Crystal structure of spinel-type Li_0.64Fe_2.15Ge_0.21O₄

Spinel-type Li_0.64Fe_2.15Ge_0.21O₄, lithium diiron(III) germanium tetra­oxide, has been formed as a by-product during flux growth of an Li–Fe–Ge pyroxene-type material. In the title compound, lithium is ordered on the octa­hedral B sites, while Ge⁴⁺ orders onto the tetra­hedral A sites, and iron distributes over both the octa­hedral and tetra­hedral sites, and is in the trivalent state as determined from Mössbauer spectroscopy. The oxygen parameter u is 0.2543; thus, the spinel is close to having an ideal cubic closed packing of the O atoms. The title spinel is compared with other Li- and Ge-containing spinels.

1. 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 LiMn₂O₄ or Li_0.5Fe_2.5O₄ 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 Fdm. Here the cations in tetra­hedral coordination occupy special position 8a (point symmetry 3m, at , , ), while the octa­hedrally coordinated cations reside on special position 16d (point symmetry m at , , ). 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 AB₂O₄, 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)[B₂]O₄. In contrast, the complete inverse spinel has a cationic distribution of (B)[AB]O₄ (O'Neill & Navrotsky, 1983). More detailed reviews on the spinel structure and crystal chemistry can be 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 Ge⁴⁺ 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 GeMg₂O₄ and Welch et al. (2001) for the mineral brunogeierite (GeFe₂O₄). For LiMn₂O₄ and LiNi_0.5Mn_1.5O₄, 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 LiCrGeO₄, Touboul & Bourée (1993) reported an almost exclusive ordering of Li⁺ for the tetra­hedral site, while Cr³⁺ and Ge⁴⁺ occupy the octa­hedral sites. Different to this is the spinel Li_0.5Fe_2.5O₄. This compound is an inverse spinel in which Fe³⁺ is ordered onto the tetra­hedral site, while Li⁺ and the remaining Fe³⁺ 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, FeFe₂O₄ (Fleet, 1981).

During the synthesis of Li–Fe–Ge pyroxenes (Redhammer et al., 2009, 2010), black octa­hedral-shaped single crystals were frequently obtained, which turned out to be a spinel-type compound with significant Li⁺ and small Ge⁴⁺ concentrations. We present here the structure refinement and ⁵⁷Fe Mössbauer spectroscopic characterization of these crystals.

2. Structural commentary

The structure of the title compound is shown in Fig. 1. The site-occupation refinement indicates that Li⁺ orders onto the octa­hedral B site, while Ge⁴⁺ is found on the tetra­hedral A site, indicating a partial inverse spinel arrangement; iron is distributed over both sites. The derived crystal chemical formula of the title compound is thus (Fe³⁺_0.79Ge⁴⁺_0.21)[Li⁺_0.64Fe³⁺_1.36]O₄, with the valence state of iron determined from ⁵⁷Fe Mössbauer spectroscopy (see below). 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_0.5Fe_2.5O₄ spinel-type materials. The shift of Li⁺ to the octa­hedral site, for example, in comparison with LiCrGeO₄ or LiMn₂O₄, can be explained by the strong preference of Fe³⁺ for the tetra­hedral site. Based on the concept of crystal field stabilization energy, Miller (1959) theoretically calculated octa­hedral site preference energies which gave a stronger preference of Fe³⁺ for the tetra­hedral site as compared, for example, to Li⁺ or Mn³⁺.

Figure 1 Polyhedral drawing of the spinel-type structure of the title compound. Anisotropic displacement parameters are drawn at the 95% probability level.

The lattice parameter of the title compound [8.2903 (3) Å] is smaller in comparison with, for example, magnetite Fe₃O₄ [a = 8.3941 (7) Å; Fleet, 1981], but larger than that observed in the Li spinels LiCrGeO₄ [a = 8.1976 (1) Å; Touboul & Bourée, 1993] or LiMn₂O₄ and LiNi_0.5Mn_1.5O₄ (a = 8.243 and 8.1685 Å, respectively; Liu et al., 2014). This is due mainly to the high amount of Fe³⁺ at the A sites, which has a larger ionic radius than Ge⁴⁺, Ni³⁺ 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, LiMn₂O₄, with the tetra­hedral site being fully occupied by Li⁺. The T—O bond length is also smaller than in magnetite (Fleet, 1981) or Li_0.5Fe_2.5O₅ (Tomas et al., 1983), with values of 1.8889 (9) and 1.880 (5) Å, respectively. In GeFe₂O₄, 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 Ge⁴⁺ 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. The M—O bond length is somewhat larger than 2.025 (3) Å in Li_0.5Fe_2.5O₄ (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 Fe³⁺ (0.645 Å; Shannon & Prewitt, 1969), thus increasing the M—O distance. Magnetite has a mixed occupation of the octa­hedral sites, with both Fe²⁺ and Fe³⁺, thus having a larger M—O bond length of 2.0582 (9) Å, while in GeFe₂O₄, 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 ⁵⁷Fe Mössbauer 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 −0.053 (17) mm s⁻¹ and a quadrupole splitting (QS) of 0.57 (3) mm s⁻¹, 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⁻¹ and an almost identical QS of 0.58 (2) mm s⁻¹, 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 Fe³⁺, the results of Mössbauer spectroscopy give a cation distribution of (Fe³⁺_0.83)[Fe³⁺_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 ⁵⁷Fe Mössbauer spectrum.

Figure 2 ^57Fe Mössbauer spectrum of the title compound, recorded at 740 K.

3. Synthesis and crystallization

The spinel formed as a by-product during the synthesis of pyroxene-type LiFeGe₂O₆ in flux-growth experiments (Redhammer et al., 2010). For the synthesis of the pyroxene, Li₂CO₃, Fe₂O₃ and GeO₂ in the stoichiometry of the compound and Li₂MoO₄/LiVO₃ 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⁻¹ 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 µm. 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% Fe₂O₃, 10.52 (25) wt% GeO₂ and 4.62 wt% Li₂O, 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)O₄ 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.

4. 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.

Table 1
Experimental details

Crystal data
Chemical formula	Li0.64Fe2.15Ge0.21O4
Mr	203.5
Crystal system, space group	Cubic, Fdm
Temperature (K)	298
a (Å)	8.2903 (3)
V (Å^3)	569.78 (6)
Z	8
Radiation type	Mo Kα
μ (mm^−1)	12.85
Crystal size (mm)	0.13 × 0.12 × 0.12
Data collection
Diffractometer	Bruker SMART APEX CCD
Absorption correction	Multi-scan (SADABS; Bruker, 2012)
Tmin, Tmax	0.83, 0.94
No. of measured, independent and observed [I > 2σ(I)] reflections	3046, 118, 114
Rint	0.021
(sin θ/λ)max (Å^−1)	0.940
Refinement
R[F^2 > 2σ(F^2)], wR(F^2), S	0.018, 0.042, 1.37
No. of reflections	118
No. of parameters	10
No. of restraints	1
Δρmax, Δρmin (e Å^−3)	0.36, −0.67
Computer programs: APEX2 and SAINT (Bruker, 2012), SHELXL2014 (Sheldrick, 2015), DIAMOND (Brandenburg, 2006) and WinGX (Farrugia, 2012).

Supporting information

Computing details

Data collection: APEX2 (Bruker, 2012); cell refinement: SAINT (Bruker, 2012); data reduction: SAINT (Bruker, 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).

Lithium diiron(III) germanium tetraoxide

Crystal data

Li0.64Fe2.15Ge0.21O4	Dx = 4.744 Mg m^−3
Mr = 203.5	Mo Kα radiation, λ = 0.71073 Å
Cubic, Fd3m	Cell parameters from 3046 reflections
Hall symbol: -F 4vw 2vw 3	θ = 7.0–41.9°
a = 8.2903 (3) Å	µ = 12.85 mm^−1
V = 569.78 (6) Å^3	T = 298 K
Z = 8	Octahedron, black
F(000) = 771	0.13 × 0.12 × 0.12 mm

Data collection

Bruker SMART APEX CCD diffractometer	118 independent reflections
Radiation source: 3-circle diffractometer	114 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.021
ω–scan at 4 different φ positions	θmax = 41.9°, θmin = 7.0°
Absorption correction: multi-scan (SADABS; Bruker, 2012)	h = −15→14
Tmin = 0.83, Tmax = 0.94	k = −14→10
3046 measured reflections	l = −15→13

Refinement

Refinement on F^2	1 restraint
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0139P)^2 + 2.542P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.018	(Δ/σ)max < 0.001
wR(F^2) = 0.042	Δρmax = 0.36 e Å^−3
S = 1.37	Δρmin = −0.67 e Å^−3
118 reflections	Extinction correction: SHELXL2014 (Sheldrick, 2015)
10 parameters	Extinction coefficient: 0.0051 (6)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Fe1	0.5	0.5	0.5	0.00795 (17)	0.678 (4)
Li1	0.5	0.5	0.5	0.00795 (17)	0.322 (4)
Fe2	0.125	0.125	0.125	0.00573 (17)	0.795 (3)
Ge2	0.125	0.125	0.125	0.00573 (17)	0.205 (3)
O2	0.25434 (14)	0.25434 (14)	0.25434 (14)	0.0095 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Fe1	0.00795 (17)	0.00795 (17)	0.00795 (17)	−0.00100 (11)	−0.00100 (11)	−0.00100 (11)
Li1	0.00795 (17)	0.00795 (17)	0.00795 (17)	−0.00100 (11)	−0.00100 (11)	−0.00100 (11)
Fe2	0.00573 (17)	0.00573 (17)	0.00573 (17)	0	0	0
Ge2	0.00573 (17)	0.00573 (17)	0.00573 (17)	0	0	0
O2	0.0095 (3)	0.0095 (3)	0.0095 (3)	0.0010 (3)	0.0010 (3)	0.0010 (3)

Geometric parameters (Å, º)

Fe1—O2^i	2.0373 (11)	Fe1—Fe1^ii	2.9311 (1)
Fe1—O2^ii	2.0373 (11)	Fe2—O2^vii	1.857 (2)
Fe1—O2^iii	2.0373 (11)	Fe2—O2^viii	1.857 (2)
Fe1—O2^iv	2.0373 (11)	Fe2—O2^ix	1.857 (2)
Fe1—O2^v	2.0373 (11)	Fe2—O2	1.857 (2)
Fe1—O2^vi	2.0373 (11)
O2^i—Fe1—O2^ii	180	O2^ii—Fe1—O2^vi	87.96 (7)
O2^i—Fe1—O2^iii	87.96 (7)	O2^iii—Fe1—O2^vi	92.04 (7)
O2^ii—Fe1—O2^iii	92.04 (7)	O2^iv—Fe1—O2^vi	87.96 (7)
O2^i—Fe1—O2^iv	92.04 (7)	O2^v—Fe1—O2^vi	180.00 (7)
O2^ii—Fe1—O2^iv	87.96 (7)	O2^vii—Fe2—O2^viii	109.5
O2^iii—Fe1—O2^iv	180	O2^vii—Fe2—O2^ix	109.5
O2^i—Fe1—O2^v	87.96 (7)	O2^viii—Fe2—O2^ix	109.5
O2^ii—Fe1—O2^v	92.04 (7)	O2^vii—Fe2—O2	109.4710 (10)
O2^iii—Fe1—O2^v	87.96 (7)	O2^viii—Fe2—O2	109.5
O2^iv—Fe1—O2^v	92.04 (7)	O2^ix—Fe2—O2	109.4710 (10)
O2^i—Fe1—O2^vi	92.04 (7)

Symmetry codes: (i) x+1/4, y+1/4, −z+1; (ii) −x+3/4, −y+3/4, z; (iii) x+1/4, −y+1, z+1/4; (iv) −x+3/4, y, −z+3/4; (v) −x+1, y+1/4, z+1/4; (vi) x, −y+3/4, −z+3/4; (vii) −x+1/4, y, −z+1/4; (viii) x, −y+1/4, −z+1/4; (ix) −x+1/4, −y+1/4, z.