Revision of the Li13Si4 structure

Besides Li17Si4, Li16.42Si4, and Li15Si4, another lithium-rich representative in the Li–Si system is the phase Li13Si4 (tridecalithium tetrasilicide), the structure of which has been determined previously [Frank et al. (1975 ▶). Z. Naturforsch. Teil B, 30, 10–13]. A careful analysis of X-ray diffraction patterns of Li13Si4 revealed discrepancies between experimentally observed and calculated Bragg positions. Therefore, we redetermined the structure of Li13Si4 on the basis of single-crystal X-ray diffraction data. Compared to the previous structure report, decisive differences are (i) the introduction of a split position for one Li site [occupancy ratio 0.838 (7):0.162 (7)], (ii) the anisotropic refinement of atomic displacement parameters for all atoms, and (iii) a high accuracy of atom positions and unit-cell parameters. The asymmetric unit of Li13Si4 contains two Si and seven Li atoms. Except for one Li atom situated on a site with symmetry 2/m, all other atoms are on mirror planes. The structure consists of isolated Si atoms as well as Si–Si dumbbells surrounded by Li atoms. Each Si atom is either 12- or 13-coordinated. The isolated Si atoms are situated in the ab plane at z = 0 and are strictly separated from the Si–Si dumbbells at z = 0.5.

Besides Li 17 Si 4 , Li 16.42 Si 4 , and Li 15 Si 4 , another lithium-rich representative in the Li-Si system is the phase Li 13 Si 4 (tridecalithium tetrasilicide), the structure of which has been determined previously [Frank et al. (1975). Z. Naturforsch. Teil B,30,[10][11][12][13]. A careful analysis of X-ray diffraction patterns of Li 13 Si 4 revealed discrepancies between experimentally observed and calculated Bragg positions. Therefore, we redetermined the structure of Li 13 Si 4 on the basis of singlecrystal X-ray diffraction data. Compared to the previous structure report, decisive differences are (i) the introduction of a split position for one Li site [occupancy ratio 0.838 (7):0.162 (7)], (ii) the anisotropic refinement of atomic displacement parameters for all atoms, and (iii) a high accuracy of atom positions and unit-cell parameters. The asymmetric unit of Li 13 Si 4 contains two Si and seven Li atoms. Except for one Li atom situated on a site with symmetry 2/m, all other atoms are on mirror planes. The structure consists of isolated Si atoms as well as Si-Si dumbbells surrounded by Li atoms. Each Si atom is either 12-or 13-coordinated. The isolated Si atoms are situated in the ab plane at z = 0 and are strictly separated from the Si-Si dumbbells at z = 0.5.

Related literature
For details of the structural description of Li 13 Si 4 , see: Frank et al. (1975). For structural data for Li 13 Si 4 based on computational methods, see: Chevrier et al.  Baran et al. (2013). For further thermodynamic investigations on the Li-Si system, see: Thomas et al. (2013); Wang et al. (2013). The behavior of silicon as anode material upon lithiation/delithiation is described by Limthongkul et al. (2003) and Obrovac & Christensen (2004). For in-situ/ex-situ solid state NMR investigations of structural changes in silicon electrodes for lithium-ion batteries, see: Key et al. (2009Key et al. ( , 2011 This work has been funded by the Fonds der Chemischen Industrie and the SolTech (Solar Technologies go Hybrid) program of the State of Bavaria.

Comment
In the last decade, the demand for high capacity lithium-ion batteries (LIBs) particularly fueled the research on the Li-Si phase system since as anode material, Si theoretically offers a specific capacity of 3579 mA h g -1 based on the formation of the metastable phase Li 15 Si 4 (Obrovac & Christensen, 2004). It is well known that Li 15 Si 4 is the only Li-Si phase that appears in crystalline form during charging and discharging processes in silicon based LIBs at room temperature (Limthongkul et al., 2003;Obrovac & Christensen, 2004). However, in order to understand the lithiation/delithiation mechanism, X-ray diffraction methods only provide sparse information and therefore other techniques such as in-situ / The latter is assigned a high temperature phase existing in a temperature range of 743-891 K, the former decomposes peritectically at 754-759 K. Li 16.42 Si 4 is compositionally embraced by the lithium-richer phase Li 17 Si 4 and the lithiumpoorer phase Li 13 Si 4 . Since the determination of the Li-Si phase diagram in the aforementioned section is carried out by thermal investigations on various samples with different Li concentrations, the structures of the relevant phases have to be ascertained for an unambiguous assignment of phases in X-ray powder diffraction patterns of those samples. However, the calculated X-ray diffraction pattern of Li 13 Si 4 based on structural data published by Frank et al. (1975) decisively differs from the experimentally observed pattern of a Li 13 Si 4 sample ( Fig. 1). More recent data based on theoretical calculations were reported by Chevrier et al. (2010). Yet, the accordingly calculated pattern is slightly but still distinctly different ( Fig. 1). Therefore, we redetermined the structure of Li 13 Si 4 based on single crystal X-ray diffraction data. As can be seen in Fig.   1, the resulting calculated pattern is in very good agreement with the experimental one. Main differences to the previous single-crystal X-ray structure determination by Frank et al. (1975) (7)).
Regarding the structure of Li 13 Si 4 we briefly elaborate on the main structure motifs since this has already been described in detail by Frank et al. (1975) to 3.2283 (7) Å and next nearest neighbor distances are clearly separated, starting off from 4.1899 (2) Å. The shortest Li -Li distance is 2.429 (7) Å and comparable to other Li-Si phases (Zeilinger & Benson et al., 2013). The Si-Si distance within the Si-Si dumbbells is 2.3852 (2) Å, further Si atoms are separated by distances larger than 4.4661 (2) Å. Whereas Si1 is coordinated by 12 Li and one Si atom, Si2 is exclusively surrounded by 12 Li atoms. In addition, dumbbells and isolated Si atoms are strictly separated from each other in a layer like fashion as they are located in different ab-planes (Figs. 2 b and c).

Experimental
In our previous work we reported on thermal investigations by differential scanning calorimetry (DSC) means which were targeting the determination of the lithium-rich section of the Li-Si phase diagram (Zeilinger & Kurylyshyn et al. 2013). Various samples with different Li-Si compositions (Li 17 Si 4 , "Li 16.5 Si 4 ", "Li 16 Si 4 " and "Li 14 Si 4 ") were synthesized.
Crystals of Li 13 Si 4 could be obtained from a sample with a nominal composition "Li 14 Si 4 ". For the synthesis of "Li 14 Si 4 " we refer to Zeilinger & Kurylyshyn et al. (2013). Li 13 Si 4 crystals were handled inside an Ar-filled glove box, selected under a microscope and sealed inside 0.3 mm glass capillaries for X-ray diffraction experiments.

Refinement
For better comparison between the first structure refinement and the current redetermination, atomic coordinates and atom labels were taken from Frank et al. (1975). During the structure refinement procedure the positions of two Si and seven Li atoms were confirmed. If refined freely, the site occupation factors of all atoms converged to values very close to full occupancy for the respective sites and were therefore constrained for full occupancy. Extinction was refined to non-significant values and thus excluded from the refinement. Furthermore, an anisotropic refinement of atomic displacement parameters was possible for all atoms. This model resulted in R-values of R 1 = 0.020 and wR 2 = 0.059 for all data and residual electron densities of +1.223 e Å -3 and -0.740 e Å -3 . However, the atomic displacement parameters for Li6 on Wyckoff position 4h (0.0895 (2), 0.25508 (9), 1/2) indicated a large prolongation in the x-direction. Additionally, significant residual electron density (+1.22 e Å -3 ) is located closely to Li6. To account for that, we introduced a split position for Li6. This resulted in markedly better R-values of R 1 = 0.016 and wR 2 = 0.044 for all data as well as acceptable residual electron densities of +0.68 e Å -3 and -0.40 e Å -3 . The refined fractions are 0.838 (7) for Li6A and 0.162 (7) for Li6B. An example for a similar introduction of an atom split in lithium-rich Li-Si phases is given by Zeilinger & Kurylyshyn et al. (2013).    Refinement. Refinement of F 2 against all reflections. The weighted R-factor wR and goodness of fit S are based on F 2 , conventional R-factors R are based on F, with F set to zero for negative F 2 . The threshold expression of F 2 > σ(F 2 ) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F 2 are statistically about twice as large as those based on F, and R-factors based on all data will be even larger.