Intricate Li–Sn Disorder in Rare-Earth Metal–Lithium Stannides

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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

Intricate Li−Sn Disorder in Rare-Earth Metal−Lithium Stannides. Crystal Chemistry of RE3Li4−xSn4+x (RE = La−Nd, Sm; x < 0.3) and Eu7Li8−xSn10+x (x ≈ 2.0) Nian-Tzu Suen,†,‡ Sheng-Ping Guo,†,‡ James Hoos,† and Svilen Bobev*,† †

Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716, United States College of Chemistry and Chemical Engineering, Yangzhou University, Yangzhou 225002, P. R. China

‡

S Supporting Information *

ABSTRACT: Reported are the syntheses, crystal structures, and electronic structures of six rare-earth metal−lithium stannides with the general formulas RE3Li4−xSn4+x (RE = La−Nd, Sm) and Eu7Li8−xSn10+x. These new ternary compounds have been synthesized by high-temperature reactions of the corresponding elements. Their crystal structures have been established using single-crystal X-ray diffraction methods. The RE3Li4−xSn4+x phases crystallize in the orthorhombic body-centered space group Immm (No. 71) with the Zr3Cu4Si4 structure type (Pearson code oI22), and the Eu7Li8−xSn10+x phase crystallizes in the orthorhombic base-centered space group Cmmm (No. 65) with the Ce7Li8Ge10 structure type (Pearson code oC50). Both structures can be consdered as part of the [RESn2]n[RELi2Sn]m homologous series, wherein the structures are intergrowths of imaginary RESn2 (AlB2-like structure type) and RELi2Sn (MgAl2Cu-like structure type) fragments. Close examination the structures indicates complex occupational Li−Sn disorder, apparently governed by the drive of the structure to achieve an optimal number of valence electrons. This conclusion based on experimental results is supported by detailed electronic structure calculations, carried out using the tight-binding linear muffin-tin orbital method.

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INTRODUCTION The synthesis and structural characterization of new lithiumcontaining solid-state compoundssilicides, germanides, stannides, and antimonidesis an ongoing project in our laboratory.1−10 Our focus has been on ternary phases with lithium and alkaline-earth or rare-earth metals, which can be broadly classified as (nearly) valence-precise compounds, i.e., Zintl phases.11,12 For example, not long ago, we identified four families of germanides, RE2Li2Ge3, RE3Li4Ge4, RE7Li8Ge10, and RE11Li12Ge16 (RE = La−Nd, Sm),3,4 which are members of an extended homologous series, [REGe2]n[RELi2Ge]m. Their structures are based on imaginary RELi2Ge (MgAl2Cu-structure type) and REGe2 (AlB2 -structure type) slabs. 13 Thus, RE2Li2Ge3 with n = 1 and m = 1 and RE3Li4Ge4 with n = 1 and m = 2 are the simplest members of the series;3 RE7Li8Ge10 = [REGe 2 ] 3 [RELi 2 Ge] 4 and RE 1 1 Li 1 2 Ge 1 6 = [REGe2]5[RELi2Ge]6 are higher homologues.4 The latter structures can also be rationalized as intergrowths of the former, as schematically shown in Figure 1. Over the course of the previous studies, it was observed that the number of valence electrons plays an important role in the overall structural stability. This conjecture is nicely demonstrated for RE3Li4Ge4, in which fewer than needed electrons for chemical bonding are available; thus, to achieve an optimal electron count, Nature allows the Li atoms to be partially replaced by Ge atoms. Such occupational Li−Ge disorder is not intuitive, which combined with the very small degree of Li and © XXXX American Chemical Society

Ge admixing leaves some doubts about the model put forth for RE3Li4−xGe4+x. To verify our hypothesis, we attempted to make the isostructural RE3Li4−xSn4+x, where the potential Li−Sn disorder on the Li site would be easier to discern by in-house Xray diffraction (XRD) methods. Indeed, Ce3Li3.69Sn4.31(1) was synthesized and structurally characterized by single-crystal XRD several years ago; the crystallographic data were included as Supporting Information in the paper discussing the RE3Li4−xGe4+x crystal chemistry.3 Follow-up work yielded four more members of the RE3Li4−xSn4+x [RE = La−Nd, Sm; 0.06(1) < x < 0.31(1)] family. Additional, and perhaps the most conclusive, evidence for extensive Li−Sn mixing was found when the nominally divalent Eu metal was employed and the new phase Eu7Li8−xSn10+x (x ≈ 2.0) was discovered. This compound is isotypic with the germanides RE7Li8Ge10 (RE = La−Nd, Sm), which are apparently line compounds and show no signs of Li−Ge disorder.4 Aliovalent substitution of a nominally trivalent rare-earth metal with the divalent Eu leads to a severe electron imbalance in the structure [ca. 7−8 fewer electrons per formula unit than needed]. The shortage is nearly offset by the substitution at an extensive level (ca. 50%) of the Li atoms with Sn atoms on one of the Li sites. With this paper, we report the synthesis and crystal structure determination of the above-mentioned new stannides. Also Received: March 6, 2018

A

DOI: 10.1021/acs.inorgchem.8b00583 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

ends of which were sealed via arc-welding. The welding was done under a high-purity argon atmosphere. The closed Nb ampules were then put into fused silica tubes, which were sealed under vacuum (below discharge). Many different heating profiles for the synthesis of RE3Li4−xSn4+x (RE = La−Nd, Sm) were explored before the best one was found; it consists of a pre-reaction step carried out via induction melting (almost instantaneous heating) to 1273 K for 10 min. The “activated” mixtures were then transferred to tube furnaces, where they were equilibrated at 1273 K for 5 h. The reactions were cooled to 873 K at rate of 5 K/h, and then the mixtures were removed from the furnaces. Other attempts to synthesize the target compounds included the use of a RE−Sn binary precursor and elemental Li added to it, as well as the heating of stoichiometric mixtures of the respective metals in tube furnaces (without the induction-melt step). In all of these cases, the desired phase formed but in poorer yields. To make Eu7Li8−xSn10+x (x ≈ 2.0), a very similar procedure was used. Our initial goal was Eu3Li4Sn4, but a phase with this composition was never obtained. All reactions set up with this stoichiometry yielded multiphase mixtures, with the main product being Eu7Li8−xSn10+x. Via optimization of the nominal composition and temperature profile, it was found that for best results the reaction mixture should be slowly cooled to 573 K (not 873 K as before) and then removed from the furnace. Later on, Sr7Li8−xSn10+x (Supporting Information), isoelectronic and isostructural with Eu7Li8−xSn10+x (x ≈ 2.0), was also synthesized via the exact same protocol. Single crystals of RE3Li4−xSn4+x (RE = La−Nd, Sm) and Eu7Li8−xSn10+x show clear signs of decomposition upon a brief (ca. 1 h) exposure to the ambient atmosphere. The air and/or moisture sensitivity of the bulk material was also confirmed by taking powder Xray diffraction (PXRD) patterns (vide infra) of the samples before and after they had been exposed to air for 3−4 h. PXRD. PXRD measurements were performed on a Rigaku Miniflex diffractometer (Cu Kα radiation; λ = 1.5418 Å). The patterns were collected using a θ−θ scan mode and at a rate of 5 s/step (step size of 0.05°). The instrument is housed in a glovebox so that air-sensitive materials can be handled. The diffraction patterns were analyzed using the JADE 6.5 software; such analyses suggest that the synthetic approaches mentioned above can provide RE3Li4−xSn4+x (RE = La− Nd, Sm) and Eu7Li8−xSn10+x samples of high purity. However, a singlephase material was never obtained; even the samples with the highest purity had small amounts of secondary phase(s), some of which were identified as RELi1−xSn2 (RE = La−Nd, Sm; CeNi1−xSi2 structure type), Eu3Sn5 (Pd5Pu3 structure type), and EuSn (AlTh structure type).5,13

Figure 1. Schematic representation of the close relationship between the structures of RE2Li2Ge3, RE3Li4Ge4, and RE7Li8Ge10. The same analogy can be extended toward the Sn-based compounds, where the latter “7−8−10” structure can be considered as an intergrowth of the former two, as illustrated.

presented and discussed are their electronic structures, computed with the aid of the tight-bonding linear-muffin-tinorbital atomic-sphere-approximation method.14 These studies complement (and extend) the previous work by our group on similar germanide chemistry and unequivocally show the role of this intricate Li−Sn disorder on alleviating the electron deficiency and stabilizing such complex bonding arrangements.

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EXPERIMENTAL SECTION

Synthesis. All steps during the synthesis were performed in an argon-filled glovebox or under vacuum. The metals were sourced from Alfa with a stated purity of >99.9 wt %; they were used as received. The surface of the Li rod had to be cleaned carefully with a blade before each use to eliminate surface contaminants (likely because of inadvertent presence nitrogen gas in the glovebox). For each reaction, the metals in the desired stoichiometric ratio were weighed out in the glovebox and loaded into Nb tubes, the open

Table 1. Selected Crystal Data and Structure Refinement Parameters for the Compounds of the RE3Li4−xSn4+x (RE = La−Nd, Sm) Seriesa empirical formula fw, g/mol λ, Å T, K a, Å b, Å c, Å V, Å3 ρcalcd, g/cm3 μ(Mo Kα), cm−1 GOF on F2 R1 [I > 2σ(I)]b wR2 [I > 2σ(I)]b R1 (all data)b wR2 (all data)b

La3Li3.94Sn4.06(1) 926.51

Ce3Li3.69Sn4.31(1) 958.08

4.7533(14) 7.282(2) 15.698(5) 543.4(3) 5.66 206.3 1.161 0.0172 0.0416 0.0193 0.0427

4.7147(6) 7.2793(9) 15.537(2) 533.2(1) 5.97 223.8 1.217 0.0223 0.0553 0.0230 0.0559

Pr3Li3.93Sn4.07(1) 960.45 0.71073 200(2) 4.6915(14) 7.204(2) 15.474(5) 523.0(3) 5.93 231.7 1.139 0.0132 0.0307 0.0137 0.0308

Nd3Li3.75Sn4.25(1) 963.18

Sm3Li3.81Sn4.19(1) 974.80

4.668(2) 7.221(2) 15.392(5) 518.8(3) 6.17 247.0 1.024 0.0137 0.0298 0.0147 0.0299

4.6253(13) 7.159(2) 15.244(4) 504.8(2) 6.41 272.6 1.241 0.0270 0.0601 0.0275 0.0604

All five compounds are isostructural, crystallizing with the orthorhombic space group Immm (No. 71) and with Z = 2. bR1 = ∑||Fo| − |Fc||/∑|Fo|; wR2 = [∑[w(Fo2 − Fc2)2]/∑[w(Fo2)2]]1/2, and w = 1/[σ2Fo2 + (AP)2 + BP], where P = (Fo2 + 2Fc2)/3; A and B are weight coefficients. For additional information, see CCDC 1827698−1827703.

a

B

DOI: 10.1021/acs.inorgchem.8b00583 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Scanning Electron Microscopy (SEM). The composition of several Eu7Li8−xSn10+x (x ≈ 2.0) single crystals was examined on a JEOL JSM-6335F scanning electron microscope equipped with an energy-dispersive X-ray (EDX) detector. The Li content, naturally, could not be probed via EDX, but the semiquantitative analysis (even though hampered by the rough surface of the specimensan apparent artifact of the brief exposure to air) confirmed the presence of the heavy elements in the expected Eu/Sn ratio. While not direct proof, the measured Eu/Sn ratio of ca. 1.6−1.7, in conjunction with the structure refinements, helps to ascertain the model (refined composition Eu7Li∼6Sn∼12 vs the devoid of disorder Eu7Li8Sn10). Single-Crystal XRD. Single-crystal XRD data were collected on a Bruker APEX II diffractometer, equipped with monochromated Mo Kα radiation and a charge-coupled-device detector. Multiple crystals were picked from each batch and checked for quality by quick scans, before the best ones were chosen for full intensity data collection. For each chosen crystal, a routine consisting of four batch runs with a frame width of 0.4° in ω and θ and with a data acquisition rate of 8−12 s/frame was used to gather almost a full sphere of reflections in reciprocal space. The angular range in 2θ extended up to ca. 60°. The Bruker-supplied software15 was used to reduce and integrate the data and to do a global unit cell refinement. Absorption correction was performed using SADABS.16 The program XPREP17 was used to sort and merge the structure factors and to determine the space groups. The structures were solved via direct methods and refined by full matrix least-squares methods on F2, as implemented in the SHELXTL software package.18 The refined parameters were the atomic positions with anisotropic displacement parameters (except for the Li positions, which were refined isotropically), extinction coefficients, occupancy factors, and scale factors. Relevant details of the crystallographic work for RE3Li4−xSn4+x (RE = La−Nd, Sm) and Eu7Li8−xSn10+x are summarized in Tables 1 and 2, respectively. Structural information for Sr7Li8−xSn10+x, which as the formula suggests is isostructural with Eu7Li8−xSn10+x, is listed in the Supporting Information.

the full potential. Calculations were done on two idealized model structures, La3Li4Sn4 and Sr7Li6Sn12, using the atomic coordinates from the structure refinements for La 3 Li 3.94 Sn 4.06(1) and Sr 7Li5.76Sn12.24(2), respectively. WS sphere radii used for the calculations were as follows: La = 2.06−2.11 Å, Li = 1.45 Å, and Sn = 1.65−1.85 Å for La3Li4Sn4 and Sr = 2.22−2.28 Å, Li = 1.58−1.64 Å, and Sn = 1.61−1.65 Å for Sr7Li6Sn12. Local density approximation was used to treat exchange and correlation.20 Scalar relativistic approximation was used to account for all relativistic effects with the exception of spin−orbit coupling.21 Using the tetrahedron method,22 the k-space integrations were performed and the self-consistent charge density was computed using 171 k points for La3Li4Sn4 and 196 k points for Sr7Li6Sn12. Crystal orbital Hamilton population (COHP) curves were generated by the procedure implemented in the LMTO code.23

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RESULTS AND DISCUSSION General Notes. As mentioned already, the title compounds were targeted after a small Li−Ge occupational disorder was discovered in RE3Li4−xGe4+x.3 Our thought was that if the isostructural RE3Li4−xSn4+x can be made, they could potentially exhibit similar Li−Sn disorder, which would be much easier to model. For example, in our paper on RE3Li4−xGe4+x, we noted that the scattering from the site where the Li atom was assigned was consistent with “heavier” elements; in model structural refinements, when the occupancy factor for the Li site was freed, it consistently exceeded unity across the series, but the magnitude of the effect was not as convincing as it could have been. In the stannides in question, the substitution of Li with the much heavier Sn makes the variation of the calculated versus observed electron-density map so much clearer; the occupancy factor for the Li site when freed would exceed full by over 250−300%. As such, the model refinement with Li and Sn co-occupying the same site proceeded without any complications and did not require any constraints. Furthermore, electron density on the order of 10−12 e/Å3 can be considered to be indirect evidence that the site cannot be occupied by a light, nonmetallic element. Synthesis. The targeted synthesis of RE3Li4−xSn4+x was not an easy task. The conditions employed earlier for the germanides were not suitable for the stannides. Several different starting compositions and temperature profiles were used to optimize the yield and quality of the crystals. In all cases, small amounts of side products were present (a representative PXRD pattern is provided in the Supporting Information). Also, unlike the germanides, where thus far four families of compounds belonging to the homologous series [REGe2]n[RELi2Ge]m (RE = La−Nd, Sm) have been characterized, namely, RE2Li2Ge3,3 RE3Li4Ge4,3 RE7Li8Ge10,4 and RE11Li12Ge16,4 the stannide chemistry appears to be limited only to one family. All attempts to make other members were unsuccessful. The above is suggestive of a very different energy landscape in the RE− Li−Sn phase diagrams, compared to the respective RE−Li−Ge ones, despite the many similarities between the binary RE−Sn and RE−Ge systems, respectively.13,24,25 As discussed already for RE3Li4−xGe4+x,3 the “3−4−4” structure is realized for the early members of the 4f block. The RE3Li4−xSn4+x family was also found to span only the lanthanides from La to Sm. The stannide Eu7Li8−xSn10+x also exists, but with the “7−8−10” structure (N.B. Eu7Li8−xGe10+x is not known to date),4 and the rare-earth metal in it is divalent (electronic configuration [Xe]4f7). Notably, Eu7Li8−xSn10+x is only the second example, after LiMgEu2Sn3 (Ce2Li2Ge3 type),26 of a Eu-bearing compound adopting similar structure.

Table 2. Selected Crystal Data and Structure Refinement Parameters for Eu7Li8−xSn10+x empirical formula fw, g/mol λ, Å T, K space group, Z a, Å b, Å c, Å V, Å3 ρcalcd, g/cm3 μ(Mo Kα), cm−1 GOF on F2 R1 [I > 2σ(I)]a wR2 [I > 2σ(I)]a R1 (all data)a wR2 (all data)a

Eu7Li6.01Sn11.99(2) 2529.64 0.71073 200(2) Cmmm (No. 65), 2 7.5551(15) 36.575(8) 4.8178(10) 1331.3(5) 6.31 272.1 1.045 0.0259 0.0527 0.0392 0.0554

a R1 = ∑||Fo| − |Fc||/∑|Fo|; wR2 = [∑[w(Fo2 − Fc2)2]/∑[w(Fo2)2]]1/2, and w = 1/[σ2Fo2 + 9.44P], where P = (Fo2 + 2Fc2)/3.

Computational Details. Tight-binding linear muffin-tin orbital (TB-LMTO) calculations were performed using the software package LMTO47.19 At the core of this level of theory is the atomic-sphereapproximation (ASA) method,14 where the space is filled with overlapping atomic spheres known as Wigner−Seitz (WS) spheres. In each WS sphere, the symmetry of the potential is considered to be spherical, and overlap between the spheres is accounted for with a combined correction. An automatic procedure within the program determined the size of the WS atomic spheres under the requirement that the overlapping potential be the best possible approximation to C

DOI: 10.1021/acs.inorgchem.8b00583 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Crystal Structure of RE3Li4−xSn4+x. Neglecting the small disorder, an idealized RE3Li4Sn4 structure will belong to the orthorhombic Zr3Cu4Si4 structure type (Pearson symbol oI22).13 Relevant crystallographic information for the five synthesized compounds is summarized in Table 1; final positional and equivalent isotropic displacement parameters are listed in Table 3.

er for the other members because the size of the rare-earth metal decreases upon moving from La to Sm, as seen in Table 4). These bond lengths are close to the sum of the Pauling covalent radii of Li (1.225 Å) and Sn (1.421 Å),27 which is suggestive that the Li−Sn interactions exhibit considerable covalent character. The other prominent fragment of the polyanionic sublattice is the [Sn2] dimer. The Sn−Sn bond distances vary within a narrow interval across the series, from 2.828(1) to 2.848(1) Å, and judging from the Pauling covalent radius of Sn (1.421 Å),27 the Sn−Sn bonds should be regarded as single covalent bonds. Unlike the above-mentioned Li−Sn contacts, one can notice that the small variations in the Sn1−Sn1 distances (Table 4) do not follow the lanthanide contraction and the respective decrease in the unit cell parameters (Table 1). Instead, a correlation can be established with the amount of Li that has been replaced by Sn (Figure 3). For instance, the shortest Sn−Sn bond distance [dSn−Sn = 2.828(1) Å] occurs in La3Li3.94Sn4.06(1), while the longest Sn− Sn bond distance [dSn−Sn = 2.848(1) Å] is observed in Ce3Li3.69Sn4.31(1). This result, while quite surprising at first glance, is easy to account for once the electronic structure is understood and it is realized that the Sn−Sn interactions have an antibonding character at the Fermi level (formally [Sn2]6−, i.e., isoelectronic with the I2 molecule, vide infra). Consequently, because La3Li3.94Sn4.06(1) is almost 1/2 electron poorer per formula unit compared to Ce3Li3.69Sn4.31(1), the population of antibonding states in the former would be lower, thereby leading to strengthening of the Sn−Sn interactions and a shorter bond in the [Sn2] dimer. A detailed discussion on the chemical bonding can be found in the electronic structure section. There are two types of rare-earth metal sites: (i) RE1, which is octahedrally coordinated by six Sn atoms (Figure 2d); (ii) RE2, which is coordinated by six Sn atoms in a trigonalprismatic fashion but more appropriately can be viewed as enclosed in a pentagonal prism that is made of Li and Sn atoms (Figure 2e). The RE−RE distances (>4 Å) in this structure are much longer than those in the structures of the elements (ca. 3.6−3.7 Å),25 which suggests a very small contribution of the RE−RE interactions to the overall bonding. On the other hand, the RE−Sn distances appear to be indicative of appreciable covalent bonding. Taking La3Li3.94Sn4.06(1) as an example, one can see that the shortest La−Sn contact measures dLa−Sn = 3.2569(8) Å and almost perfectly matches the sum of the Pauling covalent radii of the La (1.825 Å) and Sn (1.421 Å) atoms.27 The trends in the RE−Sn distances follow the lanthanide contraction (Table 4). Crystal Structure of Eu7Li6.01Sn11.99(2). This phase is isotypic with the germanides RE7Li8Ge10 (RE = La−Nd, Sm),4 which crystallize with their own type [space group Cmmm (No. 65), Pearson symbol oC50].13 This is the first stannide known to form with this structure. There are 10 independent sites in the asymmetric unit (Table 5), and based on the refinements, the structure appears to be devoid of disorder on all sites but Li1, which shows very heavy mixing with Sn. In previous studies,3,4 we have described this structure in detail and have discussed the structural relationship among all members of the [REGe2]n[RELi2Ge]m homologous series (Figure 1). Therefore, the text only provides a succinct description, with the focus being on the extensive occupational disorder between Li and Sn atoms.

Table 3. Atomic Coordinates and Equivalent Displacement Parameters (Ueqa) for the Compounds of the RE3Li4−xSn4+x (RE = La−Nd, Sm) Series atom

site

x

La1 La2 Sn1 Sn2 Lib

2a 4j 4h 4i 8l

0 1 /2 0 0 0

Ce1 Ce2 Sn1 Sn2 Lib

2a 4j 4h 4i 8l

Pr1 Pr2 Sn1 Sn2 Lib

2a 4j 4h 4i 8l

Nd1 Nd2 Sn1 Sn2 Lib

2a 4j 4h 4i 8l

Sm1 Sm2 Sn1 Sn2 Lib

2a 4j 4h 4i 8l

0 /2 0 0 0

1

0 /2 0 0 0

1

0 /2 0 0 0

1

0 /2 0 0 0

1

y La3Li3.94Sn4.06(1) 0 0 0.1942(1) 0 0.312(1) Ce3Li3.69Sn4.31(1) 0 0 0.1956(1) 0 0.3127(5) Pr3Li3.93Sn4.07(1) 0 0 0.1963(1) 0 0.3116(7) Nd3Li3.75Sn4.25(1) 0 0 0.1967(1) 0 0.3122(4) Sm3Li3.81Sn4.19(1) 0 0 0.1979(1) 0 0.3111(8)

z

Ueq, Å2

0 0.3687(1) 1 /2 0.2139(1) 0.3294(5)

0.008(1) 0.009(1) 0.009(1) 0.010(1) 0.016(3)

0 0.3708(1) 1 /2 0.2142(1) 0.3297(3)

0.009(1) 0.010(1) 0.011(1) 0.014(1) 0.013(1)

0 0.3698(1) 1 /2 0.2140(1) 0.3293(3)

0.008(1) 0.009(1) 0.009(1) 0.010(1) 0.003(1)

0 0.3712(1) 1 /2 0.2143(1) 0.3289(2)

0.009(1) 0.011(1) 0.010(1) 0.013(1) 0.011(1)

0 0.3712(1) 1 /2 0.2144(1) 0.3283(8)

0.010(1) 0.012(1) 0.011(1) 0.014(1) 0.017(2)

a

Ueq is defined as one-third of the trace of the orthogonalized Uij tensor. bLi refers to the nominal Li position, where the refinements show a statistical mixing of Li and Sn atoms with ratios 0.984:0.016(2) for La 3 Li 3.94 Sn 4.06(1) , 0.922:0.078(2) for Ce 3 Li 3.69 Sn 4.31(1) , 0.983:0.017(2) for Pr 3 Li 3 . 9 3 Sn 4 . 0 7 ( 1 ) , 0.937:0.063(2) for Nd3Li3.75Sn4.25(1), and 0.0953:0.047(3) for Sm3Li3.81Sn4.19(1).

The structure is best viewed if cut into two types of slabs: (i) RESn2 (the [Sn2] dimers in trigonal-prismatic coordination of rare-earth atoms); (ii) RELi2Sn, featuring [LiSn4] tetrahedra connected to each other by shared edges, as schematically shown in Figure 2. Formally, the RESn2 slab is akin to the AlB2 structure type, and the RELi2Sn slab is of the MgAl2Cu structure type.13 To accentuate this analogy, the tetrahedra of Sn atoms, where the Li atoms are located, are emphasized, and “bonds” are drawn between with the Sn atoms at the corners and the Li atoms in the centers. Both Li and Sn atoms can be considered to be part of the polyanionic framework. Within this framework, the Li−Sn bond distances fall in the range of 2.812(8)−2.907(7) Å (in La3Li3.94Sn4.06(1), systematically shortD

DOI: 10.1021/acs.inorgchem.8b00583 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 2. (a) Crystal structure of the compounds of the RE3Li4−xSn4+x (RE = La−Nd, Sm) series. In the schematic representation of the orthorhombic structure, the viewing direction is approximately along [100]. The unit cell is outlined in black. The rare-earth atoms are drawn as green spheres; the Li and Sn atoms are shown as purple and orange spheres, respectively. (b) Combined polyhedral and ball-and-stick representation of the edge-sharing [LiSn4] tetrahedra. Close views of the local coordination environments of (c) [Sn(1)2] dimers and (d) RE1 and (e) RE2 atoms. For the corresponding bond distances, the reader is referred to Table 4.

Table 4. Important Interatomic Distances (Å) for the Compounds of the RE3Li4−xSn4+x (RE = La−Nd, Sm) Series RE atom pair

La

Ce

Pr

Nd

Sm

RE1−Sn1 (×4) RE1−Sn2 (×2) RE2−Sn1 (×4) RE2−Sn2 (×2) RE1−Li (×6) RE2−Li (×4) RE2−Li (×2) Sn1−Sn1 Li−Sn1 Li−Sn2 (×2) Li−Sn2

3.2569(8) 3.358(1) 3.4491(7) 3.4001(8) 3.833(6) 3.345(5) 3.398(8) 2.828(1) 2.812(8) 2.826(4) 2.907(7)

3.2353(5) 3.3290(8) 3.4080(5) 3.3869(6) 3.796(3) 3.339(3) 3.401(4) 2.848(1) 2.779(4) 2.808(2) 2.898(4)

3.2076(7) 3.312(1) 3.4006(7) 3.3632(8) 3.784(4) 3.306(4) 3.367(5) 2.829(1) 2.769(5) 2.792(3) 2.867(5)

3.2005(8) 3.300(1) 3.3757(7) 3.3576(9) 3.772(2) 3.310(2) 3.365(3) 2.841(1) 2.763(3) 2.780(2) 2.862(3)

3.1662(7) 3.268(1) 3.3479(7) 3.3269(8) 3.747(4) 3.277(4) 3.328(5) 2.834(1) 2.741(5) 2.757(3) 2.823(5)

Figure 3. (a) Variation of the unit cell parameters and unit cell volume for the five refined RE3Li4−xSn4+x (RE = La−Nd, Sm) structures, plotted as a function of the size of the rare-earth metal atoms (Pauling scale for elemental radii).26 (b) Variation of the Sn−Sn bond lengths, Sn/Li ratios, and VECs per formula unit for the RE3Li4−xSn4+x (RE = La−Nd, Sm) compounds.

A structural representation of Eu7Li8−xSn10+x (x ≈ 2) is shown in Figure 4, and relevant interatomic distances are

tabulated in Table 6. The coordination environments for each atom are very similar to those in RE3Li4−xSn4+x (RE = La−Nd, E

DOI: 10.1021/acs.inorgchem.8b00583 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 5. Atomic Coordinates and Equivalent Displacement Parameters (Ueqb) for Eu7Li6.01Sn11.99(2)a atom Eu1 Eu2 Eu3 Eu4 Sn1 Sn2 Sn3 Sn4 Li1/Snc Li2

site 4j 4j 4i 2a 8p 4j 4i 4h 8q 8p

x 0 0 0 0 0.1871(1) 0 0 0.3099(1) 0.2090(2) 0.313(2)

z

Ueq, Å2

atom pair

distance (Å)

atom pair

distance (Å)

/2 1 /2 0 0 0 1 /2 0 1 /2 1 /2 0

0.014(1) 0.011(1) 0.020(1) 0.011(1) 0.011(1) 0.021(1) 0.017(1) 0.011(1) 0.013(2) 0.005(4)

Sn1−Sn1 Sn1−Sn1 Sn4−Sn4 Li1−Sn2 Li1−Sn3 (×2) Li1−Sn4 Li2−Sn1 Li2−Sn2 (×2) Li2−Sn3

2.813(1) 2.827(1) 2.873(2) 2.833(1) 2.9535(9) 2.886(1) 2.81(1) 2.857(6) 2.94(1)

Eu1−Sn1 (×4) Eu1−Sn3 (×2) Eu1−Li1 (×2) Eu1−Li2 (×4) Eu2−Sn1 (×4) Eu2−Sn1 (×4) Eu2−Sn2 Eu3−Sn2 (×2) Eu3−Sn4 (×4) Eu3−Li1 (×4) Eu3−Li2 (×2) Eu4−Sn3 (×2) Eu4−Sn4 (×4)

3.3920(7) 3.4412(9) 3.489(1) 3.452(8) 3.3864(6) 3.6630(8) 3.527(1) 3.5087(9) 3.4561(7) 3.350(1) 3.46(1) 3.438(1) 3.3592(8)

y 0.1612(1) 0.2786(1) 0.4448(1) 0 0.2138(1) 0.3750(1) 0.0940(1) 0 0.0761(2) 0.1415(3)

Table 6. Important Interatomic Distances (Å) for Eu7Li6.01Sn11.99(2)

1

a

Data for the isostructural Sr analogue are provided in the Supporting Information. bUeq is defined as one-third of the trace of the orthogonalized Uij tensor. cLi1/Sn refers to the Li1 position, where the refinements show statistical mixing of Li and Sn atoms with a ratio of 0.506:0.494(3).

the trans bond, 2.827(1) and 2.813(1) Å, respectively. Both are slightly shorter than the Sn−Sn bond of the isolated [Sn2] unit [dSn−Sn = 2.873(2) Å]. These values match well with those of the zigzag 1∞[Sn2] chains of previously reported compounds such as RELi1−xSn2 (CeNi1−xSi2 structure type),5 LiMg(Eu/ Sr)2Sn3 (Ce2Li2Ge3 structure type),26 and LiRh3Sn5 (own structure type),28 as well as compounds containing [Sn2] dimers, such as Ca5Sn3 (Cr5B3 structure type)29 and La11Sn10 (Ho11Ge10 structure type),30 to name a few. Next, we turn our attention to the occupational disorder between Li and Sn atoms in the structure of Eu7Li8−xSn10+x (x ≈ 2). The magnitude of the admixture in this case is large, Li1/ Sn ratio is ca. 50%, and its effect cannot be neglected. The average Li−Sn distances fall in the range from 2.81 to 2.96 Å, slightly longer than the sum of the Pauling covalent radii of Li (1.225 Å) and Sn (1.421 Å).27 These values are longer than the

Sm). The Li and Sn atoms, without consideration of the disorder, can be seen as forming [LiSn4] tetrahedra (Figure 4b) that connect to each other via shared edges to become corrugated layers extending along the ac plane. These layers connect to each other through Sn−Sn bonds to build the polyanionic framework, with Sr filling the open space. Unlike RE3Li4−xSn4+x (RE = La−Nd, Sm), where the only homoatomic interaction is manifested in the form of [Sn2] dumbbells (Figure 1), there are two types of [Snx] subunits in the Eu7Li8−xSn10+x structure. The first one is the very same [Sn2] dimer discussed previously, and the second one is a cis−trans 1 ∞[Sn2] chain (Figure 4). Such an alternating pattern of the Sn− Sn bonds has a noteworthy implication on the Sn−Sn distances: the length of the cis bond is greater than that of

Figure 4. (a) Schematic representation of the orthorhombic structure of Eu7Li8−xSn10+x (x ≈ 2), viewed approximately along the [001] direction. The Eu atoms are drawn as green spheres, and the Sn atoms are shown as orange spheres. (b) Combined polyhedral and ball-and-stick representation of the edge-shared [LiSn4] tetrahedra; the Li1 site is a statistical mixture of Li and Sn and is differentiated from the Li2 site by the different color. Close view of the local coordination environments of (c) the 1∞[Sn2] cis−trans chain and (d) [Sn2] dimers. F

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Figure 5. Side-by-side comparison of the [Li8Sn10] polyanionic framework in imaginary Eu7Li8Sn10 with the [Li6Sn12] polyanionic framework in a model of the Eu7Li8−xSn10+x (x ≈ 2) structure. The observed Li−Sn disorder in the latter structure is “resolved” in the model, and the resultant fully occupied Li and Sn sites are differentiated (Sn5 is shown in black).

scenario where an electron-richer element replaces Li (it contributes only one valence electron) seems logical. Because there is no experimental evidence for another inadvertent element, on the basis of coordination/distances as discussed earlier, Sn is more likely than Eu to substitute Li and bring the overall formula closer to charge balance. However, the Sn atoms in the above-presented structure rationalization are the electron acceptor and, thereby, are assigned negative formal charges; how can such a disorder be reconciled with the discussed scheme for chemical bonding? To approach this question, we had to build an imaginary “superstructure” of Eu7Li6Sn12, where the 50:50 mixture of Li and Sn on the Li1 site (Table 5) is modeled as two separate sites, one occupied by Sn and one by Li.36 This hypothetical structure is depicted in Figure 5, and the two sites are colored in black (Sn) and red (Li). Sn−Sn bonds are delineated to emphasize the presence of a lot more covalent Sn−Sn interactions in Eu7Li6Sn12 versus the “parent” Eu7Li8Sn10. As a result, the formal charge for every Sn atom except Sn1 will have to be changed. Specifically, as seen in Figure 5, the Sn2A, Sn3, and Sn4 atoms will be connected to two Sn atoms, the Sn2B atoms remain isolated (coordinated to Li only), and the newly assigned Sn5 atoms will be bonded to four Sn atoms. The corresponding electron-counting scheme for Eu7Li6Sn12 will now become (Eu2+)7(Li+)6([2b-Sn1]2−)2([2b-Sn2A]2−)([Sn2B]4−)([2b-Sn3]2−)4([2b-Sn4]2−)2([4b-Sn5]0)2(h+)2. This model shows that the introduction of more covalent Sn−Sn bonds within the structure decreases the number of electron holes, which will lead to an overall increase in the electronic stability. The electron-counting method employed above can be readily applied to RE3Li4Sn4 too, giving the following breakdown: (RE3+)3(Li+)4(Sn4−)2([1b-Sn]3−)2(h+). Partial substitution of Li with Sn will alleviate the charge imbalance and will lower the amount of h+. From simple considerations, one can see that the ideal number of valence electrons per formula unit for this type of bonding will be 30, and it will be realized for RE3Li4−xSn4+x (x = 1/3). This corresponds to 11:1 mixing of Li and Sn [specifically, the single Li site in this structure (Table 2) will have to be cooccupied by Li and Sn atoms in the ratio 0.9175:0.0825]. Admixing of Li and Sn to such an extent is unlikely to contribute to the significant deviations from the structure description presented earlier. This conjecture is

Li−Sn distances in RE3Li4−xSn4+x (RE = La−Nd, Sm), which, as shown in Table 4, range from 2.74 to 2.91 Å. Distances of ca. 2.8−2.9 Å are also “normal” for covalent Sn−Sn bonds: the elemental α-Sn allotrope with dSn−Sn = 2.810 Å is a good benchmark.25 Thus, from the point of view of crystal chemistry (bond distances and coordination environment), Sn substitution for Li in this position should not be uncommon. In fact, there are many other reports on the Li/Sn admixture within similar intermetallic compounds: relevant examples include Li9−xEuSn6+x,26 Li9−xCaSn6+x,26 RE5Li2−xSn7+x (RE = Ce, Pr, Nd, Sm),6 LixT3Sn7−x (T = Rh, Ir),31 Li3−xPt2Sn3+x,32 and Li2−xPd2Sn5+x,33 etc., which have shown that the Li atoms can be replaced by Sn atoms or vice versa. This report, however, is a rare case of disorder with such a large extent. The reason for this is rooted in the electronic structure, and before we turn our attention to it, we will briefly recap the electron count. Electron Count and Valence Rules. The Zintl−Klemm concept11,12 is a good starting point to try to partition the available valence electrons and to understand the electronic structure at a basic level. We will start this gedanken experiment with Eu7Li8−xSn10+x (x ≈ 2) and will first consider the structure of the archetype Ce7Li8Ge10, which does not exhibit any admixture between Li and Ge.4 In Ce7Li8Ge10, there are four isolated Ge (i.e., Ge4−) atoms per formula unit, two dimerized Ge atoms per formula unit (1b-Ge3−), and four polymerized Ge atoms (2b-Ge2−) per formula unit (the notations 1b and 2b denote atoms with 1 and 2 covalent bonds, respectively). Therefore, Ce 7 Li 8 Ge 10 = (Ce 3+ ) 7 (Li + ) 8 (Ge 4− ) 4 ([1bGe]3−)2([2b-Ge]2−)4(h+). h+ represents an electron hole, i.e., charge balance following the octet rule cannot be achieved for this bonding arrangement. It has been suggested that the reason for this is the nonclassical bonding in the cis−trans chains [akin to the bonding in (CH)x and (SN)x chains].34,35 Considering now Eu7Li8Sn10, one will immediately recognize that the aliovalent substitution of Ce3+ with Eu2+ will lead to a severe electron imbalance, namely, (Eu 2+ ) 7 (Li + ) 8 (Sn 4− ) 4 ([1bSn]3−)2([2b-Sn]2−)4(h+)8. It is obvious that a compound with such a structure and formula will not be stable. Taking the refined composition Eu7Li8−xSn10+x (x ≈ 2) or Eu7Li6Sn12, one can reason that the latter has 68 valence electrons per formula unit, very close to the 69 valence electrons per formula unit in Ce7Li8Ge10, bringing the number of valence electrons closer to the optimal 70. Given that, the G

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Inorganic Chemistry

while a local minimum (i.e., a pseudogap) is observed at ca. 0.5 eV above the Fermi level (dotted line). The corresponding quantity of valence electrons per formula unit (f.u.) from integration of the DOS to the Fermi level, and the local minima are 29 and 30.4 e−/f.u., respectively. If it is assumed that the rigid-band approximation is valid,37 the DOS curve suggests that increasing the valence electron concentration (VEC) for La3Li4Sn4 will be energetically favorable. This can be reconciled with the refinements from single-crystal data for all five RE3Li4−xSn4+x structures (Table1). Such a desire of polar intermetallic phases to achieve greater electronic stability is not uncommon, and similar observations have been made for a number of other compounds, for example, A2(Li1−xInx)2Ge3 (A = Sr, Ba, Eu),1 RE7Zn21Tt2 (RE = La−Nd; Tt = Ge, Sn and Pb),38 and Li1.42Pd2Sn5.58(5),33 among others. Well below the Fermi level, in the low-energy region between −9 and −6 eV, the contributions to the DOS are mostly from the Sn 5s orbitals. Significant band overlap between the Li 2s and 2p, La 5d, and Sn 5p orbitals occurs from −3.5 eV to EF, which is indicative of covalence of the bonding between these elements. In Figure 6b, analysis of the −COHP curves indicates that, at the Fermi level, the La−Sn interactions are in the bonding state, while the Sn−Sn interactions are in the antibonding state. The Li−Sn interactions are nearly optimized. Again, assuming that the rigid-band approximation is valid,37 the Fermi level can be moved up/down, according to different VECs. This means that an electron-richer structure will have the Fermi level at slightly higher energy. In such a case, one will readily notice that the La−Sn interactions would benefit from an increase in the VEC because the La−Sn bonding state requires ca. 1 e/f.u. more to be filled. We do not have refined La3Li4−xSn4+x structures with different “x” but can speculate that the greater the number of valence electrons (higher Sn content), the shorter the respective La−Sn bonds would be. In addition, variations in the electron count should also affect the Sn−Sn bonding. As mentioned earlier, the Sn−Sn bond distances across this series do not follow the lanthanide contraction (Figure 4). The experimental observation that lower VEC (lower Sn content) correlates with shorter observed Sn−Sn bond distances can be explained by the subtle change in the Sn−Sn antibonding states (Figure 6b, indicated by the arrow); using the analogy to simple diatomic molecules, the higher the occupation of the antibonding orbital, the weaker the bonding. For the ordered Sr7Li6Sn12 model, the total DOS and pDOS (Figure 7) have features similar to those of La3Li4Sn4. The main contributions from EF to ca. −3.5 eV are from the Li 2s and 2p, Sr 5d, and Sn 5p orbitals; between −9 and −6 eV, the contributions are from mostly the Sn 5s orbital (lone pair). The corresponding numbers of valence electrons are 68 e/f.u. for Sr7Li6Sn12 (solid line) and 62 e/f.u. for Sr7Li8Sn10 (dashed line), respectively. The former is near a local minimum, while the latter is situated at a peak of high DOS. Similar to the La3Li4Sn4 case, the placement of the two Fermi levels indicates that Sr7Li8−xSn10+x (x ≈ 0, i.e., Sr7Li8Sn10) is far less electronically stable than Sr7Li6Sn12. This notion is in excellent agreement with the large magnitude of the Li/Sn admixture at the Li1 site observed in this compound. The presence of an even deeper pseudogap of ca. 0.5 eV above the Fermi level is suggestive that Sr7Li8−xSn10+x (x > 2) might be more energetically favorable than Sr7Li6Sn12 because increasing the amount of valence electrons in the system beyond 68 e/f.u. will help to further stabilize the structure.

indirectly supported by the compound Eu3Li4Sb4, synthesized and structurally characterized by single-crystal XRD not too long ago.9 Eu3Li4Sb4 adopts the same structure type (Zr3Cu4Si4 structure type) as RE3Li4−xSn4+x but is completely devoid of disorder. Following the Zintl−Klemm concept,11,12 the Eu3Li4Sb4 formula can be rewritten as (Eu2+)3(Li+)4(Sb3−)2([1b-Sb]2−)2, and it is a valence-precise compound. Electronic Structure Calculations and Chemical Bonding. The electronic structures of the line compounds La3Li4Sn4 and Sr7Li6Sn12, considered to be suitable models for the RE3Li4−xSn4+x (x < 0.3) and Eu7Li8−xSn10+x (x ≈ 2) structures, were calculated based on the TB-LMTO-ASA method.14 The calculated total density of states (DOS) and partial density of states (pDOS) curves for La3Li4Sn4 are plotted in Figure 6a;

Figure 6. (a) Calculated total DOS for La3Li4Sn4. The Fermi level is set at 0 eV as an energy reference. (b) COHP curves for the La−Sn, Li−Sn, and Sn−Sn interactions. In the −COHP curves, the positive and negative signs represent bonding and antibonding states, respectively.

the individual contributions for the corresponding elements are shown in the Supporting Information. Also included are the COHP curves for the La−Sn, Li−Sn, and Sn−Sn interactions, and they are presented in Figure 6b. The analogous information for Sr7Li6Sn12 is presented in Figure 7. As seen in Figure 6a, the electronic structure of La3Li4Sn4 is very similar to that of the previously reported La3Li4Ge4.3 The Fermi level (EF) is located in a region of relatively high DOS,

Figure 7. (a) Calculated total DOS for the model Sr7Li6Sn12 structure. The Fermi level is set at 0 eV as an energy reference. (b) COHP curves. The following interactions are considered: Sr−Sn, Li−Sn, and three types of Sn−Sn interactionsd for dimer, c for chain, and td for tetrahedron. In the −COHP curves, the positive and negative signs represent bonding and antibonding states, respectively. H

DOI: 10.1021/acs.inorgchem.8b00583 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Indeed, moving the EF value slightly up will cause more Sr−Sn bonding states to be included. From the COHP analysis presented in Figure 7, it is evident that the dimer (d), chain (c), and tetrahedral (td) conformations of the Sn−Sn interactions are all nearly optimized at the current Fermi level and will remain such if there were up to ca. 70 e/f.u. In addition, we also notice that the integrated COHP of Sn−Sn (td) is substantially stronger than that of Li1−Sn (td) (Table S4). That is to say, the bond Sn−Sn strength is greater, and the substitution of Li atoms with Sn will also enhance the overall bond strengths within the system. The detailed investigations of the Sr−Li−Sn systems are ongoing, but the preliminary structural data gathered for Sr7Li5.76Sn12.24(2) (Supporting Information) seem to support this conjecture. Whether the difference between Eu7Li6.01Sn11.99(2) (68 e/f.u.) and Sr7Li5.76Sn12.24(2) (68.8 e/f.u) is an artifact of the refinements for the Sr structure from subpar data or could be an indication of EuII/EuIII valence fluctuation is yet to be confirmed.

charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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*E-mail: [email protected] (S.B.). Phone: (302) 831-8720. Fax: (302) 831-6335. ORCID

Svilen Bobev: 0000-0002-0780-4787 Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

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The authors declare no competing financial interest.

CONCLUSIONS With this study, we have successfully synthesized and structurally characterized the new ternary stannides RE3Li4−xSn4+x (RE = La−Nd, Sm) and Eu7Li8−xSn10+x. Their crystal structures are closely related, and both can be considered to be members of the [RESn 2 ]n [RELi 2Sn]m homologous series, i.e., linear intergrowths of the imaginary compounds RESn2 and RELi2Sn. On the basis of the refinements of the single-crystal data, the Li sites in all RE3Li4−xSn4+x structures show significant occupational disorder with Sn atoms, which is especially true in Eu7Li8−xSn10+x (x ≈ 2). These experimental results are supported by TB-LMTOASA calculations, confirming that the 29 valence electrons per formula for RE3Li4Sn4 and the 62 valence electrons per formula for Eu7Li8Sn10 are insufficient for bonding, mirroring trends established previously for the isotypic germanides. Our next step in this line of research will be focused on the possible stannide analogues of RE11Li12Ge16. In the latter, single-crystal X-ray data indicate a small amount of Li/Ge mixing on one of the Li sites; however, for the lower RE7Li8Ge10 homologues, the experiments have shown no obvious signs of Li−Ge disorder. The stannide analogues may yield the soughtafter clues. Besides that, the results from the additional exploratory work in the RE−Li−Sn systems could provide new information about the special role Li plays in the chemistry of intermetallic systems in general and, specifically, in Li-based materials for electrochemical energy storage.10,39

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AUTHOR INFORMATION

Corresponding Author

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ACKNOWLEDGMENTS

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REFERENCES

This work was supported by the National Science Foundation under Grants DMR-0743916 (CAREER) and DMR-1709813.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b00583. Preliminary structural data for Sr7Li5.76Sn12.24(2), integrated COHP values, a representative powder XRD pattern, the group−subgroup relationship within the Bärnighausen formalism for the symmetry reduction (k2, from space group Cmmm to Pbam) used to build the imaginary ordered Sr7Li6Sn12 model from Sr7Li8Sn10, and pDOS curves (PDF) Accession Codes

CCDC 1827698−1827703 contain the supplementary crystallographic data for this paper. These data can be obtained free of I

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electron per chain, the formal charge per Ge or Sn atom will be 1.5− and the chain will be isoelectronic (and isosteric) with the polythiazyl (SN)x chains with three π electrons per S2N2 repeating unit.35 (35) Cohen, M. J.; Garito, A. G.; Heeger, A. J.; MacDiarmid, A. G.; Mikulski, C. M.; Saran, M. S.; Kleppinger, J. Solid state polymerization of S2N2 to (SN)x. J. Am. Chem. Soc. 1976, 98, 3844−3848. (36) To fully model this imaginary “Sr7Li6Sn12”, we first considered the ordered Sr7Li8Sn10 (i.e., assuming no Li1−Sn disorder on the Li site) and lowered the space group from Cmmm to Pbam. In the lower symmetry group, the original Li1 site is split into two independent sites; one of which is then assigned to Sn (fully occupied), and the resultant structure has the formula Sr7Li6Sn12. The group−subgroup relationship within the Bärnighausen formalism for this transformation is shown in Figure S4. (37) Mizutani, U. Introduction to the Electron Theory of Metals; Cambridge University Press: Cambridge, U.K., 2001. (38) Suen, N.-T.; Bobev, S. Synthesis and structural characterization of RE7Zn21Tt2 (RE = La−Nd; Tt = Ge, Sn, and Pb): New structure type among the polar intermetallic phases. Inorg. Chem. 2013, 52, 12731−12740. (39) Park, C.-M.; Kim, J.-H.; Kim, H.; Sohn, H.-J. Li-alloy based anode materials for Li secondary batteries. Chem. Soc. Rev. 2010, 39, 3115−3141.

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DOI: 10.1021/acs.inorgchem.8b00583 Inorg. Chem. XXXX, XXX, XXX−XXX