Spinel-type Li0.64Fe2.15Ge0.21O4, 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.Günther J. Redhammer and Gerold Tippel

Redhammer, Günther J.

Tippelt, Gerold

Paris Lodron University of Salzburg

research communications
Acta Cryst. (2016). E72, 505–508 http://dx.doi.org/10.1107/S205698901600414X 505
Received 1 March 2016
Accepted 11 March 2016
Edited by M. Weil, Vienna University of
Technology, Austria
Keywords: crystal structure; spinel; Mo¨ssbauer
spectroscopy; geoscience.
CCDC reference: 1463892
Supporting information: this article has
supporting information at journals.iucr.org/e
Crystal structure of spinel-type Li0.64Fe2.15Ge0.21O4
Gu¨nther J. Redhammer* and Gerold Tippelt
University of Salzburg, Department Chemistry and Physics of Materials, Hellbrunnerstrasse 34, 5020 Salzburg, Austria.
*Correspondence e-mail: guenther.redhammer@sbg.ac.at
Spinel-type Li0.64Fe2.15Ge0.21O4, 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 tetrahedralA sites, and iron distributes over both the
octahedral and tetrahedral sites, and is in the trivalent state as determined from
Mo¨ssbauer 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
Li0.5Fe2.5O4 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; Thack-
eray 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 coordina-
tion occupy special position 8a (point symmetry 43m, at 18,
1
8,
1
8),
while the octahedrally coordinated cations reside on special
position 16d (point symmetry 3m at 12,
1
2,
1
2). The anions are at
equipoint position 32e, which requires one positional para-
meter, 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 adjust-
ment 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
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 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
LiNi0.5Mn1.5O4, 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 & Boure´e
(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 Li0.5Fe2.5O4. This compound
is an inverse spinel in which Fe3+ is ordered onto the tetra-
hedral 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 Mo¨ssbauer
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+0.79Ge
4+
0.21)-
[Li+0.64Fe
3+
1.36]O4, with the valence state of iron determined
from 57Fe Mo¨ssbauer 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 Li0.5Fe2.5O4
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 prefer-
ence energies which gave a stronger preference of Fe3+ for the
tetrahedral site as compared, for example, to Li+ or Mn3+.
The lattice parameter of the title compound [8.2903 (3) A˚]
is smaller in comparison with, for example, magnetite Fe3O4
[a = 8.3941 (7) A˚; Fleet, 1981], but larger than that observed in
the Li spinels LiCrGeO4 [a = 8.1976 (1) A˚; Touboul & Boure´e,
1993] or LiMn2O4 and LiNi0.5Mn1.5O4 (a = 8.243 and 8.1685 A˚,
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 Mn3+/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 coordi-
nated site T is 1.857 (2) A˚, 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 Li0.5Fe2.5O5 (Tomas et al., 1983),
with values of 1.8889 (9) and 1.880 (5) A˚, respectively. In
GeFe2O4, the T—O bond length is only 1.771 (2) A˚ 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) A˚, which is 1.07 times larger than the bond
length involving the tetrahedrally coordinated site. TheM—O
506 Redhammer and Tippelt  Li0.64Fe2.15Ge0.21O4 Acta Cryst. (2016). E72, 505–508
research communications
Figure 1
Polyhedral drawing of the spinel-type structure of the title compound.
Anisotropic displacement parameters are drawn at the 95% probability
level.
Figure 2
57Fe Mo¨ssbauer spectrum of the title compound, recorded at 740 K.
bond length is somewhat larger than 2.025 (3) A˚ in
Li0.5Fe2.5O4 (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 A˚)
being larger than that of Fe3+ (0.645 A˚; 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) A˚,
while in GeFe2O4, all the Fe atoms are in a divalent state and
an M—O bond length of 2.132 (2) A˚ is observed.
In order to quantify the valence state of iron in the title
compound, a 57Fe Mo¨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 0.053 (17) mm s1
and a quadrupole splitting (QS) of 0.57 (3) mm s1, and can be
assigned to the ferric iron on the tetrahedral site. The second
doublet has a larger IS of 0.115 (14) mm s1 and an almost
identical QS of 0.58 (2) mm s1, 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 Mo¨ssbauer spectroscopy give a cation distribution of
(Fe3+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 57Fe Mo¨ssbauer spectrum.
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 h1 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% 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
Li0.63 (2)Fe2.18 (1)Ge0.20 (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 tetra-
hedral site and Fe + Li = 1 for the octahedral site.
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Acta Cryst. (2016). E72, 505–508 Redhammer and Tippelt  Li0.64Fe2.15Ge0.21O4 507
Table 1
Experimental details.
Crystal data
Chemical formula Li0.64Fe2.15Ge0.21O4
Mr 203.5
Crystal system, space group Cubic, Fd3m
Temperature (K) 298
a (A˚) 8.2903 (3)
V (A˚3) 569.78 (6)
Z 8
Radiation type Mo K
 (mm1) 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 > 2(I)] reflections
3046, 118, 114
Rint 0.021
(sin /)max (A˚
1) 0.940
Refinement
R[F 2 > 2(F 2)], wR(F 2), S 0.018, 0.042, 1.37
No. of reflections 118
No. of parameters 10
No. of restraints 1
max, min (e A˚
3) 0.36, 0.67
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508 Redhammer and Tippelt  Li0.64Fe2.15Ge0.21O4 Acta Cryst. (2016). E72, 505–508
research communications
supporting information
sup-1Acta Cryst. (2016). E72, 505-508    
supporting information
Acta Cryst. (2016). E72, 505-508    [doi:10.1107/S205698901600414X]
Crystal structure of spinel-type Li0.64Fe2.15Ge0.21O4
Günther J. Redhammer and Gerold Tippelt
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
Mr = 203.5
Cubic, Fd3m
Hall symbol: -F 4vw 2vw 3
a = 8.2903 (3) Å
V = 569.78 (6) Å3
Z = 8
F(000) = 771
Dx = 4.744 Mg m−3
Mo Kα radiation, λ = 0.71073 Å
Cell parameters from 3046 reflections
θ = 7.0–41.9°
µ = 12.85 mm−1
T = 298 K
Octahedron, black
0.13 × 0.12 × 0.12 mm
Data collection 
Bruker SMART APEX CCD 
diffractometer
Radiation source: 3-circle diffractometer
Graphite monochromator
ω–scan at 4 different φ positions
Absorption correction: multi-scan 
(SADABS; Bruker, 2012)
Tmin = 0.83, Tmax = 0.94
3046 measured reflections
118 independent reflections
114 reflections with I > 2σ(I)
Rint = 0.021
θmax = 41.9°, θmin = 7.0°
h = −15→14
k = −14→10
l = −15→13
Refinement 
Refinement on F2
Least-squares matrix: full
R[F2 > 2σ(F2)] = 0.018
wR(F2) = 0.042
S = 1.37
118 reflections
10 parameters
1 restraint
w = 1/[σ2(Fo2) + (0.0139P)2 + 2.542P] 
where P = (Fo2 + 2Fc2)/3
(Δ/σ)max < 0.001
Δρmax = 0.36 e Å−3
Δρmin = −0.67 e Å−3
Extinction correction: SHELXL2014 (Sheldrick, 
2015)
Extinction coefficient: 0.0051 (6)
supporting information
sup-2Acta Cryst. (2016). E72, 505-508    
Special details 
Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full 
covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and 
torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. 
An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) 
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 (Å2) 
U11 U22 U33 U12 U13 U23
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—O2i 2.0373 (11) Fe1—Fe1ii 2.9311 (1)
Fe1—O2ii 2.0373 (11) Fe2—O2vii 1.857 (2)
Fe1—O2iii 2.0373 (11) Fe2—O2viii 1.857 (2)
Fe1—O2iv 2.0373 (11) Fe2—O2ix 1.857 (2)
Fe1—O2v 2.0373 (11) Fe2—O2 1.857 (2)
Fe1—O2vi 2.0373 (11)
O2i—Fe1—O2ii 180 O2ii—Fe1—O2vi 87.96 (7)
O2i—Fe1—O2iii 87.96 (7) O2iii—Fe1—O2vi 92.04 (7)
O2ii—Fe1—O2iii 92.04 (7) O2iv—Fe1—O2vi 87.96 (7)
O2i—Fe1—O2iv 92.04 (7) O2v—Fe1—O2vi 180.00 (7)
O2ii—Fe1—O2iv 87.96 (7) O2vii—Fe2—O2viii 109.5
O2iii—Fe1—O2iv 180 O2vii—Fe2—O2ix 109.5
O2i—Fe1—O2v 87.96 (7) O2viii—Fe2—O2ix 109.5
O2ii—Fe1—O2v 92.04 (7) O2vii—Fe2—O2 109.4710 (10)
O2iii—Fe1—O2v 87.96 (7) O2viii—Fe2—O2 109.5
O2iv—Fe1—O2v 92.04 (7) O2ix—Fe2—O2 109.4710 (10)
O2i—Fe1—O2vi 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.


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

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