Mixed-valent 1:1 oxidotellurates(IV/VI) of Na, K and Rb: superstructure and three-dimensional disorder

2.1 Synthesis

The title compounds were obtained from experiments under hydrothermal conditions. M₂CO₃ (M = Na, K, Rb), TeO₂ and Te(OH)₆ in a 4:1:1 molar ratio with a combined mass of 700 mg were thoroughly mixed and introduced into Teflon containers with ca. 3 ml inner volume. The containers were filled to three quarters with deionized water and placed in steel autoclaves. The samples were heated to 210 °C and kept under autogenous pressure at that temperature for one week. After cooling to room temperature within 3 h, the solids were separated, washed with deionized water, ethanol and acetone and dried at ambient conditions. For the Na batch, Na₂Te₂O₆·11/8H₂O was obtained as a single phase, whereas for K and Rb additionally colorless needles of the oxidotellurates(VI) KTeO₃(OH) [17] and RbTeO₃(OH) were obtained. These phases are non-isotypic but closely related to CsTeO₃(OH) and will be discussed in a subsequent publication.

2.2 Data collection and refinement

The colourless crystals were preselected under a polarizing microscope. Na₂Te₂O₆·11/8H₂O crystallizes as small tabular crystals, M₂Te₂O₄(OH)₄ (M = K, Rb) as large hexagonal pillars. The crystals were cut into fragments with a size suitable for single crystal diffraction.

Data were collected under a dry stream of nitrogen on a Bruker KAPPA ApexII diffractometer system using MoK α ‾ radiation and fine-sliced ω- and φ-scans. Data were reduced to intensity values with Saint-Plus [18] and a correction for absorption effects applied using the multi-scan approach implemented in Sadabs [18]. The structures were solved with the dual-space approach implemented in Shelxt [19] and refined against F² with Shelxl [20]. Details on data collection and refinement are summarized in Table 1. Additional crystallographic information on the title structures were deposited in the ICSD database of the FIZ Karlsruhe with the CSD deposition numbers listed at the end of Table 1.

Localization and refinement of the H positions as well as refinement of the displacement parameters of disordered O atoms was only possible after removing erroneous reflection intensities (for example owing to shadowing by the beamstop) and optimizing the weighting of reflections.

H atoms of Na₂Te₂O₆·11/8H₂O were located from difference Fourier maps and the O–H distance restrained to 0.87(2) Å. For K₂Te₂O₄(OH)₄ and Rb₂Te₂O₄(OH)₄, the single H site features a 2/3 occupancy and therefore was difficult to locate. Ultimately, a crystal-chemically reasonable position could be located and refined.

K₂Te₂O₄(OH)₄ and Rb₂Te₂O₄(OH)₄ crystallize in the space group P6₃/mmc and feature disorder about the threefold rotation axis. All attempts to resolve the disorder by refinement of models in subgroups of P6₃/mmc, with the lost operation as twin operations, failed. Indeed, distinct three-dimensional diffuse scattering, lack of superstructure reflections, and excellent reliability factors all favor the P6₃/mmc model. Moreover, the platy crystals featured a hexagonal shape and showed no birefringence when viewed perpendicular to the main plane, as expected for trigonal or hexagonal symmetry.

3.1 Na₂Te₂O₆·11/8H₂O

Na₂Te₂O₆·11/8H₂O [P2₁/n, V = 5288.5(9) Å³, Z = 32] crystallizes as an eightfold superstructure. Atoms were labeled according to their position in the basic structure with an added letter (e.g. Te1A, Te1B, etc.). The set of atoms that correspond to a single position in the basic structure will be indicated by an appended ‘x’ (e.g. Te1x stands for Te1A, Te1B, etc.).

The basic structure [C2/c, V = 1322.1(2) Å³, Z = 8] corresponds, except for the water molecules, to the Na₂Te₂O₆·3/2H₂O structure reported by [16]. The eightfold superstructure is expressed by a quadrupling of the cell volume and the loss of the C-centring. The unit cells are related by ( a , b , c ) = ( 4 a b , b b , a b + c b ) , where a subscript ‘b’ marks basis vectors of the basic structure. Equivalently, the structure can be considered as a commensurately modulated structure with the modulation wave vector q = a _b */4−c _b */4 (Figure 1).

Figure 1:

Reconstructed hk2 section of reciprocal space of Na₂Te₂O₆·11/8H₂O. The reciprocal basis of the basic structure and the q-vector are indicated.

In a crystal-chemical sense, Na₂Te₂O₆·11/8H₂O can be described as an alternation of corrugated [Te₂O₆]²⁻ layers and [Na₂·11/8H₂O]²⁺ layers extending parallel to (010) (Figure 2).

Figure 2:

The crystal structure of Na₂Te₂O₆·11/8H₂O viewed down [100]. Te (yellow), Na (pink), O (red) and H (white) atoms are represented by spheres of arbitrary radii.

The [Te₂O₆]²⁻ layers, shown including the Na1x atoms in Figure 3(a), feature a diperiodic network, which has already been described by [16]. [Te^IVO₄₊₁] units (with Te^IV in distorted square-pyramidal coordination) are connected by edges to [Te₂^IVO₈] groups (Figure 4). The [Te^VIO₆] octahedra are likewise connected via edges to [Te₂^VIO₁₀] groups (Figure 4).

Figure 3:

Layers in Na₂Te₂O₆·11/8H₂O projected on the layer plane (010): (a) [Te₂O₆]²⁻ including the Na1x atoms and (b) [Na₂·11/8H₂O]²⁺ excluding the Na1x atoms, but including the O1 atoms of the [Te^VIO₆] octahedra. Atom color codes are as in Figure 2. Super and basic structure cells are indicated in red and black, respectively. Atoms are labeled according to the basic structure for clarity. The symmetry elements of the layers in the basic structure are indicated in one cell using the standard graphical symbols [21].

Figure 4:

One of the eight [Te₂^VIO₁₀] (Te1A, Te1B) and [Te₂^IVO₈] (Te2A, Te2B) groups in Na₂Te₂O₆·11/8H₂O. For clarity, O atoms are only labeled according to the basic structure. Te and O atoms are represented by yellow and red ellipsoids drawn at the 75% probability level.

In the basic structure, both kinds of dimers ([Te₂^IVO₈] and [Te^VIO₆]) are located on centres of inversion. The dimers are connected via corner-sharing to a checkerboard pattern. The individual atoms are all located on the general position in the basic structure and therefore also in the superstructure, since the site symmetry cannot increase. This means that each position in the basic structure is split into eight positions in the superstructure.

The [Te₂O₆]²⁻ layers show a moderate modulation with respect to the basic structure, as compiled in Table 2. The largest modulation amplitude is observed for the Te2G (0.237 Å) and the O1B (0.403 Å) atoms, respectively. In most cases, the atoms are displaced by less than 0.2 Å. Owing to the modulation, the description of the [Te₂^IVO₈] dimers is ambiguous. The bridging oxygen atoms (O6x) partake in the shortest [1.8496(18)–1.8779(17) Å] and longest [2.2557(18)–2.5763(18) Å] bonds (Figure 4). Whereas the shorter of these long bonds clearly constitute 4 + 1-coordination, in some cases, where d(Te—O) > 2.5 Å, the [Te^IVO₄₊₁] units could be better described as two isolated [Te^IVO₄] units. As is common for oxidotellurates(IV) [1], a clear distinction cannot be made.

The [Na₂·11/8H₂O]²⁺ layers feature three Na positions in the basic structure. Na1 [Figure 3(a)] is located on the twofold axis and Na2 [Figure 3(b)] on a general position. In both cases, the superstructure atoms are located on general positions, leading to four (Na1x) and eight (Na2x) independent positions, which all feature mild modulation (max. 0.311 Å, Table 3). The Na3 atom is located on a centre of inversion in the basic structure, which is retained for two positions in the superstructure. These atoms therefore feature no positional modulation. The three remaining Na3x atoms are located on general positions and exhibit distinctly stronger modulation than the previously discussed atoms: 0.473–0.720 Å.

This can be explained by the connectivity to the water molecules, which can be considered as the source of the modulation [Figure 3(b)]. In the basic structure, the OW1 atom is located on the twofold axis, however the four corresponding atoms on the general position of the superstructure are strongly modulated (0.458–0.822 Å, Table 3). For the remaining water molecules, two cases can be distinguished: OW2 is realized in one fourth of the cases and located on the twofold rotation axis of the basic structure, from which it deviates slightly in the single superstructure position (0.241 Å). In the remaining three quarters of the cases, OW3 in the basic structure is located on a general position around the twofold axis. There are six independent positions in the superstructure, with modulation amplitudes of 0.149–0.638 Å.

In total, there are eleven (four OW1, one OW2 and six OW3) water positions in the superstructure resulting in the peculiar composition of Na₂Te₂O₆·11/8H₂O. Thus, the water molecules can be considered as occupationally modulated. If only OW2 or only OW3 were realized, the composition would read as Na₂Te₂O₆·H₂O or Na₂Te₂O₆·3/2H₂O, respectively. As far as we can tell from the refined H-positions, the water molecules only donate hydrogen bonds to O atoms of the [Te₂O₆]²⁻ layers and not to other water molecules. However, in some cases the situation is not entirely clear.

The strong positional modulation of the Na3x atoms is due to their direct contact to the water molecules. One of the positions in the superstructure (Na3B) is disordered in a 78.7:21.3(3) manner, whereby the second position is close to the centre of inversion in the basic structure. This could be interpreted as another Na3A- or Na3C-type position, which are located on an inversion centre of the superstructure. An Na3A-type position results in a reduced number of water molecules, because it leads to the coordination of a single OW2 position rather than two OW3 positions. However, with an Na3C-like position the composition remains unchanged, as an OW3-like coordination is established, where the Na atom coordinates to two water molecules. Thus, for now the water content is given as 11/8 molecules per formula unit.

3.2 M₂Te₂O₄(OH)₄ (M = K, Rb)

K₂Te₂O₄(OH)₄ and Rb₂Te₂O₄(OH)₄ crystallize in isotypic disordered crystal structures in the hexagonal space group P6₃/mmc. The main building blocks of the structures are [Te₂O₄(OH)₄]²⁻ rods with 6₃/mmc symmetry [Figure 5(a) and (b)]. The rods are connected by M atoms located on a site with 3m symmetry.

Figure 5:

The crystal structure of M₂Te₂O₄(OH)₄ (M = K, Rb) viewed down (a) [001] and (b) [110]; (c) a [Te₂O₄(OH)₄]²⁻ rod. M is represented by pink spheres, color codes of the other atoms are as in Figure 2. H atoms were omitted in (a) and (b) for clarity and in (b) the O atoms disordered about the .2. position were merged to a single position. In (c) only one of the three possible positions of the [Te^IVO₄] groups is shown in each case.

The [Te₂O₄(OH)₄]²⁻ rods are built of an alternation of [(Te1)^VIO₂(OH)₄] and [(Te2)^IVO₄] groups [Figure 5(c)]. The Te^VI atom is located on the 3 ‾ m position and coordinated by six O1 atoms forming a close to regular octahedron [six equal distances: 1.926(2) Å (M = K), 1.9239(18) Å (M = Rb); O–Te–O angles deviating by less than 2° from the ideal angles]. The Te^IV atom is located on an mm2 position and bonded to four O atoms within an disphenoidal coordination with short Te–O distances [1.879(7) Å (M = K) and 1.862(5) Å (M = Rb)] for the two terminal O2 atoms and longer distances [2.181(2) Å (M = K) and 2.1843(18) Å (M = Rb)] for the two bridging O1 atoms, which connect the two kinds of oxidotellurate groups.

The [Te^IVO₄] units are disordered around the threefold axis of the rod group. Hence, only one out of three positions is realized. This leaves the other two O1 atoms that are not connected to the [Te^IVO₄] units and correspond to the OH groups. The latter form strong hydrogen bonds to the O2 atoms of the [Te^IVO₄] units [O ⋯ O: 2.551(5) Å (M = K) and 2.562(3) Å (M = Rb)] [Figure 5(c)].

The disorder of the rods can be explained by application of the OD theory [22], which is usually applied to structures built of layers. Here, the rods are decomposed into two kinds of blocks. The [Te^VIO₆] octahedra (excluding H atoms) feature 3 ‾ m symmetry and will be called A¹. The [Te^IVO₄] units and OH groups form the second block and feature mm2 symmetry and will be called A². The O1 atoms are located at the interface and attributed to both adjacent blocks. Both blocks are non-polar in the sense that they are symmetric by an operation that inverts the rod directions ( 3 ‾ , .2. and m.., ..2, respectively). In analogy to structures of layers, a rod structure of two non-polar blocks can be considered as a category IV structure of two kinds of blocks [23].

By application of the threefold rotation of the A¹ block onto the A² block, it becomes evident that given an A¹ block, the adjacent A² block can be placed in three ways that result in congruent (and therefore energetically equivalent) pairs of adjacent blocks. This equivalence of pairs of modules is the crucial aspect of OD structures, since it means that all possible arrangements are locally equivalent. However, triples of adjacent objects may differ. Indeed, there are two kinds of A²A¹A² triples, namely those where the two A² blocks are related by a twofold screw rotation and those where they are related by a sixfold screw rotation in clockwise (6₅) or counterclockwise (6₁) direction (Figure 6). An example of triples with a 6₁ screw is given in Figure 5(c). The triples possess the overall symmetry .2/m. and .2., respectively.

Figure 6:

Schematic representation of the two types of A²A¹A² triples in M₂Te₂O₄(OH)₄: (a) .2/m. and (b, c) two orientations of .2.. [Te^VIO₆] units are represented by a green octahedron, the direction of the lone pair of the [Te^IVO₄] units by a yellow arrow. Symmetry elements are indicated in black.

Polytypes of a maximum degree of order (MDO) are those that cannot be decomposed into simpler polytypes [24, 25], that is into polytypes made up of only one subset of the triples, quadruples, etc. of adjacent modules. Applied to [Te₂O₄(OH)₄]²⁻, there are four MDO rods, which are schematized in Figure 7. MDO₁ (mmc, c = 2c₀) is composed only of the .2/m. triple and the generating operation is a 2₁.. operation. MDO₂ (6₁22, c = 6c₀) and MDO₂^′ (6₅22, c = 6c₀) are composed of either of the two orientations of the .2. triple and the generating operation is a 6₁.. or 6₅.. screw rotation. Finally, in MDO₃ (211, c = 2c₀) the two orientations of the 0.2. triple alternate and the generating operation is .2..

Figure 7:

Schematic representation of the MDO rods in M₂Te₂O₄(OH)₄. The electron lone pairs of [Te^IVO₄] units are represented by yellow arrows. (a) MDO₁, (b) MDO₂, (c) MDO′₂, (d) MDO₃

The M atoms (site symmetry 3m.) connect the [Te₂O₄(OH)₄]²⁻ rods [Figure 5(a)] Their coordination polyhedron can be derived from an anticuboctahedron [Figure 8]. Six O1 atoms (which make up the [Te^VIO₆] octahedra) form a central, slightly distorted hexagon [M–O distances: 3.1115(5) Å (M = K), 3.2155(5) Å (M = Rb); O–M–O angles: 66.94(10), 52.89(10)° (M = K) and 69.04(7), 50.89(7)° (M = Rb)]. Three more O1 atoms form an equilateral triangular base [M–O distances: 2.808(3) Å (M = K) and 2.938(2) Å (M = Rb)]. The second triangular base is formed by O2 atoms of the partially occupied [Te^IVO₄] units [M–O distances: 3.103(6) Å (M = K) and 3.146(4) Å (M = Rb)]. However, on average only two out of three vertices (each consisting of two possible O2 sites) are occupied and thus the M site can be considered as eleven-coordinated.

Figure 8:

M/O-network in the crystal structure of M₂Te₂O₄(OH)₄ (M = K, Rb). Atoms as in Figure 5. Non-labeled oxygen atoms are O1.

Figure 9(a) shows a section of the M₂Te₂O₄(OH)₄ crystal structure with fixed z. As stated above, the lone pairs of the Te^IV atoms point towards the threefold axis, on which the M atoms are located at a different z value. It is reasonable to assume that only one Te^IV for a given z-coordinate can point into a given channel. Thus, the distribution of the [Te^IVO₄] units in a fixed z section is restricted. In particular, one can describe such a section as a bipartite honeycomb net, where the nodes stand for the centres of the [Te₂O₄(OH)₄]⁻ rods and the channels of empty space (represented by yellow and blue disks in Figure 9).

Figure 9:

(a) Slice parallel to (001) through the Te^IVO₄ units of M₂Te₂O₄(OH)₄ (M = K, Rb). Atom colours are as in Figure 4. Only one out of three Te^IVO₄ units is realized. Centres of the Te₂O₄(OH)₄ rods and the empty space, towards which the lone pairs point are indicated, by yellow and blue circles, respectively. (b, c) Examples of dimer partitions of a honeycomb net corresponding to a valid M₂Te₂O₄(OH)₄ (M = K, Rb) structure. Arrows indicate lone pairs protruding into the channels of empty space. A grey backdrop indicates a unit cell.

Finding a valid distribution of the [Te^IVO₄] units then is equivalent to finding a dimer covering of a honeycomb net [26]. Two examples of such nets are given in Figure 9(b) and (c). In particular, these can be considered as the two ‘MDO layers’: In Figure 9(b), all lone pairs point in the same direction (layer symmetry pm2m), whereas in Figure 9(c) adjacent lone pairs always point in different directions [layer symmetry p 6 ‾ 2 m with lattice basis (2a + b, −a + b)]. These two configurations have been named ‘ladder’ and ‘columnar’, respectively [26]. In the former, all M atoms are eleven-coordinated. In the latter, a third of the M atoms are nine- and the other two thirds are twelve-coorindated. Thus, from the point of view of the M atoms, these arrangements are not equivalent. The M atoms might compensate the change in coordination number by displacement in the [001] direction.

The description in terms of disordered blocks is proved by the diffraction pattern of the M₂Te₂O₄(OH)₄ crystals, which feature distinct three-dimensional diffuse scattering (Figure 10). In the c^* direction, the diffuse scattering is entirely unstructured, which means that the orientation of succesive [Te^IVO₄] units along c is uncorrelated.

Figure 10:

Reconstructed sections of reciprocal space of M₂Te₂O₄(OH)₄. Spurious sharp diffraction spots, in particular for the K sample, are due to microcrystalline contaminations on the crystal surface. (a) K₂Te₂O₄(OH)₄, (hk0)*; (b) K₂Te₂O₄(OH)₄, (h2/3l)*; (c) Rb₂Te₂O₄(OH)₄, (hk0)*; (d) Rb₂Te₂O₄(OH)₄, (h2/3l)*.

In planes parallel to (001)^* (with constant l), the Rb analogue features distinctly less pronounced diffuse scattering than the K analogue. Thus, the distribution of the [Te^IVO₄] units is rather well ordered in the (001) plane of Rb₂Te₂O₄(OH)₄. The observed intensities at (h+1/3)a^* + (k + 1/3)b^* and (h + 2/3)a^* + (k + 2/3)b^* suggest a layer with tripled unit cell volume and the layer lattice basis (2a + b, −a + b). This cell is consistent with the ‘columnar’ arrangement [Figure 9(c)].

The layers in the K analogue are distinctly less ordered. Diffuse scattering still centres around positions suggesting a ‘columnar’ arrangement. Distinct elongation in the a^* + b^* direction suggests an increased ordering in rods running along 〈 1 1 ‾ 0 〉 with respect to the basic structure, which is equivalent to the 〈100〉 directions with respect to the basis vectors of the ’columnar’ arrangement [Figure 9(b) and (c)].