Occupational disorder of cobalt and indium in the crystal structure of Co5In3SbSi2O16

Wolflehner, T.; Weil, M.

doi:10.1107/S2056989026010960

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ISSN: 2056-9890

Volume 82| Part 11| November 2026| Pages 1338-1341

https://doi.org/10.1107/S2056989026010960

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Occupational disorder of cobalt and indium in the crystal structure of Co₅In₃SbSi₂O₁₆

Tobias Wolflehner ^a and Matthias Weil ^a ^*

^aInstitute for Chemical Technologies and Analytics, Division of Applied Solid State Chemistry, Getreidemarkt 9/E164-05-1, 1060 Vienna, Austria
^*Correspondence e-mail: [email protected]

Edited by W. T. A. Harrison, University of Aberdeen, United Kingdom (Received 8 October 2026; accepted 21 October 2026; online 23 October 2026)

Pentacobalt(II) triindium(III) antimony(V) disilicon(VI) hexadecaoxide, Co₅In₃SbSi₂O₁₆, was obtained as a single-crystalline by-product through a reaction with the silica glass ampoule during a chemical vapor transport reaction. It crystallizes isotypically with Co₈TeAs₂O₁₆ in space group Cmce, with two (out of four) Co sites co-occupied by In, the Te site replaced by Sb, and the As site replaced by Si. The crystal structure of Co₅In₃SbSi₂O₁₆ consists of [CoO₆], [(In,Co)O₆], and [SbO₆] octahedra, and [CoO₄] and [SiO₄] tetrahedra, fused by vertex- and edge-sharing into a complex three-dimensional framework.

Keywords: crystal structure; co-occupation; isotypism; framework structure; structure comparison.

CCDC reference: 2597010

1. Chemical context

First-row divalent transition-metal (M^II) antimonates with composition M₂InSbO₆ have a corundum-related crystal structure and exhibit interesting magnetic properties, including frustrated magnetism for Mn₂InSbO₆ (Ivanov et al., 2011 ), long-range incommensurate antiferromagnetic order at low temperatures for Ni₂InSbO₆ (Ivanov et al., 2013 ), or, depending on the modification of Co₂InSbO₆, a sharp ferrimagnetic transition at 65 K (Ji et al., 2022 ). The relevant materials were produced as powder samples via solid-state reactions, either at normal pressure (M = Ni, Mn) or under high-pressure conditions (M = Co). Since chemical vapour transport reactions (Binnewies et al., 2012 ) had been successfully applied for single crystal growth of Ni₂InSbO₆ in the millimetre size range (Weil et al., 2014 ), an attempt was made to apply this method to crystal growth of Co₂InSbO₆. The crystals obtained during one of these experiments did not have the desired composition, but also contained silicon as an additional element, which resulted from a reaction with the silica glass ampoule. This article reports on the corresponding crystal structure of Co₅In₃SbSi₂O₁₆, (I).

2. Structural commentary

Compound (I) is isotypic with Co₈TeAs₂O₁₆ (Staack & Müller-Buschbaum, 1997 ). It comprises two Co sites (Co1: multiplicity 8, Wyckoff letter f, site symmetry m..; Co2: 8 e, .2.), two mixed-occupied (In/Co) sites (In1/Co3: 8 f; In2/Co4: 8 e), one Si (Si1: 8 f), one Sb (Sb1: 4 a, 2/m..) and six O sites (O2–O5: 8 f; O1, O6: 16 g, 1) in the asymmetric unit. Compared with Co₈TeAs₂O₁₆, sites Co3 and Co4 of Co₅In₃SbSi₂O₁₆ are co-occupied by In, the Te site is replaced by Sb, and the As site by Si. Co-occupation of sites by Co and In was also observed for different modifications of Co₂InSbO₆ (Ji et al., 2022) or Co₂InBO₅ and Co_3–xIn_xBO₅ solid solutions (Cai et al., 2014 ).

The principal building units in the crystal structure of (I) are [Co1O₄] and [Si1O₄] tetrahedra and [Co2O₆], [(In1,Co3)O₆], [(In2,Co4)O₆] and [Sb1O₆] octahedra. Ranges and averages of bond lengths in these polyhedra comply with literature values and are summarized in Table 1.

Table 1
Details of the coordination by O atoms around the metal cations and results of BVS calculations

Site	Coordination number	Range of bond lengths (Å)	Mean bond length (Å)	Mean bond length (literature value) (Å)	BVS (valence units)
Co1	4	1.977 (2)–1.997 (3)	1.984	1.967 (22)^c	1.86
Co2	6	2.128 (2)–2.1913 (19)	2.147	2.108 (62)^c	1.82
(In1,Co3)^a	6	2.078 (3)–2.2745 (19)	2.156	Co 2.108 (62)^c, In 2.142 (42)^d	2.73
(In2,Co4)^b	6	2.084 (2)–2.219 (2)	2.137	Co 2.108 (62)^c, In 2.142 (42)^d	2.53
Sb1	6	1.9818 (19)–1.989 (3)	1.984	1.977 (34)^d	4.94
Si1	4	1.622 (3)–1.648 (3)	1.630	1.625 (24)^d	3.94
O1	4 [2Co+Sb+(In,Co)]				1.93
O2	3 [Si+Co+(In,Co)]				1.96
O3	3 [Si+2(In,Co)]				1.97
O4	5 [2Co+3(In,Co)]				1.80
O5	4 (Sb+3Co)				1.90
O6	3 [Si+2(In,Co)]				1.93
Notes: (a) In:Co ratio 0.9:0.1; (b) In:Co ratio 0.6:0.4; (c) Gagné & Hawthorne (2020 ); (d) Gagné & Hawthorne (2018 ).

The rather complex crystal structure of (I) is made up from vertex- and edge-sharing of the building units and is displayed in Fig. 1. As the structural details have already been discussed at length in connection with isotypic Co₈TeAs₂O₁₆ (Staack & Müller-Buschbaum, 1997), we will limit ourselves to the most notable features: The [Sb1O₆] octahedra are isolated from others, and a {Co1Si1O₇} double tetrahedron is formed via a bridging O atom (O2) and is also isolated from other double tetrahedra. These entities are linked by [100] chains of edge-sharing [CoO₆] and [(In,Co)O₆] octahedra into a framework structure; a fragment of this is shown in Fig. 2.

Figure 1
Polyhedral representation of the crystal structure of (I) in a view along [ $[\overline{1}]$ 00]. Displacement ellipsoids are represented at the 90% probability level. Colour codes for polyhedra: Co in tetrahedral coordination is turquoise, Co2 in octahedral coordination is blue, mixed (In,Co) sites in octahedral coordination are pink, antimonate octahedra are green and silicate tetrahedra are red.

Figure 2
Fragment of the crystal structure showing the {Co1Si1O₇} double tetrahedron linked to [(In2,Co4)O₆] and [Co2O₆] octahedra. Displacement ellipsoids are as in Fig. 1

. [Symmetry codes: (i) x − $[{1\over 2}]$ , y + $[{1\over 2}]$ , z; (ii) −x + $[{1\over 2}]$ , y + $[{1\over 2}]$ , z; (iii) x, y + $[{1\over 2}]$ , −z + $[{1\over 2}]$ ; (iv) x, y − $[{1\over 2}]$ , −z + $[{1\over 2}]$ ; (v) x + $[{1\over 2}]$ , y − $[{1\over 2}]$ , z; (vi) −x, −y + $[{1\over 2}]$ , z − $[{1\over 2}]$ ; (vii) −x + $[{1\over 2}]$ , −y + $[{1\over 2}]$ , −z + 1; (viii) x, −y + $[{1\over 2}]$ , z + $[{1\over 2}]$ ; (ix) −x + $[{1\over 2}]$ , −y + $[{1\over 2}]$ , −z; (xiii) x + $[{1\over 2}]$ , y + $[{1\over 2}]$ , z; (xiv) −x + $[{1\over 2}]$ , −y + 1, z − $[{1\over 2}]$ ; (xv) x, −y + 1, −z + 1; (xvi) −x, −y + 1, −z + 1; (xxi) x − $[{1\over 2}]$ , y + $[{1\over 2}]$ , z − 1; (xxii) −x + $[{1\over 2}]$ , y + $[{1\over 2}]$ , z − 1.]

Bond-valence-sum (BVS) calculations (Brown, 2002 ) were carried out with the ECoN21 program (Ilinca, 2022 ) to validate the structure model. The calculated bond-valence sums (Table 2) of Co1, Co2, Sb1, Si1 and the six O atoms are close to the expected values (in parentheses) for Co (2), Sb (5), Si (4) and O (2) atoms. The mixed-occupied (In1,Co3) and (In2,Co4) sites exhibit BVS values between 2 and 3, which is consistent with the formal charges of +2 for Co and +3 for In, as well as the different In:Co ratio. The strongest deviation from expectation pertains to O4, which is bonded to five metal cations [2Co, 3(In,Co)] and not to the higher-charged Si or Sb atoms. The global instability index (GII) of 0.11 valence units indicates a stable and not particularly strained crystal structure (Salinas-Sanchez et al., 1992 ; Brown, 2009 ).

Table 2
Absolute distances |u| (Å) of matching atom pairs, arithmetic mean (d_av) of distances (Å), degree of lattice distortion (S) and measure of similarity (δ) in the isotypic crystal structures of Co₅In₃SbSi₂O₁₆ and Co₈TeAs₂O₁₆

Co1	0.0523	O1	0.0526
Co2	0.0817	O2	0.1220
(In1,Co3)^a/Co3	0.0943	O3	0.1195
(In2,Co4)^b/Co4	0.1057	O4	0.0413
Sb1/Te1	0	O5	0.0243
Si1/As1	0.0489	O6	0.0709

S	0.0050
d_av	0.0694
δ	0.027
Notes: (a) In:Co ratio 0.9:0.1; (b) In:Co ratio 0.6:0.4.

Numerical data from a quantitative comparison of the isotypic structures of (I) and Co₈TeAs₂O₁₆, carried out using the compstru program (de la Flor et al., 2016 ), which is available on the Bilbao Crystallographic Server (Aroyo et al., 2006 ), are summarized in Table 2. The low values for the degree of lattice distortion (0.0050) and the measure of similarity (0.027) indicate a high degree of similarity between the two crystal structures. The highest differences in atomic positions pertain to atoms O2 and O3, both of which are part of the silicate tetrahedron and two [CoO₆] (for the arsenate) or one [CoO₆] and one [(In,Co)O₆] octahedron (for the silicate). Interestingly, the differences for O4, which is bound to five octahedrally coordinated metal atoms [Co or (In,Co)] but not to the double tetrahedron or the Sb (Te) atom (Table 2), are small.

3. Synthesis and crystallization

Co₅In₃SbSi₂O₁₆ formed serendipitously during phase-formation studies in the system Co/In/Sb/O aimed at a phase with composition Co₂InSbO₆ (Ji et al., 2022) by using chemical vapour transport reactions (CVTR; Binnewies et al., 2012). Stoichiometric amounts of Co₃O₄ (Alfa-Aesar, >99%), In₂O₃ (Merck KGaA, >99.5%) and Sb₂O₅ [Thermo Fisher Scientific, 99.998% (metals basis)] were weighted in an 1.333:1:1 ratio (altogether ca. 300 mg), intimidately ground in an agate mortar and combined with HgCl₂ (60 mg) as the transport agent. The mixture was loaded in a silica ampoule (volume ca. 20 cm³) that was evacuated, sealed and placed in a two-zone furnace using a gradient 1223 → 1123 K for 4 days. Co₅In₃SbSi₂O₁₆ crystallized in the cooler sink side by reacting with the glass ampoule in form of sub-mm blue plates; brown crystals of preliminary composition Co₈In₁₁Sb₇O₄₂ were also present at the sink side. Powder X-ray diffraction of the bulk revealed an approximate phase ratio Co₅In₃SbSi₂O₁₆:Co₈In₁₁Sb₇O₄₂ of 1:9. At the source side, CoSb₂O₆ (Reimers et al., 1989 ) and monoclinic InSbO₄ (Wolflehner, 2026 ) were identified.

An attempt to synthesize Co₅In₃SbSi₂O₁₆ specifically under the same conditions as described above, using Co₃O₄, Sb₂O₅, In₂O₃ and SiO₂ (Merck, purum) in the stoichiometric ratio 1.67:0.5:1.5:2, resulted in the formation of Co₅In₃SbSi₂O₁₆ crystals as the only product present in the sink region. In the source region, Co₅In₃SbSi₂O₁₆, CoSb₂O₆ and spinel-type Co_2.33Sb_0.67O₄ (Dulac & Durif, 1960 ) were identified in an approximate ratio of 5:1:1 according to powder X-ray diffraction of the bulk.

4. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 3. Starting atomic coordinates and the labelling scheme were taken from isotypic Co₈As₂TeO₁₆ (Staack & Müller-Buschbaum, 1997). Initial refinement considering two Co, two In, one Sb, one Si and six O sites resulted in the composition Co₄In₄SbSi₂O₁₆, i.e. a charged compound under consideration of oxidation states of +II for Co, +III for In, +V for Sb and +IV for Si. Successive free refinement of the site occupation factors of the metal sites revealed full occupation for Co1, Co2, Sb1, Si1, but a minor under-occupation for In1 and a pronounced under-occupation for In2. To achieve charge neutrality, both sites were co-occupied with Co atoms in a fixed In1:Co3 ratio of 0.9:0.1 and In2:Co4 ratio of 0.6:0.4. The remaining maximum and minimum electron densities in the final model are located 0.96 and 0.76 Å, respectively, from Sb1.

Table 3
Experimental details

Crystal data
Chemical formula	Co₅In₃SbSi₂O₁₆
M_r	1073.04
Crystal system, space group	Orthorhombic, Cmce
Temperature (K)	293
a, b, c (Å)	6.1012 (4), 23.8586 (6), 8.5282 (18)
V (Å³)	1241.4 (3)
Z	4
Radiation type	Mo Kα
μ (mm⁻¹)	14.40
Crystal size (mm)	0.10 × 0.08 × 0.05

Data collection
Diffractometer	Stoe STADIVARI
Absorption correction	Multi-scan (LANA; Koziskova et al., 2016 )
T_min, T_max	0.474, 0.874
No. of measured, independent and observed [I > 2σ(I)] reflections	6885, 1580, 1320
R_int	0.032
(sin θ/λ)_max (Å⁻¹)	0.834

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.024, 0.056, 1.01
No. of reflections	1580
No. of parameters	75
Δρ_max, Δρ_min (e Å⁻³)	1.54, −2.23
Computer programs: X-AREA (Folkers-Karlsson et al., 2026 ), SHELXT (Sheldrick, 2015a ), SHELXL (Sheldrick, 2015b ), ATOMS (Dowty, 2006 ) and publCIF (Westrip, 2010 ).

Supporting information

CCDC reference: 2597010

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2056989026010960/hb8265sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989026010960/hb8265Isup2.hkl

checkCIF report

Computing details top

Pentacobalt(II) triindium(III) antimony(V) disilicon(VI) hexadecaoxide top

Crystal data top

Co₅In₃SbSi₂O₁₆	D_x = 5.741 Mg m⁻³
M_r = 1073.04	Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, Cmce	Cell parameters from 14765 reflections
a = 6.1012 (4) Å	θ = 3.4–36.5°
b = 23.8586 (6) Å	µ = 14.40 mm⁻¹
c = 8.5282 (18) Å	T = 293 K
V = 1241.4 (3) Å³	Plate, red
Z = 4	0.10 × 0.08 × 0.05 mm
F(000) = 1956

Data collection top

Stoe STADIVARI diffractometer	1320 reflections with I > 2σ(I)
Detector resolution: 13.33 pixels mm^-1	R_int = 0.032
rotation method, ω scans	θ_max = 36.4°, θ_min = 3.4°
Absorption correction: multi-scan (LANA; Koziskova et al., 2016)	h = −3→10
T_min = 0.474, T_max = 0.874	k = −39→35
6885 measured reflections	l = −6→14
1580 independent reflections

Refinement top

Refinement on F²	75 parameters
Least-squares matrix: full	0 restraints
R[F² > 2σ(F²)] = 0.024	w = 1/[σ²(F_o²) + (0.033P)²] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.056	(Δ/σ)_max = 0.001
S = 1.01	Δρ_max = 1.54 e Å⁻³
1580 reflections	Δρ_min = −2.23 e Å⁻³

Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Co1	0.000000	0.55684 (2)	0.12353 (6)	0.00899 (10)
Co2	0.250000	0.42916 (2)	0.250000	0.00861 (10)
Co3	0.000000	0.13625 (2)	0.03647 (3)	0.00856 (6)	0.1
In1	0.000000	0.13625 (2)	0.03647 (3)	0.00856 (6)	0.9
Co4	0.250000	0.80155 (2)	0.250000	0.00934 (7)	0.4
In2	0.250000	0.80155 (2)	0.250000	0.00934 (7)	0.6
Si1	0.000000	0.68839 (4)	0.10629 (12)	0.00706 (17)
Sb1	0.000000	0.000000	0.000000	0.00677 (7)
O1	0.2222 (3)	0.06057 (8)	0.0046 (2)	0.0096 (3)
O2	0.000000	0.13256 (11)	0.2799 (3)	0.0108 (5)
O3	0.000000	0.24301 (12)	0.2804 (3)	0.0106 (5)
O4	0.000000	0.13194 (11)	0.7828 (3)	0.0089 (5)
O5	0.000000	0.99103 (12)	0.2319 (3)	0.0098 (5)
O6	0.2821 (3)	0.18631 (8)	0.9968 (2)	0.0107 (4)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Co1	0.00738 (19)	0.0093 (2)	0.0103 (2)	0.000	0.000	0.00064 (18)
Co2	0.00728 (19)	0.0091 (2)	0.0095 (2)	0.000	0.00118 (16)	0.000
Co3	0.00825 (10)	0.00913 (12)	0.00829 (12)	0.000	0.000	−0.00009 (9)
In1	0.00825 (10)	0.00913 (12)	0.00829 (12)	0.000	0.000	−0.00009 (9)
Co4	0.00864 (13)	0.00895 (15)	0.01044 (15)	0.000	−0.00114 (10)	0.000
In2	0.00864 (13)	0.00895 (15)	0.01044 (15)	0.000	−0.00114 (10)	0.000
Si1	0.0067 (4)	0.0072 (4)	0.0073 (4)	0.000	0.000	−0.0004 (4)
Sb1	0.00580 (12)	0.00698 (14)	0.00754 (15)	0.000	0.000	0.00012 (11)
O1	0.0072 (7)	0.0092 (9)	0.0123 (9)	−0.0016 (6)	−0.0006 (6)	0.0005 (8)
O2	0.0142 (12)	0.0076 (12)	0.0106 (13)	0.000	0.000	−0.0005 (10)
O3	0.0086 (10)	0.0106 (12)	0.0124 (13)	0.000	0.000	0.0023 (10)
O4	0.0085 (10)	0.0094 (12)	0.0089 (12)	0.000	0.000	0.0004 (10)
O5	0.0113 (11)	0.0083 (12)	0.0098 (12)	0.000	0.000	−0.0007 (10)
O6	0.0064 (7)	0.0130 (10)	0.0128 (9)	−0.0016 (6)	−0.0016 (6)	0.0010 (8)

Geometric parameters (Å, º) top

Co1—O1ⁱ	1.977 (2)	In2—O3ⁱⁱⁱ	2.084 (2)
Co1—O1ⁱⁱ	1.977 (2)	In2—O3^xiii	2.084 (2)
Co1—O2ⁱⁱⁱ	1.986 (3)	In2—O6^xiv	2.1340 (19)
Co1—O5^iv	1.997 (3)	In2—O6^xv	2.1340 (19)
Co2—O5^v	2.128 (2)	In2—O4^xiv	2.219 (2)
Co2—O5^iv	2.128 (2)	In2—O4^xvi	2.219 (2)
Co2—O4^vi	2.128 (2)	Sb1—O1^xvii	1.9818 (19)
Co2—O4^vii	2.128 (2)	Sb1—O1^xii	1.9818 (19)
Co2—O1^viii	2.1913 (19)	Sb1—O1^xviii	1.9818 (19)
Co2—O1^ix	2.1913 (19)	Sb1—O1	1.9818 (19)
In1—O2	2.078 (3)	Sb1—O5^xix	1.989 (3)
In1—O6^x	2.1220 (18)	Sb1—O5^xx	1.989 (3)
In1—O6^xi	2.1220 (18)	Si1—O3ⁱⁱⁱ	1.622 (3)
In1—O4^x	2.165 (3)	Si1—O6^xxi	1.6252 (19)
In1—O1	2.2744 (19)	Si1—O6^xxii	1.6252 (19)
In1—O1^xii	2.2745 (19)	Si1—O2ⁱⁱⁱ	1.648 (3)

O1ⁱ—Co1—O1ⁱⁱ	118.00 (11)	O3ⁱⁱⁱ—Si1—O6^xxii	111.51 (10)
O1ⁱ—Co1—O2ⁱⁱⁱ	99.91 (8)	O6^xxi—Si1—O6^xxii	109.78 (14)
O1ⁱⁱ—Co1—O2ⁱⁱⁱ	99.91 (8)	O3ⁱⁱⁱ—Si1—O2ⁱⁱⁱ	107.36 (15)
O1ⁱ—Co1—O5^iv	110.62 (7)	O6^xxi—Si1—O2ⁱⁱⁱ	108.28 (10)
O1ⁱⁱ—Co1—O5^iv	110.62 (7)	O6^xxii—Si1—O2ⁱⁱⁱ	108.28 (10)
O2ⁱⁱⁱ—Co1—O5^iv	117.34 (12)	O1^xvii—Sb1—O1^xii	93.67 (11)
O5^v—Co2—O5^iv	92.17 (11)	O1^xvii—Sb1—O1^xviii	86.33 (11)
O5^v—Co2—O4^vi	176.59 (10)	O1^xii—Sb1—O1^xviii	180.00 (11)
O5^iv—Co2—O4^vi	87.25 (7)	O1^xvii—Sb1—O1	180.0
O5^v—Co2—O4^vii	87.25 (7)	O1^xii—Sb1—O1	86.33 (11)
O5^iv—Co2—O4^vii	176.59 (10)	O1^xviii—Sb1—O1	93.67 (11)
O4^vi—Co2—O4^vii	93.54 (11)	O1^xvii—Sb1—O5^xix	93.38 (8)
O5^v—Co2—O1^viii	92.86 (9)	O1^xii—Sb1—O5^xix	86.62 (8)
O5^iv—Co2—O1^viii	78.17 (9)	O1^xviii—Sb1—O5^xix	93.38 (8)
O4^vi—Co2—O1^viii	83.73 (9)	O1—Sb1—O5^xix	86.62 (8)
O4^vii—Co2—O1^viii	105.22 (10)	O1^xvii—Sb1—O5^xx	86.62 (8)
O5^v—Co2—O1^ix	78.17 (9)	O1^xii—Sb1—O5^xx	93.38 (8)
O5^iv—Co2—O1^ix	92.86 (9)	O1^xviii—Sb1—O5^xx	86.62 (8)
O4^vi—Co2—O1^ix	105.22 (10)	O1—Sb1—O5^xx	93.38 (8)
O4^vii—Co2—O1^ix	83.73 (9)	O5^xix—Sb1—O5^xx	180.00 (17)
O1^viii—Co2—O1^ix	167.15 (10)	Co1^v—O1—Sb1	124.31 (10)
O2—In1—O6^x	100.54 (7)	Co1^v—O1—Co2^ix	116.55 (9)
O2—In1—O6^xi	100.54 (7)	Sb1—O1—Co2^ix	96.61 (8)
O6^x—In1—O6^xi	108.41 (10)	Co1^v—O1—In1	119.02 (9)
O2—In1—O4^x	174.85 (10)	Sb1—O1—In1	99.99 (8)
O6^x—In1—O4^x	82.40 (7)	Co2^ix—O1—In1	94.35 (7)
O6^xi—In1—O4^x	82.40 (7)	Si1^iv—O2—Co1^iv	119.41 (17)
O2—In1—O1	94.93 (8)	Si1^iv—O2—In1	123.65 (16)
O6^x—In1—O1	86.81 (7)	Co1^iv—O2—In1	116.94 (14)
O6^xi—In1—O1	155.68 (8)	Si1^iv—O3—Co4^iv	127.76 (8)
O4^x—In1—O1	80.96 (7)	Si1^iv—O3—Co4^xxiii	127.76 (8)
O2—In1—O1^xii	94.93 (8)	Co4^iv—O3—Co4^xxiii	94.07 (12)
O6^x—In1—O1^xii	155.68 (8)	Co2^xxiv—O4—Co2^vii	91.56 (11)
O6^xi—In1—O1^xii	86.81 (7)	Co2^xxiv—O4—Co3^xxv	99.44 (9)
O4^x—In1—O1^xii	80.96 (7)	Co2^vii—O4—Co3^xxv	99.44 (9)
O1—In1—O1^xii	73.18 (10)	Co2^xxiv—O4—Co4^xxvi	164.99 (15)
O3ⁱⁱⁱ—In2—O3^xiii	95.85 (12)	Co2^vii—O4—Co4^xxvi	88.89 (2)
O3ⁱⁱⁱ—In2—O6^xiv	98.43 (9)	Co3^xxv—O4—Co4^xxvi	95.28 (10)
O3^xiii—In2—O6^xiv	92.02 (9)	Co2^xxiv—O4—Co4^xvi	88.89 (2)
O3ⁱⁱⁱ—In2—O6^xv	92.02 (9)	Co2^vii—O4—Co4^xvi	164.99 (15)
O3^xiii—In2—O6^xv	98.43 (9)	Co3^xxv—O4—Co4^xvi	95.28 (10)
O6^xiv—In2—O6^xv	164.39 (11)	Co4^xxvi—O4—Co4^xvi	86.85 (10)
O3ⁱⁱⁱ—In2—O4^xiv	176.38 (8)	Sb1^xxvii—O5—Co1ⁱⁱⁱ	121.97 (15)
O3^xiii—In2—O4^xiv	87.73 (7)	Sb1^xxvii—O5—Co2ⁱ	98.44 (10)
O6^xiv—In2—O4^xiv	80.88 (9)	Co1ⁱⁱⁱ—O5—Co2ⁱ	120.04 (9)
O6^xv—In2—O4^xiv	87.96 (9)	Sb1^xxvii—O5—Co2ⁱⁱⁱ	98.44 (10)
O3ⁱⁱⁱ—In2—O4^xvi	87.73 (7)	Co1ⁱⁱⁱ—O5—Co2ⁱⁱⁱ	120.04 (9)
O3^xiii—In2—O4^xvi	176.38 (8)	Co2ⁱ—O5—Co2ⁱⁱⁱ	91.56 (11)
O6^xiv—In2—O4^xvi	87.96 (9)	Si1^xxviii—O6—Co3^xxv	126.11 (11)
O6^xv—In2—O4^xvi	80.88 (9)	Si1^xxviii—O6—Co4^xxvi	129.60 (11)
O4^xiv—In2—O4^xvi	88.68 (10)	Co3^xxv—O6—Co4^xxvi	99.15 (7)
O3ⁱⁱⁱ—Si1—O6^xxi	111.51 (10)

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

Details of the coordination by O atoms around the metal cations and results of BVS calculations top

Site	Coordination number	Range of bond lengths (Å)	Mean bond length (Å)	Mean bond length (literature value) (Å)	BVS (valence units)
Co1	4	1.977 (2)–1.997 (3)	1.984	1.967 (22)^c	1.86
Co2	6	2.128 (2)–2.1913 (19)	2.147	2.108 (62)^c	1.82
(In1,Co3)^a	6	2.078 (3)–2.2745 (19)	2.156	Co 2.108 (62)^c, In 2.142 (42)^d	2.73
(In2,Co4)^b	6	2.084 (2)–2.219 (2)	2.137	Co 2.108 (62)^c, In 2.142 (42)^d	2.53
Sb1	6	1.9818 (19)–1.989 (3)	1.984	1.977 (34)^d	4.94
Si1	4	1.622 (3)–1.648 (3)	1.630	1.625 (24)^d	3.94
O1	4 [2Co+Sb+(In,Co)]				1.93
O2	3 [Si+Co+(In,Co)]				1.96
O3	3 [Si+2(In,Co)]				1.97
O4	5 [2Co+3(In,Co)]				1.80
O5	4 (Sb+3Co)				1.90
O6	3 [Si+2(In,Co)]				1.93

Notes: (a) In:Co ratio 0.9:0.1; (b) In:Co ratio 0.6:0.4; (c) Gagné & Hawthorne (2020); (d) Gagné & Hawthorne (2018).

Absolute distances |u| (Å) of matching atom pairs, arithmetic mean (d_av) of distances (Å), degree of lattice distortion (S) and measure of similarity (δ) in the isotypic crystal structures of Co₅In₃SbSi₂O₁₆ and Co₈TeAs₂O₁₆ top

Co1	0.0523	O1	0.0526
Co2	0.0817	O2	0.1220
(In1,Co3)^a/Co3	0.0943	O3	0.1195
(In2,Co4)^b/Co4	0.1057	O4	0.0413
Sb1/Te1	0	O5	0.0243
Si1/As1	0.0489	O6	0.0709

S	0.0050
d_av	0.0694
δ	0.027

Notes: (a) In:Co ratio 0.9:0.1; (b) In:Co ratio 0.6:0.4.

Acknowledgements

The authors acknowledge the X-ray Centre of TU Wien for providing access to instrumentation and analysis software and TU Wien Bibliothek for financial support through its Open Access Funding Program.

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