Spotlight on Alkali Metals: The Structural Chemistry of Alkali Metal Thallides

: Alkali metal thallides go back to the investigative works of Eduard Zintl about base metals in negative oxidation states. In 1932, he described the crystal structure of NaTl as the ﬁrst representative for this class of compounds. Since then, a bunch of versatile crystal structures has been reported for thallium as electronegative element in intermetallic solid state compounds. For combinations of thallium with alkali metals as electropositive counterparts, a broad range of di ﬀ erent unique structure types has been observed. Interestingly, various thallium substructures at the same or very similar valence electron concentration (VEC) are obtained. This in return emphasizes that the role of the alkali metals on structure formation goes far beyond ancillary ﬁlling atoms, which are present only due to charge balancing reasons. In this review, the alkali metals are in focus and the local surroundings of the latter are discussed in terms of their crystallographic sites in the corresponding crystal structures.


Introduction
In 1932, E. Zintl and W. Dullenkopf reported on the crystal structure determination of sodium thallide NaTl [1]. They completed their publication with the statement that, in case of a base metal, the formed structure type does not correlate with the average number of valence electrons per atom (VEC) according to the prevously introduced rules by Hume-Rothery [2], Westgren, and Phragmen [3]. This set a milestone in intermetallic chemistry and was the birth of polar intermetallic compounds, including metal-metal bonding (i.e., Zintl phases) [4][5][6][7][8][9] which perceive continually increasing interest in materials science [10]. In general, the combination of an electropositive and a rather electronegative metal right to the Zintl border (between group 13 and group 14 in the periodic system of elements), results in the formation of polyanionic salts [11][12][13]. By assuming a complete electron transfer from the electropositive to the more electronegative element, a modified valence electron concentration per p-block metal is calculated (VEC Zintl ), which, in combination with the 8−N rule, gives the number of bonds of the electronegative element [9,14,15]. This model works very well for elements right to the Zintl border, but interestingly, with NaTl, this concept was demonstrated for the first time by describing a compound of an element, which is left to this imaginary line. Its position at the frontier between metallic and salt-like materials makes thallium a very interesting metal concerning its structural chemistry in formal negative oxidation states [16][17][18]. Binaries of thallium and lithium, sodium, or potassium were recently summarized in terms of the respective phase diagrams [19]. Thümmel and Klemm reported investigations on the formed binaries of the heavier congeners, rubidium and cesium, in 1970 [20]. Reviews dealing with the Zintl compounds of the p-block elements [18,21,22] also include part of the alkali metal thallides, but they usually focus on the very versatile and interesting thallide substructures. However, the role of the involved alkali metals goes far beyond a classical cation which is present only for charge balancing reasons [23]. For example, the simple binaries ATl (A = Li, Na, K, Cs) feature different structure types and thallium substructures depending on the involved alkali  11 . The reported ternary A 10 Tl 13 phases follow the formula Na 4 A 6 Tl 13 where A = K, Rb Cs. Binary ATl is known for A = Li, Na, K, Cs.  The corresponding range of distances to the adjacent atoms as well as the Wyckoff letters are given in Table 2. The compound Rb17Tl41 [39] (VEC 2.41) (K17In41 type structure [42]) is even higher in symmetry (space group Fd-3m) and only three symmetry inequivalent rubidium atoms are present (Table 3), which due to their site symmetry (96g, 32e, 8a) all are located in the center of a capped tetrahedron built by 12 coordinating thallium atoms at distances up to 4.2 Å. The surrounding is completed by The corresponding range of distances to the adjacent atoms as well as the Wyckoff letters are given in Table 2. The compound Rb 17 Tl 41 [39] (VEC 2.41) (K 17 In 41 type structure [42]) is even higher in symmetry (space group Fd-3m) and only three symmetry inequivalent rubidium atoms are present (Table 3), Crystals 2020, 10, 1013 6 of 26 which due to their site symmetry (96g, 32e, 8a) all are located in the center of a capped tetrahedron built by 12 coordinating thallium atoms at distances up to 4.2 Å. The surrounding is completed by four rubidium atoms at distances up to 4.3 Å, which gives 16 neighboring atoms for each rubidium in Rb 17 Tl 41 ( Figure 4). The thallium substructure again can be described by linked Samson polyhedra. In Figure 4 the unit cell is given, showing the three-dimensional connection of empty Tl 12 icosahedra (only shorter Tl-Tl distances are taken into account). The rubidium atoms themselves form pentagonal dodecahedra, which are connected via their pentagonal faces to form a three-dimensional network analogous to the clathrate-II structure [43][44][45]. four rubidium atoms at distances up to 4.3 Å, which gives 16 neighboring atoms for each rubidium in Rb17Tl41 (Figure 4). The thallium substructure again can be described by linked Samson polyhedra. In Figure 4 the unit cell is given, showing the three-dimensional connection of empty Tl12 icosahedra (only shorter Tl-Tl distances are taken into account). The rubidium atoms themselves form pentagonal dodecahedra, which are connected via their pentagonal faces to form a three-dimensional network analogous to the clathrate-II structure [43][44][45].  . The corresponding range of distances to the adjacent atoms as well as the Wyckoff letters are given in Table 3.

A15Tl27 (A = Rb, Cs)
The VEC of ~2.33 again falls within the range of the tetrahedral star regime (see Section 2, K6Tl17), and indeed for A15Tl27 (A = Rb, Cs) [35] the structural motif of double tetrahedral stars (DTS) is observed. Figure 4 shows parts of the crystal structure of Rb15Tl27 as representative for the A15Tl27  Table 3. The VEC of~2.33 again falls within the range of the tetrahedral star regime (see Section 2, K 6 Tl 17 ), and indeed for A 15 Tl 27 (A = Rb, Cs) [35] the structural motif of double tetrahedral stars (DTS) is observed. Figure 4 shows parts of the crystal structure of Rb 15 Tl 27 as representative for the A 15 Tl 27 structure family. This compound includes two different DTS units. Figure 5a shows the DTS arrangement, which is further condensed by forming (Tl 6/2 Tl 3/1 Tl 2/1 ) 2 (≡Tl 16 ) layers (green in Figure 5c,d). The second distorted DTS unit is represented by isolated Tl 11 7− clusters (point group D 3h , Figure 5a), which are located below and above the large pores of the layers (blue, Figure 5c,d).
Crystals 2020, 10, x 6 of 27 structure family. This compound includes two different DTS units. Figure 5a shows the DTS arrangement, which is further condensed by forming (Tl6/2Tl3/1Tl2/1)2 (≡Tl16) layers (green in Figure  5c,d). The second distorted DTS unit is represented by isolated Tl11 7− clusters (point group D3h, Figure  5a), which are located below and above the large pores of the layers (blue, Figure 5c,d). Due to the high symmetry of the space group P-62m, only four crystallographically independent alkali metal sites are present in A15Tl27 type structures. In Table 4, the number and the range of distances of the four symmetry independent alkali metal positions in Rb15Tl27, as the representative for all A15Tl27 compounds, to the neighboring atoms are given. The number of surrounding atoms for each rubidium ranges from 13 to 18. Thereby, two sets of alkali metals emerge: Rb1 and Rb3 show less contacts (Rb1: 13, Rb3: 14) within a larger range of distances between 4 and 4.9 Å. In contrast, Rb2 and Rb4 exhibit larger distances to a higher number of neighboring atoms (Rb2: 15, Rb4: 18). In particular, the position of Rb4 is conspicuous due to an outstanding high number of adjacent atoms. Figure 6 shows the unit cell of Rb15Tl27, where the two sets of alkali metal positions are also reflected. The first set occupies positions within the Tl layers (Rb4, blue) and connects the Tl11 clusters (Rb2, yellow). The second set (Rb1 (red) and Rb3 (green)) is located in between the layers of the thallium substructures.
The possibility of an ordered substitution of Rb4 by the largest alkali metal cesium was shown for the compound Rb14CsTl27 [35].
Despite the very similar VEC of K49Tl108 (VEC 2.38) and A15Tl27 (VEC 2.29), both structure types have not yet been reported vice versa concerning the type of alkali metal. Due to the high symmetry of the space group P-62m, only four crystallographically independent alkali metal sites are present in A 15 Tl 27 type structures. In Table 4, the number and the range of distances of the four symmetry independent alkali metal positions in Rb 15 Tl 27 , as the representative for all A 15 Tl 27 compounds, to the neighboring atoms are given. The number of surrounding atoms for each rubidium ranges from 13 to 18. Thereby, two sets of alkali metals emerge: Rb1 and Rb3 show less contacts (Rb1: 13, Rb3: 14) within a larger range of distances between 4 and 4.9 Å. In contrast, Rb2 and Rb4 exhibit larger distances to a higher number of neighboring atoms (Rb2: 15, Rb4: 18). In particular, the position of Rb4 is conspicuous due to an outstanding high number of adjacent atoms. Figure 6 shows the unit cell of Rb 15 Tl 27 , where the two sets of alkali metal positions are also reflected. The first set occupies positions within the Tl layers (Rb4, blue) and connects the Tl 11 clusters (Rb2, yellow). The second set (Rb1 (red) and Rb3 (green)) is located in between the layers of the thallium substructures.

Atomic Ratio M I :Tl Approximately 3:4
A further increase of the alkali metal amount results in lower VEC and higher VECZintl, respectively. This means a reduction of the number of Tl-Tl contacts, which lowers the dimensionality of the Tl sublattice and results in the formation of isolated clusters.

A8Tl11 (A = K, Rb, Cs)
A8Tl11 binary phases (A = K, Rb, Cs) [46,47] crystallize in the K8In11 type structure (space group R-3c) [48]. The anionic moiety is represented by a Tl11 cluster, but in contrast to their highest possible symmetry (D3h in A15Tl27; see Section 3.2), here only D3 symmetry for the Tl11 unit is realized, according to their site symmetry. The substitution of the extra electron in A8Tl11 by halide results in A8Tl11X, in which a less degree of distortion of the Tl11 7− cluster is observed, electronic effects of the extra electron therefore cannot be excluded [49]. Due to the high symmetry of the crystal structure, only two The possibility of an ordered substitution of Rb4 by the largest alkali metal cesium was shown for the compound Rb 14 CsTl 27 [35].
Despite the very similar VEC of K 49 Tl 108 (VEC 2.38) and A 15 Tl 27 (VEC 2.29), both structure types have not yet been reported vice versa concerning the type of alkali metal.

Atomic Ratio M I :Tl Approximately 3:4
A further increase of the alkali metal amount results in lower VEC and higher VEC Zintl , respectively. This means a reduction of the number of Tl-Tl contacts, which lowers the dimensionality of the Tl sublattice and results in the formation of isolated clusters.

A 8 Tl 11 (A = K, Rb, Cs)
A 8 Tl 11 binary phases (A = K, Rb, Cs) [46,47] crystallize in the K 8 In 11 type structure (space group R-3c) [48]. The anionic moiety is represented by a Tl 11 cluster, but in contrast to their highest possible symmetry (D 3h in A 15 Tl 27 ; see Section 3.2), here only D 3 symmetry for the Tl 11 unit is realized, according to their site symmetry. The substitution of the extra electron in A 8 Tl 11 by halide results in A 8 Tl 11 X, in which a less degree of distortion of the Tl 11 7− cluster is observed, electronic effects of the extra electron therefore cannot be excluded [49]. Due to the high symmetry of the crystal structure, only two symmetry inequivalent alkali metal sites are present in A 8 Tl 11 . In Table 5, the number of contacts and the corresponding distances to thallium as well as rubidium in Rb 8 Tl 11 as representative for all A 8 Tl 11 structures are given. While Rb2 shows contacts to altogether 15 atoms within 4.6 Å, Rb1 exhibits only 12 surrounding atoms ( Figure 7). This makes the position of Rb1 conspicuous and indeed, having a closer look at the crystal structure, this position is involved in the formation of a distorted octahedral arrangement around a void. This void can be filled by halide yielding an enlarged number of surrounding atoms of Rb1 of 13 [49]. In general, for binary A 8 Tl 11 no site occupancy preferences for different alkali metals have been reported. Table 5. Surrounding atoms of the symmetry inequivalent rubidium positions in Rb 8 Tl 11 (space group R-3c).

Number of Rb Neighbors (Distances Below)
Crystals 2020, 10, x 8 of 27 symmetry inequivalent alkali metal sites are present in A8Tl11. In Table 5, the number of contacts and the corresponding distances to thallium as well as rubidium in Rb8Tl11 as representative for all A8Tl11 structures are given. While Rb2 shows contacts to altogether 15 atoms within 4.6 Å, Rb1 exhibits only 12 surrounding atoms ( Figure 7). This makes the position of Rb1 conspicuous and indeed, having a closer look at the crystal structure, this position is involved in the formation of a distorted octahedral arrangement around a void. This void can be filled by halide yielding an enlarged number of surrounding atoms of Rb1 of 13 [49]. In general, for binary A8Tl11 no site occupancy preferences for different alkali metals have been reported.

Symmetry Independent Alkali Metal
Wyckoff Letter  Table 5.

Na4A6Tl13 (A = K, Rb, Cs) and Na3K8Tl13
In 1994, Corbett et al. demonstrated on the basis of the compound Na2K21Tl19 [50] (see Section 5.3) that the involvement of different alkali metals within one thallide compound had a significant influence on the formed crystal structure. They also introduced this concept at a ratio of 3:4 of M I :Tl and subsequently reported on Na4A6Tl13 (A = K, Rb, Cs) and Na3K8Tl13 [51]. According to the A8Tl11 compounds, we would expect isolated clusters in this area of the VEC. In fact, centered, icosahedral shaped Tl13 clusters are found when sodium and additionally a heavier congener are mixed. The shape of the open-shell Tl13 10− clusters in Na4A6Tl13 is not significantly changed for closed shell Tl13 11− in Na3K8Tl13, but the overall structure changes from former bcc (body-centred cubic) packing of Tl13 10− clusters in Na4A6Tl13 into pseudo fcc (face-centred cubic) packing of formal Tl13 11− in Na3K8Tl13. The number of sodium atoms of the first coordination sphere of the clusters is reduced from eight in Na4K6Tl13 to six in Na3K8Tl13. A loss of electronic reasons for the formation of open shell Tl13 10− emphasizes the dominant effects of packing requirements [47]. The presence of sodium is essential for the formation of these compounds. All attempts to prepare a compound including Tl13 10/11− in absence of sodium have not yet succeeded. In addition, the replacement of potassium by larger alkali The corresponding range of distances to the adjacent atoms as well as the Wyckoff letters are given in Table 5.

Na 4 A 6 Tl 13 (A = K, Rb, Cs) and Na 3 K 8 Tl 13
In 1994, Corbett et al. demonstrated on the basis of the compound Na 2 K 21 Tl 19 [50] (see Section 5.3) that the involvement of different alkali metals within one thallide compound had a significant influence on the formed crystal structure. They also introduced this concept at a ratio of 3:4 of M I :Tl and subsequently reported on Na 4 A 6 Tl 13 (A = K, Rb, Cs) and Na 3 K 8 Tl 13 [51]. According to the A 8 Tl 11 compounds, we would expect isolated clusters in this area of the VEC. In fact, centered, icosahedral shaped Tl 13 clusters are found when sodium and additionally a heavier congener are mixed. The shape of the open-shell Tl 13 10− clusters in Na 4 A 6 Tl 13 is not significantly changed for closed shell Tl 13 11− in Na 3 K 8 Tl 13 , but the overall structure changes from former bcc (body-centred cubic) packing of Tl 13 10− clusters in Na 4 A 6 Tl 13 into pseudo fcc (face-centred cubic) packing of formal Tl 13 11− in Na 3 K 8 Tl 13 .
The number of sodium atoms of the first coordination sphere of the clusters is reduced from eight in Na 4 K 6 Tl 13 to six in Na 3 K 8 Tl 13 . A loss of electronic reasons for the formation of open shell Tl 13 10− emphasizes the dominant effects of packing requirements [47]. The presence of sodium is essential for the formation of these compounds. All attempts to prepare a compound including Tl 13 10/11− in absence of sodium have not yet succeeded. In addition, the replacement of potassium by larger alkali metals rubidium or cesium did not result in Na 3 A 8 Tl 13 but always in Na 4 A 6 Tl 13 . Significant differences between Na 4 K 6 Tl 13 and Na 3 K 8 Tl 13 become apparent, when comparing the adjacent atoms and the corresponding distances of the alkali metals (Tables 6 and 7). The distorted icosahedral coordination of the sodium cations by 6 Tl atoms and 6 potassium neighbors virtually is the same in both compounds ( Figure 8). The value for the Na1-K1 distance of 4.168(2) Å in Na 4 K 6 Tl 13 is longer than both Na-K distances found in Na 3 K 8 Tl 13 (d(Na1-K1 = 3.638(6) Å; d(Na1-K2) = 4.076(6) Å).
In contrast to the similarity of the sodium environment, the surroundings of the potassium atoms are significantly different (Figure 8). In Na 4 K 6 Tl 13 , potassium is surrounded at comparably short distances up to 4 Å. In Na 3 K 8 Tl 13 , the case is different. The potassium environment is built by 12 (for K1) and 11 (for K2) atoms at shorter distances below 4.1 Å, whereas additional 3 (for K1) and 5 (for K2) atoms at larger distances up to 4.8 Å complete the altogether surrounding of 15 (for K1) and 16 (for K2) atoms, respectively. This is according to a more cylindrical shaped space for K1 and K2, respectively, compared to the rather spherical surrounding of K1 in Na 4 K 6 Tl 13 ( Figure 8).
Corbett et al. suggested that, in this kind of material, the holes in which sodium is located are too small for the larger alkali metals; therefore, this structure type can only be realized in the presence of small sodium. In general, the different sized cavities in compounds including icosahedral clusters need to be filled by the suitable alkali metal resulting in an effective packing mode. By virtue of the large K-K distances observed for Na 3 K 8 Tl 13 , the nonexistence of Na 3 Rb 8 Tl 13 and Na 3 Cs 8 Tl 13 might additionally be explained by too large Rb-Rb and Cs-Cs distances for an effective packing. Table 6. Surrounding atoms of the symmetry inequivalent rubidium positions in Na 4 K 6 Tl 13 (space group Im-3).  Table 7. Surrounding atoms of the symmetry inequivalent rubidium positions in Na 3 K 8 Tl 13 (space group R-3m). The color-coding refers to the color of the contacts in Figure 8.

Symmetry
Na1 9d 6 (<3.9 Å) 6 (<4.1 Å) - Figure 8. Atomic environment of the symmetry inequivalent sodium and potassium position(s) in Na3K8Tl13 and Na4K6Tl13. The corresponding range of distances to the adjacent atoms as well as the Wyckoff letters are given in Table 6 (Na4K6Tl13) and Table 7 (Na3K8Tl13).

ATl (A = Li, Na, K, Cs)
In the area of similar stoichiometric amounts of alkali metal and thallium, formally one negative charge per thallium atom is present. According to the Zintl-Klemm formalism, this means a fourfold bound Tl atom, which in NaTl [1,[52][53][54][55] is realized by the formation of a diamond like sublattice in terms of a three-dimensional network of tetrahedrally coordinated thallium. LiTl crystallizes in the β-brass type structure [56]. In KTl [57] (ambient conditions) and CsTl [58], octahedral Tl6 6− anions are present, in which also formally fourfold bound Tl atoms are realized. According to Wade's rules [59,60], one would expect for a closo cluster (2n + 2) skeletal electrons, which is equivalent to an eightfold charge of a Tl cluster consisting of six atoms. The reduced charge of Tl6 6− in KTl and CsTl, respectively, would result in a hypo-closo cluster with 2n skeletal electrons. This deficiency in electrons accounts for a Jahn Teller distortion with an axial compression, which was supported by extended Hückel calculations for KTl [57]. In general, the hypo-closo clusters are not only stabilized by Jahn Teller distortion, but also relativistic effects, especially spin orbit coupling [16,32]. Comparing KTl and CsTl more in detail, the differences in the shapes of the octahedral anions become apparent. In KTl, the waist of the octahedron is rectangular with two significantly differing distances (3.341 Å and 3.466 Å), the crystallographic point group here is C2h (2/m). For Tl6 6− in CsTl these distances are more similar (3.409 Å and 4.434 Å) but the rectangular arrangement is slightly tilted, the  Table 6 (Na 4 K 6 Tl 13 ) and Table 7 (Na 3 K 8 Tl 13 ). In the area of similar stoichiometric amounts of alkali metal and thallium, formally one negative charge per thallium atom is present. According to the Zintl-Klemm formalism, this means a fourfold bound Tl atom, which in NaTl [1,[52][53][54][55] is realized by the formation of a diamond like sublattice in terms of a three-dimensional network of tetrahedrally coordinated thallium. LiTl crystallizes in the β-brass type structure [56]. In KTl [57] (ambient conditions) and CsTl [58], octahedral Tl 6 6− anions are present, in which also formally fourfold bound Tl atoms are realized. According to Wade's rules [59,60], one would expect for a closo cluster (2n + 2) skeletal electrons, which is equivalent to an eightfold charge of a Tl cluster consisting of six atoms. The reduced charge of Tl 6 6− in KTl and CsTl, respectively, would result in a hypo-closo cluster with 2n skeletal electrons. This deficiency in electrons accounts for a Jahn Teller distortion with an axial compression, which was supported by extended Hückel calculations for KTl [57]. In general, the hypo-closo clusters are not only stabilized by Jahn Teller distortion, but also relativistic effects, especially spin orbit coupling [16,32]. Comparing KTl and CsTl more in detail, the differences in the shapes of the octahedral anions become apparent. In KTl, the waist of the octahedron is rectangular with two significantly differing distances (3.341 Å and 3.466 Å), the crystallographic point group here is C 2h (2/m). For Tl 6 6− in CsTl these distances are more similar (3.409 Å and 4.434 Å) but the rectangular arrangement is slightly tilted, the crystallographic point group is D 2 with only slight difference from D 4h . The reasons for the differences of Tl 6 6− in KTl and CsTl are not due to electronic effects but seem to be retrieved in size effects of the cations and their packing requirements [58]. In the following, attention will be drawn at the different local environments of the alkali metal sites in binary 1:1 alkali metal thallides (Table 8 (LiTl), Table 9 (NaTl), Table 10 (KTl), Table 11(CsTl)). Table 8. Surrounding atoms of the symmetry inequivalent alkali metal position in LiTl (space group Pm-3m). The color-coding refers to the color of the contacts in Figure 9.

Number of Li Neighbors (Distances Below)
Li1 1a 8 (<3 Å) 6 (<3.5 Å) Table 9. Surrounding atoms of the symmetry inequivalent alkali metal position in NaTl (true for both space groups Fd-3m and I4 1 /acd). The color-coding refers to the color of the contacts in Figure 9. Table 10. Surrounding atoms of the symmetry inequivalent alkali metal positions in KTl (space group Cmce). The color-coding refers to the color of the contacts in Figure 9.  Table 11. Surrounding atoms of the symmetry inequivalent alkali metal positions in CsTl (space group Fddd). The color-coding refers to the color of the contacts in Figure 9. Figure 9 shows the surroundings of the symmetry inequivalent alkali metals in ATl (A = Li, Na, K, Cs), thereby, the shorter distances are given in red, the longer are colored blue. According to the β-brass type structure, the altogether number of neighboring atoms of Li in LiTl sums up to 14, of which 8 Tl atoms are at short distances below 3 Å in a cubic arrangement. Six additional coordinating atoms are found at a Li-Li distance of 3.5 Å, which is significantly elongated, compared to the Li-Li distance of 3 Å in the bcc unit cell of elemental Lithium [61].  Tables 8-11. Shorter contacts are colored red, longer distances are given in blue. The color coding is also used in the corresponding tables. K3 and Cs3 are depicted in pink (K3) and cyan (Cs3) within their surroundings to illustrate the K3 zigzag chains and Cs3 dumbbells.

Number of Cs neighbors (Distances Below)
Summarized, according to Corbett et al. the Li-Tl distances in LiTl would be too long in the NaTl type structure, therefore, the formation of β-brass type LiTl is favored. The stuffed diamond structure of NaTl is the preferred structure type due to very similar sized sodium/thallium atoms resulting in efficient interwoven three-dimensional thallium and sodium networks. The larger cations potassium and cesium would mean too large Tl-Tl distances when a three-dimensional network would be realized, therefore cluster formation is favored. In general, the ATl series nicely allows for the discussion of differences due to size and electronic effects, but it also was emphasized that these effects are not sufficient for the occurrence of a phase.
The different structure types for 1:1 alkali metal thallides gave rise to deeper investigations by Evers et al. who could show a pressure induced formation of NaTl-type KTl [62]. This result also nicely supports the argumentation of Corbett et al. concerning observed Tl-Tl distances and effective packing.

Na9K16Tl25.25
In the area of similar amounts of alkali metal and thallium (VEC~2) also ternary compounds are reported.  Tables 8-11. Shorter contacts are colored red, longer distances are given in blue. The color coding is also used in the corresponding tables. K3 and Cs3 are depicted in pink (K3) and cyan (Cs3) within their surroundings to illustrate the K3 zig-zag chains and Cs3 dumbbells. Na1 in NaTl shows eight contacts at a short distance below 3.3 Å, four to Tl and four to sodium. Additionally, six contacts to thallium at an elongated Na-Tl distance of 3.8 Å are present. This interaction was shown to be responsible for the tetragonal distortion of NaTl at lower temperatures [52]. Altogether, there are 14 neighbors of sodium.
In KTl, each potassium atom is surrounded by 16 (for K1 and K2) or 15 (for K3) atoms. In general, two sets can be distinguished. Distances belonging to set one are found up to 4.4 Å, whereas the distances of set two are significantly elongated up to 5 Å. The three alkali metal sites can be differentiated, as there are six distances elongated for K1 and K2 and only two for K3.
Corbett et al. discuss in their publication about CsTl [58] the two striking positions of Cs3 in CsTl and K3 in KTl more in detail. Both Cs3 and K3 connect Tl 6 6− units in an unusual way by forming pairs of Cs3 (cyan colored in the surrounding of Cs3 in Figure 9) and chains of K3 (pink colored in the surrounding of K3 in Figure 9). The symmetry operations of the respective space groups is reflected within this arrangement. In CsTl, the regular arrangement of the Tl 6 6− units around the Interestingly, the surroundings of K1/Cs1 and K2/Cs2 are very much alike. In fact, the surroundings of K3 in KTl and Cs3 in CsTl are also very similar, but in KTl an additional potassium is present compared to the surrounding of Cs3 in CsTl. This additional potassium cation in the coordination sphere of K3 obviously is needed due to packing requirements.
The existence of KTl and CsTl makes the absence of any 1:1 compound in the Rb-Tl system peculiar. It was suggested that this might be due to the inability of forming an intermediate structure between KTl and CsTl, or due to the enormous stability of the Rb 8 Tl 11 phase.
In general, in case of innocent alkali metals and exclusive dominant effects of covalent interactions according to the Zintl-Klemm formalism, one would expect similar structures concerning the Tl-Tl sublattice type for all 1:1 compounds. Theoretical investigations of Miller et al. strongly support the dominant effects of size of the alkali metals on the formed thallide substructure [24].
Summarized, according to Corbett et al. the Li-Tl distances in LiTl would be too long in the NaTl type structure, therefore, the formation of β-brass type LiTl is favored. The stuffed diamond structure of NaTl is the preferred structure type due to very similar sized sodium/thallium atoms resulting in efficient interwoven three-dimensional thallium and sodium networks. The larger cations potassium and cesium would mean too large Tl-Tl distances when a three-dimensional network would be realized, therefore cluster formation is favored. In general, the ATl series nicely allows for the discussion of differences due to size and electronic effects, but it also was emphasized that these effects are not sufficient for the occurrence of a phase.
The different structure types for 1:1 alkali metal thallides gave rise to deeper investigations by Evers et al. who could show a pressure induced formation of NaTl-type KTl [62]. This result also nicely supports the argumentation of Corbett et al. concerning observed Tl-Tl distances and effective packing.

Na 9 K 16 Tl 25.25
In the area of similar amounts of alkali metal and thallium (VEC~2) also ternary compounds are reported.
In Na 9 K 16 Tl 25.25 [63] the VEC Zintl = 3.99 is very close to the previously discussed binary compounds. The thallium substructure includes pentagonal bipyramidal Tl 7 7− anions, additional one thallium position with a reduced occupancy of 70% complements this pentagonal bipyramidal cluster by forming a nine atom Tl 9 9− cluster anion. This gives a 70:30 mixture of Tl 9 and Tl 7 units at the same site, which is necessary to meet the given electron count of the alkali metals. Three fully occupied Tl 9 9− clusters would give the fictitious composition (Na,K) 27 Tl 27 of which the synthesis has failed.
To meet the given alkali metal count, which seems to be a structure-determining factor, less thallium is assembled. This makes it worth having a closer look at the alkali metal positions and their surroundings. The asymmetric unit of Na 9 K 16 Tl 25.25 (space group P6 3 /m) contains two sodium and five potassium positions (Table 12, Figure 10). Each sodium atom is surrounded by 12 atoms, at distances up to 4.2 Å to potassium and up to 3.5 Å to thallium. The available space around sodium is very limited and probably makes the formation of a binary compound unfavored, when exclusively potassium is included. The binary phases preferably form other, more stable structure types. In Na 9 K 16 Tl 25.25 , the major differences in the surroundings of the symmetry inequivalent potassium positions are found in the farther surroundings. The environment of K1 (Wyckoff 2d) is completed by six K4 atoms at a large distance of 4.514(4) Å. K1 also is the only alkali metal without sodium neighboring atoms. The large anisotropic displacement parameter of K5 was supposed to be caused by the large void around K5. In general, the possibility of replacing potassium by rubidium was mentioned by Corbett et al., the sodium cavities in contrast seem to be delimitated to small guests.   Table 12. Shorter contacts are colored red, longer distances are given in blue, the color coding is also used in the corresponding table (Table 12).

Na2K21Tl19
A slightly increased amount of alkali metal is observed in the compound Na2K21Tl19 [50], which in fact was the first structure where dominant effects of mixed alkali metals could be demonstrated. By supplying more electrons than one per Tl atom and therefore increasing the VECZintl, the classical trigonal bipyramidal shaped thallide cluster Tl5 7− is observed. The shape of Tl5 7− is directly related to isoelectronic Pb5 2− . Additionally, the hypoelectronic Tl9 9− anions are present. In the asymmetric unit of the crystal structure (space group Cmcm), eight potassium atoms and one sodium are present (Table 13, Figure 11). Sodium is surrounded by ten neighbors, of which five are potassium atoms up to 3.9 Å. The remaining five neighbors are represented by thallium up to 3.3 Å. At a larger distance  Table 12. Shorter contacts are colored red, longer distances are given in blue, the color coding is also used in the corresponding table (Table 12).

Na 2 K 21 Tl 19
A slightly increased amount of alkali metal is observed in the compound Na 2 K 21 Tl 19 [50], which in fact was the first structure where dominant effects of mixed alkali metals could be demonstrated. By supplying more electrons than one per Tl atom and therefore increasing the VEC Zintl , the classical trigonal bipyramidal shaped thallide cluster Tl 5 7− is observed. The shape of Tl 5 7− is directly related to isoelectronic Pb 5 2− . Additionally, the hypoelectronic Tl 9 9− anions are present. In the asymmetric unit of the crystal structure (space group Cmcm), eight potassium atoms and one sodium are present (Table 13, Figure 11). Sodium is surrounded by ten neighbors, of which five are potassium atoms up to 3.9 Å. The remaining five neighbors are represented by thallium up to 3.3 Å. At a larger distance of 4.1 Å one additional thallium atom is present, which is in the same range of distance like the second Na-Tl coordination sphere in NaTl (d(Na-Tl) = 3.8 Å). Two additional Tl neighbors are found at distances up to 4.1 Å. The resulting overall surrounding resembles the one of K1, but the void obviously is too small for potassium. Concerning potassium, attentions needs to be drawn at K8, as it turned out to be peculiar in terms of crystallography. Its site occupancy only is 50%, due to the direct vicinity to a mirror plane. Symmetry reduction (space group Cmc2 1 and A2am) was checked by the authors and did not result in an ordered model. Lower temperatures (−60 • C) gave only one maximum in the Fourier maps located on the mirror plane, but the large anisotropic displacement parameters still suggested disordering.  Figure 11. Atomic environment of the symmetry inequivalent sodium and potassium positions in Na2K21Tl19. The corresponding range of distances to the adjacent atoms as well as the Wyckoff letters are given in Table 13. Shorter contacts are colored red, longer distances are given in blue, the color coding is also used in the corresponding table. Figure 11. Atomic environment of the symmetry inequivalent sodium and potassium positions in Na 2 K 21 Tl 19 . The corresponding range of distances to the adjacent atoms as well as the Wyckoff letters are given in Table 13. Shorter contacts are colored red, longer distances are given in blue, the color coding is also used in the corresponding table. Table 13. Surrounding atoms of the symmetry inequivalent alkali metal positions in Na 2 K 21 Tl 19 (space group Cmcm). The color-coding refers to the color of the contacts in Figure 11.

Symmetry Independent Alkali Metal
Wyckoff Letter

Atomic Ratio M I :Tl Approximately 3:2
K 10 Tl 7 The composition of K 10 Tl 7 [64] is unique for potassium as in this area of VEC no other alkali metal thallide is known so far. K 10 Tl 7 also represents the potassium-richest binary thallide phase. The included polyanionic species is, according to MO (molecular orbital) extended Hückel calculations, represented by a pentagonal bipyramidal, hypocloso Tl 7 7− anion. Additionally, three extra electrons are present which allow for the favored composition for an effective packing of Tl 7 7− anions and potassium cations. The geometry of the anion is close to D 5h , the crystallographic symmetry is C 1 as all atoms lie on general positions of the space group P2 1 /c. The potassium atoms are also located on general positions around this anion. The number of surrounding atoms and the respective distances of the potassium atoms are given in Table 14. The coordination numbers are between 11 and 15, if distances up to 5 Å are taken into account. At farther distances up to 5.5 Å, the coordination number is 13 to 15. The potassium atoms can be subdivided into two groups concerning their role in the overall crystal structure. Six cations (red: K2, K3, K4, K6, K7, and K10) connect the clusters to form layers, while the remaining (pink: K1, K5, K8, and K9) are situated between these layers and connect them to form a three-dimensional network ( Figure 12). The surroundings of all ten symmetry inequivalent potassium atoms are given in Figure 12. The coloring of the contacts refers to the given range of distances in Table 14. The perceivable surrounding of K3 is worth mentioning, as 15 neighbors at comparably small distances (6 × K-Tl (< 4 Å); 9 × K-K (< 4.7 Å)) form the smallest cavity within the crystal structure of K 10 Tl 7 . Table 14. Surrounding atoms of the symmetry inequivalent alkali metal positions in K 10 Tl 7 (space group P2 1 /c). The color-coding refers to the color of the contacts in Figure 12.   Table 14. Shorter contacts are colored red, longer distances are given in blue. The color coding is also used in the corresponding table.  2 Ga type structure and includes Tl-Tl zig-zag chains. Both symmetry inequivalent Li atoms are located at special position 4c of space group Cmcm. The first coordination sphere of both Li atoms below 3 Å is distorted cubically arranged (red contacts in Figure 10), but the atom type on the vertices differs, as two different interwoven tetrahedral arrangements are built by Li and Tl, respectively. In the second coordination sphere up to 3.5 Å (blue contacts in Figure 13) one Tl atom and five Li atoms are found for Li1, which gives an altogether coordination number (first and second coordination sphere) of 14 for Li1. Li2 is surrounded by six Li and two Tl in the distorted cubic arrangement. The second coordination sphere is, vice versa to Li1, built by one additional Li and five additional Tl.

Atomic Ratio M I :Tl
Na2Tl [66] includes classical, tetrahedrally shaped Tl4 8− anions as anionic moiety. Na2Tl was the first structurally characterized trielide compound, which contains isolated clusters and therefore represents a milestone in alkali metal trielide chemistry. This result goes back to the works of Hansen in 1967 [66], who was encouraged during his PhD works by J.D. Corbett to perform the structure determination of the latter compound. Tetrahedral shaped anions in solid state structures are wellknown in tetrelide chemistry [67], where the binaries of 1:1 stoichiometry form E4 4− anions. The coordination number within the different observed structure types in these cases is 12 (NaGe and NaSi type) and 16 (KGe and NaPb type). According to the higher alkali metal content in trielides, the coordination of the Tl4 8− in Na2Tl sums up to 23 sodium cations. This very dense packing of alkali metal atoms around the tetrahedra might prevent the formation of a pure binary, when larger congeners of the alkali metals are provided [18]. Having a closer look at the alkali metal positions shows that two of the five symmetry inequivalent sodium atoms are located on special positions 4a and 4b of space group C2221 (Table 15, Figure 13). The remaining three alkali metals reside on general positions. Figure 13 shows the symmetry inequivalent sodium atoms and their local environments, thereby the shorter distances are given in red, longer contacts are colored blue (according to the colorcoding in Table 15). 12 to 14 atoms at distances between 3.1 and 4.2 Å surround each sodium atom. The densest surrounding is observed for Na1, as there are 12 distances below 3.7 Å to the adjacent atoms. More space is available for Na5, which only features nine neighbors at shorter distances up to 3.8 Å, additional three longer distances up to 4.2 Å complete the local surrounding. Figure 13. Atomic environment of the symmetry inequivalent alkali metals in Na2Tl. The corresponding range of distances to the adjacent atoms as well as the Wyckoff letters are given in Table 15. Shorter contacts are colored red, longer distances are given in blue.  Table 15. Shorter contacts are colored red, longer distances are given in blue. Table 15. Surrounding atoms of the symmetry inequivalent alkali metal positions in Na 2 Tl (space group C222 1 ). The color-coding refers to the color of the contacts in Figure 13.

Symmetry Independent
Alkali  [66], who was encouraged during his PhD works by J.D. Corbett to perform the structure determination of the latter compound. Tetrahedral shaped anions in solid state structures are well-known in tetrelide chemistry [67], where the binaries of 1:1 stoichiometry form E 4 4− anions.
The coordination number within the different observed structure types in these cases is 12 (NaGe and NaSi type) and 16 (KGe and NaPb type). According to the higher alkali metal content in trielides, the coordination of the Tl 4 8− in Na 2 Tl sums up to 23 sodium cations. This very dense packing of alkali metal atoms around the tetrahedra might prevent the formation of a pure binary, when larger congeners of the alkali metals are provided [18]. Having a closer look at the alkali metal positions shows that two of the five symmetry inequivalent sodium atoms are located on special positions 4a and 4b of space group C222 1 (Table 15, Figure 13). The remaining three alkali metals reside on general positions. Figure 13 shows the symmetry inequivalent sodium atoms and their local environments, thereby the shorter distances are given in red, longer contacts are colored blue (according to the color-coding in Table 15). 12 to 14 atoms at distances between 3.1 and 4.2 Å surround each sodium atom. The densest surrounding is observed for Na1, as there are 12 distances below 3.7 Å to the adjacent atoms. More space is available for Na5, which only features nine neighbors at shorter distances up to 3.8 Å, additional three longer distances up to 4.2 Å complete the local surrounding.

Na 23 K 9 Tl 15.3
At a slight increased VEC Zintl of 5.1, the compound Na 23 K 9 Tl 15.3 [68] could be realized. This compound includes tetrahedral Tl 4 8− as well as trigonal bipyramidal Tl 5 7− anions. Additionally, a Tl 3 trimer is present. This trimer overlaps with an isolated Tl 5− mono-anion. Multiple bonding is discussed for the Tl 3 trimer in analogy to higher reduced alkaline earth tetrelide phases, which include tetrelide linear chains [69]. The mixed alkali metals seem to prevent the crystallization of a classical M I :Tl 2:1 stoichiometric compound. Slightly more alkali metal positions are needed for stabilization, which also means an excess of electrons. Therefore, thallium is further reduced under the formation of higher charged thallide species. Na 23 K 9 Tl 15.3 so far is the alkali-metal-richest thallide phase, where isolated polyanions are present. The alkali metal positions are very specific, as sodium caps edges and faces of Tl 4 8− and Tl 5 7− , whereas potassium coordinates to the vertices of the clusters ( Figure 14, Table 16). Altogether, there are two symmetry inequivalent potassium and five sodium sites. Concerning the sodium environments, one can distinguish between two main surroundings. Na1 and Na3 exhibit 12 neighbors at distances between 3.3 Å and 4.1 Å. Na2, Na4, and Na5 feature 13 surrounding atoms between 3.5 and 4.2 Å. Na1 and Na3 are distorted icosahedrally surrounded while Tl 4 8− and Tl 5 7− clusters are involved.
For Na2, Na4, and Na5 this icosahedral environment is "disturbed" due to the participation of the Tl 3 chain.
Crystals 2020, 10, x 21 of 27 Figure 14. Atomic environment of the symmetry inequivalent alkali metals in Na23K9Tl15. 3. The corresponding range of distances to the adjacent atoms as well as the Wyckoff letters are given in Table 16. Thallides very rich in alkali metal are only reported for lithium and sodium and in general, a high content of alkali metal increases the complexity of the compounds [70,71]. Lithium compounds crystallize in known intermetallic structure types, interestingly they are isotypic to lithium tetrelides, Figure 14. Atomic environment of the symmetry inequivalent alkali metals in Na 23 K 9 Tl 15.3 . The corresponding range of distances to the adjacent atoms as well as the Wyckoff letters are given in Table 16. The surroundings of both potassium atoms is similar, the main discrepancy is due to the involvement of the Tl 3 trimer instead of a sodium atom for K2. Additionally, fewer contacts to potassium and more contacts to sodium are observed for K2 ( Figure 14).

Atomic Ratio M I :Tl > 2:1
Thallides very rich in alkali metal are only reported for lithium and sodium and in general, a high content of alkali metal increases the complexity of the compounds [70,71]. Lithium compounds crystallize in known intermetallic structure types, interestingly they are isotypic to lithium tetrelides, which emphasizes the subsidiary role of the VEC for phase stability. Li 5 Tl 2 [72] crystallizes in the Li 5 Sn 2 structure type and includes Tl 2 dimers with a short Tl-Tl distances of 3 Å. Li 3 Tl [72] (Li 3 Pb type structure) includes monomeric Tl anions. In Li 22 Tl 5 [65] (Li 22 Pb 5 structure), also isolated Tl atoms are present. The alkali metal thallide with the highest content of alkali metal is found for the complex cubic compound Na 43.8 Tl 7 (space group F-43m) [73]. The compound includes eleven sodium and three Tl symmetry inequivalent positions. A topological analysis for Na 44 Tl 7 was reported by Shevchenko et al. in 2017 [74]. The local environment of ten symmetry independent sodium atoms sums up to 12 atoms, one exception is reported for one sodium position, which only shows nine direct contacts below 4 Å.

Comparison of Binary and Ternary Compounds Including Sodium and Potassium
The number of reported alkali metal thallides is very limited, but the majority involve sodium or potassium. In addition, some ternary compounds are known involving these elements. Table 17 lists alkali metal thallides, which involve sodium and/or potassium. Additionally, the distances are given, up to which a surrounding atom is found in terms of the above described atomic environment. In general, the distances between the alkali metals seem to remain within the same range for binary and ternary materials. Moreover, the Na-Tl distances stay the same or at least are little shorter than in the known binaries. In contrast, the K-Tl distances attract attention, as they seem to be significantly shifted to smaller values, when sodium is additionally present in the crystal structure. This demonstrates that the impact of mixing sodium and potassium is not only limited to the local environments, but also the overall crystal structure is affected. Of course, this trend is based on data of only a few crystal structures, future ternary compounds will show, if this trend is confirmed or refuted. Table 17. The comparison of the distances within the hitherto reported alkali metal thallides which involve sodium and/or potassium suggests that an involvement of sodium results in shorter K-Tl distances (bold).

Compound
Na-Tl K-Tl Na-Na K-K Na-K

Conclusions
The size and nature of the alkali metals play an important role in structure formation of alkali metal thallides, which goes far beyond a classical counter cation, respectively filling atom in terms of reasonable numbers for the VEC. The analyses of the local surroundings of the different crystallographic sites on which the alkali metals reside, clearly show discrepancies, even in binary compounds. Rb 14 CsTl 27 proves that an ordered substitution of one position in a structure type can be realized if different sized voids are available in the respective crystal structure. In contrast, the surrounding of only one alkali metal is supposed to be responsible for the change in the overall crystal structure of KTl and CsTl, respectively. In the ternary compounds Na 4 A 6 Tl 13 (A = K, Rb, Cs), Na 3 K 8 Tl 13 , Na 9 K 16 Tl 25.25 , Na 2 K 21 Tl 19 and Na 23 K 9 Tl 15.3 the size dependent arrangement and impact on the overall crystal structure could be demonstrated by Corbett et al.
The analyses of the different surroundings of the alkali metal sites in the binary compounds also emerges continuative potential. This is especially interesting, where obviously a disruption concerning formed structure types is given. For example, K 49 Tl 108 is only known for potassium, whereas at a similar VEC A 15 Tl 27 (A = Rb, Cs) is reported. The question arises, if the compounds K 15 Tl 27 or Rb 49 Tl 108 exist or if the formed structure type is unique for potassium respectively rubidium/cesium. An approach could be the employment of mixed alkali metals in order to prove, if there are site preferences and if yes, which alkali metal on which site is essential for structure formation. A similar approach is conceivable for all unique thallide compounds in order to introduce heavier or lighter alkali metals. This procedure might also allow approximating still unknown RbTl or heavier congeners of K 10 Tl 7 or Na 2 Tl. The involvement of lithium in ternary compounds has not yet been reported at all and seems to be very promising, especially in combination with the heavier alkali metals K, Rb and Cs, as for lithium even smaller voids can be realized.
Of course, directed synthesis based on size effects would be very desirable, but is essentially impossible due to effects other than size (e.g., electronic or thermodynamic). Nevertheless, in virtue of J. D. Corbett: "First comes the synthesis", unknown alkali metal thallides might be observed when more than one alkali metal is provided at a certain VEC. This accounts for a deeper understanding of the role of the alkali metals on the structure formation of alkali metal thallides. Investigative works within the vacant areas of the map of hitherto reported compounds ( Figure 1) might provide new insights for this class of materials. With brighter X-ray sources and highly resolving detector techniques this might now be the time to readopt the characterization of these compounds including also the heavier congeners of the alkali metals, which in combination with thallium naturally possess very high absorption coefficients. In conclusion, the structural chemistry of alkali metal thallides still provides exciting aspects even more than 90 years after the very meticulous structural characterization of NaTl by Eduard Zintl.