The binary alkaline-earth (A) indides [1–4] as well as mercurides [5–8] represent intermetallic phases with a pronounced electron transfer from A to In/Hg (M), caused by rather high differences between the electronegativity of the A and M element. Accordingly, M polyanions are formed exhibiting strong covalent bonds with structurally very interesting valence electron (v.e.) concentrations around v.e./M = 3, i.e., the electron count of boron. The electron-richer indides are mainly electron precise and their structures and electronic properties, which are characterized by small or pseudo band gaps, can be rationalized according to the Zintl concept [9–11], in some cases extended by the Wade–Mingos or mno rules [12–15]. The mercurides likewise exhibit strong covalent bonding in their polyanions. Their structures are even isotypic to the analogous indides, however no longer electron precise and easily rationalized. Consequently, these mercurides are metallic and do not show minima of the DOS at the Fermi level. Due to the similar atomic properties of Hg and In and their common ability to form longer “secondary” bonds in addition to the strong covalent 2e2c bonds [4, 8, 16], these two elements are able to substitute each other inside the polyanions and, thus, allow to continuously adjust the v.e. concentration in ternary mixed indides/mercurides [16–19]. At the same time, first effects of “coloring,” i.e., partial ordering of the two atoms at different M sites, appear . Among the different compositions A:M, the 1:4 compounds are particulary interesting: The pseudo-binary section between AHg4 and AIn4 allows to vary the range of v.e./M from 2.5 to 3.5, i.e., around the electron concentration of elemental boron. While calcium compounds CaIn4 and CaHg4 do not exist for geometric reasons [3, 15, 21] and the barium systems are dominated by the simple BaAl4-type structure , the nearly singular tetraindide SrIn4 [3, 4] and the closely related compound Sr3In11 [4, 22, 23] are structurally and electronically very attractive starting compounds for a study of electronic stability ranges. For mixed mercurides/indides Sr(Hg1–xInx)4, we recently demonstrated that depending on the indium content x, and, thus, the v.e. concentration different variants of the EuIn4-type exist at higher (3.5–3.36) and lower (2.82–2.74) v.e./M, surprisingly interrupted by a stability range of the common BaAl4-type structure at intermediate v.e. concentrations (3.26–3.0) . In the present work, we report on the results of a related study on mixed mercurides/stannides Sr(Hg1–xSnx)4. By changing indium against tin, the v.e. concentration is obviously increased, but with a 1:1 mixture of the two elements isoelectronic indides with a coloring of the polyanion can be “imitated.” This has already been demonstrated for the 1:2 compound SrHgSn , which represents the only known compound of the ternary system Sr–Hg–Sn reported to date. It crystallizes in the LiGaGe-type structure and exhibits a tetrahedral network, similar to SrIn2 , with a strictly alternating Hg/Sn distribution. As for the Hg/In (and the related Hg/Tl ) substitution, the Hg/Sn exchange is possible due to the similar radii and electronegativities of the two elements (Hg: r = 157.3 pm, χ = 1.9; In: r = 166.3 pm, χ = 1.7; Sn: r = 162.3 pm, χ = 1.8). However, for the Hg/Sn element combination the increased difference of the v.e. numbers is assumed to reduce, if not even prevent, phase widths.
2.1 Preparation and phase analysis
The synthesis of the title compounds of the series Sr(Hg1–xSnx)4 was generally performed starting from the elements strontium, mercury and tin as obtained from commercial sources (Sr: Metallhandelsgesellschaft Maassen, Bonn, Germany, 99 %; Hg: Merck, p.A.; Sn: Shots, ABCR Karlsruhe, 99.9 %). The elements were filled into tantalum crucibles in a glovebox under an argon atmosphere and the sealed containers were heated up to a maximum temperature of 800–1000 °C. Subsequently, the crystallization was performed by a slow cooling rate of 5–20 K/h. The details of the temperature programs can be found in Table 1, together with the weighed sample compositions, which were restricted to the stoichiometric 1:4 (for Sr:Hg/Sn) element ratio. After the syntheses, representative parts of the reguli were ground in the glovebox and sealed in capillaries with a diameter of 0.3 mm. Powder X-ray diffraction diagrams were collected on transmission powder diffraction systems (STADI-P, linear PSD, Stoe & Cie, Darmstadt, Germany, MoKα radiation, graphite monochromator). The exactly stoichiometric compound SrHg2Sn2 forms over a wide composition range at Sn proportions x in Sr(Hg1–xSnx)4 between 0.85 and 0.47, where the tin-rich samples contain in addition the known binary stannide SrSn4 . According to our single crystal data, the latter compound does not take up any mercury. From a series of single crystal data and also from the positions of characteristic reflections of the EuIn4-I-type structure of SrHg2Sn2 in the powder patterns, no phase width could be observed for this compound. At a tin content x of 0.43 (SrHg2.28Sn1.72), the powder diagrams of the samples change and additional reflections appear, which clearly indicate the larger unit cell of a superstructure. Several data sets collected from crystals taken from samples around the composition SrHg2.5Sn1.5 show a small phase width of the superstructure compound not larger than from SrHg2.48Sn1.52 to SrHg2.52Sn1.48. A further decreased tin content in samples of compositions like SrHg2.75Sn1.25 and SrHg3Sn yielded only the distorted EuIn4-II-type structure. Again, from several single crystal data sets a small phase width ranging from SrHg2.56Sn1.44 to SrHg3.22Sn0.77 has been obtained for the electron-poor form II of the EuIn4 structure.
2.2 Crystal structure determination
For the crystal structure determinations, irregularly shaped single crystals of silver metallic luster were selected using a stereo microscope and mounted in glass capillaries (diameter 0.1 mm) under dried paraffine oil. The crystals were centered on diffractometers equipped with an image plate (Stoe IPDS, sealed tube) or a CCD (Bruker Apex-II Quazar, microfocus source) detector.
The reflections of the border compound SrHg2Sn2 could be indexed using a C-centered monoclinic lattice. Due to the lack of further absence conditions (and thus C2/m as a possible space group) and the similarities of the lattice parameters with the indide SrIn4 , the latter model has been used for the structure refinement (program Shelxs-2013 ). The refinement of the Hg/Sn site occupation factors of the four original indium positions easily showed the fully ordered Hg/Sn distribution in SrHg2Sn2. This also holds for all four data sets collected from crystals of different samples (see the section 2.1 Preparation and phase analysis).
Crystals isolated from the most Hg-rich samples of the series Sr(Hg1–xSnx)4 also exhibit the monoclinic C-centered EuIn4-type unit cell, but the ratios of the lattice parameters are significantly different: While the a axis is decreased from 1258 (Sn-rich EuIn4-I-type) to 1173 pm, the c axis increases from 998 to 1010 pm. As expected from the slightly smaller metallic radius of mercury (r = 157.3 pm) compared to tin (r = 162.3 pm), the unit cell is about 5 % smaller at the Hg-rich border of the series. Nevertheless, the structure of SrHg3.2Sn0.8 could be refined starting from the atomic coordinates of SrIn4. The statistically occupied Hg/Sn positions M(2), M(3) and M(4) were refined with constrained positional and thermal parameters. The significant shifting of the atomic parameters (see the differences of the related x and z parameter values in Table 2, top and bottom) results in a distorted EuIn4 variant (hereafter referred to as EuIn4-II-type). The distortion is associated with the formation of additional, primarily Hg–Hg, bonds (see section 3 Results and discussion). Similar electronically driven structural changes have already been observed for the related series Sr(Hg1–xInx)4 .
The reflections of the crystals of the “intermediate” compounds (SrHg2.5Sn1.5) could likewise be indexed using a C-centered monoclinic lattice. In this case, however, only the length of the lattice parameter b fits the EuIn4-type structure. A closer inspection of the precession photographs calculated from the image plate data revealed the presence of a superstructure of the original EuIn4 unit cell, which is connected with a tripling of the monoclinic a–c basis. Also in this case, the lack of further absence conditions reduced the possible space groups to C2/m, C2 and Cm. The structure was solved using Direct Methods (program Shelxs-2013 ) in the centrosymmetric space group C2/m. This solution already yielded the three strontium and 10 of the 12 Hg/Sn atomic positions. After the completion of the model, the assignment of the pure Hg and Sn positions and the refinement of the Hg/Sn occupation for five mixed M positions, all displacement parameters converged to plausible values and the data refined to a low R1 value of 0.0475. The residual difference electron density maxima of 2.8 e– × 10–6 pm–3 are located in the vicinity of the M atoms.
The crystallographic data and the refined atomic parameters of the three compounds are summarized in Tables 2 and 3, respectively . Selected interatomic distances are collected in Table 4 (EuIn4-type structures I and II) and 6 (tripled superstructure of SrHg2.5Sn1.5).
2.3 Band structure calculations
DFT calculations of the electronic band structures were performed using the FP-LAPW method (program Wien2k ). Whereas the fully ordered compound SrHg2Sn2 could be calculated directly, ‘SrHg3Sn’ and ‘SrHg4’ were set up as model compounds for the second electron-poor variant of the EuIn4-type structure using the crystal data of SrHg3.2Sn0.8. For the Sn-containing model, the position M(2), which shows the highest tin content, was treated as a pure Sn site. In all calculations, the exchange-correlation contribution was described by the generalized gradient approximation (GGA) functional of Perdew, Burke, and Ernzerhof . Muffin-tin radii were chosen as 127.0 pm (2.4 a.u.) for all atoms. Cutoff energies used are = 190 eV (potential) and = 170 eV (interstitial plane waves). Electron densities and Fermi surfaces were calculated and visualized using the programs XCrysDen  and DrawXTL . A Bader  analysis of the electron density map was performed to evaluate the charge distribution between the atoms, the bond critical points (3, –1; BCP) and the volumes of the Bader basins (VBB). Details and selected results of the calculations are summarized in Table 5. The total and partial Sr, Hg, and Sn densities of states are depicted in Fig. 1.
3 Results and discussion
3.1 Description of the crystal structure of SrHg2Sn2 (EuIn4-I)
SrHg2Sn2 crystallizes with a fully ordered variant of the EuIn4-type structure. This very rare monoclinic structure type occurs only for the isoelectronic (14 v.e./f.u.) binary indides EuIn4 and SrIn4 [3, 4], the latter with a very small substitution of In by Hg . The structure has nevertheless been repeatedly described in the literature emphazising different structural elements [3, 4, 24]. For the ordered phase SrHg2Sn2 (I), the mercury-rich variant (II) and also the superstructure (S) reported herein, a description of the structures is given following, which focusses on the Hg/Sn distribution and the similarities with the structure elements found in SrHgSn  (LiGaGe type) and in binary and ternary Hg-rich alkaline-earth mercurides [16, 17, 19].
For the structure description and comparison, the shorter M–M distances are denoted by the bold characters a to e. They are found in the range 280–300 pm and, thus, vary around the Hg–Sn bond length observed in the electron precise compound SrHgSn (dHg–Sn = 290.1 pm). These distances are well separated from those of the multicenter/metallic bonds above 315 pm. This gap in the bond length distribution has been similarly reported for the binary alkaline-earth indides [1, 4], as well as for the corresponding mercurides [8, 16]. The distances f, g, and h alternate between the shorter and longer group of contacts within the different structure variants. The longer contacts u and v (314–335 pm) still have bond critical points in the calculated electron densities (see following). In Tables 4 and 6 the coordination numbers of Hg/Sn are designated (N + M) for the N shorter (280–300 pm) and the M longer/“secondary” (314–335 pm) bonds.
The left-hand side of Fig. 2 shows the unit cell of the fully ordered compound SrHg2Sn2 (x = 0.5) forming the “usual” (I) EuIn4-type structure. As in the other variants of this structure, all atoms are located at y = 0 and i.e., on the mirror planes perpendicular to the short b axis. In SrHg2Sn2, the atoms Hg(2) and Sn(3) at the one hand, and Hg(1) and Sn(4), on the other hand, are alternatingly forming zig-zag chains running along the b axis. These two types of chains are interconnected (via Hg–Sn bonds only) to form folded ladders like in the TiNiSi/KHg2-type structures. In Fig. 3a these two types of zig-zag ladders A [formed by Sn(2) and Hg(3)] and B [Sn(1)/Hg(4)] are indicated by medium gray (A) and transparent light gray (B) planes. The Hg–Sn bonds d (A) and c (B) along the zig-zag chains are strong with interatomic distances of 287.0 and 282.0 pm, respectively (Table 4). In contrast, the rungs of the folded ladders, the Hg–Sn contacts f/u (for ladders A/B), are elongated significantly (317.6/323.3 pm). The square planar rings of the ladders B are only slightly distorted forming a rectangle with angles of 96.5/83.5° at the Hg/Sn corners, whereas the ladders A are strongly distorted toward rhombs (107.2/72.8° for Hg/Sn). Similar to the situation in the KHg2 structure, both ladder types A and B are further connected along  via the Sn–Sn bonds a/h (dSn–Sn = 289.8/285.0 pm). In the resulting layers, six-membered rings are formed between the ladders, which are nearly planar between the ladders A and heavily puckered (chair conformation) between the ladders B (see dashed boxes in Fig. 2a). The two layers are further connected by strong Hg–Sn bonds b and e (285.0 and 289.1 pm) resulting in five-membered rings on the mirror planes (see Fig. 4a). The Sr cations are interspersed between two such pentagons exhibiting an overall coordination by (10 + 5) Hg/Sn and 2 Sr cations. The coordination number of Sn(1) amounts to 4 + 1 (with the neighbor atoms forming a trigonal-bipyramidal arrangement), whereas Sn(2), Hg(3) and Hg(4) show a distorted tetrahedral 3 + 1 coordination (Table 4). With the exception of the increased coordination number of Sn(1), the structure of SrHg2Sn2 can be described as a network of tetrahedra with four-, five- and six-membered rings similar to the nets observed in SrHgSn (LiGaGe-type ), SrIn2 (CaIn2-type ) (both with six-membered rings only) and SrHg2 (KHg2-type , four-, six- and eight-membered rings). Also related to the situation in SrHgSn, Hg–Sn bonds with a small polarity dominate the complex polyanion. The only exception are the two strong Sn–Sn bonds a and h, which connect the folded ladders to layers. Neglecting the weaker M–M bonds longer than 300 pm, the characteristic building blocks of the structure of SrHg2Sn2 are double tubes of connected cages consisting of five- and six-membered Hg/Sn rings. These structural elements are located around the b axis (0, y, 0) and are marked by ellipses in Figs. 2 and 5. The tubes are connected by the Sn(2)–Sn(2) bonds a resulting in complex layers in the b–c plane. Very similar layers (in this case formed by connected triple tubes) are found in the structure of the electron precise compound SiAs . The Si positions are taken by the similarly four-bonded Sn atoms, which form Sn–Sn dumbbells inside [Sn(1)] and between [Sn(2)] the tubes. The As positions are occupied by the likewise three-bonded Hg(3,4) atoms. Compared to the electron precise compound SiAs (3bAs and 4bSi) with 9 v.e./f.u., all Hg/Sn atoms in the 7 v.e. unit [HgSn]– of SrHg2Sn2 are additionally connected to the neigboring layers via the longer secondary Hg/Sn contacts of the folded ladders as described. This compensates for the two electron difference resulting also in an electron precise bonding situation for SrHg2Sn2 (see section Electronic structure and chemical bonding, following).
3.2 Comparison with the electron-poor EuIn4-II-type of SrHg3.2Sn0.8
As expected from the slightly smaller metallic radius of mercury relative to tin, the unit cell volume of the Hg-rich compound decreased by 5 % compared to SrHg2Sn2. Whereas the a and the b lattice parameter are also decreased, c unexpectedly increases from 998 to 1010 pm, indicating a significant change of the bonding situation in the two variants of the EuIn4-type structure. The interchanged Hg/Sn distribution also points to significant differences between the two structure variants: The pure tin position Sn(1) of SrHg2Sn2 is fully occupied by Hg in SrHg3.2Sn0.8 and vice versa Hg(3) is the site occupied by the highest Sn content in the Hg-richer compound. Initially, the folded ladders A and B appear to be similar. Admittedly, the bonds f of the ladders A are significantly decreased from 317.6 to 297.7 pm. In addition, the distortion of the folded ladders is inverted: In SrHg2Sn2, the meshes of the ladders A are strongly sheared to give paralellograms, whereas in SrHg3.2Sn0.8 the four-membered rings of the ladders B are those which deviate significantly from rectangularity [77.5/102.5° at Hg(4)/Hg(1)]. Here, the ladders A are with 87.7/92.4° [M(2)/M(3)] next to rectangular. The reduced distortion of the ladders A not only decreases the bonds f but results in the formation of the new contacts v and additionally decreases the bonds g. In return, the strong bond h between two Sn(1) atoms (285.0 pm) is elongated to a secondary contact of lengths 329.9 pm between the two Hg(1) atoms. These modifications of the bond lengths are associated with a change of the ultimately resulting structural elements located around the b axis: Whereas SrHg2Sn2 exhibits the SiAs-like tubes formed by five- and six-membered rings as described, the Hg-rich derivative SrHg3.2Sn0.8 exhibits M8 rhombohedra as characteristic building blocks in this part of the structure, which are similarily found in elemental mercury and Hg-rich mercurides [7, 16, 17]. The rhombohedra, which are depicted as dark polyhedra in Fig. 3, are connected via common edges to form rods along .
The differences of the two EuIn4-type structure variants also lead to different coordination numbers, especially of the positions M(1) and M(4) forming the ladders B (Table 4). Due to the formation of the new contacts g and v at a higher Hg content, the coordination number of the very Hg-rich position M(4) is clearly increased from (3 + 1) to (4 + 3). As expected for a reduced v.e. number, the average connectivity of the atoms increases and, thus, the averaged coordination numbers (M + N) increase from (3.5 + 1) in the more electron rich compound SrHg2Sn2 to (4 + 1.75) in the Hg-rich derivative. With a value of 15 in SrHg2Sn2 and 16 in SrHg3.2Sn0.8 (Sr–M distances of 346–410 pm) the M coordination of the Sr cations is also slightly increased.
3.3 The superstructure of the EuIn4-type in SrHg2.5Sn1.5
The compound SrHg2.5Sn1.5 with an intermediate Sn-content crystallizes in an isomorphous superstructure of index 3 of the EuIn4-type structure (C2/m; Pearson code mS60, Figs. 3c and 5). The tripled unit cell is crystallographically achieved by the transformation matrix 1 0 –2, 0 1 0, 1 0 1 (see dotted small unit cell in Fig. 4c). Conversely, the corresponding small unit cell dimensions are a = 1195.2, b = 493.9, c = 991.1 pm, and β = 114.38°. Its volume Vu.c. of 532.9 × 106 pm3 is consequently of intermediate size compared to those of the Sn-richer (545.2 × 106pm3, I) and the Hg-richer (516.6 × 106 pm3, II) EuIn4-type structures. According to this tripling, the structure exhibits three Sr and 12 Hg/Sn sites. Two of the M sites, Sn(12) and Sn(22), are pure tin positions, five are pure mercury sites, and the other five are statistically occupied by the two elements (Table 2, middle). The atom labels of the M atoms, in general M(ij), are chosen in such a way, that i (with i = 1–4) corresponds to the label of the atom in the simple EuIn4-type structures as discussed. The second part of the label, j (with j = 1–3), has been selected so that atoms with the same j form the zig-zag chains running along . Bond labels (bold numbers) are also chosen to match the labeling in the simple structure type (e.g., a splits into a, a′ and a″, Table 6).
Similar to the two EuIn4 variants, atoms M(1j) alternating with M(4j) and likewise M(2j) alternating with M(3j) form zig-zag chains running along the b axis. Two chains are again connected via bonds u and f to form the characteristic folded ladders A [two chains M(21)/M(31)], A′ [chains Sn(22)/Hg(32) and M(23)/Hg(33)], B [2 × Hg(11)/M(41)], and B′ [M(12)/Hg(42) + Sn(13)-Hg(43)]. The folded ladders A/A′ are connected to sheets forming flat six-membered rings in between the ladders. In contrast, the six-membered rings between the ladders B/B′ are again heavily puckered. The sheets formed by the ladders A/A′ are very similar in the two variants of the two EuIn4-type structure; therefore, it is not surprising that they are also equal in the superstructure. In the sheets formed by the ladders B and B′ the building blocks of the variants I (SiAs-like double tubes, solid gray ellipses in Fig. 5) and II (rods of rhombohedra, dashed ellipses) of the two EuIn4-derivatives alternate in a 1:2 ratio. The distribution of Hg and Sn also corresponds to the two more simple structure variants: The tubes of the “original” EuIn4-type I are built up by the Hg/Sn atoms Sn(13), Sn(22), Hg(32) and Hg(43), which are–with the exception of the Sn(13)–Sn(13) bond h″–alternately connected. Comparable with the Hg-rich EuIn4 variant II, the remaining mixed Hg-rich/pure Hg atoms Hg(11), M(12), M(21), M(31), Hg(33), M(41), and Hg(42) form rods of edge-sharing rhombohedra (black polyhedra in Fig. 3c), dashed ellipses in Fig. 5). In this mercury-rich region of the structure, additional longer M–M bonds are formed, which are missing in the open tubes: The bond v [M(12)– M(41)] newly appears, and the bond u between Hg(11) and M(41) is strengthened from a secondary to a short M–M contact.
According to this 1:2 structure relation, the Sr cations also exhibit the two coordination numbers of the EuIn4 type variants, 16 (1×) and 15 (2×), in parallel.
Figure 4 shows the three variants of the EuIn4-type structure observed in the title compounds Sr(Hg1–xSnx)4 in a projection along b, which is also a useful description to compare the structures with related compounds like BaIn4 (BaAl4 type), Sr3In11 (La3Al11) or several Hg-rich mercurides (see figures and discussion in [3, 24]). These projections, in which the short (long) bonds below (above) 300 pm are depicted with thick (thin) sticks, easily show the different connection of the double pentagons inside the layers of similar y parameters (bold/thin atoms and bonds). In the original EuIn4-I-type (Fig. 4a) the double pentagons are connected via the short Sn–Sn bond h along the diagonal  of the monoclinic unit cell. In contrast, this strong bond h is elongated in the mercury richer compound, some longer bonds appear and the new short Hg(4)–Hg(4) bond g connects the double pentagons to form ribbons running along  (Fig. 4b). Consequently, the connection of the pentagon dimers in the superstructure (Fig. 4c) is a combination of both the EuIn4-I- and the -II-type structure, resulting in very wide (lengths of the large a lattice parameter) ribbons running along the  direction of the superstructure cell.
3.4 Comparison of the two series Sr(Hg1–xSnx)4 and Sr(Hg1–xInx)4
The series of the mixed mercuride indides Sr(Hg1–xInx)4  and the mixed stannides Sr(Hg1–xSnx)4 examined herein, show some similarities but also some distinct differences. At first, the electron-rich EuIn4-type structure exists for the binary tetraindide (v.e./M = 3.5), as well as for the isoelectronic mixed stannide SrHg2Sn2. In the case of the indide, a small phase width due to In to Hg exchange is observed reaching down to a valence electron concentration of 3.36 in SrHg0.56In3.44. In contrast, no additional Hg incorporation is observed for SrHg2Sn2. A partial occupation of the Sn positions by Hg in this coumpound would result in a loss of the strong Sn–Sn bonds. Second, the EuIn4-II-type occurs in both series at significantly reduced v.e. concentrations. In the case of the indides, this structure type is found in the v.e./M range 2.82 to 2.74, and for the tin compounds at somewhat larger values of v.e./M from 3.22 to 2.88. Also similar for both compound series, the stability range of the two different EuIn4-type structures is interrupted by the occurence of an alternative structure: In constrast to the superstructure found for the stannides at v.e./M = 3.25, the common BaAl4-type is observed in the indium system at intermediate v.e. concentrations from v.e./M 3.26 to the stoichiometric compound SrHg2In2 with v.e./M = 3.0. The composition of the isoelectronic hypothetic tin compound would be SrHg3Sn, which already lies in the stability region of the EuIn4-II variant. The absence of a BaAl4-type structure in the Sr/Hg/Sn system is presumably caused by the smaller radius of tin (and the high content of likewise small mercury atoms). The geometric stability range of the BaAl4 structure, which is observed for larger A and smaller M atoms only, is already exceeded for this composition.
3.5 Electronic structures and chemical bonding
For the band structure calculations of the title compounds, the fully ordered electron-rich compound SrHg2Sn2 and, as model systems for the electron-poor compounds, ‘SrHg4’ and ‘SrHg3Sn’ with the crystal data taken from SrHg3.2Sn0.8 were used. For the latter model compound, the statistically occupied M(3) position was treated as a pure tin site (see the Experimental section).
In the calculated valence electron density of all compounds, distinct bond critical points of heights 0.21–0.33 e– × 10–6 pm–3 (Table 5) are located on each short Hg–Sn bond up to 300 pm. The short Sn–Sn bonds a and h (in SrHg2Sn2) are found at the upper end of this range (ρBCP = 0.30–0.33 e– × 10–6 pm–3). In accordance with the electronegativities of Hg (χ = 1.9) and Sn (χ = 1.8), the bond critical points at the Hg–Sn bonds are slightly (approximately 10 pm) shifted toward the less electronegative tin atom. The reduced Bader charges of tin (0 to –0.18) compared to the charges of mercury of –0.57 to –0.60 are also in agreement with this observation. Thus, the always higher charge of mercury also leads to very similar volumes of the Bader basins for both M elements: Even though mercury has a smaller metallic radius (157.3 pm compared to tin (162.3 pm) (see the trends in the unit cell volumes along with the tin-content x), the smaller radius of mercury is “compensated” by the increased negative charge. The longer contacts f, h, and u, which are found inside the Hg-rich rhombohedra, still exhibit bond critical points with reduced electron densities. These weaker bonds, which are clearly separated by their lengths, as well as by their ρBCP values from the purely covalent 2e2c bonds, are a very characteristic feature in most of the electron-poor polar intermetallics of mercury and the heavier p block elements Sn, Pb, In, and Tl.
For SrHg2Sn2 and both Hg-rich model compounds the calculated total density of states (DOS) and the partial DOS (pDOS) of the different Hg/Sn and Sr sites are plotted in Fig. 1 in the range between –10.5 and +2 eV relative to the Fermi level. The electronic stability range of the Hg-rich EuIn4-II-type structure is marked by a hatched bar, numbers indicate v.e./M. As expected, the occupied bands are primarily of Hg and Sn character. The s and p states of all M atoms (not shown) are extensivly mixed, resulting in broad bands typical for an extended three-dimensional polyanion. The Hg d states are mainly situated between –9 and –5 eV below EF, but they also spread out to higher energy and show a pronounced mixing in particular with the Hg- s states. This corresponds to a considerable contribution of Hg- d states to the covalent bonding. The Sr pDOS found below the Fermi level is mainly composed of d states. The contribution of these Sr states to the chemical bonding, which indicates an incomplete electron transfer from Sr towards M, is in the same order of magnitude as in electron precise Zintl phases with pseudo band gaps. The Bader charges of the Sr atoms, which are +1.35 and +1.40 in the calculated compounds (Table 5) are also similar to those in electron precise Sr indides .
The tDOS of SrHg2Sn2, similar to the observation for the isoelectronic indide [1, 3, 4, 24], exhibits a very pronounced pseudo band gap (Fig. 1, top). However, the distinct local minimum of the tDOS is located slightly below the Fermi energy (see discussion for the “hypoelectronic” SrIn4 on the basis of a Hückel calculation ). In contrast to the related Hg/In tetrametallides , no phase width toward this slightly decreased v.e. concentration of 3.45 v.e./M is observed. The tDOS of ‘SrHg3Sn’ (Fig. 1, bottom), which serves as a model compound for the Hg-rich version of the EuIn4-type structure, shows that the structural distortion leads to a new, though not too pronounced, broad minimum of the tDOS around EF, which nicely corresponds with the compositions of the observed variants of the Hg-rich EuIn4-II type (see hatched bar in Fig. 1, bottom). Although simple electron counting rules cannot be applied for both variants of the EuIn4 type (i.e., due to the larger secondary bonds found inside the folded ladders and the Hg-rich parts of the structures), the results of the bandstructure calculations prove that the structural distorsions are governed by electronic factors.
4 Summary and outlook
In the series of mixed 1:4 mercurides/stannides Sr(Hg1–xSnx)4 (x = 0.5–0.2) several compounds forming three different variants of the EuIn4-type structure were synthesized and structurally characterized. The most electron-rich compound SrHg2Sn2 (x = 0.5, no phase width) is isoelectronic and isotypic with SrIn4 and crystallizes in a fully ordered EuIn4-type variant. In the structure, folded ladders composed of alternating Hg/Sn atoms are connected via six-membered rings to form open tubes resembling the structure motif and atom connectivity of SiAs. The most electron-poor phase SrHg3.2Sn0.8 (phase width: x = 0.2–0.36) crystallizes in a distorted variant of this structure, in which additional weaker M–M (primarily Hg–Hg) bonds appear and the open Hg/Sn tubes are distorted toward rods of edge-sharing Hg-rich rhombohedra resembling the motifs of elemental Hg. At an intermediate tin content of x = 0.37–0.38 (SrHg2.5Sn1.5) an isomorphous tripled superstructure is formed, where the building blocks of the two variants of the EuIn4-type structure alternate in a 1:2 ratio. The calculated tDOS of the electron-rich compound SrHg2Sn2, similar to the isoelectronic SrIn4, exhibits a pronounced pseudo band gap, whereas a broad less pronounced minimum, which exactly fits the observed phase width of the Hg-rich compounds, appears for the model compound ‘SrHg3Sn’. Consistent with the electronegativities of M, Hg always serves as the more negatively charged bonding partner in the polyanion. The M–M bond lengths, as well as the magnitudes of the bond critical points, are clearly separated into strong shorter (280–300 pm) covalent 2e2c bonds and additional longer (315–335 pm) multicenter/metallic M–M contacts. This distribution of the interatomic distances is likewise characteristic for binary electron-poor alkaline-earth polymetallides of the heavy p-block elements and of mercury. It leads to an increased structural diversity while preventing the application of simple electron counting rules. For this reason, related synthetic, structural, and bond theoretical studies in the systems AII-Hg-Sn are under way. The investigation of geometric criteria and the coloring of the polyanions is also in progress, e.g., the partial substitution of indium by aluminium or gallium.
We would like to thank the Deutsche Forschungsgemeinschaft for financial support.
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Published Online: 2015-03-25
Published in Print: 2015-04-01