33.45 (2)	Tl2ⁱ—Se2—Se4	50.873 (12)
Tl1^vi—Tl2—Se2ⁱⁱ	33.45 (2)	Tl2—Se2—In2	125.34 (2)
Tl1^vi—Tl2—Se2^viii	146.55 (2)	Tl2—Se2—In2^v	147.42 (2)
Tl1^vi—Tl2—Se2^ix	146.55 (2)	Tl2—Se2—In2^vi	95.178 (13)
Tl1^vi—Tl2—Se4	91.70 (5)	Tl2—Se2—Se1	123.962 (15)
Tl1^vi—Tl2—Se4ⁱⁱ	91.70 (5)	Tl2—Se2—Se2ⁱ	121.093 (19)
Tl1^vi—Tl2—Se4^viii	88.30 (5)	Tl2—Se2—Se2ⁱⁱ	58.907 (12)
Tl1^vi—Tl2—Se4^ix	88.30 (5)	Tl2—Se2—Se2^v	167.79 (2)
Tl2ⁱ—Tl2—Tl2ⁱⁱ	180.0 (5)	Tl2—Se2—Se2^vi	117.058 (10)
Tl2ⁱ—Tl2—Se2	58.907 (6)	Tl2—Se2—Se3^x	97.822 (17)
Tl2ⁱ—Tl2—Se2ⁱⁱ	121.093 (6)	Tl2—Se2—Se3^xi	67.384 (13)
Tl2ⁱ—Tl2—Se2^viii	58.907 (6)	Tl2—Se2—Se4	50.873 (12)
Tl2ⁱ—Tl2—Se2^ix	121.093 (6)	In2—Se2—In2^v	86.47 (2)
Tl2ⁱ—Tl2—Se4	52.785 (7)	In2—Se2—In2^vi	86.47 (2)
Tl2ⁱ—Tl2—Se4ⁱⁱ	127.215 (7)	In2—Se2—Se1	96.79 (3)
Tl2ⁱ—Tl2—Se4^viii	52.785 (7)	In2—Se2—Se2^v	43.875 (14)
Tl2ⁱ—Tl2—Se4^ix	127.215 (7)	In2—Se2—Se2^vi	43.875 (14)
Tl2ⁱⁱ—Tl2—Se2	121.093 (6)	In2—Se2—Se3^x	136.53 (2)
Tl2ⁱⁱ—Tl2—Se2ⁱⁱ	58.907 (6)	In2—Se2—Se3^xi	136.53 (2)
Tl2ⁱⁱ—Tl2—Se2^viii	121.093 (6)	In2—Se2—Se4	89.96 (2)
Tl2ⁱⁱ—Tl2—Se2^ix	58.907 (6)	In2^v—Se2—In2^vi	93.52 (3)
Tl2ⁱⁱ—Tl2—Se4	127.215 (7)	In2^v—Se2—Se1	47.915 (14)
Tl2ⁱⁱ—Tl2—Se4ⁱⁱ	52.785 (7)	In2^v—Se2—Se2ⁱ	43.241 (14)
Tl2ⁱⁱ—Tl2—Se4^viii	127.215 (7)	In2^v—Se2—Se2ⁱⁱ	136.76 (3)
Tl2ⁱⁱ—Tl2—Se4^ix	52.785 (7)	In2^v—Se2—Se2^v	42.593 (15)
Se2—Tl2—Se2ⁱⁱ	62.186 (10)	In2^v—Se2—Se2^vi	90.05 (2)
Se2—Tl2—Se2^viii	117.814 (10)	In2^v—Se2—Se3^x	50.066 (15)
Se2—Tl2—Se2^ix	180.0 (5)	In2^v—Se2—Se3^xi	95.31 (2)
Se2—Tl2—Se4	63.828 (16)	In2^v—Se2—Se4	133.020 (14)
Se2—Tl2—Se4ⁱⁱ	100.580 (14)	In2^vi—Se2—Se1	47.915 (14)
Se2—Tl2—Se4^viii	79.420 (14)	In2^vi—Se2—Se2ⁱ	136.76 (3)
Se2—Tl2—Se4^ix	116.172 (16)	In2^vi—Se2—Se2ⁱⁱ	43.241 (14)
Se2ⁱⁱ—Tl2—Se2^viii	180.0 (5)	In2^vi—Se2—Se2^v	90.05 (2)
Se2ⁱⁱ—Tl2—Se2^ix	117.814 (10)	In2^vi—Se2—Se2^vi	42.593 (15)
Se2ⁱⁱ—Tl2—Se4	100.580 (14)	In2^vi—Se2—Se3^x	95.31 (2)
Se2ⁱⁱ—Tl2—Se4ⁱⁱ	63.828 (16)	In2^vi—Se2—Se3^xi	50.066 (15)
Se2ⁱⁱ—Tl2—Se4^viii	116.172 (16)	In2^vi—Se2—Se4	133.020 (14)
Se2ⁱⁱ—Tl2—Se4^ix	79.420 (14)	Se1—Se2—Se2^v	67.339 (17)
Se2^viii—Tl2—Se2^ix	62.186 (10)	Se1—Se2—Se2^vi	67.339 (17)
Se2^viii—Tl2—Se4	79.420 (14)	Se1—Se2—Se3^x	56.591 (16)
Se2^viii—Tl2—Se4ⁱⁱ	116.172 (16)	Se1—Se2—Se3^xi	56.591 (16)
Se2^viii—Tl2—Se4^viii	63.828 (16)	Se1—Se2—Se4	173.25 (2)
Se2^viii—Tl2—Se4^ix	100.580 (14)	Se2ⁱ—Se2—Se2ⁱⁱ	180.0 (5)
Se2^ix—Tl2—Se4	116.172 (16)	Se2ⁱ—Se2—Se2^v	59.612 (13)
Se2^ix—Tl2—Se4ⁱⁱ	79.420 (14)	Se2ⁱ—Se2—Se2^vi	120.388 (19)
Se2^ix—Tl2—Se4^viii	100.580 (14)	Se2ⁱ—Se2—Se3^x	59.729 (11)
Se2^ix—Tl2—Se4^ix	63.828 (16)	Se2ⁱ—Se2—Se3^xi	120.271 (16)
Se4—Tl2—Se4ⁱⁱ	74.429 (12)	Se2ⁱⁱ—Se2—Se2^v	120.388 (19)
Se4—Tl2—Se4^viii	105.571 (12)	Se2ⁱⁱ—Se2—Se2^vi	59.612 (13)
Se4—Tl2—Se4^ix	180.0 (5)	Se2ⁱⁱ—Se2—Se3^x	120.271 (16)
Se4ⁱⁱ—Tl2—Se4^viii	180.0 (5)	Se2ⁱⁱ—Se2—Se3^xi	59.729 (11)
Se4ⁱⁱ—Tl2—Se4^ix	105.571 (12)	Se2^v—Se2—Se2^vi	60.777 (14)
Se4^viii—Tl2—Se4^ix	74.429 (12)	Se2^v—Se2—Se3^x	92.659 (16)
In1ⁱ—In1—In1ⁱⁱ	180.0 (5)	Se2^v—Se2—Se3^xi	123.81 (2)
In1ⁱ—In1—In3^x	57.447 (5)	Se2^v—Se2—Se4	118.249 (18)
In1ⁱ—In1—In3^xi	122.553 (5)	Se2^vi—Se2—Se3^x	123.81 (2)
In1ⁱ—In1—In3^xii	57.447 (5)	Se2^vi—Se2—Se3^xi	92.659 (16)
In1ⁱ—In1—In3^xiii	122.553 (5)	Se2^vi—Se2—Se4	118.249 (18)
In1ⁱ—In1—Se3^x	42.872 (10)	Se3^x—Se2—Se3^xi	60.542 (13)
In1ⁱ—In1—Se3^xi	137.128 (10)	Se3^x—Se2—Se4	117.94 (2)
In1ⁱ—In1—Se3^xii	42.872 (10)	Se3^xi—Se2—Se4	117.94 (2)
In1ⁱ—In1—Se3^xiii	137.128 (10)	Tl1ⁱⁱⁱ—Se3—In1^iv	97.18 (2)
In1ⁱ—In1—Se4^xiv	90	Tl1ⁱⁱⁱ—Se3—In1^vii	97.18 (2)
In1ⁱ—In1—Se4^viii	90	Tl1ⁱⁱⁱ—Se3—Cr^iv	97.18 (2)
In1ⁱⁱ—In1—Crⁱ	180.0 (5)	Tl1ⁱⁱⁱ—Se3—Cr^vii	97.18 (2)
In1ⁱⁱ—In1—In3^x	122.553 (5)	Tl1ⁱⁱⁱ—Se3—In2ⁱⁱⁱ	74.45 (2)
In1ⁱⁱ—In1—In3^xi	57.447 (5)	Tl1ⁱⁱⁱ—Se3—In3^xv	172.46 (3)
In1ⁱⁱ—In1—In3^xii	122.553 (5)	Tl1ⁱⁱⁱ—Se3—Se1^iv	107.29 (2)
In1ⁱⁱ—In1—In3^xiii	57.447 (5)	Tl1ⁱⁱⁱ—Se3—Se1^vii	107.29 (2)
In1ⁱⁱ—In1—Se3^x	137.128 (10)	Tl1ⁱⁱⁱ—Se3—Se2^iv	49.567 (17)
In1ⁱⁱ—In1—Se3^xi	42.872 (10)	Tl1ⁱⁱⁱ—Se3—Se2^vii	49.567 (17)
In1ⁱⁱ—In1—Se3^xii	137.128 (10)	Tl1ⁱⁱⁱ—Se3—Se3^xv	100.59 (3)
In1ⁱⁱ—In1—Se3^xiii	42.872 (10)	Tl1ⁱⁱⁱ—Se3—Se4^xvi	141.961 (17)
In1ⁱⁱ—In1—Se4^xiv	90	Tl1ⁱⁱⁱ—Se3—Se4^xvii	141.961 (17)
In1ⁱⁱ—In1—Se4^viii	90	Tl1ⁱⁱⁱ—Se3—Se4^v	52.372 (17)
Crⁱ—In1—Crⁱⁱ	180.0 (5)	Tl1ⁱⁱⁱ—Se3—Se4^vi	52.372 (17)
Crⁱ—In1—In3^x	57.447 (5)	In1^iv—Se3—In1^vii	94.256 (19)
Crⁱ—In1—In3^xi	122.553 (5)	In1^iv—Se3—Cr^vii	94.256 (19)
Crⁱ—In1—In3^xii	57.447 (5)	In1^iv—Se3—In2ⁱⁱⁱ	132.673 (10)
Crⁱ—In1—In3^xiii	122.553 (5)	In1^iv—Se3—In3^xv	87.929 (17)
Crⁱ—In1—Se3^x	42.872 (10)	In1^iv—Se3—Se1^iv	94.758 (12)
Crⁱ—In1—Se3^xi	137.128 (10)	In1^iv—Se3—Se1^vii	152.58 (2)
Crⁱ—In1—Se3^xii	42.872 (10)	In1^iv—Se3—Se2^iv	95.340 (12)
Crⁱ—In1—Se3^xiii	137.128 (10)	In1^iv—Se3—Se2^vii	146.30 (2)
Crⁱⁱ—In1—In3^x	122.553 (5)	In1^iv—Se3—Se3ⁱ	42.872 (9)
Crⁱⁱ—In1—In3^xi	57.447 (5)	In1^iv—Se3—Se3ⁱⁱ	137.128 (19)
Crⁱⁱ—In1—In3^xii	122.553 (5)	In1^iv—Se3—Se3^xv	47.128 (10)
Crⁱⁱ—In1—In3^xiii	57.447 (5)	In1^iv—Se3—Se4^xvi	45.411 (12)
Crⁱⁱ—In1—Se3^x	137.128 (10)	In1^iv—Se3—Se4^xvii	93.072 (18)
Crⁱⁱ—In1—Se3^xi	42.872 (10)	In1^iv—Se3—Se4^v	45.298 (13)
Crⁱⁱ—In1—Se3^xii	137.128 (10)	In1^iv—Se3—Se4^vi	92.907 (19)
Crⁱⁱ—In1—Se3^xiii	42.872 (10)	In1^vii—Se3—Cr^iv	94.256 (19)
In3^x—In1—In3^xi	65.105 (9)	In1^vii—Se3—Cr^vii	0.0 (5)
In3^x—In1—In3^xii	114.895 (9)	In1^vii—Se3—In2ⁱⁱⁱ	132.673 (10)
In3^x—In1—In3^xiii	180.0 (5)	In1^vii—Se3—In3^xv	87.929 (17)
In3^x—In1—Se3^x	85.411 (15)	In1^vii—Se3—Se1^iv	152.58 (2)
In3^x—In1—Se3^xi	135.128 (16)	In1^vii—Se3—Se1^vii	94.758 (12)
In3^x—In1—Se3^xii	44.872 (16)	In1^vii—Se3—Se2^iv	146.30 (2)
In3^x—In1—Se3^xiii	94.589 (15)	In1^vii—Se3—Se2^vii	95.340 (12)
In3^x—In1—Se4^xiv	134.936 (11)	In1^vii—Se3—Se3ⁱ	137.128 (19)
In3^x—In1—Se4^viii	45.064 (11)	In1^vii—Se3—Se3ⁱⁱ	42.872 (9)
In3^xi—In1—In3^xii	180.0 (5)	In1^vii—Se3—Se3^xv	47.128 (10)
In3^xi—In1—In3^xiii	114.895 (9)	In1^vii—Se3—Se4^xvi	93.072 (18)
In3^xi—In1—Se3^x	135.128 (16)	In1^vii—Se3—Se4^xvii	45.411 (12)
In3^xi—In1—Se3^xi	85.411 (15)	In1^vii—Se3—Se4^v	92.907 (19)
In3^xi—In1—Se3^xii	94.589 (15)	In1^vii—Se3—Se4^vi	45.298 (13)
In3^xi—In1—Se3^xiii	44.872 (16)	Cr^iv—Se3—Cr^vii	94.256 (19)
In3^xi—In1—Se4^xiv	134.936 (11)	Cr^iv—Se3—In2ⁱⁱⁱ	132.673 (10)
In3^xi—In1—Se4^viii	45.064 (11)	Cr^iv—Se3—In3^xv	87.929 (17)
In3^xii—In1—In3^xiii	65.105 (9)	Cr^iv—Se3—Se1^iv	94.758 (12)
In3^xii—In1—Se3^x	44.872 (16)	Cr^iv—Se3—Se1^vii	152.58 (2)
In3^xii—In1—Se3^xi	94.589 (15)	Cr^iv—Se3—Se2^iv	95.340 (12)
In3^xii—In1—Se3^xii	85.411 (15)	Cr^iv—Se3—Se2^vii	146.30 (2)
In3^xii—In1—Se3^xiii	135.128 (16)	Cr^iv—Se3—Se3ⁱ	42.872 (9)
In3^xii—In1—Se4^xiv	45.064 (11)	Cr^iv—Se3—Se3ⁱⁱ	137.128 (19)
In3^xii—In1—Se4^viii	134.936 (11)	Cr^iv—Se3—Se3^xv	47.128 (10)
In3^xiii—In1—Se3^x	94.589 (15)	Cr^iv—Se3—Se4^xvi	45.411 (12)
In3^xiii—In1—Se3^xi	44.872 (16)	Cr^iv—Se3—Se4^xvii	93.072 (18)
In3^xiii—In1—Se3^xii	135.128 (16)	Cr^iv—Se3—Se4^v	45.298 (13)
In3^xiii—In1—Se3^xiii	85.411 (15)	Cr^iv—Se3—Se4^vi	92.907 (19)
In3^xiii—In1—Se4^xiv	45.064 (11)	Cr^vii—Se3—In2ⁱⁱⁱ	132.673 (10)
In3^xiii—In1—Se4^viii	134.936 (11)	Cr^vii—Se3—In3^xv	87.929 (17)
Se3^x—In1—Se3^xi	94.256 (15)	Cr^vii—Se3—Se1^iv	152.58 (2)
Se3^x—In1—Se3^xii	85.744 (15)	Cr^vii—Se3—Se1^vii	94.758 (12)
Se3^x—In1—Se3^xiii	180.0 (5)	Cr^vii—Se3—Se2^iv	146.30 (2)
Se3^x—In1—Se4^xiv	89.889 (17)	Cr^vii—Se3—Se2^vii	95.340 (12)
Se3^x—In1—Se4^viii	90.111 (17)	Cr^vii—Se3—Se3ⁱ	137.128 (19)
Se3^xi—In1—Se3^xii	180.0 (5)	Cr^vii—Se3—Se3ⁱⁱ	42.872 (9)
Se3^xi—In1—Se3^xiii	85.744 (15)	Cr^vii—Se3—Se3^xv	47.128 (10)
Se3^xi—In1—Se4^xiv	89.889 (17)	Cr^vii—Se3—Se4^xvi	93.072 (18)
Se3^xi—In1—Se4^viii	90.111 (17)	Cr^vii—Se3—Se4^xvii	45.411 (12)
Se3^xii—In1—Se3^xiii	94.256 (15)	Cr^vii—Se3—Se4^v	92.907 (19)
Se3^xii—In1—Se4^xiv	90.111 (17)	Cr^vii—Se3—Se4^vi	45.298 (13)
Se3^xii—In1—Se4^viii	89.889 (17)	In2ⁱⁱⁱ—Se3—In3^xv	98.01 (3)
Se3^xiii—In1—Se4^xiv	90.111 (17)	In2ⁱⁱⁱ—Se3—Se1^iv	47.708 (13)
Se3^xiii—In1—Se4^viii	89.889 (17)	In2ⁱⁱⁱ—Se3—Se1^vii	47.708 (13)
In1ⁱ—Cr—In3^x	57.447 (5)	In2ⁱⁱⁱ—Se3—Se2^iv	43.670 (13)
In1ⁱ—Cr—In3^xi	122.553 (5)	In2ⁱⁱⁱ—Se3—Se2^vii	43.670 (13)
In1ⁱ—Cr—In3^xii	57.447 (5)	In2ⁱⁱⁱ—Se3—Se3ⁱ	90.000 (11)
In1ⁱ—Cr—In3^xiii	122.553 (5)	In2ⁱⁱⁱ—Se3—Se3ⁱⁱ	90.000 (11)
In1ⁱ—Cr—Se3^x	42.872 (10)	In2ⁱⁱⁱ—Se3—Se3^xv	175.04 (3)
In1ⁱ—Cr—Se3^xi	137.128 (10)	In2ⁱⁱⁱ—Se3—Se4^xvi	122.44 (2)
In1ⁱ—Cr—Se3^xii	42.872 (10)	In2ⁱⁱⁱ—Se3—Se4^xvii	122.44 (2)
In1ⁱ—Cr—Se3^xiii	137.128 (10)	In2ⁱⁱⁱ—Se3—Se4^v	114.61 (2)
In1ⁱⁱ—Cr—In3^x	122.553 (5)	In2ⁱⁱⁱ—Se3—Se4^vi	114.61 (2)
In1ⁱⁱ—Cr—In3^xi	57.447 (5)	In3^xv—Se3—Se1^iv	66.595 (18)
In1ⁱⁱ—Cr—In3^xii	122.553 (5)	In3^xv—Se3—Se1^vii	66.595 (18)
In1ⁱⁱ—Cr—In3^xiii	57.447 (5)	In3^xv—Se3—Se2^iv	124.62 (2)
In1ⁱⁱ—Cr—Se3^x	137.128 (10)	In3^xv—Se3—Se2^vii	124.62 (2)
In1ⁱⁱ—Cr—Se3^xi	42.872 (10)	In3^xv—Se3—Se3ⁱ	90.000 (14)
In1ⁱⁱ—Cr—Se3^xii	137.128 (10)	In3^xv—Se3—Se3ⁱⁱ	90.000 (14)
In1ⁱⁱ—Cr—Se3^xiii	42.872 (10)	In3^xv—Se3—Se3^xv	86.96 (2)
Crⁱ—Cr—Crⁱⁱ	180.0 (5)	In3^xv—Se3—Se4^xvi	42.569 (14)
Crⁱ—Cr—In3^x	57.447 (5)	In3^xv—Se3—Se4^xvii	42.569 (14)
Crⁱ—Cr—In3^xi	122.553 (5)	In3^xv—Se3—Se4^v	133.180 (18)
Crⁱ—Cr—In3^xii	57.447 (5)	In3^xv—Se3—Se4^vi	133.180 (18)
Crⁱ—Cr—In3^xiii	122.553 (5)	Se1^iv—Se3—Se1^vii	66.594 (15)
Crⁱ—Cr—Se3^x	42.872 (10)	Se1^iv—Se3—Se2^iv	58.029 (16)
Crⁱ—Cr—Se3^xi	137.128 (10)	Se1^iv—Se3—Se2^vii	91.374 (18)
Crⁱ—Cr—Se3^xii	42.872 (10)	Se1^iv—Se3—Se3ⁱ	56.703 (12)
Crⁱ—Cr—Se3^xiii	137.128 (10)	Se1^iv—Se3—Se3ⁱⁱ	123.297 (18)
Crⁱⁱ—Cr—In3^x	122.553 (5)	Se1^iv—Se3—Se3^xv	135.502 (16)
Crⁱⁱ—Cr—In3^xi	57.447 (5)	Se1^iv—Se3—Se4^xvi	75.321 (16)
Crⁱⁱ—Cr—In3^xii	122.553 (5)	Se1^iv—Se3—Se4^xvii	108.22 (2)
Crⁱⁱ—Cr—In3^xiii	57.447 (5)	Se1^iv—Se3—Se4^v	111.678 (12)
Crⁱⁱ—Cr—Se3^x	137.128 (10)	Se1^iv—Se3—Se4^vi	159.11 (2)
Crⁱⁱ—Cr—Se3^xi	42.872 (10)	Se1^vii—Se3—Se2^iv	91.374 (18)
Crⁱⁱ—Cr—Se3^xii	137.128 (10)	Se1^vii—Se3—Se2^vii	58.029 (16)
Crⁱⁱ—Cr—Se3^xiii	42.872 (10)	Se1^vii—Se3—Se3ⁱ	123.297 (18)
In3^x—Cr—In3^xi	65.105 (9)	Se1^vii—Se3—Se3ⁱⁱ	56.703 (12)
In3^x—Cr—In3^xii	114.895 (9)	Se1^vii—Se3—Se3^xv	135.502 (16)
In3^x—Cr—In3^xiii	180.0 (5)	Se1^vii—Se3—Se4^xvi	108.22 (2)
In3^x—Cr—Se3^x	85.411 (15)	Se1^vii—Se3—Se4^xvii	75.321 (16)
In3^x—Cr—Se3^xi	135.128 (16)	Se1^vii—Se3—Se4^v	159.11 (2)
In3^x—Cr—Se3^xii	44.872 (16)	Se1^vii—Se3—Se4^vi	111.678 (12)
In3^x—Cr—Se3^xiii	94.589 (15)	Se2^iv—Se3—Se2^vii	60.542 (13)
In3^x—Cr—Se4^xiv	134.936 (11)	Se2^iv—Se3—Se3ⁱ	59.729 (11)
In3^x—Cr—Se4^viii	45.064 (11)	Se2^iv—Se3—Se3ⁱⁱ	120.271 (16)
In3^xi—Cr—In3^xii	180.0 (5)	Se2^iv—Se3—Se3^xv	132.827 (19)
In3^xi—Cr—In3^xiii	114.895 (9)	Se2^iv—Se3—Se4^xvi	116.325 (11)
In3^xi—Cr—Se3^x	135.128 (16)	Se2^iv—Se3—Se4^xvii	164.40 (2)
In3^xi—Cr—Se3^xi	85.411 (15)	Se2^iv—Se3—Se4^v	71.825 (16)
In3^xi—Cr—Se3^xii	94.589 (15)	Se2^iv—Se3—Se4^vi	101.93 (2)
In3^xi—Cr—Se3^xiii	44.872 (16)	Se2^vii—Se3—Se3ⁱ	120.271 (16)
In3^xi—Cr—Se4^xiv	134.936 (11)	Se2^vii—Se3—Se3ⁱⁱ	59.729 (11)
In3^xi—Cr—Se4^viii	45.064 (11)	Se2^vii—Se3—Se3^xv	132.827 (19)
In3^xii—Cr—In3^xiii	65.105 (9)	Se2^vii—Se3—Se4^xvi	164.40 (2)
In3^xii—Cr—Se3^x	44.872 (16)	Se2^vii—Se3—Se4^xvii	116.325 (11)
In3^xii—Cr—Se3^xi	94.589 (15)	Se2^vii—Se3—Se4^v	101.93 (2)
In3^xii—Cr—Se3^xii	85.411 (15)	Se2^vii—Se3—Se4^vi	71.825 (16)
In3^xii—Cr—Se3^xiii	135.128 (16)	Se3ⁱ—Se3—Se3ⁱⁱ	180.0 (5)
In3^xii—Cr—Se4^xiv	45.064 (11)	Se3ⁱ—Se3—Se3^xv	90.000 (12)
In3^xii—Cr—Se4^viii	134.936 (11)	Se3ⁱ—Se3—Se4^xvi	58.969 (11)
In3^xiii—Cr—Se3^x	94.589 (15)	Se3ⁱ—Se3—Se4^xvii	121.031 (17)
In3^xiii—Cr—Se3^xi	44.872 (16)	Se3ⁱ—Se3—Se4^v	59.036 (12)
In3^xiii—Cr—Se3^xii	135.128 (16)	Se3ⁱ—Se3—Se4^vi	120.964 (19)
In3^xiii—Cr—Se3^xiii	85.411 (15)	Se3ⁱⁱ—Se3—Se3^xv	90.000 (12)
In3^xiii—Cr—Se4^xiv	45.064 (11)	Se3ⁱⁱ—Se3—Se4^xvi	121.031 (17)
In3^xiii—Cr—Se4^viii	134.936 (11)	Se3ⁱⁱ—Se3—Se4^xvii	58.969 (11)
Se3^x—Cr—Se3^xi	94.256 (15)	Se3ⁱⁱ—Se3—Se4^v	120.964 (19)
Se3^x—Cr—Se3^xii	85.744 (15)	Se3ⁱⁱ—Se3—Se4^vi	59.036 (12)
Se3^x—Cr—Se3^xiii	180.0 (5)	Se3^xv—Se3—Se4^xvi	61.541 (16)
Se3^x—Cr—Se4^xiv	89.889 (17)	Se3^xv—Se3—Se4^xvii	61.541 (16)
Se3^x—Cr—Se4^viii	90.111 (17)	Se3^xv—Se3—Se4^v	61.336 (16)
Se3^xi—Cr—Se3^xii	180.0 (5)	Se3^xv—Se3—Se4^vi	61.336 (16)
Se3^xi—Cr—Se3^xiii	85.744 (15)	Se4^xvi—Se3—Se4^xvii	62.063 (14)
Se3^xi—Cr—Se4^xiv	89.889 (17)	Se4^xvi—Se3—Se4^v	90.709 (15)
Se3^xi—Cr—Se4^viii	90.111 (17)	Se4^xvi—Se3—Se4^vi	122.88 (2)
Se3^xii—Cr—Se3^xiii	94.256 (15)	Se4^xvii—Se3—Se4^v	122.88 (2)
Se3^xii—Cr—Se4^xiv	90.111 (17)	Se4^xvii—Se3—Se4^vi	90.709 (15)
Se3^xii—Cr—Se4^viii	89.889 (17)	Se4^v—Se3—Se4^vi	61.929 (14)
Se3^xiii—Cr—Se4^xiv	90.111 (17)	Tl1^x—Se4—Tl1^xi	72.644 (18)
Se3^xiii—Cr—Se4^viii	89.889 (17)	Tl1^x—Se4—Tl1^v	26.78 (3)
In2ⁱ—In2—In2^v	57.450 (8)	Tl1^x—Se4—Tl1^vi	78.44 (2)
In2ⁱ—In2—In2^vi	122.550 (12)	Tl1^x—Se4—Tl2ⁱ	13.482 (18)
In2ⁱ—In2—Se1^v	43.568 (12)	Tl1^x—Se4—Tl2	75.169 (16)
In2ⁱ—In2—Se1^vi	136.432 (19)	Tl1^x—Se4—In1^xviii	105.91 (3)
In2ⁱ—In2—Se2^v	43.241 (14)	Tl1^x—Se4—Cr^xviii	105.91 (3)
In2ⁱ—In2—Se2^vi	136.76 (2)	Tl1^x—Se4—In3^v	93.230 (15)
In2ⁱ—In2—Se3ⁱⁱⁱ	90.000 (9)	Tl1^x—Se4—In3^vi	162.86 (3)
In2ⁱⁱ—In2—In2^v	122.550 (12)	Tl1^x—Se4—Se2	78.09 (2)
In2ⁱⁱ—In2—In2^vi	57.450 (8)	Tl1^x—Se4—Se3^xix	104.602 (16)
In2ⁱⁱ—In2—Se1^v	136.432 (19)	Tl1^x—Se4—Se3^xx	149.63 (3)
In2ⁱⁱ—In2—Se1^vi	43.568 (12)	Tl1^x—Se4—Se3^v	61.88 (2)
In2ⁱⁱ—In2—Se2^v	136.76 (2)	Tl1^x—Se4—Se3^vi	97.94 (2)
In2ⁱⁱ—In2—Se2^vi	43.241 (14)	Tl1^x—Se4—Se4ⁱ	53.678 (12)
In2^v—In2—In2^vi	65.100 (11)	Tl1^x—Se4—Se4ⁱⁱ	126.322 (19)
In2^v—In2—Se1^v	95.040 (13)	Tl1^xi—Se4—Tl1^v	78.44 (2)
In2^v—In2—Se1^vi	150.17 (2)	Tl1^xi—Se4—Tl1^vi	26.78 (3)
In2^v—In2—Se2	47.491 (14)	Tl1^xi—Se4—Tl2ⁱ	75.169 (16)
In2^v—In2—Se2^v	46.041 (16)	Tl1^xi—Se4—Tl2	13.482 (18)
In2^v—In2—Se2^vi	95.149 (19)	Tl1^xi—Se4—In1^xviii	105.91 (3)
In2^v—In2—Se3ⁱⁱⁱ	132.304 (17)	Tl1^xi—Se4—Cr^xviii	105.91 (3)
In2^vi—In2—Se1^v	150.17 (2)	Tl1^xi—Se4—In3^v	162.86 (3)
In2^vi—In2—Se1^vi	95.040 (13)	Tl1^xi—Se4—In3^vi	93.230 (15)
In2^vi—In2—Se2	47.491 (14)	Tl1^xi—Se4—Se2	78.09 (2)
In2^vi—In2—Se2^v	95.149 (19)	Tl1^xi—Se4—Se3^xix	149.63 (3)
In2^vi—In2—Se2^vi	46.041 (16)	Tl1^xi—Se4—Se3^xx	104.602 (16)
In2^vi—In2—Se3ⁱⁱⁱ	132.304 (17)	Tl1^xi—Se4—Se3^v	97.94 (2)
Se1^v—In2—Se1^vi	92.86 (2)	Tl1^xi—Se4—Se3^vi	61.88 (2)
Se1^v—In2—Se2	102.70 (2)	Tl1^xi—Se4—Se4ⁱ	126.322 (19)
Se1^v—In2—Se2^v	84.510 (16)	Tl1^xi—Se4—Se4ⁱⁱ	53.678 (12)
Se1^v—In2—Se2^vi	163.74 (3)	Tl1^v—Se4—Tl1^vi	71.529 (18)
Se1^v—In2—Se3ⁱⁱⁱ	77.503 (18)	Tl1^v—Se4—Tl2ⁱ	13.300 (18)
Se1^vi—In2—Se2	102.70 (2)	Tl1^v—Se4—Tl2	74.560 (17)
Se1^vi—In2—Se2^v	163.74 (3)	Tl1^v—Se4—In1^xviii	130.51 (2)
Se1^vi—In2—Se2^vi	84.510 (16)	Tl1^v—Se4—Cr^xviii	130.51 (2)
Se1^vi—In2—Se3ⁱⁱⁱ	77.503 (18)	Tl1^v—Se4—In3^v	84.600 (17)
Se2—In2—Se2^v	93.53 (2)	Tl1^v—Se4—In3^vi	142.48 (3)
Se2—In2—Se2^vi	93.53 (2)	Tl1^v—Se4—Se2	52.84 (2)
Se2—In2—Se3ⁱⁱⁱ	179.70 (3)	Tl1^v—Se4—Se3^xix	113.150 (12)
Se2^v—In2—Se2^vi	93.52 (2)	Tl1^v—Se4—Se3^xx	174.69 (2)
Se2^v—In2—Se3ⁱⁱⁱ	86.26 (2)	Tl1^v—Se4—Se3^v	85.96 (2)
Se2^vi—In2—Se3ⁱⁱⁱ	86.26 (2)	Tl1^v—Se4—Se3^vi	122.07 (3)
In1^iv—In3—In1^vii	65.105 (11)	Tl1^v—Se4—Se4ⁱ	54.236 (13)
In1^iv—In3—Cr^iv	0.0 (5)	Tl1^v—Se4—Se4ⁱⁱ	125.764 (19)
In1^iv—In3—Cr^vii	65.105 (11)	Tl1^vi—Se4—Tl2ⁱ	74.560 (17)
In1^iv—In3—In3ⁱ	57.447 (8)	Tl1^vi—Se4—Tl2	13.300 (18)
In1^iv—In3—In3ⁱⁱ	122.553 (14)	Tl1^vi—Se4—In1^xviii	130.51 (2)
In1^iv—In3—Se1	146.097 (7)	Tl1^vi—Se4—Cr^xviii	130.51 (2)
In1^iv—In3—Se1^xii	81.246 (13)	Tl1^vi—Se4—In3^v	142.48 (3)
In1^iv—In3—Se1^xiii	117.067 (18)	Tl1^vi—Se4—In3^vi	84.600 (17)
In1^iv—In3—Se3^xv	47.199 (12)	Tl1^vi—Se4—Se2	52.84 (2)
In1^iv—In3—Se4^v	47.930 (17)	Tl1^vi—Se4—Se3^xix	174.69 (2)
In1^iv—In3—Se4^vi	98.44 (2)	Tl1^vi—Se4—Se3^xx	113.150 (12)
In1^vii—In3—Cr^iv	65.105 (11)	Tl1^vi—Se4—Se3^v	122.07 (3)
In1^vii—In3—Cr^vii	0.0 (5)	Tl1^vi—Se4—Se3^vi	85.96 (2)
In1^vii—In3—In3ⁱ	122.553 (14)	Tl1^vi—Se4—Se4ⁱ	125.764 (19)
In1^vii—In3—In3ⁱⁱ	57.447 (8)	Tl1^vi—Se4—Se4ⁱⁱ	54.236 (13)
In1^vii—In3—Se1	146.097 (7)	Tl2ⁱ—Se4—Tl2	74.429 (15)
In1^vii—In3—Se1^xii	117.067 (18)	Tl2ⁱ—Se4—In1^xviii	118.427 (18)
In1^vii—In3—Se1^xiii	81.246 (13)	Tl2ⁱ—Se4—Cr^xviii	118.427 (18)
In1^vii—In3—Se3^xv	47.199 (12)	Tl2ⁱ—Se4—In3^v	88.858 (13)
In1^vii—In3—Se4^v	98.44 (2)	Tl2ⁱ—Se4—In3^vi	153.93 (3)
In1^vii—In3—Se4^vi	47.930 (17)	Tl2ⁱ—Se4—Se2	65.299 (14)
Cr^iv—In3—Cr^vii	65.105 (11)	Tl2ⁱ—Se4—Se3^xix	109.398 (10)
Cr^iv—In3—In3ⁱ	57.447 (8)	Tl2ⁱ—Se4—Se3^xx	162.88 (2)
Cr^iv—In3—In3ⁱⁱ	122.553 (14)	Tl2ⁱ—Se4—Se3^v	73.913 (13)
Cr^iv—In3—Se1	146.097 (7)	Tl2ⁱ—Se4—Se3^vi	110.197 (19)
Cr^iv—In3—Se1^xii	81.246 (13)	Tl2ⁱ—Se4—Se4ⁱ	52.785 (10)
Cr^iv—In3—Se1^xiii	117.067 (18)	Tl2ⁱ—Se4—Se4ⁱⁱ	127.215 (17)
Cr^iv—In3—Se3^xv	47.199 (12)	Tl2—Se4—In1^xviii	118.427 (18)
Cr^iv—In3—Se4^v	47.930 (17)	Tl2—Se4—Cr^xviii	118.427 (18)
Cr^iv—In3—Se4^vi	98.44 (2)	Tl2—Se4—In3^v	153.93 (3)
Cr^vii—In3—In3ⁱ	122.553 (14)	Tl2—Se4—In3^vi	88.858 (13)
Cr^vii—In3—In3ⁱⁱ	57.447 (8)	Tl2—Se4—Se2	65.299 (14)
Cr^vii—In3—Se1	146.097 (7)	Tl2—Se4—Se3^xix	162.88 (2)
Cr^vii—In3—Se1^xii	117.067 (18)	Tl2—Se4—Se3^xx	109.398 (10)
Cr^vii—In3—Se1^xiii	81.246 (13)	Tl2—Se4—Se3^v	110.197 (19)
Cr^vii—In3—Se3^xv	47.199 (12)	Tl2—Se4—Se3^vi	73.913 (13)
Cr^vii—In3—Se4^v	98.44 (2)	Tl2—Se4—Se4ⁱ	127.215 (17)
Cr^vii—In3—Se4^vi	47.930 (17)	Tl2—Se4—Se4ⁱⁱ	52.785 (10)
In3ⁱ—In3—In3ⁱⁱ	180.0 (5)	In1^xviii—Se4—Cr^xviii	0.0 (5)
In3ⁱ—In3—Se1^xii	55.649 (9)	In1^xviii—Se4—In3^v	87.01 (2)
In3ⁱ—In3—Se1^xiii	124.351 (13)	In1^xviii—Se4—In3^vi	87.01 (2)
In3ⁱ—In3—Se4^v	40.619 (12)	In1^xviii—Se4—Se2	174.94 (2)
In3ⁱ—In3—Se4^vi	139.381 (18)	In1^xviii—Se4—Se3^xix	44.701 (13)
In3ⁱⁱ—In3—Se1^xii	124.351 (13)	In1^xviii—Se4—Se3^xx	44.701 (13)
In3ⁱⁱ—In3—Se1^xiii	55.649 (9)	In1^xviii—Se4—Se3^v	44.590 (12)
In3ⁱⁱ—In3—Se4^v	139.381 (18)	In1^xviii—Se4—Se3^vi	44.590 (12)
In3ⁱⁱ—In3—Se4^vi	40.619 (12)	In1^xviii—Se4—Se4ⁱ	90.000 (14)
Se1—In3—Se1^xii	71.494 (18)	In1^xviii—Se4—Se4ⁱⁱ	90.000 (14)
Se1—In3—Se1^xiii	71.494 (18)	Cr^xviii—Se4—In3^v	87.01 (2)
Se1—In3—Se3^xv	133.67 (3)	Cr^xviii—Se4—In3^vi	87.01 (2)
Se1—In3—Se4^v	113.92 (2)	Cr^xviii—Se4—Se2	174.94 (2)
Se1—In3—Se4^vi	113.92 (2)	Cr^xviii—Se4—Se3^xix	44.701 (13)
Se1^xii—In3—Se1^xiii	68.701 (13)	Cr^xviii—Se4—Se3^xx	44.701 (13)
Se1^xii—In3—Se3^xv	70.606 (18)	Cr^xviii—Se4—Se3^v	44.590 (12)
Se1^xii—In3—Se4^v	95.083 (14)	Cr^xviii—Se4—Se3^vi	44.590 (12)
Se1^xii—In3—Se4^vi	160.95 (2)	Cr^xviii—Se4—Se4ⁱ	90.000 (14)
Se1^xiii—In3—Se3^xv	70.606 (18)	Cr^xviii—Se4—Se4ⁱⁱ	90.000 (14)
Se1^xiii—In3—Se4^v	160.95 (2)	In3^v—Se4—In3^vi	98.76 (2)
Se1^xiii—In3—Se4^vi	95.083 (14)	In3^v—Se4—Se2	89.70 (2)
Se3^xv—In3—Se4^v	95.08 (2)	In3^v—Se4—Se3^xix	42.356 (17)
Se3^xv—In3—Se4^vi	95.08 (2)	In3^v—Se4—Se3^xx	92.50 (2)
Se4^v—In3—Se4^vi	98.76 (2)	In3^v—Se4—Se3^v	83.236 (17)
In2^v—Se1—In2^vi	92.86 (2)	In3^v—Se4—Se3^vi	131.55 (3)
In2^v—Se1—In3	112.287 (19)	In3^v—Se4—Se4ⁱ	40.619 (12)
In2^v—Se1—In3^xii	84.802 (14)	In3^v—Se4—Se4ⁱⁱ	139.38 (2)
In2^v—Se1—In3^xiii	136.64 (2)	In3^vi—Se4—Se2	89.70 (2)
In2^v—Se1—Se1ⁱ	43.568 (12)	In3^vi—Se4—Se3^xix	92.50 (2)
In2^v—Se1—Se1ⁱⁱ	136.43 (2)	In3^vi—Se4—Se3^xx	42.356 (17)
In2^v—Se1—Se1^xii	100.184 (12)	In3^vi—Se4—Se3^v	131.55 (3)
In2^v—Se1—Se1^xiii	166.119 (16)	In3^vi—Se4—Se3^vi	83.236 (17)
In2^v—Se1—Se2	47.575 (13)	In3^vi—Se4—Se4ⁱ	139.38 (2)
In2^v—Se1—Se3^x	54.788 (16)	In3^vi—Se4—Se4ⁱⁱ	40.619 (12)
In2^v—Se1—Se3^xi	102.65 (2)	Se2—Se4—Se3^xix	131.745 (18)
In2^vi—Se1—In3	112.287 (19)	Se2—Se4—Se3^xx	131.745 (18)
In2^vi—Se1—In3^xii	136.64 (2)	Se2—Se4—Se3^v	138.720 (15)
In2^vi—Se1—In3^xiii	84.802 (14)	Se2—Se4—Se3^vi	138.720 (15)
In2^vi—Se1—Se1ⁱ	136.43 (2)	Se2—Se4—Se4ⁱ	90.000 (14)
In2^vi—Se1—Se1ⁱⁱ	43.568 (12)	Se2—Se4—Se4ⁱⁱ	90.000 (14)
In2^vi—Se1—Se1^xii	166.119 (16)	Se3^xix—Se4—Se3^xx	62.063 (14)
In2^vi—Se1—Se1^xiii	100.184 (12)	Se3^xix—Se4—Se3^v	57.123 (15)
In2^vi—Se1—Se2	47.575 (13)	Se3^xix—Se4—Se3^vi	89.291 (19)
In2^vi—Se1—Se3^x	102.65 (2)	Se3^xix—Se4—Se4ⁱ	58.969 (12)
In2^vi—Se1—Se3^xi	54.788 (16)	Se3^xix—Se4—Se4ⁱⁱ	121.031 (18)
In3—Se1—In3^xii	108.51 (2)	Se3^xx—Se4—Se3^v	89.291 (19)
In3—Se1—In3^xiii	108.51 (2)	Se3^xx—Se4—Se3^vi	57.123 (15)
In3—Se1—Se1^xiii	67.047 (18)	Se3^xx—Se4—Se4ⁱ	121.031 (18)
In3—Se1—Se2	135.19 (2)	Se3^xx—Se4—Se4ⁱⁱ	58.969 (12)
In3—Se1—Se3^x	143.728 (13)	Se3^v—Se4—Se3^vi	61.929 (14)
In3—Se1—Se3^xi	143.728 (13)	Se3^v—Se4—Se4ⁱ	59.036 (13)
In3^xii—Se1—In3^xiii	68.701 (13)	Se3^v—Se4—Se4ⁱⁱ	120.964 (19)
In3^xii—Se1—Se1ⁱ	55.649 (10)	Se3^vi—Se4—Se4ⁱ	120.964 (19)
In3^xii—Se1—Se1ⁱⁱ	124.351 (15)	Se3^vi—Se4—Se4ⁱⁱ	59.036 (13)
In3^xii—Se1—Se1^xii	41.459 (14)	Se4ⁱ—Se4—Se4ⁱⁱ	180.0 (5)

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

Funding information

Funding for this research was provided by: Agence Nationale de la Recherche, program Investissements d'Avenir, LabEx EMC3 (award No. ANR-10-LABX-09–01).

References

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