A new form of Cd3TeO6 revealing dimorphism

Weil, M.; Veyer, T.

doi:10.1107/S2056989018014214

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ISSN: 2056-9890

Volume 74| Part 11| November 2018| Pages 1561-1564

https://doi.org/10.1107/S2056989018014214

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A new form of Cd₃TeO₆ revealing dimorphism

Matthias Weil ^a ^* and Théo Veyer ^b

^aInstitute for Chemical Technologies and Analytics, Division of Structural Chemistry, TU Wien, Getreidemarkt 9/164-SC, A-1060 Vienna, Austria, and ^bIUT Bordeaux 1, 15 Rue Naudet, 33175 Gradignan, France
^*Correspondence e-mail: matthias.weil@tuwien.ac.at

Edited by A. Van der Lee, Université de Montpellier II, France (Received 2 October 2018; accepted 8 October 2018; online 12 October 2018)

Phase-formation studies in the system CdO–TeO₃ using a CsCl/NaCl melt at comparatively low temperatures revealed that tricadmium orthotellurate(VI), Cd₃TeO₆, is dimorphic. The new modification of Cd₃TeO₆ is denoted as the β-form and adopts the rhombohedral Mg₃TeO₆ structure type with one Cd and two O sites in general positions, and two Te sites with site symmetry $[\overline{3}]$ each. In comparison with the previously reported monoclinic cryolite-type α-form that was prepared at higher temperatures, β-Cd₃TeO₆ has a much lower density and most likely represents a metastable modification. Whereas the [TeO₆] octahedra in both polymorphs are very similar and show only minor deviations from ideal values, the polyhedra around the Cd^II sites are different, with a distorted [CdO₆] octahedron in both modifications but an additional [CdO₈] polyhedron with a [4 + 4] coordination in the α-form.

Keywords: crystal structure; dimorphism; Mg₃TeO₆ structure type; solid solution.

CCDC reference: 1872058

1. Chemical context

Various salts of meta-telluric acid, H₂TeO₄, have been reported as a result of high-pressure and high-temperature experiments (3000 atm; 973 K) aiming at various M^IITeO₄ phases, where M = Mg, Ca, Sr, Ba, Cd or Pb (Sleight et al., 1972 ). Meanwhile, the crystal structures of the Ca, Sr and Ba salts were determined (Hottentot & Loopstra, 1979 ; Weil et al., 2016 ) whereas those of the other phases remain unknown to date. In a recent project on single-crystal growth of the Cd salt of meta-telluric acid, we used a CsCl/NaCl salt mixture (Źemcźuźny & Rambach, 1909 ) at temperatures < 800 K as a flux. Instead of the target phase CdTeO₄, we obtained a new form of Cd₃TeO₆. The previously reported Cd₃TeO₆ polymorph crystallizes as a monoclinically distorted cryolite-type material in space-group type P2₁/n (Burckhardt et al., 1982 ) while the new form adopts the rhombohedral Mg₃TeO₆ structure type.

Prior to the current study, solid solutions Cd_3–xMn_xTeO₆ with x = 3, 2, 1.5 and 1 were prepared in polycrystalline form (Ivanov et al., 2012 ), but not the cadmium end member, i.e. where x = 0. We report here the crystal structure of the new polymorph of Cd₃TeO₆, together with a comparative discussion of isostructural solid solutions Cd_3–xMn_xTeO₆. In the following, we refer to the previously reported monoclinic polymorph of Cd₃TeO₆ (Burckhardt et al., 1982) as the α-form, and the new rhombohedral polymorph as the β-form of Cd₃TeO₆.

2. Structural commentary

The crystal structure of β-Cd₃TeO₆ (Fig. 1) is made up from a distorted close packing of hexagonal oxygen layers extending parallel to (001). The Cd site (site symmetry 1) and the two unique Te sites (each with site symmetry $[\overline{3}]$ ) are situated in the octahedral interstices of this arrangement. The distorted [CdO₆] octahedron has Cd—O distances ranging from 2.2348 (17)–2.4658 (19) Å (Table 1) and shares one edge with a [Te1O₆] octahedron, another edge with a [Te2O₆] octahedron, and four edges with neighbouring [CdO₆] octahedra. Both [TeO₆] octahedra show only minute deviations from the ideal octahedral symmetry. They are isolated from each other and are connected to six [CdO₆] octahedra by sharing edges. The average Te—O bond length in β-Cd₃TeO₆ (1.931 Å) is in very good agreement with the mean Te—O bond length of 1.923 Å calculated for numerous (> 100) oxotellurates with octahedrally coordinated Te^VI (Christy et al., 2016 ; Gagné & Hawthorne, 2018 ). Both unique O atoms are bonded to one Te and three Cd atoms in the form of a distorted tetrahedron.

Table 1
Selected bond lengths (Å) in rhombohedral β-Cd₃TeO₆ and in isotypic (Cd_1.5Mn_1.5)TeO₆ and Mn₃TeO₆

	β-Cd₃TeO₆^a	Cd_1.5Mn_1.5TeO₆^b	Mn₃TeO₆^c
M1—O1	2.2348 (17)	2.147	2.1055 (14)
M1—O2ⁱ	2.2455 (17)	2.150	2.1275 (13)
M1—O1ⁱⁱ	2.2907 (19)	2.240	2.2009 (13)
M1—O2ⁱⁱⁱ	2.3051 (18)	2.260	2.2311 (12)
M1—O2	2.3370 (18)	2.273	2.2313 (13)
M1—O1^iv	2.4658 (19)	2.412	2.3841 (13)
Te1—O1	1.9339 (17)	1.955	1.9247 (13)
Te2—O2	1.9290 (17)	1.959	1.9214 (12)
Notes: (a) This study; (b) Ivanov et al. (2012) on the basis of X-ray powder diffraction data at room temperature (no s.u. given in original publication); (c) Weil (2006) on the basis of single-crystal X-ray data at room temperature. [Symmetry codes: (i) y − $[{1\over 3}]$ , −x + y + $[{1\over 3}]$ , −z + $[{1\over 3}]$ ; (ii) −x + $[{1\over 3}]$ , y + $[{2\over 3}]$ , −z + $[{2\over 3}]$ ; (iii) −y, x − y, z; (iv) −y + $[{1\over 3}]$ , x − y + $[{2\over 3}]$ , z − $[{1\over 3}]$ .]

Figure 1
The crystal structure of β-Cd₃TeO₆ in polyhedral view in a projection along [0 $[\overline{1}]$ 0]. [CdO₆] octahedra are blue and [TeO₆] octahedra are red. Displacement ellipsoids are drawn at the 90% probability level.

Like β-Cd₃TeO₆, Mn₃TeO₆ (Weil, 2006 ) as well as phases with x = 2, 1.5 and 1 of the Cd_3–xMn_xTeO₆ solid-solution series (Ivanov et al., 2012) adopt the rhombohedral Mg₃TeO₆ structure type. A comparison of the bond lengths of the [MO₆] (M = Cd, Mn) octahedra in the end members β-Cd₃TeO₆ and Mn₃TeO₆ and the solid solution Cd_1.5Mn_1.5TeO₆ (mixed occupancy for the M site) shows intermediate values for the solid solution, consistent with the different ionic radii for six-coordinate Cd^II and Mn^II of 0.95 and 0.83 (high-spin) Å, respectively (Shannon, 1976 ). For a quantitative structural comparison of the end members β-Cd₃TeO₆ and Mn₃TeO₆ the program compstru (de la Flor et al., 2016 ) available at the Bilbao Crystallographic Server (Aroyo et al., 2006 ) was used. The degree of lattice distortion is 0.0204, the maximum distance between the atomic positions of paired atoms is 0.0680 Å for pair O2, the arithmetic mean of all distances is 0.0417 Å, and the measure of similarity is 0.011. All these values show a high similarity between the two crystal structures.

The structure of the monoclinic α-form of Cd₃TeO₆ (Burckhardt et al., 1982) comprises of two cadmium sites (one on a general position and one on an inversion centre), one tellurium site on an inversion centre and three oxygen sites in general positions. While the [TeO₆] octahedra in both Cd₃TeO₆ polymorphs have nearly the same bond length distribution [2 × 1.904 (4), 2 × 1.924 (5), 2 × 1.948 (4) Å in the α-form; for the β-form, see: Table 1], the set of coordination polyhedra around the two Cd^II cations in the two structures is different. In β-Cd₃TeO₆, the cadmium site has a coordination number (CN) of six with an octahedral oxygen environment whereas in α-Cd₃TeO₆, only one site is octahedrally surrounded [range of Cd—O bond lengths: 2.211 (5)–2.350 (4) Å] and the other site exhibits a distorted [4 + 4] coordination [range of Cd—O bond lengths: 2.237 (5)–3.010 (5) Å].

As noted above, the end members β-Cd₃TeO₆ and Mn₃TeO₆ crystallize in the same structure type, suggesting a full miscibility over the complete range of x for the solid-solution series Cd_3–xMn_xTeO₆. However, the adopted structure type for the complete range of x appears to be dependent on the reaction temperature. Single crystals of α-Cd₃TeO₆ for structure analysis were grown from a 9 CdO: 11 TeO₂ mixture that was heated in air at 1350 K for three h (Burckhardt et al., 1982) while single crystals of β-Cd₃TeO₆ were obtained at much lower temperatures (793 K) using a flux method. This suggests that the high-temperature synthesis yields the thermodynamically stable modification. The rule of thumb that in the majority of cases the denser polymorph represents also the thermodynamically stable modification supports this assumption because α-Cd₃TeO₆ [D_x = 7.490 (2) g cm⁻³; Burckhardt et al., 1982] is much denser than β-Cd₃TeO₆ [D_x = 6.941 g cm⁻³]. Under consideration of the similar reaction conditions for preparation of monoclinic α-Cd₃TeO₆ and the given solid solutions Cd_3–xMn_xTeO₆ (1270 K following a ceramic route; Ivanov et al., 2012), it appears likely that the rhombohedral β-Cd₃TeO₆ end member can be prepared only at lower temperatures whereas certain amounts of manganese substituting cadmium in the Cd_3–xMn_xTeO₆ solid-solution series stabilize the Mg₃TeO₆ structure type at higher temperatures. Unfortunately, because of the scarcity of β-Cd₃TeO₆ material, a detailed investigation of the thermal behaviour of this phase, e.g. in terms of stability and a possible phase transition to α-Cd₃TeO₆, could not be undertaken.

3. Database survey

According to a search of the Inorganic Crystal Structure Database (ICSD; Belsky et al., 2002 ), the Mg₃TeO₆ structure type is realized for eponymous Mg₃TeO₆ (Schulz & Bayer, 1971 ), Ca₃UO₆ (Holc & Golic, 1983 ), Mn₃WO₆ (Klüver & Müller-Buschbaum, 1994 ), Li₃AlD₆ (Brinks & Hauback, 2003 ; Løvvik et al., 2004 ), Mn₃TeO₆ (Weil, 2006), selected solid solutions Cd_3–xMn_xTeO₆ (Ivanov et al., 2012), Mn_3-xCo_xTeO₆ (Singh et al., 2014 ; Ivanov et al., 2014 ), Mn_2.4Cu_0.6TeO₆ (Wulff et al., 1998 ), (Ca_0.2667 Y_0.7333)₃(Y_0.2Sn_0.3)Sn_0.5O6 (Kaminaga et al., 2006 ), Mn₂InSbO₆ and Mn₂ScSbO₆ (Ivanov et al., 2011 ), Sc₃(Sc_0.295 Al_0.705)O₆ (Müller et al., 2004 ) and Ho₃ScO₆ (Badie, 1973 ).

4. Synthesis and crystallization

The rhombohedral β-form of Cd₃TeO₃ was obtained as one of the products from a flux synthesis using a CsCl/NaCl salt mixture (molar ratio 0.65/0.35). To 1.7 g of the salt mixture were added CdO (0.13 g) and TeO₃ (0.18 g). TeO₃ had previously been prepared by heating H₆TeO₆ at 573 K for 8 h. The reaction mixture was evacuated and sealed in a silica ampoule, heated from room temperature within 3 h to 793 K, kept at that temperature for 90 h and cooled within 10 h back to room temperature. The silica ampoule was subsequently broken and the solidified melt leached out with water for 2 h. The off-white product was filtered off, washed with water and was air-dried. The title compound was present in the form of a few nearly spherical colourless crystals. Other phases identified by single-crystal X-ray diffraction measurements of selected crystals were α-Cd₃TeO₆ (Burckhardt et al., 1982), the mixed-valent Te^IV/VI compound Cd₂Te₂O₇ (Weil, 2004 ) and a new form of incommensurately modulated CdTe₂O₅ (Weil & Stöger, 2018 ). Estimated on optical inspection with a microscope, all these phases represent minor by-products. Powder X-ray diffraction measurements of the bulk additionally revealed triple-perovskite-type CsCdCl₃ (Siegel & Gebert, 1964 ) as the main phase and the Te^IV compound CdTeO₃ (Krämer & Brandt, 1985 ) as a minority phase. Some additional reflections in the X-ray powder diffraction pattern of the bulk could not be assigned to the phases mentioned above or to any other known phase(s).

5. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 2. Standardized coordinates (Gelato & Parthé, 1987 ) from the isotypic phase Mn₃TeO₆ (Weil, 2006) were taken as starting parameters for refinement. The highest and lowest remaining electron density peaks are located 1.56 and 1.53 Å from sites Te2 and O1, respectively.

Table 2
Experimental details

Crystal data
Chemical formula	Cd₃TeO₆
M_r	560.80
Crystal system, space group	Trigonal, R $[\overline{3}]$ :H
Temperature (K)	296
a, c (Å)	9.1620 (2), 11.0736 (3)
V (Å³)	805.01 (4)
Z	6
Radiation type	Mo Kα
μ (mm⁻¹)	17.06
Crystal size (mm)	0.08 (radius)

Data collection
Diffractometer	Bruker APEXII CCD
Absorption correction	Multi-scan (SADABS; Krause et al., 2015 )
T_min, T_max	0.527, 0.749
No. of measured, independent and observed [I > 2σ(I)] reflections	11351, 1623, 1526
R_int	0.033
(sin θ/λ)_max (Å⁻¹)	1.025

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.023, 0.046, 1.29
No. of reflections	1623
No. of parameters	33
Δρ_max, Δρ_min (e Å⁻³)	2.57, −1.53
Computer programs: APEX3 and SAINT (Bruker, 2015 ), SHELXL2017/1 (Sheldrick, 2015 ), ATOMS for Windows (Dowty, 2006 ) and publCIF (Westrip, 2010 ).

Supporting information

CCDC reference: 1872058

Crystal structure: contains datablocks I, global. DOI: https://doi.org/10.1107/S2056989018014214/vn2137sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989018014214/vn2137Isup2.hkl

checkCIF report

Computing details top

Data collection: APEX3 (Bruker, 2015); cell refinement: SAINT (Bruker, 2015); data reduction: SAINT (Bruker, 2015); program(s) used to solve structure: coordinates from isotypic structure; program(s) used to refine structure: SHELXL2017/1 (Sheldrick, 2015); molecular graphics: ATOMS for Windows (Dowty, 2006); software used to prepare material for publication: publCIF (Westrip, 2010).

Tricadmium orthotellurate(VI) top

Crystal data top

Cd₃TeO₆	D_x = 6.941 Mg m⁻³
M_r = 560.80	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3:H	Cell parameters from 6637 reflections
a = 9.1620 (2) Å	θ = 5.0–46.6°
c = 11.0736 (3) Å	µ = 17.06 mm⁻¹
V = 805.01 (4) Å³	T = 296 K
Z = 6	Spherical, colourless
F(000) = 1464	0.08 × 0.08 × 0.08 × 0.08 (radius) mm

Data collection top

Bruker APEXII CCD diffractometer	1526 reflections with I > 2σ(I)
ω– and φ–scans	R_int = 0.033
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	θ_max = 46.8°, θ_min = 3.2°
T_min = 0.527, T_max = 0.749	h = −18→18
11351 measured reflections	k = −18→16
1623 independent reflections	l = −22→22

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	w = 1/[σ²(F_o²) + (0.0021P)² + 11.2674P] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.023	(Δ/σ)_max < 0.001
wR(F²) = 0.046	Δρ_max = 2.57 e Å⁻³
S = 1.29	Δρ_min = −1.53 e Å⁻³
1623 reflections	Extinction correction: SHELXL-2017/1 (Sheldrick 2015), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
33 parameters	Extinction coefficient: 0.00434 (9)

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
Cd1	0.03947 (2)	0.26424 (2)	0.21210 (2)	0.00731 (4)
Te1	0.000000	0.000000	0.500000	0.00444 (5)
Te2	0.000000	0.000000	0.000000	0.00424 (5)
O1	0.0289 (2)	0.1903 (2)	0.40560 (16)	0.0087 (2)
O2	0.1800 (2)	0.1509 (2)	0.10570 (16)	0.0078 (2)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Cd1	0.00657 (6)	0.00745 (6)	0.00789 (6)	0.00348 (5)	−0.00052 (4)	−0.00099 (4)
Te1	0.00419 (7)	0.00419 (7)	0.00492 (10)	0.00210 (3)	0.000	0.000
Te2	0.00403 (7)	0.00403 (7)	0.00464 (10)	0.00202 (3)	0.000	0.000
O1	0.0102 (6)	0.0074 (6)	0.0082 (5)	0.0043 (5)	−0.0001 (5)	0.0024 (4)
O2	0.0058 (5)	0.0069 (6)	0.0094 (6)	0.0021 (5)	−0.0024 (4)	−0.0017 (4)

Geometric parameters (Å, º) top

Cd1—O1	2.2348 (17)	Te1—O1^viii	1.9339 (18)
Cd1—O2ⁱ	2.2455 (17)	Te1—O1ⁱⁱⁱ	1.9339 (17)
Cd1—O1ⁱⁱ	2.2907 (19)	Te1—O1^ix	1.9339 (17)
Cd1—O2ⁱⁱⁱ	2.3051 (18)	Te1—O1^x	1.9339 (17)
Cd1—O2	2.3370 (18)	Te1—O1^xi	1.9339 (17)
Cd1—O1^iv	2.4658 (19)	Te1—O1	1.9339 (17)
Cd1—Te2	3.2608 (2)	Te2—O2	1.9290 (17)
Cd1—Te1^v	3.3420 (2)	Te2—O2^xii	1.9290 (17)
Cd1—Cd1ⁱⁱ	3.3606 (3)	Te2—O2ⁱⁱⁱ	1.9290 (17)
Cd1—Cd1^vi	3.4239 (3)	Te2—O2^xiii	1.9291 (17)
Cd1—Cd1^vii	3.4537 (2)	Te2—O2^xiv	1.9291 (17)
Cd1—Cd1ⁱ	3.4538 (2)	Te2—O2^xi	1.9291 (17)

O1—Cd1—O2ⁱ	94.05 (7)	O1^x—Te1—Cd1^xvii	79.65 (6)
O1—Cd1—O1ⁱⁱ	84.10 (7)	O1^xi—Te1—Cd1^xvii	100.35 (6)
O2ⁱ—Cd1—O1ⁱⁱ	120.35 (7)	O1—Te1—Cd1^xvii	138.37 (6)
O1—Cd1—O2ⁱⁱⁱ	107.98 (7)	Cd1^xv—Te1—Cd1^xvii	117.776 (1)
O2ⁱ—Cd1—O2ⁱⁱⁱ	82.41 (7)	Cd1^xvi—Te1—Cd1^xvii	62.224 (1)
O1ⁱⁱ—Cd1—O2ⁱⁱⁱ	154.11 (6)	Cd1ⁱⁱ—Te1—Cd1^xvii	180.0
O1—Cd1—O2	107.37 (6)	O1^viii—Te1—Cd1^xviii	100.35 (6)
O2ⁱ—Cd1—O2	148.88 (4)	O1ⁱⁱⁱ—Te1—Cd1^xviii	79.65 (6)
O1ⁱⁱ—Cd1—O2	84.88 (6)	O1^ix—Te1—Cd1^xviii	46.92 (5)
O2ⁱⁱⁱ—Cd1—O2	69.79 (8)	O1^x—Te1—Cd1^xviii	138.37 (6)
O1—Cd1—O1^iv	144.36 (6)	O1^xi—Te1—Cd1^xviii	41.63 (6)
O2ⁱ—Cd1—O1^iv	82.90 (6)	O1—Te1—Cd1^xviii	133.08 (5)
O1ⁱⁱ—Cd1—O1^iv	67.58 (8)	Cd1^xv—Te1—Cd1^xviii	62.225 (1)
O2ⁱⁱⁱ—Cd1—O1^iv	106.78 (6)	Cd1^xvi—Te1—Cd1^xviii	117.775 (1)
O2—Cd1—O1^iv	91.75 (6)	Cd1ⁱⁱ—Te1—Cd1^xviii	117.775 (1)
O1—Cd1—Te2	119.57 (5)	Cd1^xvii—Te1—Cd1^xviii	62.225 (1)
O2ⁱ—Cd1—Te2	113.76 (5)	O1^viii—Te1—Cd1^xix	79.65 (6)
O1ⁱⁱ—Cd1—Te2	118.53 (5)	O1ⁱⁱⁱ—Te1—Cd1^xix	100.35 (6)
O2ⁱⁱⁱ—Cd1—Te2	35.59 (4)	O1^ix—Te1—Cd1^xix	133.08 (5)
O2—Cd1—Te2	35.72 (4)	O1^x—Te1—Cd1^xix	41.63 (6)
O1^iv—Cd1—Te2	93.60 (4)	O1^xi—Te1—Cd1^xix	138.37 (6)
O1—Cd1—Te1^v	111.58 (5)	O1—Te1—Cd1^xix	46.92 (5)
O2ⁱ—Cd1—Te1^v	97.31 (5)	Cd1^xv—Te1—Cd1^xix	117.775 (1)
O1ⁱⁱ—Cd1—Te1^v	34.11 (4)	Cd1^xvi—Te1—Cd1^xix	62.225 (1)
O2ⁱⁱⁱ—Cd1—Te1^v	140.34 (4)	Cd1ⁱⁱ—Te1—Cd1^xix	62.225 (1)
O2—Cd1—Te1^v	95.47 (4)	Cd1^xvii—Te1—Cd1^xix	117.775 (1)
O1^iv—Cd1—Te1^v	34.95 (4)	Cd1^xviii—Te1—Cd1^xix	180.0
Te2—Cd1—Te1^v	116.088 (5)	O2—Te2—O2^xii	93.00 (8)
O1—Cd1—Cd1ⁱⁱ	42.69 (5)	O2—Te2—O2ⁱⁱⁱ	87.00 (8)
O2ⁱ—Cd1—Cd1ⁱⁱ	113.04 (5)	O2^xii—Te2—O2ⁱⁱⁱ	180.00 (11)
O1ⁱⁱ—Cd1—Cd1ⁱⁱ	41.41 (4)	O2—Te2—O2^xiii	180.0
O2ⁱⁱⁱ—Cd1—Cd1ⁱⁱ	144.94 (5)	O2^xii—Te2—O2^xiii	87.00 (8)
O2—Cd1—Cd1ⁱⁱ	97.92 (4)	O2ⁱⁱⁱ—Te2—O2^xiii	93.00 (8)
O1^iv—Cd1—Cd1ⁱⁱ	106.29 (4)	O2—Te2—O2^xiv	93.00 (8)
Te2—Cd1—Cd1ⁱⁱ	130.823 (8)	O2^xii—Te2—O2^xiv	87.00 (8)
Te1^v—Cd1—Cd1ⁱⁱ	71.352 (5)	O2ⁱⁱⁱ—Te2—O2^xiv	93.00 (8)
O1—Cd1—Cd1^vi	104.72 (5)	O2^xiii—Te2—O2^xiv	87.00 (8)
O2ⁱ—Cd1—Cd1^vi	41.86 (5)	O2—Te2—O2^xi	87.00 (8)
O1ⁱⁱ—Cd1—Cd1^vi	159.57 (5)	O2^xii—Te2—O2^xi	93.00 (8)
O2ⁱⁱⁱ—Cd1—Cd1^vi	40.55 (4)	O2ⁱⁱⁱ—Te2—O2^xi	87.00 (8)
O2—Cd1—Cd1^vi	109.20 (4)	O2^xiii—Te2—O2^xi	93.00 (8)
O1^iv—Cd1—Cd1^vi	96.51 (4)	O2^xiv—Te2—O2^xi	180.00 (13)
Te2—Cd1—Cd1^vi	73.547 (5)	O2—Te2—Cd1^xiii	134.98 (5)
Te1^v—Cd1—Cd1^vi	126.995 (8)	O2^xii—Te2—Cd1^xiii	44.06 (5)
Cd1ⁱⁱ—Cd1—Cd1^vi	143.877 (10)	O2ⁱⁱⁱ—Te2—Cd1^xiii	135.94 (5)
O1—Cd1—Cd1^vii	104.17 (5)	O2^xiii—Te2—Cd1^xiii	45.02 (5)
O2ⁱ—Cd1—Cd1^vii	153.98 (5)	O2^xiv—Te2—Cd1^xiii	96.56 (5)
O1ⁱⁱ—Cd1—Cd1^vii	45.47 (5)	O2^xi—Te2—Cd1^xiii	83.44 (5)
O2ⁱⁱⁱ—Cd1—Cd1^vii	108.67 (4)	O2—Te2—Cd1^xi	44.06 (5)
O2—Cd1—Cd1^vii	40.10 (4)	O2^xii—Te2—Cd1^xi	83.44 (5)
O1^iv—Cd1—Cd1^vii	71.44 (4)	O2ⁱⁱⁱ—Te2—Cd1^xi	96.56 (5)
Te2—Cd1—Cd1^vii	73.148 (6)	O2^xiii—Te2—Cd1^xi	135.94 (5)
Te1^v—Cd1—Cd1^vii	58.887 (1)	O2^xiv—Te2—Cd1^xi	134.98 (5)
Cd1ⁱⁱ—Cd1—Cd1^vii	71.628 (5)	O2^xi—Te2—Cd1^xi	45.02 (5)
Cd1^vi—Cd1—Cd1^vii	143.600 (10)	Cd1^xiii—Te2—Cd1^xi	106.152 (5)
O1—Cd1—Cd1ⁱ	122.01 (5)	O2—Te2—Cd1	45.02 (5)
O2ⁱ—Cd1—Cd1ⁱ	42.10 (5)	O2^xii—Te2—Cd1	135.94 (5)
O1ⁱⁱ—Cd1—Cd1ⁱ	90.20 (4)	O2ⁱⁱⁱ—Te2—Cd1	44.06 (5)
O2ⁱⁱⁱ—Cd1—Cd1ⁱ	101.62 (5)	O2^xiii—Te2—Cd1	134.98 (5)
O2—Cd1—Cd1ⁱ	129.56 (4)	O2^xiv—Te2—Cd1	83.44 (5)
O1^iv—Cd1—Cd1ⁱ	41.48 (4)	O2^xi—Te2—Cd1	96.56 (5)
Te2—Cd1—Cd1ⁱ	113.622 (7)	Cd1^xiii—Te2—Cd1	180.0
Te1^v—Cd1—Cd1ⁱ	58.888 (1)	Cd1^xi—Te2—Cd1	73.847 (5)
Cd1ⁱⁱ—Cd1—Cd1ⁱ	110.788 (6)	O2—Te2—Cd1^xiv	135.94 (5)
Cd1^vi—Cd1—Cd1ⁱ	69.450 (8)	O2^xii—Te2—Cd1^xiv	96.56 (5)
Cd1^vii—Cd1—Cd1ⁱ	111.882 (5)	O2ⁱⁱⁱ—Te2—Cd1^xiv	83.44 (5)
O1^viii—Te1—O1ⁱⁱⁱ	180.0	O2^xiii—Te2—Cd1^xiv	44.06 (5)
O1^viii—Te1—O1^ix	93.54 (7)	O2^xiv—Te2—Cd1^xiv	45.02 (5)
O1ⁱⁱⁱ—Te1—O1^ix	86.46 (7)	O2^xi—Te2—Cd1^xiv	134.98 (5)
O1^viii—Te1—O1^x	93.54 (7)	Cd1^xiii—Te2—Cd1^xiv	73.848 (5)
O1ⁱⁱⁱ—Te1—O1^x	86.46 (7)	Cd1^xi—Te2—Cd1^xiv	180.0
O1^ix—Te1—O1^x	93.54 (7)	Cd1—Te2—Cd1^xiv	106.153 (5)
O1^viii—Te1—O1^xi	86.46 (7)	O2—Te2—Cd1^xii	83.44 (5)
O1ⁱⁱⁱ—Te1—O1^xi	93.54 (7)	O2^xii—Te2—Cd1^xii	45.02 (5)
O1^ix—Te1—O1^xi	86.46 (7)	O2ⁱⁱⁱ—Te2—Cd1^xii	134.98 (5)
O1^x—Te1—O1^xi	180.0	O2^xiii—Te2—Cd1^xii	96.56 (5)
O1^viii—Te1—O1	86.46 (7)	O2^xiv—Te2—Cd1^xii	44.06 (5)
O1ⁱⁱⁱ—Te1—O1	93.54 (7)	O2^xi—Te2—Cd1^xii	135.94 (5)
O1^ix—Te1—O1	180.0	Cd1^xiii—Te2—Cd1^xii	73.848 (5)
O1^x—Te1—O1	86.46 (7)	Cd1^xi—Te2—Cd1^xii	106.152 (5)
O1^xi—Te1—O1	93.54 (7)	Cd1—Te2—Cd1^xii	106.153 (5)
O1^viii—Te1—Cd1^xv	41.63 (6)	Cd1^xiv—Te2—Cd1^xii	73.848 (5)
O1ⁱⁱⁱ—Te1—Cd1^xv	138.37 (6)	O2—Te2—Cd1ⁱⁱⁱ	96.56 (5)
O1^ix—Te1—Cd1^xv	79.65 (6)	O2^xii—Te2—Cd1ⁱⁱⁱ	134.98 (5)
O1^x—Te1—Cd1^xv	133.08 (6)	O2ⁱⁱⁱ—Te2—Cd1ⁱⁱⁱ	45.02 (5)
O1^xi—Te1—Cd1^xv	46.92 (6)	O2^xiii—Te2—Cd1ⁱⁱⁱ	83.44 (5)
O1—Te1—Cd1^xv	100.35 (6)	O2^xiv—Te2—Cd1ⁱⁱⁱ	135.94 (5)
O1^viii—Te1—Cd1^xvi	138.37 (6)	O2^xi—Te2—Cd1ⁱⁱⁱ	44.06 (5)
O1ⁱⁱⁱ—Te1—Cd1^xvi	41.63 (6)	Cd1^xiii—Te2—Cd1ⁱⁱⁱ	106.152 (5)
O1^ix—Te1—Cd1^xvi	100.35 (6)	Cd1^xi—Te2—Cd1ⁱⁱⁱ	73.848 (5)
O1^x—Te1—Cd1^xvi	46.92 (6)	Cd1—Te2—Cd1ⁱⁱⁱ	73.847 (5)
O1^xi—Te1—Cd1^xvi	133.08 (6)	Cd1^xiv—Te2—Cd1ⁱⁱⁱ	106.152 (5)
O1—Te1—Cd1^xvi	79.65 (6)	Cd1^xii—Te2—Cd1ⁱⁱⁱ	180.000 (11)
Cd1^xv—Te1—Cd1^xvi	180.0	Te1—O1—Cd1	139.23 (10)
O1^viii—Te1—Cd1ⁱⁱ	46.92 (5)	Te1—O1—Cd1ⁱⁱ	104.25 (8)
O1ⁱⁱⁱ—Te1—Cd1ⁱⁱ	133.08 (5)	Cd1—O1—Cd1ⁱⁱ	95.90 (7)
O1^ix—Te1—Cd1ⁱⁱ	138.37 (6)	Te1—O1—Cd1^xix	98.13 (7)
O1^x—Te1—Cd1ⁱⁱ	100.35 (6)	Cd1—O1—Cd1^xix	116.00 (7)
O1^xi—Te1—Cd1ⁱⁱ	79.65 (6)	Cd1ⁱⁱ—O1—Cd1^xix	93.05 (7)
O1—Te1—Cd1ⁱⁱ	41.63 (6)	Te2—O2—Cd1^vii	147.03 (10)
Cd1^xv—Te1—Cd1ⁱⁱ	62.223 (1)	Te2—O2—Cd1^xi	100.35 (7)
Cd1^xvi—Te1—Cd1ⁱⁱ	117.776 (1)	Cd1^vii—O2—Cd1^xi	97.59 (7)
O1^viii—Te1—Cd1^xvii	133.08 (5)	Te2—O2—Cd1	99.25 (7)
O1ⁱⁱⁱ—Te1—Cd1^xvii	46.92 (5)	Cd1^vii—O2—Cd1	97.80 (7)
O1^ix—Te1—Cd1^xvii	41.63 (6)	Cd1^xi—O2—Cd1	115.12 (8)

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

Selected bond lengths (Å) in rhombohedral β-Cd₃TeO₆ and in isotypic (Cd_1.5Mn_1.5)TeO₆ and Mn₃TeO₆ top

	β-Cd₃TeO₆^a	Cd_1.5Mn_1.5TeO₆^b	Mn₃TeO₆^c
M1—O1	2.2348 (17)	2.147	2.1055 (14)
M1—O2ⁱ	2.2455 (17)	2.150	2.1275 (13)
M1—O1ⁱⁱ	2.2907 (19)	2.240	2.2009 (13)
M1—O2ⁱⁱⁱ	2.3051 (18)	2.260	2.2311 (12)
M1—O2	2.3370 (18)	2.273	2.2313 (13)
M1—O1^iv	2.4658 (19)	2.412	2.3841 (13)
Te1—O1	1.9339 (17)	1.955	1.9247 (13)
Te2—O2	1.9290 (17)	1.959	1.9214 (12)

Notes: (a) This study; (b) Ivanov et al. (2012) on basis of X-ray powder diffraction data at room temperature (no s.u. given in original publication); (c) Weil (2006) on the basis of single-crystal X-ray data at room temperature. [Symmetry codes: (i) y - 1/3, -x + y + 1/3, -z + 1/3; (ii) -x + 1/3, y + 2/3, -z + 2/3; (iii) -y, x - y, z; (iv) -y + 1/3, x - y + 2/3, z - 1/3.]

Acknowledgements

The X-ray centre of the TU Wien is acknowledged for financial support and for providing access to the single-crystal and powder X-ray diffractometers.

Funding information

TV acknowledges the Erasmus+ programme for an educational exchange.

References

Aroyo, M. I., Perez-Mato, J. M., Capillas, C., Kroumova, E., Ivantchev, S., Madariaga, G., Kirov, A. & Wondratschek, H. (2006). Z. Kristallogr. 221, 15–27. Web of Science CrossRef CAS Google Scholar
Badie, J. M. (1973). C. R. Acad. Sci. Ser. C, 277, 1365–1366. Google Scholar
Belsky, A., Hellenbrandt, M., Karen, V. L. & Luksch, P. (2002). Acta Cryst. B58, 364–369. Web of Science CrossRef CAS IUCr Journals Google Scholar
Brinks, H. W. & Hauback, B. C. (2003). J. Alloys Compd. 354, 143–147. Web of Science CrossRef Google Scholar
Bruker (2015). APEX3 and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA. Google Scholar
Burckhardt, H.-G., Platte, C. & Trömel, M. (1982). Acta Cryst. B38, 2450–2452. CrossRef CAS Web of Science IUCr Journals Google Scholar
Christy, A. G., Mills, S. J. & Kampf, A. R. (2016). Miner. Mag. 80, 415–545. Web of Science CrossRef Google Scholar
Dowty, E. (2006). ATOMS for Windows. Shape Software, Kingsport, TN, USA. Google Scholar
Flor, G. de la, Orobengoa, D., Tasci, E., Perez-Mato, J. M. & Aroyo, M. I. (2016). J. Appl. Cryst. 49, 653–664. Web of Science CrossRef IUCr Journals Google Scholar
Gagné, O. C. & Hawthorne, F. C. (2018). Acta Cryst. B74, 63–78. Web of Science CrossRef IUCr Journals Google Scholar
Gelato, L. M. & Parthé, E. (1987). J. Appl. Cryst. 20, 139–143. CrossRef Web of Science IUCr Journals Google Scholar
Holc, J. & Golic, L. (1983). J. Solid State Chem. 48, 396–400. CrossRef Web of Science Google Scholar
Hottentot, D. & Loopstra, B. O. (1979). Acta Cryst. B35, 728–729. CrossRef CAS IUCr Journals Web of Science Google Scholar
Ivanov, S. A., Mathieu, R., Nordblad, P., Politova, E., Tellgren, R., Ritter, C. & Proidakova, V. (2012). J. Magn. Magn. Mater. 324, 1637–1644. Web of Science CrossRef Google Scholar
Ivanov, S. A., Mathieu, R., Nordblad, P., Ritter, C., Tellgren, R., Golubko, N., Mosunov, A., Politova, E. D. & Weil, M. (2014). Mater. Res. Bull. 50, 42–56. Web of Science CrossRef Google Scholar
Ivanov, S., Nordblad, P., Mathieu, R., Tellgren, R., Politova, E. & André, G. (2011). Eur. J. Inorg. Chem. pp. 4691–4699. Web of Science CrossRef Google Scholar
Kaminaga, Y., Yamane, H. & Yamada, T. (2006). Acta Cryst. C62, i57–i58. Web of Science CrossRef CAS IUCr Journals Google Scholar
Klüver, E. & Müller-Buschbaum, H. (1994). Z. Anorg. Allg. Chem. 620, 733–736. Google Scholar
Krämer, V. & Brandt, G. (1985). Acta Cryst. C41, 1152–1154. CrossRef Web of Science IUCr Journals Google Scholar
Krause, L., Herbst-Irmer, R., Sheldrick, G. M. & Stalke, D. (2015). J. Appl. Cryst. 48, 3–10. Web of Science CSD CrossRef CAS IUCr Journals Google Scholar
Løvvik, O. M., Opalka, S. M., Brinks, H. W. & Hauback, B. C. (2004). Phys. Rev. B, 69, 134117-, 1–1341179. Google Scholar
Müller, D., Assenmacher, W. & Mader, W. (2004). Z. Anorg. Allg. Chem. 630, 2483–2489. Google Scholar
Schulz, H. & Bayer, G. (1971). Acta Cryst. B27, 815–821. CrossRef IUCr Journals Web of Science Google Scholar
Shannon, R. D. (1976). Acta Cryst. A32, 751–767. CrossRef CAS IUCr Journals Web of Science Google Scholar
Sheldrick, G. M. (2015). Acta Cryst. A71, 3–8. Web of Science CrossRef IUCr Journals Google Scholar
Siegel, S. & Gebert, E. (1964). Acta Cryst. 17, 790. CrossRef IUCr Journals Web of Science Google Scholar
Singh, H., Sinha, A. K., Ghosh, H., Singh, M. N., Rajput, P., Prajapat, C. L., Singh, M. R. & Ravikumar, G. (2014). J. Appl. Phys. 116, 074904. Web of Science CrossRef Google Scholar
Sleight, A. W., Foris, C. M. & Licis, M. S. (1972). Inorg. Chem. 11, 1157–1158. CrossRef Web of Science Google Scholar
Weil, M. (2004). Solid State Sci. 6, 29–37. Web of Science CrossRef CAS Google Scholar
Weil, M. (2006). Acta Cryst. E62, i244–i245. Web of Science CrossRef IUCr Journals Google Scholar
Weil, M. & Stöger, B. (2018). Unpublished results. Google Scholar
Weil, M., Stöger, B., Gierl-Mayer, C. & Libowitzky, E. (2016). J. Solid State Chem. 241, 187–197. Web of Science CrossRef Google Scholar
Westrip, S. P. (2010). J. Appl. Cryst. 43, 920–925. Web of Science CrossRef CAS IUCr Journals Google Scholar
Wulff, L., Wedel, B. & Müller-Buschbaum, H. (1998). Z. Naturforsch. Teil B, 53, 49–52. CrossRef CAS Google Scholar
Źemcźuźny, S. & Rambach, F. (1909). Z. Anorg. Allg. Chem. 65, 403–428. Google Scholar