Order–disorder (OD) polytypism of K3FeTe2O8(OH)2(H2O)1+x

Wolflehner, T.; Stöger, B.

doi:10.1107/S2052520623009162

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STRUCTURAL SCIENCE
CRYSTAL ENGINEERING
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ISSN: 2052-5206

Volume 79| Part 6| December 2023| Pages 510-518

https://doi.org/10.1107/S2052520623009162

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Order–disorder (OD) polytypism of K₃FeTe₂O₈(OH)₂(H₂O)_1+x

Tobias Wolflehner ^a and Berthold Stöger ^a ^*

^aX-Ray Centre, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
^*Correspondence e-mail: bstoeger@mail.tuwien.ac.at

Edited by K. E. Knope, Georgetown University, USA (Received 27 June 2023; accepted 18 October 2023; online 7 November 2023)

K₃FeTe₂O₈(OH)₂(H₂O)₂ was synthesized under hydrothermal conditions from Te(OH)₆, FeSO₄·7H₂O and 85 wt% KOH in a 1:2:6 molar ratio. The crystal structure is built of a triperiodic network. One disordered water molecule per formula unit is located in a channel and can be partially removed by heating. Systematic one-dimensional diffuse scattering indicates a polytypic character, which is best described by application of the order–disorder theory. The major polytype is monoclinic with pseudo-orthorhombic metrics. It is interrupted by fragments of an orthorhombic polytype. The diffraction intensities are analyzed using structure factor calculations.

Keywords: polytypism; OD theory; X-ray diffraction; tellurate.

CCDC references: 2301936; 2301937

1. Introduction

Single crystals of the hydrous potassium iron(III) tellurium(VI) oxide K₃FeTe₂O₈(OH)₂(H₂O)₂ were grown under hydrothermal conditions in an attempt to synthesize Fe analogues of K₂Ni₂TeO₆, a fast potassium ion conductor with potential application as battery materials (Masese et al., 2018 ). On heating, weakly-bound water is gradually lost, resulting in K₃FeTe₂O₈(OH)₂(H₂O)_1+x (0 ≤ x < 1) with otherwise unchanged structure. The fully hydrated compound and the partially dehydrated products can be formulated as K₃FeTe₂O₈(OH)₂(H₂O)_1+x.

The title compounds feature order–disorder (OD) polytypism (Dornberger-Schiff & Grell-Niemann, 1961 ). This means that the structure is built of layers that can be stacked in different ways and all are locally equivalent. In particular, adjacent pairs of layers contact in such a way that the resulting pairs are geometrically equivalent. The OD theory thus interprets the common occurrence of polytypism and provides a unified description of families of OD structures.

Herein, a detailed OD description of K₃FeTe₂O₈(OH)₂(H₂O)_1+x is given. The diffraction pattern is analyzed using structure factor calculations.

2. Experimental

2.1. Synthesis

A mixture of Te(OH)₆, FeSO₄·7H₂O and 85 wt% KOH in a 1:2:6 molar ratio were introduced into PTFE inlays with ∼3 ml inner volume. The inlays were three-quarters filled with deionized water, introduced into steel autoclaves and placed in a pre-heated drying closet at 210°C. After three days, the autoclaves were cooled in air for ∼4 h. The solid residue was washed twice with water and twice with isopropanol and finally dried at 35°C in air to give single phase K₃FeTe₂O₈(OH)₂(H₂O)₂ according to powder X-ray diffraction. The product was obtained as a mixture of microcrystalline powder and tiny lath-shaped single crystals.

2.2. Single crystal diffraction

Single crystals of K₃FeTe₂O₈(OH)₂(H₂O)₂ were selected under a polarizing microscope. A 300 K dataset was collected on a Bruker KAPPA APEX II diffractometer system equipped with a Mo Kα sealed tube, a CCD detector and an Oxford Cryosystems Cryostream 800. High temperature measurements and reciprocal space maps were collected on a STOE Stadivari diffractometer system equipped with a Mo Kα microsource, a DECTRIS Eiger CdTe hybrid photon-counting (HPC) detector and a STOE Heatstream heating system. To reconstruct the diffuse scattering, a room temperature dataset with very long exposure times (120 s per degree) was collected, taking advantage of the practically zero-noise of HPC detectors.

Data were processed using the APEX4 suite (Bruker, 2022 ) and X-Area (STOE & Cie GmbH, 2021 ). Corrections for absorption effects were applied using the multi-scan approach followed by a spherical absorption correction implemented in SADABS (Bruker, 2022) and LANA (STOE & Cie, 2021). Data collection and refinement details are compiled in Table 1.

Table 1
Data collection and refinement details

	K₃FeTe₂O₈(OH)₂(H₂O)₂	K₃FeTe₂O₈(OH)₂(H₂O)_1.43 (5)
Crystal data
Chemical formula	FeH₆K₃O₁₂Te₂	FeH_4.86K₃O_11.43Te₂
M_r	626.40	616.17
Crystal system, space group	Monoclinic, I2/m	Monoclinic, I2/m
Temperature (K)	300	436
a, b, c (Å)	12.8036 (6), 14.9042 (8), 5.9782 (3)	12.7660 (6), 14.9470 (6), 5.9706 (2)
β (°)	90.002 (2)	90.047 (3)
V (Å³)	1140.80 (10)	1139.27 (8)
Z	4	4
Radiation type	Mo Kα	Mo Kα
ρ_calc (g cm⁻³)	3.647	3.592
μ (mm⁻¹)	7.487	7.491
Crystal size (mm)	0.32 × 0.25 × 0.12	0.18 × 0.08 × 0.01

Data collection
Diffractometer	Bruker KAPPA APEX II	STOE Stadivari
Absorption correction	Multi-scan (SADABS)	Multi-scan (LANA)
T_min, T_max	0.198, 0.467	0.346, 0.929
No. of measured, independent and observed [I > 2σ(I)] reflections
	9677, 2649, 2347	14095, 2711, 2207
R_int	0.0280	0.0431
$[(\sin\theta/\lambda)_{\rm {max}}]$ (Å⁻¹)	0.83	0.83

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.0204, 0.0446, 1.012	0.0370, 0.1011, 1.026
No. of parameters	98	98
Δρ_max, Δρ_min (e Å⁻³)	−0.960, 1.331	−1.670, 3.771
Extinction (SHELXL)	0.00039 (6)	–
Twin operation	2_[100]	2_[100]
Twin volume ratio	53.25 : 46.75 (13)	53.0 : 47.0 (3)
Occupancy Te1:Fe1′	79.2 : 20.8 (2)	79.6 : 20.4 (4)
Computer programs: X-AREA, LANA (STOE & Cie, 2021), SHELXL2014/7 (Sheldrick, 2015a), SHELXT (Sheldrick, 2015b), OLEX2 (Dolomanov et al., 2009 ).

2.3. Structure solution and refinement

The unit-cell parameters strongly suggested an orthorhombic I-centered (oI) lattice. A first structural model was obtained using the dual-space methods implemented in SHELXT (Sheldrick, 2015b ) in the space group Imma. The structure was refined using SHELXL (Sheldrick, 2015a ). Non-hydrogen atoms were refined using anisotropic displacement parameters (ADPs).

The central atom of an [MO₆] octahedron had to be modeled as an occupationally disordered Te/Fe site (labeled as Te1/Fe1) with an 1:1 occupation ratio. Refinements resulted in reasonable reliability factors {R[F² > 2σ(F²)] ≈ 0.06}, however, the ADP tensors were highly anisotropic.

Since we suspected ordering of the Te/Fe site, we attempted structure solutions in the maximal subgroups of Imma with the same translation lattice, also called translationengleiche subgroups (Müller, 2013 ), namely Im2a, I2ma, Imm2, I2₁2₁2₁, I2/m11, I12/m1 and I112/a. The lost symmetry operations survive in the crystalline edifice as twin operations and define the twin law that was applied in the subsequent refinements.

A satisfying structure model was only obtained in I2/m11. The Te/Fe site of the orthorhombic Imma structure split into two sites with distinctly different electron densities. Yet, both sites still had to be modeled as mixed Te/Fe sites (Te1:Fe1′ and Fe1:Te1′) with the overall Te:Fe ratio being fixed to 1:1. For convenience, the axes were permuted to the standard setting of monoclinic space groups (b unique). In this setting, the space group of the final model is I2/m and that of the orthorhombic parent structure is Ibmm.

H atoms were located from difference Fourier maps and the O—H distances were restrained to 0.870 Å. The H atoms of the disordered water molecule in channels of the structure could not be localized. The occupancy of the disordered water molecule refined to 1 within experimental precision for the 300 K dataset and to 43 (5)% for the dataset collected at 436 K.

A further dataset was collected at 489 K, though was of even worse quality and is therefore not presented here. Increasing the temperature to 540 K let to a decomposition of the crystal, as evidenced by planes of diffuse scattering normal to b* (though no formation of powder rings).

3. Results and discussion

3.1. Structure overview

The crystal structures of K₃FeTe₂O₈(OH)₂(H₂O)_1+x (Fig. 1) are built of wavy sheets of a FeTe₂O₈(OH)₂ network extending in the (010) plane. The sheets are connected by K atoms and a water molecule (O6) located on a (010) reflection plane (see Table 2). Channels in the structure extending along [001] are filled with a varying number of water molecules (O7) depending on measurement temperature. Owing to the loss of water, the unit-cell volume decreases marginally from 300 K to 436 K (see Table 1). However, as expected, the overall density decreases on heating. The a parameter decreases by ∼0.3%, owing to a shrinking of the channels.

Table 2
Hydrogen-bond geometries (Å, °) in K₃FeTe₂O₈(OH)₂(H₂O)₂ at 300 K

	O—H	H⋯O	O⋯O	∠(O—H⋯O)
O5—H1⋯O1	0.87	1.927 (17)	2.723 (2)	151 (3)
O6—H2⋯O4 (2×)	0.87	1.816 (14)	2.653 (3)	161 (4)

Figure 1
The crystal structure of K₃FeTe₂O₈(OH)₂(H₂O)₂ viewed along [001]. H (white), O (red) and K (pink) are represented by spheres of arbitrary radius, [TeO₆] and [FeO₆] units by yellow and orange polyhedra, respectively. Hydrogen bonds are indicated by dotted lines.

3.2. OD interpretation

Faint one-dimensional diffuse scattering perpendicular to (010) (Fig. 2) clearly indicated a non-negligible stacking fault probability, i.e. polytypism, which is consistent with the observed twinning and the disorder of the Te1, Fe1 positions. As noted in the introduction, the OD theory often provides convincing arguments for the polytype character of a structure. The crucial step in an OD interpretation is the identification of the OD layers. This is performed by identifying pseudo-symmetry operations that apply only to a part of the structure. These partial operations (POs) may map layers onto themselves or onto a different layer.

Figure 2
Examples of (a) l even and (b) l odd sections through reciprocal space of a K₃FeTe₂O₈(OH)₂(H₂O)₂ crystal reconstructed from a measurement with long exposition times. The indicated reciprocal base is the dual base of (a, b₀, c).

For K₃FeTe₂O₈(OH)₂(H₂O)_1+x, the POs correspond to the lost symmetry operations when descending from the Ibmm parent structure with the equally disordered Fe1/Te1 position to the I2/m polytype with two oppositely disordered positions. Since it is known from diffuse scattering along b* that the OD layers extend in the (010) plane, an OD interpretation in terms of two kinds of layers imposes itself as follows.

The K₃FeTe₂O₈(OH)₂(H₂O)_1+x structures are category IV (Grell & Dornberger-Schiff, 1982 ) OD structures of two kinds of non-polar (with respect to the stacking directions) layers, named A¹ and A². The symbol A is reserved for non-polar layers and the superscript identifies the kind of the layer (Grell & Dornberger-Schiff, 1982). The two kinds of layers appear alternately as indicated in Fig. 1 (right), where the subscript is a sequential number. Note that the exact choice of layer boundary is not relevant as will be shown below and therefore we choose here an interpretation according to crystal chemistry.

The A¹ layers comprise a network of K and water molecules [Fig. 3(a)]. The disordered O7 water molecule is not shown, since it is irrelevant for the OD description. The A² layers [Fig. 3(b)] contain the diperiodic FeTe₂O₈(OH)₂ network where intra-layer hydrogen bonds connect the [TeO₄(OH)₂] units to the [Te1O₆] and [Fe1O₆] octahedra (see O5 atom in Table 2).

Figure 3
The (a) A¹ and (b) A² layers of K₃FeTe₂O₈(OH)₂(H₂O)_1+x projected on the layer plane (010). The idealized symmetry elements according to the OD interpretation are indicated using the usual graphical symbols.

The layers possess Pc(m)m and P1(2/n)1 symmetry according to the OD interpretation, which, as is typical for OD structures, requires a small degree of idealization. The (pseudo-)symmetry operations are given in Fig. 3 using the usual graphical symbols. In the OD literature, layer groups are written with capital Bravais symbols to indicate the three-dimensional nature of the layers and with parentheses marking the direction lacking translations. In contrast, the International Tables for Crystallography use lowercase Bravais symbols owing to the two-dimensionality of the lattice (Kopsky & Litvin, 2006 ). However, the latter symbols imply a stacking direction of [001] and therefore have not found use in the OD literature where alternative stacking directions are often preferable.

The symmetry of a particular OD structure is given by a space groupoid (Ito & Sadanaga, 1976 ) of all its POs, which lacks group character, because POs can only be composed if the target layer of the first is the source layer of the second (Ehresmann, 1957 ). All OD groupoids of structures built according to the same symmetry principle (Fichtner, 1979 ) belong to the same OD groupoid family, which can be considered as a generalization of the 230 space group types. The OD groupoid family symbol of K₃FeTe₂O₈(OH)₂(H₂O)_1+x is

according to the notation of Grell & Dornberger-Schiff (1982

The first line indicates the layer names and the second line the symmetry of the layers. The third line gives the relative position of two adjacent layers in one possible stacking arrangement. [r, s] means that the origins of the layers are related by rc + sa + b₀/2, r and s being metric parameters in addition to the unit-cell parameters (Fichtner, 1979). b₀ is the vector perpendicular to the layer planes and the length corresponding to the width of an A¹A² layer packet (see Fig. 1). For K₃FeTe₂O₈(OH)₂(H₂O)_1+x, the metric parameters adopt the fixed values $[(r,s)=({{1} \over {4}},{{1} \over {4}})]$ . Indeed, the centers of inversion of the A² layers, which define the origin of its layer group, are located at c/4 + a/4 + b₀/2 with respect to the centers of inversion of the A¹ layers (Fig. 3).

3.3. NFZ relationship

The stacking possibilities are derived using the NFZ (Z = N/F) relationship (Ďurovič, 1997 ). In the case of layers of different kinds, the procedure is as follows: the groups of layer operations that do not invert the orientations of the layers with respect to the stacking directions are determined. These groups can be associated with one of the 17 wallpaper group types. One obtains Pc(2)m for A¹ and P1(2)1 for A², respectively. In a second step, the intersection of the groups is formed, i.e. the common operations, called continuations in the OD literature, are determined. Here, the values of (r,s) = $[({{1} \over {4}},{{1} \over {4}})]$ are critical. They cause the 2_[010] rotation axes of both layers to overlap perfectly and therefore the group of common operations is P1(2)1. Finally, a coset decomposition gives the number and orientations of possible stacking arrangements.

For an A¹ → A² contact, there are [Pc(2)m:P1(2)1] = 2 cosets and therefore two ways of placing the A² layer. The second possibility is obtained by applying the c_[100] or equivalently the m_[010] operation of the A¹ layer onto the A² layer. This operation exchanges the Te1 and Fe1 positions [Fig. 3(b)]. In contrast, for an A² → A¹ contact, there is only [P1(2)1:P1(2)1] = 1 way of placing the A¹ layer.

3.4. MDO polytypes and family structure

According to the OD construction, A¹_nA²_n+1 pairs are geometrically equivalent. Likewise, all A¹_nA²_n+1A¹_n+2 triples are equivalent, since there is only one way of placing the A¹ layers (see previous section). However, there are two kinds of A²_nA¹_n+1A²_n+2 triples, namely those where the A² layers are related by the m_[010] operation of the central A¹ layer and those where they are related by the 2_[100] operation.

The polytypes containing only one of the two kinds of triples are said to be of a maximum degree of order (MDO) (Dornberger-Schiff & Grell, 1982 ). Assuming that the two triples are energetically slightly different, and therefore one is preferred during crystallization, one would assume that ordered polytypes are usually of the MDO kind. Even though a simplistic view, this is indeed very often the case, though exceptions do exist (Nespolo, 2001 ; Hybler, 2016 ). MDO polytypes are particularly important in an OD interpretation, as all other polytypes can be decomposed into fragments of the MDO polytypes.

The layer symmetries of the two MDO polytypes of K₃FeTe₂O₈(OH)₂(H₂O)_1+x are schematized in Figs. 4(a) and 4(b). Operations valid for the whole polytype are indicated in red. The geometric elements of the layers (their symmetry frameworks) are located at the same positions in all polytypes, but the global symmetries differ. The MDO₁ polytype has I2/m symmetry, lattice basis vector b = 2b₀ in the conventional setting and corresponds to the major polytype of the crystals under investigation. The MDO₂ polytype has Pbnn symmetry with the same unit-cell parameters as MDO₁, but a primitive lattice. The P1(2/n)1 symmetry of the A² layers is retained in both polytypes. The idealized Pc(m)m symmetry of the A¹ layers is reduced to P1(2/m)1 (MDO₁) and P2(2)2₁ (MDO₂), respectively.

Figure 4
Layer symmetries of the (a) MDO₁, (b) MDO₂ and (c) family structure of K₃FeTe₂O₈(OH)₂(H₂O)_1+x according to the OD description. Symmetry elements of the layers are indicated by the usual graphical symbols. Elements that apply to the whole structure are drawn in red. The unit cells are indicated by a grey rectangle.

The family structure is a fictitious disordered polytype, where all stacking possibilities are realized to the same degree. Its symmetry is schematized in Fig. 4(c). Here the Pc(m)m symmetry of the A¹ layers is retained and the symmetry of the A² layers increases from P1(2/n)1 to Pc(n)m. The family structure corresponds to the disordered Ibmm structure of the first refinement attempts described above.

Since the point group of the MDO₁ polytype (2/m) is a subgroup of the point group of the family structure (mmm) of index 2, stacking faults lead to domains with two different orientions. The domain orientations are related by the point operations of the family structure that are not point operations of the polytype: 2_[100], m_[100], 2_[001] and m_[001]. If the domain size is smaller than the coherence length of the radiation, one obtains a disordered structure with higher symmetry. If it is distinctly larger, then the crystal is a twin and the given operations constitute the twin law. If the twin domains are distinctly smaller than the crystal size, the twin volume fractions are approximately equal for statistical reasons. If there are only few stacking faults per crystal, one may obtain twins with unequal volume fractions.

The crystals under investigation were refined at the same time as disordered and twins with equal twin volume fractions, which indicates domain sizes in the region of the coherence length (see Table 1). This is consistent with the observed weak diffuse scattering.

MDO₂ and the family structure share the same point group, which means that stacking faults in MDO₂ give domains with the same orientation, but different translation states. Since translations lead to a phase shift of the scattered radiation, these are called antiphase domains.

3.5. Desymmetrization

Since the actual symmetry of the layers is in general decreased compared to the idealized OD description, one can expect a certain degree of desymmetrization (Ďurovič, 1979 ), i.e. deviation from the idealized symmetry. A full quantification of desymmetrization requires structural data of distinct polytypes (Ďurovič, 1979), which are not available for the title compounds. One can, however, create an idealized version of the layers with symmetry according to the OD description and quantify the deviation from that idealized structure.

Table 3 lists the distances of the actual A¹ layer atoms to the idealized layer. Here, some atoms of the [MO₆] octahedra have been included in the layer, even though crystal-chemically they belong to the A² layers. This is justified by the minute desymmetrization, with the largest deviation of only 0.053 Å. Clearly, the OD description of the A¹ layers is valid.

Table 3
Distances d of atoms in the actual A¹ layer from those in the idealized A¹ layer, obtained by moving the atoms onto the idealized Wyckoff positions

Data derived from the model of K₃FeTe₂O₈(OH)₂(H₂O)₂. The disordered O7 water molecule and the H atoms were ignored.

Atom	Site symmetry	d (Å)
K1	.m.	0.011
K2	2mm	0.017
O4	.m.	0.053
O5	.m.	0.033
O6	2mm	0.042

The A² layers possess their full symmetry in the MDO polytypes and therefore cannot be idealized. It is nevertheless interesting to quantify the deviation from the Ibmm family structure obtained by applying the m_[001] symmetry, averaging close atoms and moving the atoms onto the Ibmm Wyckoff positions (see Table 4). In this idealized layer, the Te1 and Fe1 atoms share a single position. Apart from that, the deviation from Pc(n)m symmetry is surprisingly minute (max. 0.065 Å). This shows that in principle the whole structure with exception of the Te1 and Fe1 positions adopts the Ibmm family structure symmetry, a crucial fact used in the next section to analyze the diffraction pattern. Moreover, it means that the choice of interface between the OD layers is not important as long as the Te1/Fe1 atoms are located in the A² layer.

Table 4
Distances d of atoms in the actual A² layer to those in the hypothetical A² layers

Data derived from the model of K₃FeTe₂O₈(OH)₂(H₂O)₂.

Atom	Site symmetry	d (Å)
Fe1/Te1	.2.	0.002
Te2	..2/m	0
O1	..m	0.065
O2/O3	1	0.012

3.6. Diffraction intensities of the MDO polytypes

The diffraction patterns of the title compounds will be described with respect to the basis $[({\bf a}^{*},{\bf b}_{0}^{*},{\bf c}^{*})]$ , which is the dual basis of (a, b₀, c). Since all layers possess a translation lattice spanned by (a, c), diffraction intensities can only appear on rods $[h{\bf a}^{*}+\nu{\bf b}_{0}^{*}+l{\bf c}^{*}]$ , whereby h and l are integers, and ν is a real number.

The reflections corresponding to the family structure are called family reflections and are always sharp. Those of other polytypes are called characteristic reflections and may be more or less diffuse, depending on the degree of order. In many OD structures, the intensities of the family reflections are identical for all polytypes (up to a scaling factor). This is the case if the polytypes can be decomposed into layers that are translationally equivalent, i.e. the polytypes differ only in the origin of the layers, but not their orientation. For the title compounds however, the A² layers appear with different orientations and therefore the family reflections may possess different intensities. The diffraction intensities therefore deserve a closer look.

The diffraction patterns of disordered polytypic structures are characterized by a coexistence of discrete and diffuse scattering. Such intensity distributions cannot be expressed using real density functions. Instead, they are properly described by measures or distributions [see Bricogne (2010 ), Baake & Grimm (2013 )]. The classical example of a measure that is not a proper real function is the Dirac measure δ, which associates the weight of 1 to the point x = 0. Since the integral of a function that is zero everywhere except at x = 0 is 0, δ cannot be a function.

Here, we will disregard such subtleties and use the `equivalence'

$[\sum_{n\in{\bb Z}}\exp(2\pi{\rm i}n\nu)=\sum_{k\in{\bb Z }}\delta(\nu-k), \eqno(1)]$

where δ(ν − k) is the Dirac measure centered at the point k. The equivalence is to be understood in a weak sense, as the function series to the left side does not converge at any point and the right side is not a function.

Since only the positions of the Te1 and Fe1 atoms differ among polytypes, it is useful to consider the contributions of these and the remaining atoms separately. Instead of partitioning the polytypes into two kinds of layers as in the OD description above, it will be described in terms of layers L_n of one kind (Fig. 1, left side), which are further decomposed into the Te1/Fe1 atoms ( L_n¹) and the remaining atoms ( L_n⁰). The corresponding structure factors are F_n¹ and F_n⁰, respectively.

Owing to the I-centering of the family structure L_n⁰ is derived from L₀⁰ by a translation of n(a/2 + c/2 + b₀). The Te1/Fe1 atoms may additionally be translated by c/2 and thus the corresponding translation vector is n(a/2) + (n + a_n)(c/2) + nb₀, where $[(a_{n})_{n\in{\bb Z}}]$ is a bi-infinite sequence with a_n = 0, 1. This sequence fully describes the polytype.

In consequence, the structure factor of the L_n layer is

$[F_{n}(h\nu l)=F_{n}^{0}(h\nu l)+F_{n}^{1}(h\nu l) \eqno(2)]$

with

$[F_{n}^{0}(h\nu l)=F_{0}^{0}(h\nu l)\exp\Big[2\pi{\rm i}n\big(\textstyle{h\over 2}+\nu+ \textstyle{l\over 2}\big)\Big] \eqno(3)]$

and

$[F_{n}^{1}(h\nu l)=F_{0}^{1}(h\nu l)\exp(2\pi{\rm i}a_{n}\textstyle{l\over 2}) \exp\Big[2\pi{\rm i}n\big(\textstyle{h\over 2}+\nu+\textstyle{l\over 2}\big)\Big]. \eqno(4)]$

For l even, $[\exp(2\pi{\rm i}a_{n}\textstyle{l\over 2})=1]$ and therefore

$[F_{n}(h\nu l)=\Big[F_{0}^{0}(h\nu l)+F_{0}^{1}(h\nu l)]\exp[2\pi {\rm i}n\big(\textstyle{h\over 2}+\nu+\textstyle{l\over 2}\big)\Big]\eqno(5)]$

Since this expression is independent of $[(a_{n})_{n\in{\bb Z}}]$ , all polytypes possess the same diffraction pattern on rods l even, which consists of sharp reflections corresponding to the family structure. This is in agreement experimental observations [Fig. 2(a)].

Henceforth, only the case l odd will be considered and the function arguments hνl will be omitted for brevity. Diffraction intensities of polytypes formally calculate as

$[I=\left|\sum_{n\in{\bb Z}}F_{n}\right|^{2}=\left(\sum_{n\in {\bb Z}}F_{n}\right)\left(\sum_{n\in{\bb Z}}F_{n}^{*}\right)\eqno(6)]$

$[=\sum_{n\in{\bb Z}}\sum_{\Delta n\in{\bb Z}}F_{n+\Delta n}\,F _{n}^{*}\eqno(7)]$

$[=\sum_{n\in{\bb Z}}\sum_{\Delta n\in{\bb Z}}\left(F_{n+ \Delta n}^{0}F_{n}^{0*}+F_{n+\Delta n}^{0}F_{n}^{1*}+F_{n+\Delta n}^{1}F_{n}^{ 0*}+F_{n+\Delta n}^{1}F_{n}^{1*}\right),\eqno(8)]$

where an asterisk indicates the complex conjugate and it should be stressed again that these function series do not converge at any point. Let us consider the individual terms of equation (8) and introduce the abbreviation φ_Δn = 2πΔn[(h/2) + ν + (l/2)]. The first term is independent of $[(a_{n})_{n\in{\bb Z}}]$ and can be expressed in terms of F₀⁰ by substituting equation (3) as

$[\displaystyle F_{n+\Delta n}^{0}F_{n}^{0*}=F_{0}^{0}F_{0}^{0*}\exp({\rm i} \varphi_{\Delta n}).\eqno(9)]$

The second and third cross terms depend on $[(a_{n})_{n\in{\bb Z}}]$ and can be written in terms of F₀⁰ and F₀¹ as [see equations (3), (4)]

$[ F_{n+\Delta n}^{0}F_{n}^{1*}=F_{0}^{0}F_{0}^{1*}\exp(2\pi {\rm i}a_{n+\Delta_{n}}\textstyle{l\over 2})\exp\big({\rm i}\varphi_{\Delta n}\big)\eqno(10)]$

$[=F_{0}^{0}F_{0}^{1*}(-1)^{a_{n+\Delta_{n}}}\exp\big({\rm i}\varphi _{\Delta n}\big)\eqno(11)]$

and

$[F_{n+\Delta n}^{1}F_{n}^{0*}=F_{0}^{1}F_{0}^{0*}\exp\big(-2\pi {\rm i}a_{n+\Delta_{n}}\textstyle{l\over 2}\big)\exp\big({\rm i}\varphi_{\Delta n}\big)\eqno(12)]$

$[=F_{0}^{1}F_{0}^{0*}(-1)^{a_{n+\Delta_{n}}}\exp\big({\rm i}\varphi _{\Delta n}\big),\eqno(13)]$

where we used the fact that l is odd and a_n = 0, 1. Finally, the forth term depends on the differences a_n+Δn − a_n [see equation (4)]:

$[F_{n+\Delta n}^{1}F_{n}^{1*}=F_{0}^{1}F_{0}^{1*}\exp[2\pi {\rm i}\big(a_{n+\Delta_{n}}\big)\textstyle{l\over 2}-a_{n}]\exp\big({\rm i}\varphi_{\Delta n}\big)\eqno(14)]$

$[\displaystyle=F_{0}^{1}F_{0}^{1*}(-1)^{a_{n+\Delta_{n}}-a_{n}}\exp\big({\rm i} \varphi_{\Delta n}\big).\eqno(15)]$

Combining these terms, the overall intensity I can be expressed using two kinds of probabilities. Let P be the probability that a_n = 0 for any n. Moreover, let P_Δn be the probability that a_n+Δn = a_n. The probabilities are compiled for the MDO polytypes and the family structure in Table 5. Note that P = 0, 1 both correspond to the MDO₁ polytype, however to the two different twin individuals. Moreover, $[P\approx{1\over 2}]$ for any structure with a substantial stacking fault probability.

Table 5
Probabilities P, P_Δn and the derived `correlations' c = 2P − 1 and c_Δn = 2P_Δn − 1 for the MDO polytypes, the family structure and disordered structures with a substantial stacking fault probability

	MDO₁	MDO₂	Family	Disordered
P	0 or 1	$[1\over 2]$	$[1\over 2]$	$[1\over 2]$
c	− 1 or 1	0	0	0
P_Δn	1	0 (Δn odd), 1 (Δn even)	$[1\over 2]$ (Δn ≠ 0), 1 (Δn = 0)	Depends
c_Δn	1	(−1)^Δn	0 (Δn ≠ 0), 1 (Δn = 0)	Depends

Then, equation (8) becomes

$[\eqalignno{I &\propto F_{0}^{0}F_{0}^{0*}\Bigg(\sum_{\Delta n\in{\bb Z}} \exp\big({\rm i}\varphi_{\Delta n}\big)\Bigg)+ c\big(F_{0}^{0}F_{0}^{1*} + F_{0}^{1}F_{0} ^{0*}\big)\cr &\times\Bigg(\sum_{\Delta n\in{\bb Z}}\!\exp\big({\rm i}\varphi_{\Delta n}\big) \Bigg)+F_{0}^{1}F_{0}^{1*}\Bigg(\sum_{\Delta n\in{\bb Z}}c_{\Delta n}\exp\big( {\rm i}\varphi_{\Delta n}\big)\Bigg) &(16)}]$

$[\eqalignno{\,\,&=\Big[F_{0}^{0}F_{0}^{0*}+c\big(F_{0}^{0}F_{0}^{1*}+F_{0}^{1}F_{0}^{ 0*}\big)\Big]\sum_{k\in{\bb Z}}\delta\bigg(\nu-\textstyle{h\over 2}-k-{l\over 2}\bigg)\cr &+ F_{0}^{1}F_{0}^{1*}\Bigg (\sum_{\Delta n\in{\bb Z}}c_{\Delta n}\exp\big({\rm i}\varphi_{\Delta n}\big) \Bigg), &(17)}]$

where c = 2P − 1 and c_Δn = 2P_Δn − 1 (c being a form of correlation). Thus, there are two distinct contributions to the intensities on rods l odd. The first term describes Dirac (Bragg) peaks located at the positions of the family reflections. For MDO₂, the family structure and substantially disordered stacking arrangements, c = 0 (see Table 5) and thus the reflection intensities are given only by $[F_{0}^{0}F_{0}^{0*}=|F_{0}|^{2}]$ . In contrast, for MDO₁ the intensity is modified by the cross term $[\pm(F_{0}^{0}F_{0}^{1*}+F_{0}^{1}F_{0}^{0*})]$ , where the sign depends on the orientation of the twin domain. Note that an expression of the form AB* + B*A is real, but may be negative. Geometrically, it corresponds to the scalar product of A and B in the complex number plane.

Only the second term of equation (17) with the $[F_{0}^{1}F_{0}^{1*}=|F_{0}^{1}|^{2}]$ factor may result in diffuse scattering in the case of disordered stacking arrangements, which means that only the Te1/Fe1 atoms contribute to diffuse scattering. The term may however also produce Dirac peaks when the stacking is ordered. In particular, it may add additional intensity to the family reflections. Substituting the c_Δn value from Table 5, the F₀¹F₀^1* contribution to the diffraction intensities calculates as:

MDO₁: $[F_{0}^{1}F_{0}^{1*}\sum_{k\in{\bb Z}}\delta(\nu-{h\over 2}-k-{l\over2})]$ ,

MDO₂: $[F_{0}^{1}F_{0}^{1*}\sum_{k\in{\bb Z}}\delta(\nu-{h \over 2}-k-{l \over 2}-{1 \over 2})]$ ,

Family structure: F₀¹F₀^1*.

For MDO₁, additional intensity is added to the family reflections, for MDO₂ additional peaks between the family reflections, as expected given its lack if I-centering. The family structure produces an unstructured streak with the form given by F₀¹F₀^1*. Even though in general $[F_{0}^{1}F_{0}^{1*}>0]$ , technically the diffuse scattering of the family structure does not contribute to the intensities of the Dirac peaks. The latter is given as the integral of an infinitesimally area below the peak, which is non-zero for a Dirac peak, but vanishes for a regular distribution (i.e. a distribution corresponding to a real function). However, in actual crystals, the Bragg peaks possess a non-zero width owing to experimental artifacts and imperfect crystals and therefore Bragg intensities will be affected by diffuse scattering.

Table 6 summarizes the diffraction intensities of the MDO polytypes and the family structure on rods l odd. The MDO polytypes (two twin domains in case of MDO₁) and the family structure can be clearly distinguished from Bragg intensities. For MDO₁, the L_n layers are all translationally equivalent, and therefore the diffraction intensity corresponds to the structure amplitude of a single layer $[|F_{0}^{0}+F_{0}^{1}|^{2}]$ . In the other twin domain, the L⁰_n components are unchanged by the twin operation, because L⁰ possesses the point symmetry of the family structure. The exchange of the Fe and Te atoms in the L¹_n components can also be described by a translation along c/2, which corresponds on rods l odd to a phase shift of π and thus the structure factor here is $[|F_{0}^{0}-F_{0}^{1}|^{2}]$ . In MDO₂ and disordered stacking arrangements, such as the family structure, phases of the L¹_n components cancel out systematically or randomly and the structure factor is accordingly $[|F_{0}^{0}|^{2}]$ .

Table 6
Contributions to Bragg peaks on rods l odd

	$[\textstyle{h\over 2}+k+{l\over 2}\in{\bb Z}]$ (family reflections)	$[\textstyle{h\over 2}+k+{l\over 2}+{1\over 2}\in{\bb Z}]$
MDO₁	$[F_{0}^{0}F_{0}^{0}+(F_{0}^{0}F_{0}^{1}+F_{0}^{1}F_{0}^{0})+F_{0}^{1}F_{0}^{ 1}=\|F_{0}^{0}+F_{0}^{1}\|^{2}]$	0
MDO₁ (m_[001])	$[F_{0}^{0}F_{0}^{0}-(F_{0}^{0}F_{0}^{1}+F_{0}^{1}F_{0}^{0})+F_{0}^{1}F_{0}^{ 1}=\|F_{0}^{0}-F_{0}^{1}\|^{2}]$	0
1:1 MDO₁ twin	$[F_{0}^{0}F_{0}^{0}+F_{0}^{1}F_{0}^{1}=\|F_{0}^{0}\|^{2}+\|F_{0}^{1}\|^{2}]$	0
MDO₂	$[F_{0}^{0}F_{0}^{0*}=\|F_{0}^{0}\|^{2}]$	$[F_{0}^{1}F_{0}^{1*}=\|F_{0}^{1}\|^{2}]$
Family structure	$[F_{0}^{0}F_{0}^{0*}=\|F_{0}^{0}\|^{2}]$	0

A quantification of the contribution of the different terms is given in Fig. 5 for the (1ν3)* rod of MDO₁ (both twin domains) and MDO₂. The intensities of the polytypes are indicated by blue dots. Note that for MDO₁ the intensities correspond perfectly to the calculated $[|F_{0}^{0}+F_{0}^{1}|^{2}]$ value since MDO₁ is generated by repeated translation of a single layer. In contrast for the alternative twin domain and MDO₂ the values differ slightly from $[|F_{0}^{0}-F_{0}^{1}|^{2}]$ owing to desymmetrization (deviation from m_[100] symmetry of the actual layers). Nevertheless, the tiny deviation proves the validity of the idealization.

Figure 5
Diffraction intensities of (a) MDO₁, (b) its m_[100] twin domain and (c) MDO₂ on the (1ν3)* rod, represented by blue dots. The relevant factors contributing to the diffraction intensities are given by green ( $[|F_{0}^{0}|^{2}]$ ), blue ( $[|F_{0}^{1}|^{2}]$ ) and yellow ( F₀⁰F₀^1*+F₀¹F₀^0*) curves.

The cross term F₀⁰F₀^1*+F₀¹F₀^0* is surprisingly pronounced and changes sign, which makes the MDO polytypes clearly distinguishable based on the intensities of the family reflections. The $[|F_{0}^{1}|^{2}]$ term, which is responsible for the diffuse scattering though is weak. In fact, assuming equal displacement parameters T of Te1 and Fe1, $[|F_{0}^{1}|^{2}]$ calculates as T²|f_Te − f_Fe|², where f stands for the atomic form factors. In other words, the contribution to the diffuse scattering is given by the difference of an Fe and a Te atom (23 electrons).

The same small contribution is also the only difference between a twin of MDO₁ and a fully disordered Imm2 structure as shown in Fig. 6 (also see rows 3 and 5 in Table 6). Thus, these two models are surprisingly hard to distinguish.

Figure 6
Diffraction intensities of a 1:1 MDO₁ twin (yellow dots) and the fully disordered family structure (blue circles). The relevant factors contributing to the diffraction intensities are given by green ( $[|F_{0}^{0}|^{2}]$ ) and blue ( $[|F_{0}^{1}|^{2}]$ ) curves.

The intensities of the crystal under investigation lie between these two cases, whence the Te1/Fe1 positions had to be modelled as disordered in a ∼ 80 : 20 manner. There must therefore be rather large MDO₁ domains on the order of magnitude of the coherence length of the employed X-ray radiation. Yet, there must also be rather frequent stacking faults resulting in apparent disorder. This shows a fundamental problem in evaluating such data: the coherence length is not precisely known. In fact, it cannot even be assumed to be a fixed value. In other words, the refined Te1/Fe1 ratio cannot be used to estimate the size of the respective domains as the extent of the twin character (i.e. the ratio of coherent and non-coherent diffraction between the domains) is not known.

Even though with long exposition times the diffuse scattering is clearly observed [Fig. 2(b)], its intensity is too weak for quantitative analysis (Fig. 7). This is due to the weak contribution of Fe1/Te1 and because the crystals are at the border between disordered and twinned crystals. The one-dimensional streaks are unstructured, as would be expected for occasional stacking faults.

Figure 7
Comparison of the experimental (3ν1)* and (3ν2)* rods of diffuse scattering (compare Fig. 2

). Splitting of the Bragg reflections at ν = −2 and $[\nu=-2{{1} \over {2}}]$ is due to a small secondary domain, also seen in Fig. 2

4. Conclusion and outlook

Application of the OD theory has again confirmed its status as `the theory of polytypism' by rationalizing the occurrence of stacking disorder and by classifying the polytype family according to its symmetry principle. However, it remains poorly known in significant parts of the structural science community, even though polytypism is an universal phenomenon. This is certainly due to poor accessibility (e.g. lack of software support and standardized notations), but also shortcomings in the theory itself (e.g. ambiguities in the choice of layers). Therefore effort should be put into improving the accessibility and the foundation of the theory.

We also showed that single-crystal diffraction in such a case is an unrivaled tool to structurally characterize the average crystal structure. When it comes to the real structure, however, such as quantification of stacking fault probabilities, complementary methods are required.

Supporting information

CCDC references: 2301936; 2301937

Crystal structure: contains datablocks 300K, 436K. DOI: https://doi.org/10.1107/S2052520623009162/yv5013sup1.cif

Structure factors: contains datablock 300K. DOI: https://doi.org/10.1107/S2052520623009162/yv5013300Ksup2.hkl

Structure factors: contains datablock 436K. DOI: https://doi.org/10.1107/S2052520623009162/yv5013436Ksup3.hkl

Computing details top

(300K) top

Crystal data top

FeH₆K₃O₁₂Te₂	F(000) = 1156
M_r = 626.40	D_x = 3.647 Mg m⁻³
Monoclinic, I2/m	Mo Kα radiation, λ = 0.71073 Å
a = 12.8036 (6) Å	Cell parameters from 4769 reflections
b = 14.9042 (8) Å	θ = 2.7–36.0°
c = 5.9782 (3) Å	µ = 7.49 mm⁻¹
β = 90.002 (2)°	T = 300 K
V = 1140.80 (10) Å³	Needle
Z = 4	0.32 × 0.25 × 0.12 mm

Data collection top

Bruker KAPPA APEX II CCD diffractometer	2347 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.028
ω– and φ–scans	θ_max = 36.2°, θ_min = 2.7°
Absorption correction: multi-scan SADABS	h = −20→13
T_min = 0.261, T_max = 0.344	k = −24→23
9677 measured reflections	l = −9→9
2649 independent reflections

Refinement top

Refinement on F²	Hydrogen site location: difference Fourier map
Least-squares matrix: full	Only H-atom coordinates refined
R[F² > 2σ(F²)] = 0.020	w = 1/[σ²(F_o²) + (0.0219P)²] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.045	(Δ/σ)_max = 0.015
S = 1.01	Δρ_max = 1.33 e Å⁻³
2649 reflections	Δρ_min = −0.96 e Å⁻³
98 parameters	Extinction correction: SHELXL-2014/7 (Sheldrick 2014, Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
2 restraints	Extinction coefficient: 0.00039 (6)

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.

Refinement. Refined as a 2-component inversion twin.

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Te1	0.0000	0.28339 (2)	0.5000	0.00689 (7)	0.792 (2)
Te1'	0.5000	0.21637 (4)	0.5000	0.00821 (13)	0.208 (2)
Te2	0.2500	0.2500	0.7500	0.00768 (5)
Fe1	0.5000	0.21637 (4)	0.5000	0.00821 (13)	0.792 (2)
Fe1'	0.0000	0.28339 (2)	0.5000	0.00689 (7)	0.208 (2)
K1	0.20295 (4)	0.13035 (4)	0.2484 (4)	0.01802 (10)
K2	0.35236 (6)	0.0000	0.7465 (8)	0.02345 (17)
O1	0.00444 (14)	0.19541 (11)	0.2607 (3)	0.0119 (3)
O2	0.15493 (15)	0.28558 (17)	0.5192 (8)	0.0096 (5)
O3	0.34349 (15)	0.21544 (17)	0.5149 (11)	0.0151 (5)
O4	−0.00836 (13)	0.36920 (11)	0.7399 (4)	0.0114 (3)
O5	0.19305 (13)	0.12767 (12)	0.7469 (13)	0.0148 (3)
H1	0.1270 (7)	0.133 (2)	0.716 (6)	0.022*
O6	0.3513 (2)	0.0000	0.257 (3)	0.0231 (7)
H2	0.3942 (18)	−0.0427 (14)	0.219 (7)	0.035*
O7	0.0425 (5)	0.0000	0.250 (2)	0.149 (3)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Te1	0.00437 (10)	0.01069 (15)	0.00561 (10)	0.000	−0.0012 (3)	0.000
Te1'	0.00572 (18)	0.0124 (3)	0.00653 (18)	0.000	−0.0012 (7)	0.000
Te2	0.00415 (7)	0.01205 (9)	0.00684 (7)	0.00048 (6)	0.0000 (5)	0.00006 (9)
Fe1	0.00572 (18)	0.0124 (3)	0.00653 (18)	0.000	−0.0012 (7)	0.000
Fe1'	0.00437 (10)	0.01069 (15)	0.00561 (10)	0.000	−0.0012 (3)	0.000
K1	0.0189 (2)	0.0192 (2)	0.0159 (2)	0.00463 (19)	0.0002 (7)	0.0004 (7)
K2	0.0168 (3)	0.0223 (4)	0.0312 (4)	0.000	−0.0017 (12)	0.000
O1	0.0097 (6)	0.0122 (7)	0.0139 (7)	0.0001 (6)	0.0017 (16)	−0.0010 (8)
O2	0.0048 (7)	0.0211 (10)	0.0029 (14)	0.0004 (9)	0.0017 (10)	0.0006 (15)
O3	0.0059 (7)	0.0223 (11)	0.0170 (16)	0.0015 (10)	0.0033 (14)	−0.0034 (19)
O4	0.0105 (6)	0.0116 (7)	0.0120 (7)	0.0003 (6)	0.0007 (13)	−0.0006 (8)
O5	0.0099 (7)	0.0134 (7)	0.0210 (8)	−0.0007 (6)	−0.003 (2)	0.003 (2)
O6	0.0132 (11)	0.0140 (12)	0.042 (2)	0.000	−0.001 (4)	0.000
O7	0.045 (3)	0.082 (5)	0.321 (11)	0.000	0.014 (8)	0.000

Geometric parameters (Å, º) top

Te1—O4ⁱ	1.925 (2)	K1—O3	2.717 (5)
Te1—O4	1.925 (2)	K1—O6	2.718 (2)
Te1—O1	1.9414 (18)	K1—O1	2.7214 (18)
Te1—O1ⁱ	1.9414 (18)	K1—O2ⁱⁱⁱ	2.728 (4)
Te1—O2	1.9872 (19)	K1—O7	2.827 (4)
Te1—O2ⁱ	1.9873 (19)	K1—O3ⁱⁱⁱ	2.848 (4)
Te1—Te1'ⁱⁱ	2.9891 (1)	K1—O2	2.890 (4)
Te1—Fe1ⁱⁱⁱ	2.9891 (1)	K1—O5	2.983 (6)
Te1—Fe1ⁱⁱ	2.9891 (1)	K1—O5^viii	3.001 (6)
Te1—Te1'ⁱⁱⁱ	2.9891 (1)	K1—Te2^viii	3.524 (2)
Te1—K1	3.7707 (11)	K1—K1ⁱⁱⁱ	3.7647 (11)
Te1—K1ⁱ	3.7707 (11)	K1—H1	2.96 (4)
Te1'—O3	2.0060 (19)	K2—O5^ix	2.7896 (18)
Te1'—O3^iv	2.0060 (19)	K2—O5	2.7896 (18)
Te1'—O4^v	2.014 (2)	K2—O4ⁱⁱ	2.7922 (17)
Te1'—O4ⁱⁱ	2.014 (2)	K2—O4^x	2.7922 (17)
Te1'—O1^vi	2.0399 (19)	K2—O6	2.924 (11)
Te1'—O1ⁱⁱⁱ	2.0399 (19)	K2—O6^vii	3.054 (11)
Te1'—Te1ⁱⁱⁱ	2.9891 (1)	K2—Te2^x	3.9499 (3)
Te1'—Te1ⁱⁱ	2.9891 (1)	K2—Te1'^xi	4.0180 (19)
Te1'—Fe1'ⁱⁱⁱ	2.9891 (1)	K2—Te1ⁱⁱ	4.0362 (18)
Te1'—Fe1'ⁱⁱ	2.9891 (1)	K2—Te1^xii	4.0362 (18)
Te1'—K1^vi	3.7651 (11)	O1—Fe1ⁱⁱⁱ	2.0399 (19)
Te1'—K1ⁱⁱⁱ	3.7651 (11)	O1—Te1'ⁱⁱⁱ	2.0399 (19)
Te2—O2ⁱⁱ	1.915 (4)	O2—K1ⁱⁱⁱ	2.728 (4)
Te2—O2	1.915 (4)	O3—K1ⁱⁱⁱ	2.848 (4)
Te2—O3ⁱⁱ	1.917 (5)	O4—Fe1ⁱⁱ	2.014 (2)
Te2—O3	1.917 (5)	O4—Te1'ⁱⁱ	2.014 (2)
Te2—O5	1.9637 (17)	O4—K2ⁱⁱ	2.7922 (17)
Te2—O5ⁱⁱ	1.9637 (17)	O5—K1^vii	3.001 (6)
Te2—K1^vii	3.524 (2)	O5—H1	0.8699 (10)
Te2—K1ⁱⁱⁱ	3.524 (2)	O6—K1^ix	2.718 (2)
Te2—K1ⁱⁱ	3.541 (2)	O6—K2^viii	3.054 (11)
Te2—K1	3.541 (2)	O6—H2	0.8700 (10)
Te2—K2ⁱⁱ	3.9499 (3)	O7—K1^ix	2.827 (4)
Te2—K2	3.9499 (3)

O4ⁱ—Te1—O4	96.72 (12)	K1ⁱⁱⁱ—Te2—K2	114.59 (7)
O4ⁱ—Te1—O1	84.15 (8)	K1ⁱⁱ—Te2—K2	115.03 (7)
O4—Te1—O1	178.30 (7)	K1—Te2—K2	64.97 (7)
O4ⁱ—Te1—O1ⁱ	178.29 (7)	K2ⁱⁱ—Te2—K2	180.0
O4—Te1—O1ⁱ	84.15 (8)	O3—K1—O6	81.9 (2)
O1—Te1—O1ⁱ	95.03 (11)	O3—K1—O1	115.86 (9)
O4ⁱ—Te1—O2	88.66 (13)	O6—K1—O1	155.11 (7)
O4—Te1—O2	90.09 (13)	O3—K1—O2ⁱⁱⁱ	71.81 (5)
O1—Te1—O2	91.40 (13)	O6—K1—O2ⁱⁱⁱ	82.7 (2)
O1ⁱ—Te1—O2	89.87 (13)	O1—K1—O2ⁱⁱⁱ	118.37 (9)
O4ⁱ—Te1—O2ⁱ	90.09 (12)	O3—K1—O7	143.1 (3)
O4—Te1—O2ⁱ	88.66 (13)	O6—K1—O7	90.95 (9)
O1—Te1—O2ⁱ	89.87 (13)	O1—K1—O7	64.30 (9)
O1ⁱ—Te1—O2ⁱ	91.40 (13)	O2ⁱⁱⁱ—K1—O7	143.4 (3)
O2—Te1—O2ⁱ	178.12 (15)	O3—K1—O3ⁱⁱⁱ	94.91 (15)
O4ⁱ—Te1—Te1'ⁱⁱ	138.11 (6)	O6—K1—O3ⁱⁱⁱ	137.2 (3)
O4—Te1—Te1'ⁱⁱ	41.75 (6)	O1—K1—O3ⁱⁱⁱ	62.13 (7)
O1—Te1—Te1'ⁱⁱ	137.53 (6)	O2ⁱⁱⁱ—K1—O3ⁱⁱⁱ	56.25 (6)
O1ⁱ—Te1—Te1'ⁱⁱ	42.60 (5)	O7—K1—O3ⁱⁱⁱ	113.91 (19)
O2—Te1—Te1'ⁱⁱ	86.69 (14)	O3—K1—O2	55.86 (6)
O2ⁱ—Te1—Te1'ⁱⁱ	93.31 (14)	O6—K1—O2	135.2 (3)
O4ⁱ—Te1—Fe1ⁱⁱⁱ	41.75 (6)	O1—K1—O2	60.06 (6)
O4—Te1—Fe1ⁱⁱⁱ	138.11 (6)	O2ⁱⁱⁱ—K1—O2	95.90 (11)
O1—Te1—Fe1ⁱⁱⁱ	42.60 (5)	O7—K1—O2	113.15 (18)
O1ⁱ—Te1—Fe1ⁱⁱⁱ	137.53 (6)	O3ⁱⁱⁱ—K1—O2	67.62 (5)
O2—Te1—Fe1ⁱⁱⁱ	93.31 (14)	O3—K1—O5	56.54 (13)
O2ⁱ—Te1—Fe1ⁱⁱⁱ	86.68 (14)	O6—K1—O5	90.0 (3)
Te1'ⁱⁱ—Te1—Fe1ⁱⁱⁱ	179.86 (3)	O1—K1—O5	86.45 (7)
O4ⁱ—Te1—Fe1ⁱⁱ	138.11 (6)	O2ⁱⁱⁱ—K1—O5	128.35 (11)
O4—Te1—Fe1ⁱⁱ	41.75 (6)	O7—K1—O5	87.5 (3)
O1—Te1—Fe1ⁱⁱ	137.53 (6)	O3ⁱⁱⁱ—K1—O5	123.64 (12)
O1ⁱ—Te1—Fe1ⁱⁱ	42.60 (5)	O2—K1—O5	56.08 (9)
O2—Te1—Fe1ⁱⁱ	86.69 (14)	O3—K1—O5^viii	128.31 (13)
O2ⁱ—Te1—Fe1ⁱⁱ	93.31 (14)	O6—K1—O5^viii	92.3 (3)
Te1'ⁱⁱ—Te1—Fe1ⁱⁱ	0.00 (2)	O1—K1—O5^viii	89.56 (8)
Fe1ⁱⁱⁱ—Te1—Fe1ⁱⁱ	179.86 (3)	O2ⁱⁱⁱ—K1—O5^viii	56.52 (10)
O4ⁱ—Te1—Te1'ⁱⁱⁱ	41.75 (6)	O7—K1—O5^viii	88.0 (3)
O4—Te1—Te1'ⁱⁱⁱ	138.11 (6)	O3ⁱⁱⁱ—K1—O5^viii	56.62 (12)
O1—Te1—Te1'ⁱⁱⁱ	42.60 (5)	O2—K1—O5^viii	124.15 (10)
O1ⁱ—Te1—Te1'ⁱⁱⁱ	137.53 (6)	O5—K1—O5^viii	174.91 (7)
O2—Te1—Te1'ⁱⁱⁱ	93.31 (14)	O3—K1—Te2^viii	98.41 (12)
O2ⁱ—Te1—Te1'ⁱⁱⁱ	86.68 (14)	O6—K1—Te2^viii	105.0 (3)
Te1'ⁱⁱ—Te1—Te1'ⁱⁱⁱ	179.86 (3)	O1—K1—Te2^viii	90.13 (6)
Fe1ⁱⁱⁱ—Te1—Te1'ⁱⁱⁱ	0.0	O2ⁱⁱⁱ—K1—Te2^viii	32.61 (8)
Fe1ⁱⁱ—Te1—Te1'ⁱⁱⁱ	179.9	O7—K1—Te2^viii	118.4 (3)
O4ⁱ—Te1—K1	93.80 (6)	O3ⁱⁱⁱ—K1—Te2^viii	32.88 (9)
O4—Te1—K1	137.53 (6)	O2—K1—Te2^viii	96.02 (8)
O1—Te1—K1	43.72 (6)	O5—K1—Te2^viii	149.16 (4)
O1ⁱ—Te1—K1	84.58 (6)	O5^viii—K1—Te2^viii	33.84 (4)
O2—Te1—K1	49.09 (10)	O3—K1—Te2	32.40 (10)
O2ⁱ—Te1—K1	132.43 (11)	O6—K1—Te2	103.0 (3)
Te1'ⁱⁱ—Te1—K1	113.56 (4)	O1—K1—Te2	87.51 (6)
Fe1ⁱⁱⁱ—Te1—K1	66.53 (4)	O2ⁱⁱⁱ—K1—Te2	98.74 (9)
Fe1ⁱⁱ—Te1—K1	113.56 (4)	O7—K1—Te2	117.8 (3)
Te1'ⁱⁱⁱ—Te1—K1	66.53 (4)	O3ⁱⁱⁱ—K1—Te2	95.57 (11)
O4ⁱ—Te1—K1ⁱ	137.53 (6)	O2—K1—Te2	32.70 (7)
O4—Te1—K1ⁱ	93.80 (6)	O5—K1—Te2	33.68 (4)
O1—Te1—K1ⁱ	84.58 (6)	O5^viii—K1—Te2	149.32 (4)
O1ⁱ—Te1—K1ⁱ	43.72 (6)	Te2^viii—K1—Te2	115.599 (16)
O2—Te1—K1ⁱ	132.44 (10)	O3—K1—K1ⁱⁱⁱ	48.92 (9)
O2ⁱ—Te1—K1ⁱ	49.09 (10)	O6—K1—K1ⁱⁱⁱ	116.96 (5)
Te1'ⁱⁱ—Te1—K1ⁱ	66.53 (4)	O1—K1—K1ⁱⁱⁱ	87.77 (4)
Fe1ⁱⁱⁱ—Te1—K1ⁱ	113.56 (4)	O2ⁱⁱⁱ—K1—K1ⁱⁱⁱ	49.78 (7)
Fe1ⁱⁱ—Te1—K1ⁱ	66.53 (4)	O7—K1—K1ⁱⁱⁱ	152.07 (8)
Te1'ⁱⁱⁱ—Te1—K1ⁱ	113.56 (4)	O3ⁱⁱⁱ—K1—K1ⁱⁱⁱ	45.99 (9)
K1—Te1—K1ⁱ	105.55 (3)	O2—K1—K1ⁱⁱⁱ	46.11 (8)
O3—Te1'—O3^iv	179.21 (15)	O5—K1—K1ⁱⁱⁱ	91.21 (8)
O3—Te1'—O4^v	88.67 (16)	O5^viii—K1—K1ⁱⁱⁱ	91.79 (8)
O3^iv—Te1'—O4^v	90.83 (17)	Te2^viii—K1—K1ⁱⁱⁱ	58.01 (5)
O3—Te1'—O4ⁱⁱ	90.83 (17)	Te2—K1—K1ⁱⁱⁱ	57.59 (5)
O3^iv—Te1'—O4ⁱⁱ	88.67 (16)	O3—K1—H1	70.0 (4)
O4^v—Te1'—O4ⁱⁱ	101.42 (11)	O6—K1—H1	102.8 (6)
O3—Te1'—O1^vi	89.90 (16)	O1—K1—H1	70.3 (2)
O3^iv—Te1'—O1^vi	90.61 (16)	O2ⁱⁱⁱ—K1—H1	140.1 (6)
O4^v—Te1'—O1^vi	178.35 (7)	O7—K1—H1	76.5 (6)
O4ⁱⁱ—Te1'—O1^vi	79.44 (7)	O3ⁱⁱⁱ—K1—H1	116.2 (6)
O3—Te1'—O1ⁱⁱⁱ	90.61 (16)	O2—K1—H1	52.4 (7)
O3^iv—Te1'—O1ⁱⁱⁱ	89.90 (16)	O5—K1—H1	16.83 (8)
O4^v—Te1'—O1ⁱⁱⁱ	79.44 (7)	O5^viii—K1—H1	158.39 (13)
O4ⁱⁱ—Te1'—O1ⁱⁱⁱ	178.35 (7)	Te2^viii—K1—H1	148.0 (7)
O1^vi—Te1'—O1ⁱⁱⁱ	99.73 (10)	Te2—K1—H1	41.3 (6)
O3—Te1'—Te1ⁱⁱⁱ	92.55 (19)	K1ⁱⁱⁱ—K1—H1	95.0 (7)
O3^iv—Te1'—Te1ⁱⁱⁱ	87.45 (19)	O5^ix—K2—O5	86.02 (7)
O4^v—Te1'—Te1ⁱⁱⁱ	39.53 (5)	O5^ix—K2—O4ⁱⁱ	177.9 (2)
O4ⁱⁱ—Te1'—Te1ⁱⁱⁱ	140.61 (6)	O5—K2—O4ⁱⁱ	92.68 (5)
O1^vi—Te1'—Te1ⁱⁱⁱ	139.75 (6)	O5^ix—K2—O4^x	92.68 (5)
O1ⁱⁱⁱ—Te1'—Te1ⁱⁱⁱ	40.11 (5)	O5—K2—O4^x	177.9 (2)
O3—Te1'—Te1ⁱⁱ	87.45 (19)	O4ⁱⁱ—K2—O4^x	88.57 (7)
O3^iv—Te1'—Te1ⁱⁱ	92.55 (19)	O5^ix—K2—O6	89.9 (2)
O4^v—Te1'—Te1ⁱⁱ	140.61 (6)	O5—K2—O6	89.9 (2)
O4ⁱⁱ—Te1'—Te1ⁱⁱ	39.53 (5)	O4ⁱⁱ—K2—O6	91.84 (11)
O1^vi—Te1'—Te1ⁱⁱ	40.11 (5)	O4^x—K2—O6	91.84 (11)
O1ⁱⁱⁱ—Te1'—Te1ⁱⁱ	139.75 (6)	O5^ix—K2—O6^vii	89.8 (2)
Te1ⁱⁱⁱ—Te1'—Te1ⁱⁱ	179.86 (3)	O5—K2—O6^vii	89.8 (2)
O3—Te1'—Fe1'ⁱⁱⁱ	92.55 (19)	O4ⁱⁱ—K2—O6^vii	88.52 (11)
O3^iv—Te1'—Fe1'ⁱⁱⁱ	87.45 (19)	O4^x—K2—O6^vii	88.52 (11)
O4^v—Te1'—Fe1'ⁱⁱⁱ	39.53 (5)	O6—K2—O6^vii	179.50 (11)
O4ⁱⁱ—Te1'—Fe1'ⁱⁱⁱ	140.61 (6)	O5^ix—K2—Te2^x	27.61 (3)
O1^vi—Te1'—Fe1'ⁱⁱⁱ	139.75 (6)	O5—K2—Te2^x	113.63 (4)
O1ⁱⁱⁱ—Te1'—Fe1'ⁱⁱⁱ	40.11 (5)	O4ⁱⁱ—K2—Te2^x	153.62 (4)
Te1ⁱⁱⁱ—Te1'—Fe1'ⁱⁱⁱ	0.000 (13)	O4^x—K2—Te2^x	65.07 (3)
Te1ⁱⁱ—Te1'—Fe1'ⁱⁱⁱ	179.86 (3)	O6—K2—Te2^x	90.22 (7)
O3—Te1'—Fe1'ⁱⁱ	87.45 (19)	O6^vii—K2—Te2^x	89.62 (7)
O3^iv—Te1'—Fe1'ⁱⁱ	92.55 (19)	O5^ix—K2—Te2	113.63 (4)
O4^v—Te1'—Fe1'ⁱⁱ	140.61 (6)	O5—K2—Te2	27.61 (3)
O4ⁱⁱ—Te1'—Fe1'ⁱⁱ	39.53 (5)	O4ⁱⁱ—K2—Te2	65.07 (3)
O1^vi—Te1'—Fe1'ⁱⁱ	40.11 (5)	O4^x—K2—Te2	153.62 (4)
O1ⁱⁱⁱ—Te1'—Fe1'ⁱⁱ	139.75 (6)	O6—K2—Te2	90.22 (7)
Te1ⁱⁱⁱ—Te1'—Fe1'ⁱⁱ	179.86 (3)	O6^vii—K2—Te2	89.62 (7)
Te1ⁱⁱ—Te1'—Fe1'ⁱⁱ	0.000 (13)	Te2^x—K2—Te2	141.24 (2)
Fe1'ⁱⁱⁱ—Te1'—Fe1'ⁱⁱ	179.86 (3)	O5^ix—K2—Te1'	153.09 (19)
O3—Te1'—K1^vi	132.54 (12)	O5—K2—Te1'	78.28 (8)
O3^iv—Te1'—K1^vi	48.11 (13)	O4ⁱⁱ—K2—Te1'	27.59 (5)
O4^v—Te1'—K1^vi	136.50 (5)	O4^x—K2—Te1'	103.56 (6)
O4ⁱⁱ—Te1'—K1^vi	92.47 (6)	O6—K2—Te1'	68.61 (7)
O1^vi—Te1'—K1^vi	44.63 (5)	O6^vii—K2—Te1'	111.64 (7)
O1ⁱⁱⁱ—Te1'—K1^vi	85.95 (6)	Te2^x—K2—Te1'	156.22 (12)
Te1ⁱⁱⁱ—Te1'—K1^vi	113.18 (4)	Te2—K2—Te1'	53.197 (14)
Te1ⁱⁱ—Te1'—K1^vi	66.73 (4)	O5^ix—K2—Te1'^xi	78.28 (8)
Fe1'ⁱⁱⁱ—Te1'—K1^vi	113.18 (4)	O5—K2—Te1'^xi	153.10 (19)
Fe1'ⁱⁱ—Te1'—K1^vi	66.73 (4)	O4ⁱⁱ—K2—Te1'^xi	103.56 (6)
O3—Te1'—K1ⁱⁱⁱ	48.11 (13)	O4^x—K2—Te1'^xi	27.59 (5)
O3^iv—Te1'—K1ⁱⁱⁱ	132.54 (12)	O6—K2—Te1'^xi	68.61 (7)
O4^v—Te1'—K1ⁱⁱⁱ	92.47 (6)	O6^vii—K2—Te1'^xi	111.64 (7)
O4ⁱⁱ—Te1'—K1ⁱⁱⁱ	136.50 (5)	Te2^x—K2—Te1'^xi	53.197 (14)
O1^vi—Te1'—K1ⁱⁱⁱ	85.95 (6)	Te2—K2—Te1'^xi	156.22 (12)
O1ⁱⁱⁱ—Te1'—K1ⁱⁱⁱ	44.63 (5)	Te1'—K2—Te1'^xi	106.75 (7)
Te1ⁱⁱⁱ—Te1'—K1ⁱⁱⁱ	66.73 (4)	O5^ix—K2—Te1ⁱⁱ	152.59 (19)
Te1ⁱⁱ—Te1'—K1ⁱⁱⁱ	113.18 (4)	O5—K2—Te1ⁱⁱ	78.26 (8)
Fe1'ⁱⁱⁱ—Te1'—K1ⁱⁱⁱ	66.73 (4)	O4ⁱⁱ—K2—Te1ⁱⁱ	25.27 (5)
Fe1'ⁱⁱ—Te1'—K1ⁱⁱⁱ	113.18 (4)	O4^x—K2—Te1ⁱⁱ	102.27 (6)
K1^vi—Te1'—K1ⁱⁱⁱ	105.29 (3)	O6—K2—Te1ⁱⁱ	112.18 (7)
O2ⁱⁱ—Te2—O2	180.00 (9)	O6^vii—K2—Te1ⁱⁱ	68.07 (7)
O2ⁱⁱ—Te2—O3ⁱⁱ	86.74 (7)	Te2^x—K2—Te1ⁱⁱ	155.22 (12)
O2—Te2—O3ⁱⁱ	93.26 (7)	Te2—K2—Te1ⁱⁱ	53.052 (14)
O2ⁱⁱ—Te2—O3	93.26 (7)	Te1'—K2—Te1ⁱⁱ	43.569 (5)
O2—Te2—O3	86.74 (7)	Te1'^xi—K2—Te1ⁱⁱ	124.01 (2)
O3ⁱⁱ—Te2—O3	180.0 (3)	O5^ix—K2—Te1^xii	78.26 (8)
O2ⁱⁱ—Te2—O5	89.18 (17)	O5—K2—Te1^xii	152.59 (19)
O2—Te2—O5	90.82 (18)	O4ⁱⁱ—K2—Te1^xii	102.27 (6)
O3ⁱⁱ—Te2—O5	91.41 (19)	O4^x—K2—Te1^xii	25.27 (5)
O3—Te2—O5	88.59 (19)	O6—K2—Te1^xii	112.18 (7)
O2ⁱⁱ—Te2—O5ⁱⁱ	90.82 (18)	O6^vii—K2—Te1^xii	68.07 (7)
O2—Te2—O5ⁱⁱ	89.18 (17)	Te2^x—K2—Te1^xii	53.052 (14)
O3ⁱⁱ—Te2—O5ⁱⁱ	88.59 (19)	Te2—K2—Te1^xii	155.22 (12)
O3—Te2—O5ⁱⁱ	91.41 (19)	Te1'—K2—Te1^xii	124.01 (2)
O5—Te2—O5ⁱⁱ	180.0	Te1'^xi—K2—Te1^xii	43.569 (5)
O2ⁱⁱ—Te2—K1^vii	50.16 (9)	Te1ⁱⁱ—K2—Te1^xii	106.23 (7)
O2—Te2—K1^vii	129.84 (9)	Te1—O1—Fe1ⁱⁱⁱ	97.29 (7)
O3ⁱⁱ—Te2—K1^vii	53.79 (13)	Te1—O1—Te1'ⁱⁱⁱ	97.29 (7)
O3—Te2—K1^vii	126.21 (13)	Fe1ⁱⁱⁱ—O1—Te1'ⁱⁱⁱ	0.0
O5—Te2—K1^vii	58.3 (2)	Te1—O1—K1	106.74 (9)
O5ⁱⁱ—Te2—K1^vii	121.7 (2)	Fe1ⁱⁱⁱ—O1—K1	103.59 (8)
O2ⁱⁱ—Te2—K1ⁱⁱⁱ	129.84 (9)	Te1'ⁱⁱⁱ—O1—K1	103.59 (8)
O2—Te2—K1ⁱⁱⁱ	50.16 (9)	Te2—O2—Te1	132.2 (2)
O3ⁱⁱ—Te2—K1ⁱⁱⁱ	126.21 (13)	Te2—O2—K1ⁱⁱⁱ	97.22 (8)
O3—Te2—K1ⁱⁱⁱ	53.79 (13)	Te1—O2—K1ⁱⁱⁱ	129.8 (2)
O5—Te2—K1ⁱⁱⁱ	121.7 (2)	Te2—O2—K1	92.68 (9)
O5ⁱⁱ—Te2—K1ⁱⁱⁱ	58.3 (2)	Te1—O2—K1	99.60 (12)
K1^vii—Te2—K1ⁱⁱⁱ	180.0	K1ⁱⁱⁱ—O2—K1	84.10 (11)
O2ⁱⁱ—Te2—K1ⁱⁱ	54.63 (10)	Te2—O3—Te1'	130.9 (3)
O2—Te2—K1ⁱⁱ	125.37 (10)	Te2—O3—K1	98.15 (9)
O3ⁱⁱ—Te2—K1ⁱⁱ	49.44 (11)	Te1'—O3—K1	129.7 (2)
O3—Te2—K1ⁱⁱ	130.56 (11)	Te2—O3—K1ⁱⁱⁱ	93.33 (10)
O5—Te2—K1ⁱⁱ	122.6 (2)	Te1'—O3—K1ⁱⁱⁱ	100.28 (15)
O5ⁱⁱ—Te2—K1ⁱⁱ	57.4 (2)	K1—O3—K1ⁱⁱⁱ	85.09 (15)
K1^vii—Te2—K1ⁱⁱ	64.400 (16)	Te1—O4—Fe1ⁱⁱ	98.72 (7)
K1ⁱⁱⁱ—Te2—K1ⁱⁱ	115.600 (16)	Te1—O4—Te1'ⁱⁱ	98.72 (7)
O2ⁱⁱ—Te2—K1	125.37 (10)	Fe1ⁱⁱ—O4—Te1'ⁱⁱ	0.0
O2—Te2—K1	54.63 (10)	Te1—O4—K2ⁱⁱ	116.47 (11)
O3ⁱⁱ—Te2—K1	130.56 (11)	Fe1ⁱⁱ—O4—K2ⁱⁱ	112.44 (12)
O3—Te2—K1	49.44 (11)	Te1'ⁱⁱ—O4—K2ⁱⁱ	112.44 (12)
O5—Te2—K1	57.4 (2)	Te2—O5—K2	111.21 (7)
O5ⁱⁱ—Te2—K1	122.6 (2)	Te2—O5—K1	88.9 (2)
K1^vii—Te2—K1	115.599 (16)	K2—O5—K1	88.7 (2)
K1ⁱⁱⁱ—Te2—K1	64.401 (16)	Te2—O5—K1^vii	87.9 (2)
K1ⁱⁱ—Te2—K1	180.0	K2—O5—K1^vii	88.80 (19)
O2ⁱⁱ—Te2—K2ⁱⁱ	117.93 (11)	K1—O5—K1^vii	174.91 (7)
O2—Te2—K2ⁱⁱ	62.07 (11)	Te2—O5—H1	106 (2)
O3ⁱⁱ—Te2—K2ⁱⁱ	62.31 (12)	K2—O5—H1	141 (2)
O3—Te2—K2ⁱⁱ	117.68 (12)	K1—O5—H1	80 (3)
O5—Te2—K2ⁱⁱ	138.82 (5)	K1^vii—O5—H1	105 (3)
O5ⁱⁱ—Te2—K2ⁱⁱ	41.18 (5)	K1^ix—O6—K1	91.25 (8)
K1^vii—Te2—K2ⁱⁱ	114.59 (7)	K1^ix—O6—K2	91.3 (3)
K1ⁱⁱⁱ—Te2—K2ⁱⁱ	65.41 (7)	K1—O6—K2	91.3 (3)
K1ⁱⁱ—Te2—K2ⁱⁱ	64.97 (7)	K1^ix—O6—K2^viii	89.0 (3)
K1—Te2—K2ⁱⁱ	115.03 (7)	K1—O6—K2^viii	89.0 (3)
O2ⁱⁱ—Te2—K2	62.07 (10)	K2—O6—K2^viii	179.50 (11)
O2—Te2—K2	117.93 (11)	K1^ix—O6—H2	85.0 (19)
O3ⁱⁱ—Te2—K2	117.69 (12)	K1—O6—H2	163 (3)
O3—Te2—K2	62.32 (12)	K2—O6—H2	105 (3)
O5—Te2—K2	41.18 (5)	K2^viii—O6—H2	75 (3)
O5ⁱⁱ—Te2—K2	138.82 (5)	K1—O7—K1^ix	86.82 (16)
K1^vii—Te2—K2	65.41 (7)

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

(436K) top

Crystal data top

FeH_4.86K₃O_11.43Te₂	F(000) = 1133
M_r = 616.17	D_x = 3.592 Mg m⁻³
Monoclinic, I2/m	Mo Kα radiation, λ = 0.71073 Å
a = 12.7660 (6) Å	Cell parameters from 14095 reflections
b = 14.9470 (6) Å	θ = 2.7–36.2°
c = 5.9706 (2) Å	µ = 7.49 mm⁻¹
β = 90.047 (3)°	T = 432 K
V = 1139.27 (8) Å³	Lath, colourless
Z = 4	0.18 × 0.08 × 0.01 × 0.10 (radius) mm

Data collection top

STOE STADIVARI diffractometer	2711 independent reflections
Radiation source: Axo_Mo	2207 reflections with I > 2σ(I)
Graded multilayer mirror monochromator	R_int = 0.043
Detector resolution: 13.33 pixels mm^-1	θ_max = 36.0°, θ_min = 2.7°
rotation method, ω scans	h = −21→20
Absorption correction: multi-scan STOE LANA, absorption correction by scaling of reflection intensities. J. Koziskova, F. Hahn, J. Richter, J. Kozisek, "Comparison of different absorption corrections on the model structure of tetrakis(µ₂-acetato)- diaqua-di-copper(II)", Acta Chimica Slovaca, vol. 9, no. 2, 2016, pp. 136 - 140. Afterwards a spherical absorption correction was performed within STOE LANA.	k = −24→24
T_min = 0.062, T_max = 0.104	l = −9→3
10382 measured reflections

Refinement top

Refinement on F²	2 restraints
Least-squares matrix: full	Hydrogen site location: difference Fourier map
R[F² > 2σ(F²)] = 0.037	Only H-atom coordinates refined
wR(F²) = 0.101	w = 1/[σ²(F_o²) + (0.0687P)²] where P = (F_o² + 2F_c²)/3
S = 1.03	(Δ/σ)_max < 0.001
2711 reflections	Δρ_max = 3.77 e Å⁻³
98 parameters	Δρ_min = −1.67 e Å⁻³

Special details top

Refinement. Refined as a 2-component inversion twin.

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Te1	0.0000	0.28586 (4)	0.5000	0.01448 (14)	0.796 (4)
Te1'	0.5000	0.21398 (6)	0.5000	0.0148 (3)	0.204 (4)
Te2	0.2500	0.2500	0.7500	0.01511 (11)
Fe1	0.5000	0.21398 (6)	0.5000	0.0148 (3)	0.796 (4)
Fe1'	0.0000	0.28586 (4)	0.5000	0.01448 (14)	0.204 (4)
K1	0.19952 (8)	0.13172 (7)	0.2520 (5)	0.0272 (2)
K2	0.35101 (13)	0.0000	0.7442 (12)	0.0356 (4)
O1	0.0044 (3)	0.1984 (2)	0.2595 (6)	0.0203 (6)
O2	0.1557 (2)	0.2878 (3)	0.5123 (18)	0.0209 (8)
O3	0.3426 (3)	0.2133 (3)	0.5234 (13)	0.0197 (11)
O4	−0.0085 (2)	0.3715 (2)	0.7416 (7)	0.0201 (6)
O5	0.1899 (2)	0.1287 (2)	0.7577 (17)	0.0239 (7)
H5	0.127 (3)	0.138 (5)	0.712 (13)	0.036*
O6	0.3471 (4)	0.0000	0.246 (4)	0.0365 (13)
H6	0.392 (5)	−0.043 (4)	0.245 (16)	0.055*
O7	0.036 (3)	0.0000	0.258 (13)	0.21 (3)	0.43 (5)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Te1	0.00881 (17)	0.0213 (3)	0.0133 (2)	0.000	−0.0034 (4)	0.000
Te1'	0.0106 (3)	0.0198 (5)	0.0139 (4)	0.000	−0.0061 (7)	0.000
Te2	0.00865 (15)	0.02181 (16)	0.01485 (18)	0.00073 (11)	−0.0043 (5)	−0.00005 (16)
Fe1	0.0106 (3)	0.0198 (5)	0.0139 (4)	0.000	−0.0061 (7)	0.000
Fe1'	0.00881 (17)	0.0213 (3)	0.0133 (2)	0.000	−0.0034 (4)	0.000
K1	0.0231 (4)	0.0314 (4)	0.0272 (5)	0.0048 (4)	−0.0043 (9)	−0.0027 (11)
K2	0.0255 (6)	0.0354 (7)	0.0458 (11)	0.000	−0.0040 (19)	0.000
O1	0.0129 (11)	0.0240 (12)	0.0241 (16)	0.0003 (10)	−0.006 (3)	−0.0011 (14)
O2	0.0103 (11)	0.031 (2)	0.021 (2)	0.0009 (14)	−0.006 (2)	0.003 (3)
O3	0.0095 (11)	0.035 (2)	0.015 (3)	0.0007 (14)	−0.0024 (18)	−0.003 (2)
O4	0.0171 (12)	0.0220 (12)	0.0211 (14)	0.0001 (10)	−0.006 (2)	0.0011 (15)
O5	0.0161 (12)	0.0235 (13)	0.0321 (18)	−0.0010 (10)	0.002 (3)	−0.005 (4)
O6	0.019 (2)	0.030 (2)	0.061 (4)	0.000	0.002 (6)	0.000
O7	0.09 (3)	0.06 (2)	0.46 (10)	0.000	0.00 (4)	0.000

Geometric parameters (Å, º) top

Te1—Te1'ⁱ	2.9853 (1)	Te2—O5	1.970 (3)
Te1—Te1'ⁱⁱ	2.9853 (1)	K1—Te2^viii	3.539 (3)
Te1—Fe1ⁱⁱ	2.9853 (1)	K1—O1	2.683 (3)
Te1—Fe1ⁱ	2.9853 (1)	K1—O2	2.858 (7)
Te1—K1ⁱⁱⁱ	3.7410 (18)	K1—O2ⁱⁱ	2.713 (8)
Te1—K1	3.7410 (18)	K1—O3	2.729 (6)
Te1—O1ⁱⁱⁱ	1.943 (3)	K1—O3ⁱⁱ	2.890 (6)
Te1—O1	1.943 (3)	K1—O5^viii	2.954 (8)
Te1—O2	1.989 (3)	K1—O5	3.022 (8)
Te1—O2ⁱⁱⁱ	1.989 (3)	K1—H5	2.90 (8)
Te1—O4	1.932 (4)	K1—O6	2.726 (4)
Te1—O4ⁱⁱⁱ	1.932 (4)	K1—O7	2.87 (3)
Te1'—Te1ⁱ	2.9853 (1)	K2—Te1'^ix	3.997 (3)
Te1'—Te1ⁱⁱ	2.9853 (1)	K2—Te2^x	3.9531 (6)
Te1'—Fe1'ⁱ	2.9853 (1)	K2—Fe1^ix	3.997 (3)
Te1'—Fe1'ⁱⁱ	2.9853 (1)	K2—O4ⁱ	2.782 (3)
Te1'—K1^iv	3.7502 (16)	K2—O4^x	2.782 (3)
Te1'—K1ⁱⁱ	3.7502 (16)	K2—O5	2.817 (4)
Te1'—O1ⁱⁱ	2.030 (4)	K2—O5^xi	2.817 (4)
Te1'—O1^iv	2.030 (4)	K2—O6	2.977 (19)
Te1'—O3^v	2.014 (4)	K2—O6^vii	2.994 (19)
Te1'—O3	2.014 (4)	O1—Te1'ⁱⁱ	2.030 (4)
Te1'—O4ⁱ	2.006 (4)	O1—Fe1ⁱⁱ	2.030 (4)
Te1'—O4^vi	2.006 (4)	O2—K1ⁱⁱ	2.713 (8)
Te2—K1ⁱⁱ	3.539 (3)	O3—K1ⁱⁱ	2.890 (6)
Te2—K1ⁱ	3.518 (3)	O4—Te1'ⁱ	2.006 (4)
Te2—K1^vii	3.539 (3)	O4—Fe1ⁱ	2.006 (4)
Te2—K1	3.519 (3)	O4—K2ⁱ	2.782 (3)
Te2—K2ⁱ	3.9532 (6)	O5—K1^vii	2.954 (8)
Te2—K2	3.9531 (6)	O5—H5	0.86 (2)
Te2—O2ⁱ	1.944 (7)	O6—K1^xi	2.726 (4)
Te2—O2	1.944 (7)	O6—K2^viii	2.994 (19)
Te2—O3	1.879 (6)	O6—H6	0.87 (2)
Te2—O3ⁱ	1.879 (6)	O7—K1^xi	2.87 (3)
Te2—O5ⁱ	1.970 (3)

Te1'ⁱ—Te1—Te1'ⁱⁱ	179.91 (5)	O3—Te2—O5ⁱ	90.4 (3)
Te1'ⁱ—Te1—Fe1ⁱ	0.00 (3)	O3ⁱ—Te2—O5ⁱ	89.6 (3)
Te1'ⁱ—Te1—Fe1ⁱⁱ	179.91 (5)	O3—Te2—O5	89.6 (3)
Te1'ⁱ—Te1—K1	113.39 (5)	O5ⁱ—Te2—K1^vii	123.4 (3)
Te1'ⁱⁱ—Te1—K1	66.68 (5)	O5—Te2—K1ⁱⁱ	123.4 (3)
Te1'ⁱ—Te1—K1ⁱⁱⁱ	66.68 (5)	O5ⁱ—Te2—K1	120.9 (3)
Te1'ⁱⁱ—Te1—K1ⁱⁱⁱ	113.39 (5)	O5—Te2—K1	59.1 (3)
Fe1ⁱ—Te1—Te1'ⁱⁱ	179.9	O5ⁱ—Te2—K1ⁱ	59.1 (3)
Fe1ⁱⁱ—Te1—Te1'ⁱⁱ	0.0	O5—Te2—K1^vii	56.6 (3)
Fe1ⁱⁱ—Te1—Fe1ⁱ	179.91 (5)	O5ⁱ—Te2—K1ⁱⁱ	56.6 (3)
Fe1ⁱ—Te1—K1ⁱⁱⁱ	66.68 (5)	O5—Te2—K1ⁱ	120.9 (3)
Fe1ⁱⁱ—Te1—K1ⁱⁱⁱ	113.39 (5)	O5—Te2—K2ⁱ	137.99 (10)
Fe1ⁱⁱ—Te1—K1	66.68 (5)	O5ⁱ—Te2—K2	138.00 (10)
Fe1ⁱ—Te1—K1	113.39 (5)	O5ⁱ—Te2—K2ⁱ	42.00 (10)
K1—Te1—K1ⁱⁱⁱ	103.97 (5)	O5—Te2—K2	42.00 (10)
O1ⁱⁱⁱ—Te1—Te1'ⁱⁱ	137.70 (11)	O5—Te2—O5ⁱ	180.0
O1ⁱⁱⁱ—Te1—Te1'ⁱ	42.39 (10)	Te2—K1—Te2^viii	115.55 (3)
O1—Te1—Te1'ⁱ	137.70 (11)	Te2—K1—H5	40.8 (14)
O1—Te1—Te1'ⁱⁱ	42.39 (10)	Te2^viii—K1—H5	147.6 (16)
O1ⁱⁱⁱ—Te1—Fe1ⁱⁱ	137.70 (11)	O1—K1—Te2^viii	89.91 (10)
O1—Te1—Fe1ⁱ	137.70 (11)	O1—K1—Te2	88.21 (10)
O1ⁱⁱⁱ—Te1—Fe1ⁱ	42.39 (10)	O1—K1—O2ⁱⁱ	118.56 (14)
O1—Te1—Fe1ⁱⁱ	42.39 (10)	O1—K1—O2	60.38 (11)
O1ⁱⁱⁱ—Te1—K1	84.15 (11)	O1—K1—O3	116.42 (15)
O1—Te1—K1ⁱⁱⁱ	84.15 (11)	O1—K1—O3ⁱⁱ	62.60 (12)
O1—Te1—K1	43.36 (10)	O1—K1—O5^viii	89.12 (12)
O1ⁱⁱⁱ—Te1—K1ⁱⁱⁱ	43.36 (10)	O1—K1—O5	87.16 (13)
O1ⁱⁱⁱ—Te1—O1	95.4 (2)	O1—K1—H5	71.0 (6)
O1ⁱⁱⁱ—Te1—O2ⁱⁱⁱ	90.4 (3)	O1—K1—O6	155.55 (11)
O1ⁱⁱⁱ—Te1—O2	90.7 (3)	O1—K1—O7	65.2 (5)
O1—Te1—O2ⁱⁱⁱ	90.7 (3)	O2—K1—Te2	33.51 (14)
O1—Te1—O2	90.4 (3)	O2ⁱⁱ—K1—Te2^viii	32.99 (15)
O2—Te1—Te1'ⁱ	87.9 (3)	O2—K1—Te2^viii	95.09 (18)
O2ⁱⁱⁱ—Te1—Te1'ⁱⁱ	87.9 (3)	O2ⁱⁱ—K1—Te2	98.29 (19)
O2—Te1—Te1'ⁱⁱ	92.1 (3)	O2ⁱⁱ—K1—O2	95.1 (3)
O2ⁱⁱⁱ—Te1—Te1'ⁱ	92.1 (3)	O2ⁱⁱ—K1—O3ⁱⁱ	55.96 (11)
O2ⁱⁱⁱ—Te1—Fe1ⁱ	92.1 (3)	O2—K1—O3ⁱⁱ	67.61 (11)
O2—Te1—Fe1ⁱ	87.9 (3)	O2ⁱⁱ—K1—O3	72.00 (11)
O2—Te1—Fe1ⁱⁱ	92.1 (3)	O2ⁱⁱ—K1—O5^viii	56.9 (2)
O2ⁱⁱⁱ—Te1—Fe1ⁱⁱ	87.9 (3)	O2—K1—O5	57.38 (19)
O2ⁱⁱⁱ—Te1—K1ⁱⁱⁱ	48.9 (2)	O2ⁱⁱ—K1—O5	128.0 (2)
O2—Te1—K1ⁱⁱⁱ	132.4 (2)	O2—K1—O5^viii	123.2 (2)
O2—Te1—K1	48.9 (2)	O2ⁱⁱ—K1—H5	139.1 (14)
O2ⁱⁱⁱ—Te1—K1	132.4 (2)	O2—K1—H5	52.9 (16)
O2—Te1—O2ⁱⁱⁱ	178.4 (3)	O2ⁱⁱ—K1—O6	80.8 (3)
O4—Te1—Te1'ⁱⁱ	138.27 (11)	O2ⁱⁱ—K1—O7	143.9 (15)
O4ⁱⁱⁱ—Te1—Te1'ⁱⁱ	41.64 (11)	O2—K1—O7	114.3 (10)
O4ⁱⁱⁱ—Te1—Te1'ⁱ	138.27 (11)	O3ⁱⁱ—K1—Te2	96.43 (14)
O4—Te1—Te1'ⁱ	41.64 (11)	O3—K1—Te2	31.94 (14)
O4ⁱⁱⁱ—Te1—Fe1ⁱⁱ	41.64 (11)	O3—K1—Te2^viii	99.05 (16)
O4—Te1—Fe1ⁱⁱ	138.27 (11)	O3ⁱⁱ—K1—Te2^viii	32.00 (12)
O4ⁱⁱⁱ—Te1—Fe1ⁱ	138.27 (11)	O3—K1—O2	56.19 (11)
O4—Te1—Fe1ⁱ	41.64 (11)	O3—K1—O3ⁱⁱ	95.95 (18)
O4ⁱⁱⁱ—Te1—K1	94.23 (10)	O3ⁱⁱ—K1—O5	124.94 (16)
O4—Te1—K1	137.95 (10)	O3ⁱⁱ—K1—O5^viii	55.70 (16)
O4ⁱⁱⁱ—Te1—K1ⁱⁱⁱ	137.95 (10)	O3—K1—O5^viii	128.86 (18)
O4—Te1—K1ⁱⁱⁱ	94.23 (10)	O3—K1—O5	56.02 (18)
O4—Te1—O1ⁱⁱⁱ	83.82 (15)	O3ⁱⁱ—K1—H5	117.0 (14)
O4ⁱⁱⁱ—Te1—O1ⁱⁱⁱ	178.26 (13)	O3—K1—H5	68.8 (10)
O4—Te1—O1	178.26 (13)	O3—K1—O7	141.8 (15)
O4ⁱⁱⁱ—Te1—O1	83.82 (15)	O5—K1—Te2^viii	149.44 (8)
O4—Te1—O2ⁱⁱⁱ	87.8 (3)	O5^viii—K1—Te2	149.26 (9)
O4ⁱⁱⁱ—Te1—O2ⁱⁱⁱ	91.1 (3)	O5—K1—Te2	33.99 (7)
O4ⁱⁱⁱ—Te1—O2	87.8 (3)	O5^viii—K1—Te2^viii	33.81 (7)
O4—Te1—O2	91.1 (3)	O5^viii—K1—O5	174.98 (13)
O4—Te1—O4ⁱⁱⁱ	97.0 (2)	O5^viii—K1—H5	158.9 (5)
Te1ⁱⁱ—Te1'—Te1ⁱ	179.90 (5)	O5—K1—H5	16.6 (4)
Te1ⁱⁱ—Te1'—Fe1'ⁱ	179.90 (5)	O6—K1—Te2	104.4 (5)
Te1ⁱ—Te1'—Fe1'ⁱⁱ	179.90 (5)	O6—K1—Te2^viii	102.9 (5)
Te1ⁱⁱ—Te1'—Fe1'ⁱⁱ	0.00 (2)	O6—K1—O2	137.1 (4)
Te1ⁱ—Te1'—Fe1'ⁱ	0.00 (2)	O6—K1—O3ⁱⁱ	134.4 (4)
Te1ⁱ—Te1'—K1ⁱⁱ	113.58 (5)	O6—K1—O3	82.5 (3)
Te1ⁱⁱ—Te1'—K1ⁱⁱ	66.35 (5)	O6—K1—O5	91.8 (5)
Te1ⁱⁱ—Te1'—K1^iv	113.58 (5)	O6—K1—O5^viii	90.2 (5)
Te1ⁱ—Te1'—K1^iv	66.35 (5)	O6—K1—H5	105.0 (12)
Fe1'ⁱⁱ—Te1'—Fe1'ⁱ	179.90 (5)	O6—K1—O7	90.4 (5)
Fe1'ⁱ—Te1'—K1ⁱⁱ	113.58 (5)	O7—K1—Te2^viii	119.1 (15)
Fe1'ⁱⁱ—Te1'—K1ⁱⁱ	66.35 (5)	O7—K1—Te2	117.8 (15)
Fe1'ⁱⁱ—Te1'—K1^iv	113.58 (5)	O7—K1—O3ⁱⁱ	115.0 (10)
Fe1'ⁱ—Te1'—K1^iv	66.35 (5)	O7—K1—O5^viii	88.4 (16)
K1^iv—Te1'—K1ⁱⁱ	104.10 (5)	O7—K1—O5	86.9 (16)
O1^iv—Te1'—Te1ⁱⁱ	139.71 (10)	O7—K1—H5	77 (2)
O1ⁱⁱ—Te1'—Te1ⁱⁱ	40.20 (9)	Te1'—K2—Te1'^ix	106.29 (12)
O1^iv—Te1'—Te1ⁱ	40.20 (9)	Te1'—K2—Fe1^ix	106.3
O1ⁱⁱ—Te1'—Te1ⁱ	139.71 (10)	Te1'^ix—K2—Fe1^ix	0.000 (15)
O1^iv—Te1'—Fe1'ⁱⁱ	139.71 (10)	Te2—K2—Te1'^ix	156.19 (19)
O1ⁱⁱ—Te1'—Fe1'ⁱⁱ	40.20 (9)	Te2^x—K2—Te1'^ix	53.29 (2)
O1ⁱⁱ—Te1'—Fe1'ⁱ	139.71 (10)	Te2—K2—Te1'	53.29 (2)
O1^iv—Te1'—Fe1'ⁱ	40.20 (9)	Te2^x—K2—Te1'	156.19 (19)
O1^iv—Te1'—K1ⁱⁱ	85.84 (11)	Te2^x—K2—Te2	141.91 (5)
O1ⁱⁱ—Te1'—K1^iv	85.84 (11)	Te2—K2—Fe1^ix	156.19 (19)
O1^iv—Te1'—K1^iv	43.83 (10)	Te2^x—K2—Fe1^ix	53.29 (2)
O1ⁱⁱ—Te1'—K1ⁱⁱ	43.83 (10)	O4^x—K2—Te1'	102.68 (11)
O1^iv—Te1'—O1ⁱⁱ	99.60 (19)	O4^x—K2—Te1'^ix	27.69 (9)
O3^v—Te1'—Te1ⁱⁱ	86.0 (2)	O4ⁱ—K2—Te1'^ix	102.68 (11)
O3—Te1'—Te1ⁱⁱ	94.0 (2)	O4ⁱ—K2—Te1'	27.69 (9)
O3—Te1'—Te1ⁱ	86.0 (2)	O4ⁱ—K2—Te2^x	152.64 (8)
O3^v—Te1'—Te1ⁱ	94.0 (2)	O4^x—K2—Te2	152.64 (8)
O3—Te1'—Fe1'ⁱⁱ	94.0 (2)	O4ⁱ—K2—Te2	65.35 (6)
O3^v—Te1'—Fe1'ⁱ	94.0 (2)	O4^x—K2—Te2^x	65.35 (6)
O3—Te1'—Fe1'ⁱ	86.0 (2)	O4^x—K2—Fe1^ix	27.69 (9)
O3^v—Te1'—Fe1'ⁱⁱ	86.0 (2)	O4ⁱ—K2—Fe1^ix	102.68 (11)
O3—Te1'—K1^iv	130.71 (18)	O4ⁱ—K2—O4^x	87.33 (13)
O3—Te1'—K1ⁱⁱ	49.72 (18)	O4^x—K2—O5^xi	93.18 (9)
O3^v—Te1'—K1ⁱⁱ	130.71 (18)	O4ⁱ—K2—O5^xi	176.6 (3)
O3^v—Te1'—K1^iv	49.72 (18)	O4ⁱ—K2—O5	93.18 (9)
O3—Te1'—O1ⁱⁱ	91.7 (2)	O4^x—K2—O5	176.6 (3)
O3^v—Te1'—O1^iv	91.7 (2)	O4^x—K2—O6^vii	88.97 (18)
O3—Te1'—O1^iv	88.7 (2)	O4ⁱ—K2—O6^vii	88.97 (18)
O3^v—Te1'—O1ⁱⁱ	88.7 (2)	O4ⁱ—K2—O6	92.40 (19)
O3—Te1'—O3^v	179.5 (3)	O4^x—K2—O6	92.40 (19)
O4^vi—Te1'—Te1ⁱⁱ	39.78 (10)	O5^xi—K2—Te1'^ix	79.15 (10)
O4ⁱ—Te1'—Te1ⁱⁱ	140.32 (11)	O5^xi—K2—Te1'	154.7 (2)
O4^vi—Te1'—Te1ⁱ	140.32 (11)	O5—K2—Te1'	79.15 (10)
O4ⁱ—Te1'—Te1ⁱ	39.78 (10)	O5—K2—Te1'^ix	154.7 (2)
O4ⁱ—Te1'—Fe1'ⁱⁱ	140.32 (11)	O5—K2—Te2	27.90 (7)
O4^vi—Te1'—Fe1'ⁱⁱ	39.78 (10)	O5^xi—K2—Te2^x	27.90 (7)
O4^vi—Te1'—Fe1'ⁱ	140.32 (11)	O5—K2—Te2^x	114.01 (8)
O4ⁱ—Te1'—Fe1'ⁱ	39.78 (10)	O5^xi—K2—Te2	114.01 (8)
O4^vi—Te1'—K1ⁱⁱ	92.68 (10)	O5^xi—K2—Fe1^ix	79.15 (10)
O4^vi—Te1'—K1^iv	137.44 (10)	O5—K2—Fe1^ix	154.7 (2)
O4ⁱ—Te1'—K1ⁱⁱ	137.44 (10)	O5^xi—K2—O5	86.12 (14)
O4ⁱ—Te1'—K1^iv	92.68 (10)	O5^xi—K2—O6^vii	87.6 (2)
O4ⁱ—Te1'—O1ⁱⁱ	178.36 (12)	O5—K2—O6^vii	87.6 (2)
O4ⁱ—Te1'—O1^iv	79.78 (14)	O5^xi—K2—O6	91.0 (2)
O4^vi—Te1'—O1^iv	178.36 (12)	O5—K2—O6	91.0 (2)
O4^vi—Te1'—O1ⁱⁱ	79.78 (14)	O6—K2—Te1'	69.07 (11)
O4ⁱ—Te1'—O3	89.8 (2)	O6^vii—K2—Te1'^ix	111.90 (11)
O4ⁱ—Te1'—O3^v	89.8 (2)	O6^vii—K2—Te1'	111.90 (11)
O4^vi—Te1'—O3^v	89.8 (2)	O6—K2—Te1'^ix	69.07 (11)
O4^vi—Te1'—O3	89.8 (2)	O6^vii—K2—Te2^x	89.17 (12)
O4^vi—Te1'—O4ⁱ	100.9 (2)	O6^vii—K2—Te2	89.17 (12)
K1^vii—Te2—K1ⁱⁱ	180.0	O6—K2—Te2^x	90.21 (11)
K1ⁱ—Te2—K1ⁱⁱ	115.55 (3)	O6—K2—Te2	90.21 (11)
K1ⁱ—Te2—K1^vii	64.45 (3)	O6—K2—Fe1^ix	69.07 (11)
K1—Te2—K1ⁱⁱ	64.45 (3)	O6^vii—K2—Fe1^ix	111.90 (11)
K1ⁱ—Te2—K1	180.0	O6—K2—O6^vii	178.1 (2)
K1—Te2—K1^vii	115.55 (3)	Te1—O1—Te1'ⁱⁱ	97.41 (14)
K1ⁱ—Te2—K2	115.02 (9)	Te1—O1—Fe1ⁱⁱ	97.41 (14)
K1ⁱ—Te2—K2ⁱ	64.98 (9)	Te1—O1—K1	106.83 (15)
K1^vii—Te2—K2ⁱ	113.90 (10)	Te1'ⁱⁱ—O1—K1	104.59 (15)
K1—Te2—K2	64.98 (9)	Fe1ⁱⁱ—O1—Te1'ⁱⁱ	0.0
K1—Te2—K2ⁱ	115.02 (9)	Fe1ⁱⁱ—O1—K1	104.59 (15)
K1^vii—Te2—K2	66.10 (10)	Te1—O2—K1	99.5 (2)
K1ⁱⁱ—Te2—K2	113.90 (10)	Te1—O2—K1ⁱⁱ	131.8 (4)
K1ⁱⁱ—Te2—K2ⁱ	66.10 (10)	Te2—O2—Te1	129.9 (5)
K2—Te2—K2ⁱ	180.0	Te2—O2—K1ⁱⁱ	97.55 (14)
O2—Te2—K1	54.3 (2)	Te2—O2—K1	92.21 (16)
O2—Te2—K1^vii	130.5 (2)	K1ⁱⁱ—O2—K1	84.9 (3)
O2—Te2—K1ⁱⁱ	49.5 (2)	Te1'—O3—K1ⁱⁱ	98.2 (2)
O2ⁱ—Te2—K1	125.7 (2)	Te1'—O3—K1	128.9 (3)
O2—Te2—K1ⁱ	125.7 (2)	Te2—O3—Te1'	132.6 (3)
O2ⁱ—Te2—K1^vii	49.5 (2)	Te2—O3—K1	97.86 (15)
O2ⁱ—Te2—K1ⁱⁱ	130.5 (2)	Te2—O3—K1ⁱⁱ	93.39 (18)
O2ⁱ—Te2—K1ⁱ	54.3 (2)	K1—O3—K1ⁱⁱ	84.05 (18)
O2ⁱ—Te2—K2ⁱ	118.02 (19)	Te1—O4—Te1'ⁱ	98.59 (13)
O2—Te2—K2	118.02 (19)	Te1—O4—Fe1ⁱ	98.59 (13)
O2ⁱ—Te2—K2	61.98 (19)	Te1—O4—K2ⁱ	116.05 (19)
O2—Te2—K2ⁱ	61.98 (19)	Te1'ⁱ—O4—K2ⁱ	112.2 (2)
O2ⁱ—Te2—O2	180.0	Fe1ⁱ—O4—Te1'ⁱ	0.0
O2ⁱ—Te2—O5	87.5 (3)	Fe1ⁱ—O4—K2ⁱ	112.2 (2)
O2—Te2—O5	92.5 (3)	Te2—O5—K1	86.9 (3)
O2ⁱ—Te2—O5ⁱ	92.5 (3)	Te2—O5—K1^vii	89.6 (3)
O2—Te2—O5ⁱ	87.5 (3)	Te2—O5—K2	110.10 (13)
O3—Te2—K1ⁱⁱ	54.61 (18)	Te2—O5—H5	102 (6)
O3ⁱ—Te2—K1ⁱ	50.20 (15)	K1^vii—O5—K1	174.98 (13)
O3ⁱ—Te2—K1	129.80 (15)	K1^vii—O5—H5	110 (5)
O3ⁱ—Te2—K1ⁱⁱ	125.39 (18)	K1—O5—H5	74 (5)
O3—Te2—K1	50.20 (15)	K2—O5—K1	87.2 (2)
O3—Te2—K1^vii	125.39 (18)	K2—O5—K1^vii	90.5 (2)
O3—Te2—K1ⁱ	129.80 (15)	K2—O5—H5	142 (6)
O3ⁱ—Te2—K1^vii	54.61 (18)	K1^xi—O6—K1	92.49 (16)
O3—Te2—K2	60.8 (2)	K1—O6—K2	89.8 (5)
O3ⁱ—Te2—K2ⁱ	60.8 (2)	K1—O6—K2^viii	91.5 (5)
O3—Te2—K2ⁱ	119.2 (2)	K1^xi—O6—K2	89.8 (5)
O3ⁱ—Te2—K2	119.2 (2)	K1^xi—O6—K2^viii	91.5 (5)
O3—Te2—O2ⁱ	92.94 (15)	K1^xi—O6—H6	86 (6)
O3ⁱ—Te2—O2	92.94 (15)	K1—O6—H6	178 (6)
O3—Te2—O2	87.06 (15)	K2—O6—K2^viii	178.1 (2)
O3ⁱ—Te2—O2ⁱ	87.06 (15)	K2^viii—O6—H6	89 (7)
O3—Te2—O3ⁱ	180.0	K2—O6—H6	90 (7)
O3ⁱ—Te2—O5	90.4 (3)	K1—O7—K1^xi	86.8 (10)

K1ⁱ—Te2—O3—Te1'	8.8 (5)	K2ⁱ—Te2—O3—K1ⁱⁱ	−15.07 (19)
K1^vii—Te2—O3—Te1'	−75.7 (4)	K2ⁱ—Te2—O3—K1	−99.52 (16)
K1—Te2—O3—Te1'	−171.2 (5)	O2—Te2—O3—Te1'	144.7 (4)
K1ⁱⁱ—Te2—O3—Te1'	104.3 (4)	O2ⁱ—Te2—O3—Te1'	−35.3 (4)
K1ⁱ—Te2—O3—K1	180.0	O2—Te2—O3—K1ⁱⁱ	40.36 (19)
K1^vii—Te2—O3—K1ⁱⁱ	180.000 (1)	O2ⁱ—Te2—O3—K1	135.9 (2)
K1—Te2—O3—K1ⁱⁱ	84.45 (19)	O2—Te2—O3—K1	−44.1 (2)
K1ⁱⁱ—Te2—O3—K1	−84.45 (19)	O2ⁱ—Te2—O3—K1ⁱⁱ	−139.64 (19)
K1ⁱ—Te2—O3—K1ⁱⁱ	−95.55 (19)	O5—Te2—O3—Te1'	−122.8 (5)
K1^vii—Te2—O3—K1	95.55 (19)	O5ⁱ—Te2—O3—Te1'	57.2 (5)
K2—Te2—O3—Te1'	−90.7 (4)	O5—Te2—O3—K1	48.4 (2)
K2ⁱ—Te2—O3—Te1'	89.3 (4)	O5ⁱ—Te2—O3—K1ⁱⁱ	−47.1 (2)
K2—Te2—O3—K1ⁱⁱ	164.93 (19)	O5ⁱ—Te2—O3—K1	−131.6 (2)
K2—Te2—O3—K1	80.48 (16)	O5—Te2—O3—K1ⁱⁱ	132.9 (2)

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

Acknowledgements

The authors acknowledge TU Wien Bibliothek for financial support through its Open Access Funding Program.

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