The Role of Different Alkali Metals in the A15Tl27 Type Structure and the Synthesis and X-ray Structure Analysis of a New Substitutional Variant Cs14.53Tl28.4

Alkali metal thallides have been known since the report of E. Zintl on NaTl in 1932. Subsequently, binary and ternary thallides of alkali metals have been characterized. At an alkali metal proportion of approximately 33% (A:Tl~1:2, A = alkali metal), three different unique type structures are reported: K49Tl108, Rb17Tl41 and A15Tl27 (A = Rb, Cs). Whereas Rb17Tl41 and K49Tl108 feature a three-dimensional sublattice of Tl atoms, the A15Tl27 structure type includes isolated Tl11 clusters as well as two-dimensional Tl-layers. This unique arrangement is only known so far when the heavier alkali metals Rb and Cs are included. In our contribution, we present single-crystal X-ray structure analyses of new ternary and quaternary compounds of the A15Tl27 type structure, which include different amounts of potassium. The crystal structures allow for the discussion of the favored alkali metal for each of the four Wyckoff positions and clearly demonstrate alkali metal dependent site preferences. Thereby, the compound Cs2.27K12.73Tl27 unambiguously proves the possibility of a potassium-rich A15Tl27 phase, even though a small amount of cesium appears to be needed for the stabilization of the latter structure type. Furthermore, we also present two compounds that show an embedding of Tl instead of alkali metal into the two-dimensional substructure, being equivalent to the formal oxidation of the latter. Cs14.53Tl28.4 represents the binary compound with the so far largest proportion of incorporated Tl in the structure type A15Tl27.


Introduction
Alkali metal thallides represent a very interesting class of materials in terms of structural chemistry as they involve versatile thallium substructures depending on the amount of alkali metal involved, which is equitable to the valence electron concentration [1]. The electronic description of the latter compounds is not trivial, as part of them are diamagnetic and show a real band gap; therefore, the description by the Zintl-Klemm formalism is permissible in a narrow sense [2][3][4][5]. In contrast, quite a large number of these compounds show metallic and paramagnetic behavior [6,7] and the basis of this concept, the complete electron transfer from the electropositive to the electronegative element, is not true for these materials. Nevertheless, in many cases, the formed anionic partial structures can be described according to this theory [8][9][10]. This still makes this concept a very powerful tool in solid state chemistry at the frontier between metallic and ionic bonding. The first Zintl phase goes back to the investigations of E. Zintl, who described the crystal structure of NaTl, in which the thallium substructure follows the Zintl-Klemm formalism by forming a diamond sublattice [11]. Interestingly, thallium as a "parental" element for this concept is found left to the so-called Zintl border in the periodic table of elements [12,13]. This actually makes it a very interesting element to point out and describe structural effects of The received products are very sensitive towards moisture and oxygen; therefore, they were stored in a glove box (Labmaster 130 G Fa. M. Braun, Garching, Germany). In advance of the characterization by single crystal X-ray diffraction techniques, a small number of crystals was transferred into dried mineral oil. Subsequently, a suitable crystal was isolated and mounted on the Rigaku SuperNova diffractometer (Rigaku Polska Sp. Z o. o. Ul, Wroclaw, Poland) (X-ray: Mo-source, Eos detector) using MiTeGen loops, before collecting data at 123 K. The program CrysAlisPro was used for data collection and data reduction [31]. The solution of the structure and subsequent refinements were accomplished in Olex2 [32] using ShelXT [33,34]. For generating representations of the crystal structures, the software Diamond was used [35].

Results
All compounds crystallize in the A 15 Tl 27 (A = Cs, Rb)-type structure (hexagonal, space group P-62m) [14]. These alkali metal thallides naturally possess very high absorption coefficients (MoKα, µ > 70 mm −1 ), hence small single crystals were selected for the X-ray diffraction experiments, but the data sets still suffered from severe absorption effects, which could be reduced by applying absorption correction. The high redundancy of the collected data sets additionally allowed a shape adjustment by the "shape optimization" tool in the CrysAlisPro software (diffractometer software, Rigaku).
We first observed the evidence of the mixed A 15 Tl 27 phases (K 6.96 Rb 8.04 Tl 27 and Cs 8.21 Rb 6.76 Tl 27.09 ) during our studies concerning A 8 T 11 X compounds, where they crystallized as a by-product together with K 3.98 Rb 4.02 Tl 11 Cl 0.1 and Cs 5.13 Rb 2.87 Tl 11 Cl 0.49 , respectively. The smaller amount of incorporated chloride in these compounds, which simultaneously means a higher degree of reduction, facilitated the formation of the less reduced A 15 Tl 27 phases, which include less alkali metal per Tl. As the results of these crystal structure determinations allowed deeper insights in the alkali metal dependent site preferences, we subsequently started to prepare and characterize mixed alkali metal approaches following the composition A 15 Tl 27 (A = K, Rb, Cs). Table 1 shows the data of the structure determinations of all approaches, including potassium and at least one other alkali metal.  For the ternary approaches including potassium, we additionally obtained the less reduced A 49 Tl 108 phases as side products [15,23]. This is reasonable, as the amount of alkali metal is very similar in both compounds (0.357 for A 15 Tl 27 and 0.312 for K 49 Tl 108 ). Additionally, we observed formations of multicrystals between the A 15 Tl 27 and A 49 Tl 108 phases. This might be due to the fact that the longest side of the unit cell of the A 15 Tl 27 and the cell vector of the A 49 Tl 108 (cubic, Pm-3, a~17Å) are close in length. Cs 8.21 Rb 6.76 Tl 27.09 exhibits residual electron density near the alkali metal position A4 (d(A4-q) > 2.7 Å), for which the assignment of Tl is reasonable in terms of the observed Tl-Tl distances (see Section 4.3 Discussion). However, the obtained s.o.f. of less than 10% thallium made this interpretation suspicious; therefore, binary samples involving cesium and a higher amount of thallium were prepared which all led to the composition Cs 14.53 Tl 28.4 . Corbett's Cs 15 Tl 27 was prepared in addition and the absence of additional thallium in this phase was confirmed. Table 2 gives the data of the structure solution and refinement of Cs 8

Occupation Trends of the Alkali Metal Positions
During our search for binary K 15 Tl 27 and the role of the different alkali metal sites in A 15 Tl 27 in general, different ternary and quaternary approaches were applied. Those new compounds gave insight into the site preferences of the different alkali metals. In A 15 Tl 27 , four different alkali metal sites are present (see Figure 1). Corbett et al. showed for Rb 14 CsTl 27 , that cesium preferably resides at position A4, as the rather large pore within the two-dimensional layer allows more space for the larger alkali metal [14]. By having a closer look at the surroundings of the remaining alkali metals, additional site preferences would be conceivable [1]. In further detail, the alkali metal positions A1 and A3 are distinguished from A2 and A4 by their number and distances of surrounding atoms, which is also reflected in their crystallographic site symmetry (see Figure 1). Alkali metals on the Wyckoff-position 6i separate the Tl-layer from the isolated Tl 11 clusters. Here, less contacts within a smaller range of distances are observed, whereas alkali metal atoms on position 1b (within the pores of the Tl-layer) and 2c (between the isolated clusters) show larger distances to a higher number of neighboring atoms [1,14]. As the positions A2 and A4 show contacts to a larger number of neighboring atoms and additionally more space around them is available, they are likely to be preferable positions for the heavier alkali metals. This assumption can be reinforced by the new ternary and quaternary compounds ( Table 3). The distances from alkali metal to thallium atoms naturally increases with increasing size of the alkali metal. This trend is also reflected in the unit cell parameters. Larger alkali metals on position A2 and A4 result in an increased value for the a-axis, whereas smaller alkali metals on A1 and A3 result in decreasing values for c. This compression along c upon an increasing content of potassium is also reflected in the decreasing c/a value (Tables 1 and 2). tinguished from A2 and A4 by their number and distances of surrounding atoms, which is also reflected in their crystallographic site symmetry (see Figure 1). Alkali metals on the Wyckoff-position 6i separate the Tl-layer from the isolated Tl11 clusters. Here, less contacts within a smaller range of distances are observed, whereas alkali metal atoms on position 1b (within the pores of the Tl-layer) and 2c (between the isolated clusters) show larger distances to a higher number of neighboring atoms [1,14]. As the positions A2 and A4 show contacts to a larger number of neighboring atoms and additionally more space around them is available, they are likely to be preferable positions for the heavier alkali metals. This assumption can be reinforced by the new ternary and quaternary compounds ( Table 3). The distances from alkali metal to thallium atoms naturally increases with increasing size of the alkali metal. This trend is also reflected in the unit cell parameters. Larger alkali metals on position A2 and A4 result in an increased value for the a-axis, whereas smaller alkali metals on A1 and A3 result in decreasing values for c. This compression along c upon an increasing content of potassium is also reflected in the decreasing c/a value (Tables 1 and 2).    The values for the quaternary compound in Tables 1 and 3 represent our best possible model for the structure solution involving three different alkali metals yielding the sum formula Cs 3.57 K 4.55 Rb 6.92 Tl 27 . Of course, a definitive statement about the alkali metal proportions, when three alkali metals are involved, is not possible; therefore, this compound is listed, but will not be discussed in detail.
In general, the size of the pore, which is reflected in the Tl4-A4 and Tl5-A4 distances (Table 3), is not only affected by the size of the (mixed) alkali metals on position A4, but also by the differently occupied remaining alkali metal sites.
The layer and the cluster separating positions A1 and A3 show fewer contacts within smaller distances, which is equitable to a smaller void; therefore, a preferred occupation by lighter alkali metals should be expected. This can be confirmed by the observed compounds. Again, the occupation tendencies differ for both sites. The alkali metal position next to the two-dimensional Tl 16 8layer (A3) consistently shows a higher amount of lighter alkali metals than the one next to the Tl 11 clusters (A1). This is in accordance with the surroundings of A1 and A3, as the distances between the thallium atoms and A3 are smaller (<4.14 Å) than the Tl-A1 distances (d(Tl-A1) < 4.29 Å). In other words, the smallest void is observed around A3, where preferably smaller alkali metal resides.

Influence of Mixed Alkali Metal Sites on the Thallium Substructures
In A 15 Tl 27 , isolated Tl 11 clusters are present; additionally, the two-dimensional layer which can be regarded as connected Tl 11 clusters via common Tl5-Tl5 edges ( Figure 2) is also present.  Table 5.
By comparing those two different Tl11 entities, the Tl3-Tl3 distances (isolated Tl11 7-) and Tl5-Tl5 distances (Tl16 8-layer) refer to the stretching or compression of the clusters in horizontal and vertical directions (Figure 3a,b).  Table 5.
By comparing those two different Tl 11 entities, the Tl3-Tl3 distances (isolated Tl 11 7-) and Tl5-Tl5 distances (Tl 16 8layer) refer to the stretching or compression of the clusters in horizontal and vertical directions (Figure 3a,b).

Figure 2.
The two-dimensional layer in A15Tl27 type structures consists of Tl11 clusters (a) which are interconnected by a common Tl5-Tl5 edge and a Tl4-Tl4 inter-cluster distance is formed (b). Altogether, six Tl11 cluster entities define the pore (c). In A15Tl27, this pore is filled by alkali metal. Cs8.21Rb6.76Tl27.09 and Cs14.53Tl28.4 prove the possibility of substituting this alkali metal position by thallium. Selected distances for both compounds are given in Table 5.
By comparing those two different Tl11 entities, the Tl3-Tl3 distances (isolated Tl11 7-) and Tl5-Tl5 distances (Tl16 8-layer) refer to the stretching or compression of the clusters in horizontal and vertical directions (Figure 3a,b). For the isolated Tl11 clusters (Figure 3a, Table 4), the distance from the trigonal prism (Tl3) to the quadrangular face capping Tl2 atoms increases, whereas the distance between the Tl3 atoms diminishes when the potassium proportion is enlarged. This is according to the observed c/a value for the unit cell parameters. Generally, Tl3-Tl3 distances in the isolated clusters are shorter compared with the Tl5-Tl5 distances of the fused clusters within For the isolated Tl 11 clusters (Figure 3a, Table 4), the distance from the trigonal prism (Tl3) to the quadrangular face capping Tl2 atoms increases, whereas the distance between the Tl3 atoms diminishes when the potassium proportion is enlarged. This is according to the observed c/a value for the unit cell parameters. Generally, Tl3-Tl3 distances in the isolated clusters are shorter compared with the Tl5-Tl5 distances of the fused clusters within the layer, which already was observed by Corbett in his three compounds (Rb 15 Tl 27 , Cs 15 Tl 27 and Rb 14 CsTl 27 ) [14]. This trend can be confirmed for our ternary and quaternary thallides.  (3) 3.0816 (12) Ideal Tl 11 7clusters exhibit D 3h symmetry. In contrast, the Tl 11 cluster fragment of the two-dimensional layer shows C 3h symmetry due to missing vertical mirror planes for this point group. As a result, two different values for Tl4-Tl5 distances are observed. For the evaluation of the distortion of the layer, the deviation from C 3h to the higher D 3h symmetry can be taken into account. For this purpose, we already introduced a cdd/cd av ratio (cdd: capping distance difference; cd av : average capping distance; Equation (1)) for isolated Tl 11 7clusters [18], which allows a quick estimation of the degree of distortion. This approach was employed again in order to gain deeper insight in the degree of distortion of the layer-forming Tl 11 entities.
It becomes apparent, that as soon as potassium is present, the degree of distortion gives larger values compared with compounds without potassium. The K-Rb approach shows the greatest degree of distortion with almost 7%. This indicates that additional distortion can be expected when rubidium is used instead of cesium, which we focused on in our current investigations. Considering the Cs-K approaches, the degree of distortion increases with increasing potassium content (Table 5). Therefore, the substitution of cesium by lighter alkali metals has a clear influence on the two-dimensional Tl layer structure.
The large pores in the two-dimensional layer were shown to be preferably occupied by larger alkali metals. In K14Cd9Tl21 [22], it was reported, that instead of alkali metal also cadmium can be present, yielding an alkali metal-free [Cd9Tl10] 7-layer. Unusually large residual electron density beside cesium in cadmium-free Cs8.22Rb6.75Tl27.09 created the idea that it might be possible to introduce thallium in this place. In this compound, the electron density was refined to a value of 3% for thallium (see Figure 4), which of course does not prove this theory. Subsequently, larger amounts of thallium were employed during the solid-state synthesis to prove the idea of thallium being embedded into the pores of the Tl16 8-layers of Cs15Tl27 (see 3. Results). The obtained single crystals undoubtedly confirmed the presence of additional thallium in the pores to an extent of 0.473(5). The s.o.f.'s of Cs4 accordingly reduced to 0.527(5)). Additionally, split positions for Tl5 could be refined, which are induced by the thallium incorporation in the pore (Figures 5 and 6). This leads to two settings being present in Cs14.53Tl28.4: On the one hand a pore description is obtained, equivalent to Cs15Tl27, with two-dimensional [Tl16] 8-layers with cesium (Cs4, 1b) residing in the pore (Figure 5a). On the other hand, pores are present, where instead of cesium on the Wyckoff position 1b, three thallium atoms (Tl7, 3g) are present in the [Tl19] 7-layer ( Figure 5b). The assignment of the charge of the layer is due to the known charge of the Tl11 7-clusters [14] and by assuming a complete electron transfer from the alkali metal to thallium, which is according to the approach of Tillard et al. and Corbett et al. In comparison with the cadmium compound, where Cd2 atoms form a triangle in the pores, the distances between the Tl7 atoms in our triangle are longer (d(Cd2-Cd2) = 2.816(7) Å [22], d(Tl7-Tl7)=3.126(4) Å ). The two symmetrically inequivalent Tl4-Tl4 distances in Cs14.53Tl28.4 (3.2860(14) Å and 3.1423(15) Å ) become more similar compared with Tl4-Tl4 in Cs15Tl27 (3.322(2) Å and 3.102(3) Å ). In the related compound K14Cd9Tl21, a similar trend is noticed [22].

Effects of Incorporation of Tl in the Two-Dimensional Layers
The large pores in the two-dimensional layer were shown to be preferably occupied by larger alkali metals. In K 14 Cd 9 Tl 21 [22], it was reported, that instead of alkali metal also cadmium can be present, yielding an alkali metal-free [Cd 9 Tl 10 ] 7layer. Unusually large residual electron density beside cesium in cadmium-free Cs 8.22 Rb 6.75 Tl 27.09 created the idea that it might be possible to introduce thallium in this place. In this compound, the electron density was refined to a value of 3% for thallium (see Figure 4), which of course does not prove this theory.
Subsequently, larger amounts of thallium were employed during the solid-state synthesis to prove the idea of thallium being embedded into the pores of the Tl 16 8layers of Cs 15 Tl 27 (see Section 3. Results). The obtained single crystals undoubtedly confirmed the presence of additional thallium in the pores to an extent of 0.473 (5). The s.o.f.'s of Cs4 accordingly reduced to 0.527(5)). Additionally, split positions for Tl5 could be refined, which are induced by the thallium incorporation in the pore (Figures 5 and 6). This leads to two settings being present in Cs 14.53 Tl 28.4 : On the one hand a pore description is obtained, equivalent to Cs 15 Tl 27 , with two-dimensional [Tl 16 ] 8layers with cesium (Cs4, 1b) residing in the pore (Figure 5a). On the other hand, pores are present, where instead of cesium on the Wyckoff position 1b, three thallium atoms (Tl7, 3g) are present in the [Tl 19 ] 7layer ( Figure 5b). The assignment of the charge of the layer is due to the known charge of the Tl 11 7clusters [14] and by assuming a complete electron transfer from the alkali metal to thallium, which is according to the approach of Tillard et al.  The change in the overall thallium substructure of the layer upon thallium substitution can be directly demonstrated by the position of Tl5. This position showed prolate anisotropic displacement, which could be reduced by introducing split positions. The free  The change in the overall thallium substructure of the layer upon thallium substitution can be directly demonstrated by the position of Tl5. This position showed prolate anisotropic displacement, which could be reduced by introducing split positions. The free Figure 6. When Cs4 is replaced by Tl7, the unusually short Tl7-Tl5 distance would be observed. Prolate displacement of Tl5 indicated split positions, which were refined according to the s.o.f. of Tl7 and Cs4, respectively. This model yields a reasonable Tl5A-Tl7 distance and improved residual density description.
The change in the overall thallium substructure of the layer upon thallium substitution can be directly demonstrated by the position of Tl5. This position showed prolate anisotropic displacement, which could be reduced by introducing split positions. The free refinement of the split Tl positions gives s.o.f. values of 0.527 (16) and 0.473 (16). As these values are according to the s.o.f.s of Cs4 (0.527(5)) and Tl7 (0.473(5)), respectively, the free refinement of the split position was performed using the same s.o.f. parameter. The reason for this movement of Tl5 upon Tl substitution can be found in the newly formed Tl7-Tl5 distance: if Tl5 was not split, this would mean a short Tl5-Tl7 distance (<2.900(2) Å), which seems to be unfavorable. The splitting of this position demonstrates how the layer structure is able to respond to a change of the host in the pores. As in the above-discussed A 15 Tl 27 compounds, a degree of distortion within the layer can be calculated. In the present case of Cs 14.53 Tl 28.4 , two different degrees of distortion are observed, as the Tl5 position is split (see Figures 5 and 6). The partial structure with the additionally embedded thallium shows a significantly smaller degree of distortion compared with all other compounds (4.3%). The second partial structure with A4 occupied by Cs gives a degree of distortion similar to that of the Cs-K phases (see Table 5).
Altogether, the formal oxidation of the former Tl 16 8layer by forming layers of Tl 19 7-upon thallium substitution yields a less distorted thallium substructure. We observed similar effects previously for A 8 Tl 11 X, where less distorted Tl 11 7was observed when halide was incorporated [18], which is equivalent to a formal oxidation of thallium in A 8 Tl 11 . A speculative compound A 14 Tl 30 would mean that solely cesium-free layers are present. Further attempts to increase the thallium content by using the mixed alkali metal approach are currently in progress.

Conclusions
In summary, it can be stated that substitution of the larger alkali metals in the A 15 Tl 27 type structure by potassium is possible to a certain extent. The presence of large alkali metals in the pores of the two-dimensional Tl 16 8layer is essential for the stabilization of the A 15 Tl 27 type structure. If the amount of potassium is enlarged, instead of binary K 15 Tl 27 , only K 49 Tl 108 is observed, which is the more stable phase at appr. 1:2 (A:Tl) composition involving this lighter homologue of the alkali metals. Therefore, Cs 2.27 K 12.73 Tl 27 is currently the first and at the same time the potassium-richest compound found in the A 15 Tl 27 type structure. The change in alkali metals is also reflected in the distortion of the Tl 16 8layer structure. When cesium is involved, less distorted layer structures are observed. Furthermore, it could be shown in Cs 14.53 Tl 28.4 , that cesium in the pore of Cs 15 Tl 27 can be partially substituted by three thallium atoms yielding formally oxidized, less distorted two-dimensional Tl 19 7layers.

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Data Availability Statement: Further details on the crystal structure investigation(s) may be obtained free of charge from The Cambridge Crystallographic data center CCDC (Access Structures) on quoting the deposition number given in the crystallographic tables (CSD-xxxxxx or the deposition number CCDC-xxxxxxx).