Crystal structure of spinel-type Li0.64Fe2.15Ge0.21O4

The synthetic spinel Li0.64Fe2.15Ge0.21O4 shows a partially inverse cationic arrangement with Ge4+ on the tetrahedral sites and Li+ on the octahdral sites. Iron is in the trivalent state and is distributed over both type of sites.


Chemical context
The minerals of the spinel group are widely occurring compounds in the geosphere and are important not only in geoscience but also in many other disciplines. In recent years, in particular, Li-containing spinels like LiMn 2 O 4 or Li 0.5 Fe 2.5 O 4 have attracted much interest in battery technology as possible candidates for cathode materials in lithium ion secondary batteries (Liu et al., 2014;Patil et al., 2016;Thackeray et al., 1983). The ideal spinel structure consists of a closed packing of anions X, with one-eighth of the tetrahedral interstices and one-half of the octahedral interstices occupied by the cations. The vast majority of spinels crystallize in the space group Fd3m. Here the cations in tetrahedral coordination occupy special position 8a (point symmetry 43m, at 1 8 , 1 8 , 1 8 ), while the octahedrally coordinated cations reside on special position 16d (point symmetry 3m at 1 2 , 1 2 , 1 2 ). The anions are at equipoint position 32e, which requires one positional parameter, often denoted as the u parameter. For u = 0.25, an ideal cubic closed packing of anions is realized and the octahedral bond length is 1.155 times larger than the tetrahedral one. Following Hill et al. (1979), variations in u reflect the adjustment of the structure to accommodate cations of different size in octahedral and tetrahedral positions. Increasing the value of u above 0.25 moves the anions away along [111] from the nearest tetrahedral cation, thereby increasing the size of the tetrahedron at the extent of the size of the octahedron. The majority of the spinels can be described with the general formula AB 2 O 4 , with the A and B cations having the formal charges A = 2 and B = 3 (2,3 spinels) or A = 4 and B = 2 (4,2 spinels). The perfect normal spinel is one in which the single A cation occupies the tetrahedral site and the two B cations reside at the two equivalent octahedral positions. Introducing parentheses, i.e. ( . . . ) and brackets, i.e. [ . . . ], for tetrahedral and octahedral coordination, respectively, one may write the normal spinels in the form (A) [B 2 ]O 4 . In contrast, the complete inverse spinel has a cationic distribution of (B)[AB]O 4 (O'Neill & Navrotsky, 1983). More detailed reviews on the spinel structure and crystal chemistry can be ISSN 2056-9890 found, for example, in Biagioni & Pasero (2014), Harrison & Putnis (1998), Hill et al. (1979) and O'Neill & Navrotsky (1983. Germanium-containing spinels are considered to belong to the normal spinels, with a full ordering of Ge 4+ onto the tetrahedral A site, while metal cations M order onto the octahedral B sites. This was demonstrated by, among others, Von Dreele et al. (1977) for GeMg 2 O 4 and Welch et al. (2001) for the mineral brunogeierite (GeFe 2 O 4 ). For LiMn 2 O 4 and LiNi 0.5 Mn 1.5 O 4 , which represent excellent cathode materials, it was found that Li + orders onto the tetrahedral site (Berg et al., 1998;Liu et al., 2014). Also for LiCrGeO 4 , Touboul & Bouré e (1993) reported an almost exclusive ordering of Li + for the tetrahedral site, while Cr 3+ and Ge 4+ occupy the octahedral sites. Different to this is the spinel Li 0.5 Fe 2.5 O 4 . This compound is an inverse spinel in which Fe 3+ is ordered onto the tetrahedral site, while Li + and the remaining Fe 3+ are distributed over the octahedral site (Hankare et al., 2009;Patil et al., 2016;Tomas et al., 1983). This cationic distribution is thus similar to that in the inverse spinel magnetite, FeFe 2 O 4 (Fleet, 1981).
During the synthesis of Li-Fe-Ge pyroxenes (Redhammer et al., 2009(Redhammer et al., , 2010, black octahedral-shaped single crystals were frequently obtained, which turned out to be a spinel-type compound with significant Li + and small Ge 4+ concentrations. We present here the structure refinement and 57 Fe Mö ssbauer spectroscopic characterization of these crystals.

Structural commentary
The structure of the title compound is shown in Fig. 1 . This formula is balanced in charge and agrees very well with the chemical composition determined from electron microprobe analysis. Generally, the title compound is similar to the Li 0.5 Fe 2.5 O 4 spinel-type materials. The shift of Li + to the octahedral site, for example, in comparison with LiCrGeO 4 or LiMn 2 O 4 , can be explained by the strong preference of Fe 3+ for the tetrahedral site. Based on the concept of crystal field stabilization energy, Miller (1959) Liu et al., 2014). This is due mainly to the high amount of Fe 3+ at the A sites, which has a larger ionic radius than Ge 4+ , Ni 3+ or Mn 3+/4+ (Shannon & Prewitt, 1969). The oxygen parameter u = 0.2543 is close to the ideal value for cubic closed packing, reflecting some distinct differences to the spinels which have the A site fully occupied by Li + . In the title compound, the bond length of the tetrahedrally coordinated site T is 1.857 (2) Å , which is distinctly smaller than in, for example, LiMn 2 O 4 , with the tetrahedral site being fully occupied by Li + . The T-O bond length is also smaller than in magnetite (Fleet, 1981) or Li 0.5 Fe 2.5 O 5 (Tomas et al., 1983), with values of 1.8889 (9) and 1.880 (5) Å , respectively. In GeFe 2 O 4 , the T-O bond length is only 1.771 (2) Å and this smaller value of T-O compared to, for example, magnetite is due to the substitution of Ge 4+ onto the A site and can be seen as additional proof for the correctness of the derived cationic distribution.
The bond length involving the octahedrally coordinated site M is 2.0373 (11) Å , which is 1.07 times larger than the bond length involving the tetrahedrally coordinated site. Polyhedral drawing of the spinel-type structure of the title compound. Anisotropic displacement parameters are drawn at the 95% probability level. bond length is somewhat larger than 2.025 (3) Å in Li 0.5 Fe 2.5 O 4 (Tomas et al., 1983). This agrees well with the observed higher Li content in the title compound, with the ionic radius for Li + in an octahedral coordination (0.740 Å ) being larger than that of Fe 3+ (0.645 Å ; Shannon & Prewitt, 1969), thus increasing the M-O distance. Magnetite has a mixed occupation of the octahedral sites, with both Fe 2+ and Fe 3+ , thus having a larger M-O bond length of 2.0582 (9) Å , while in GeFe 2 O 4 , all the Fe atoms are in a divalent state and an M-O bond length of 2.132 (2) Å is observed.
In order to quantify the valence state of iron in the title compound, a 57 Fe Mö ssbauer spectrum was recorded at 340 K. It shows a broad, slightly asymmetric, doublet, which can be evaluated with two Lorentzian-shaped doublets (Fig. 2). The first doublet shows an isomer shift (IS) of À0.053 (17) mm s À1 and a quadrupole splitting (QS) of 0.57 (3) mm s À1 , and can be assigned to the ferric iron on the tetrahedral site. The second doublet has a larger IS of 0.115 (14) mm s À1 and an almost identical QS of 0.58 (2) mm s À1 , and is assigned to ferric iron at the octahedral site. No indications for ferrous iron are present. The QS values suggest low polyhedral distortion, which is almost identical in both sites. The relative area ratio of tetrahedral to octahedral sites is 38.6 (8) to 61.4 (9)%. Assuming a total amount of 2.15 formula units Fe 3+ , the results of Mö ssbauer spectroscopy give a cation distribution of (Fe 3+ 0.83 )[Fe 3+ 1.32 ], which is in good agreement with that obtained from the site-occupation refinement of the X-ray data. At room temperature, the title compound is magnetically ordered, as revealed by its 57 Fe Mö ssbauer spectrum.

Synthesis and crystallization
The spinel formed as a by-product during the synthesis of pyroxene-type LiFeGe 2 O 6 in flux-growth experiments (Redhammer et al., 2010). For the synthesis of the pyroxene, Li 2 CO 3 , Fe 2 O 3 and GeO 2 in the stoichiometry of the compound and Li 2 MoO 4 /LiVO 3 as a flux (mass ratio sample to flux = 1:10) were mixed together, heated to 1473 K in a platinum crucible, covered with a lid, held at this temperature for 24 h and cooled afterwards at a rate of 1.5 K h À1 to 973 K. The experimental batch consisted of large pyroxene crystals and a distinct amount of black crystals with idiomorphic octahedral habit, up to 200 mm. Semi-quantitative EDX (energy-dispersive X-ray) analysis revealed iron and some germanium as the main elements; powder X-ray diffraction analysis revealed the crystals as a spinel-type material. An electron microprobe analysis on polished/embedded crystals (three different grains with five measurement points each) yielded a chemical composition of 84.86 (30) wt% Fe 2 O 3 , 10.52 (25) wt% GeO 2 and 4.62 wt% Li 2 O, with the latter calculated from the difference to 100 oxide%. There is no evidence for Mo or V from the flux, nor for any other chemical elements. From the oxide percentage, a chemical formula of Li 0.63 (2) Fe 2.18 (1) Ge 0.20 (2) O 4 was calculated, which is in good agreement with that obtained from the structure refinement. Individual crystals are homogeneous in composition, with no significant systematic variation from rim-core; also, there is no systematic variation in composition from crystal to crystal.

Refinement
Crystal data, data collection and structure refinement details are summarized in Table 1. In a first stage of refinement, only iron was considered on the A and B sites, thereby allowing unconstrained refinement of the site-occupation factors. This gave a surplus of electron density (higher occupation than allowed by the multiplicity) at the tetrahedral site, while a lower occupation than possible was found for the octahedral site. From this it was concluded that Li enters the octahedral site and Ge enters the tetrahedral site. In the final refinements, it was assumed that both tetrahedral and octahedral sites are fully occupied, with Fe + Ge = 1 as a restraint for the tetrahedral site and Fe + Li = 1 for the octahedral site. Computer programs: APEX2 and SAINT (Bruker, 2012), SHELXL2014 (Sheldrick, 2015), DIAMOND (Brandenburg, 2006) and WinGX (Farrugia, 2012). program(s) used to solve structure: coordinates from an isotypic structure; program(s) used to refine structure: SHELXL2014 (Sheldrick, 2015); molecular graphics: DIAMOND (Brandenburg, 2006); software used to prepare material for publication: WinGX (Farrugia, 2012).