Li5Sn, the Most Lithium-Rich Binary Stannide: A Combined
Experimental and Computational Study
Robert U. Stelzer, Yuji Ikeda,* Prashanth Srinivasan, Tanja S. Lehmann, Blazej Grabowski,
and Rainer Niewa

Cite This: J. Am. Chem. Soc. 2022, 144, 7096−7110 Read Online

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ABSTRACT: From reaction of excess lithium with tin, we isolate well-
crystallized Li5Sn and solve the crystal structure from single-crystal X-ray
diffraction data. The orthorhombic structure (space group Cmcm)
features the same coordination polyhedra around tin and lithium as
previously predicted by electronic structure calculations for this
composition, however differently arranged. An extensive ab initio analysis,
including thermodynamic integration using Langevin dynamics in
combination with a machine-learning potential (moment tensor
potential), is conducted to understand the thermodynamic stability of
this Cmcm Li5Sn structure observed in our experiments. Among the 108
Li5Sn structures systematically derived using the structure enumeration
algorithm, including the experimental Cmcm structure and those obtained in previous ab initio studies, another new structure with
the space group Immm is found to be energetically most stable at 0 K. This computationally discovered Immm structure is also found
to be thermodynamically more stable than the Cmcm structure at finite temperatures, indicating that the Cmcm Li5Sn structure
observed in our experiments is favored likely due to kinetic reasons rather than thermodynamics.

1. INTRODUCTION

Since the beginning of the 21st century, lithium ion batteries
have conquered the market of portable electronic devices.
However, to meet the increasing requirements of electro-
mobility, the commercial graphite anodes with a maximum
capacity of 372 mAh/g need to be replaced by materials with
an increased specific lithium uptake and thus enhanced
capacity.1 Particularly the tetrels Si and Sn offer an increased
storage capacity via the formation of binary intermetallic
phases with Li. For Si a remarkable maximum capacity of 1978
mAh/g upon formation of Li17Si4 can be achieved. Sn delivers
a similarly noteworthy capacity of 769 mAh/g during
formation of Li17Sn4, though smaller than Si due to the larger
relative volumes and masses. Both tetrels Si and Sn are
nontoxic, comparably inexpensive, and readily available.
Disadvantages are still the severe volume changes during
cycling, which result in capacity losses2 and mechanical
challenges to the cell design, although some problems were
minimized during recent years.3−5 Volume changes and the
resulting disadvantages are generally less pronounced in the
Li−Sn system, which is in the focus of the present study.
First investigations concerning the Li−Sn system date back

to the beginning of the last century, when the existence of the
three phases Li4Sn, Li3Sn2, and Li2Sn5 was postulated6 (cf.
Figure 1). For Li4Sn the possibility of an even higher lithium
content in this phase was already noted, according to
observations during crystallization. Indeed, the composition

of this phase was subsequently revised to Li22Sn5 (Li4.4Sn)
based on crystal structure refinements,7 though only
temporarily, as should become clear later. Baroni8,9 apparently
also observed Li2Sn5, but gave the composition as LiSn4.
Shortly after, the presence of several intermetallic compounds
in the binary phase diagram was proposed, namely, Li4Sn,
Li7Sn2, Li5Sn2, Li2Sn, α-LiSn, and LiSn2, highlighting the
complexity of the Li−Sn system. Li3Sn2 and LiSn4 were not
observed during these studies.10 In the 1970s Li7Sn2,

11

Li5Sn2,
12 and α-LiSn13 were affirmed by crystal structure

determinations, while the compositions Li2Sn and LiSn2 were
corrected to Li7Sn3

14 and Li2Sn5,
15 respectively. In the

following a new phase with a composition of Li13Sn5 was
introduced,16 and a second polymorph, β-LiSn, was obtained
from a Ga-containing melt.17 Thermodynamic studies aiming
for the construction of an improved phase diagram indicated
one more compound denoted as Li8Sn3, but this phase was not
further characterized.18

In the beginning of this century, structure refinements based
on single-crystal X-ray and powder neutron diffraction

Received: October 8, 2021
Published: April 13, 2022

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demanded to once again reconsider the composition of Li22Sn5
(Li4.4Sn). Specifically, the composition was refined to Li17Sn4
(Li4.25Sn),

19,20 which, to the best of our knowledge, is the Li-
richest binary stannide reported so far. This compound
exhibits poor metallic behavior20 and might be understood in
a simple ionic picture according to (Li+)17[Sn

4−]4·e
− based on

band structure and electron localization function calcula-
tions.21 Difficulties in determining the composition and
inconsistencies in occupations of crystallographic Li positions
from different investigations might be related to a significant
homogeneity range of this phase spanning from Li17Sn4 to
Li17.42Sn4 (= “Li21.8Sn5”).

22

Figure 1a summarizes the Li−Sn chronology, and Figure 1b
emphasizes the Li concentration of the verified phases. Phase
diagrams including Li17Sn4, Li7Sn2, Li13Sn5, Li5Sn2, Li7Sn3,
LiSn, Li2Sn5, and Li8Sn3 can be found in the literature.18,23

Moreover, all known stable phases were recently studied with
solid state NMR and Mössbauer spectroscopy to produce
reference data for battery operando studies.24

Further metastable lithium-rich stannides with compositions
of Li5Sn and Li7Sn were predicted based on ab initio
calculations.25,26 For Li5Sn, two crystal structures were derived,
both closely related in their local atomic surroundings,
however, with differences in the arrangement and intercon-
nection of the resulting coordination polyhedra.
In the present work, we describe the successful synthesis and

structural characterization of Li5Sn, which contains the already
predicted coordination polyhedra, but again differently
arranged. The thermodynamic stability of the obtained and
various competing structures is investigated based on ab initio
density functional theory (DFT) calculations, considering
atomic vibrations, including anharmonicity, as well as
electronic excitations at finite temperatures.

2. EXPERIMENTAL DETAILS
All manipulations were carried out in an Ar-filled glovebox (MBraun,
Garching, Germany; p(O2) < 0.1 ppm, moisture and oxygen
constantly removed by copper catalyst and molecular sieve), due to
severe air and moisture sensitivity of lithium and the title compound.
Synthesis was successful from tin powder (99.9%, Alfa Aesar) with an
excess of lithium metal (rods, Merck) as flux and reaction medium
with an overall Sn to Li molar ratio of 1:10 in a welded tantalum

ampule (Aldrich). The tantalum ampule was heated in an Ar-filled
fused silica tube at 100 K/h to 1073 K and directly allowed to cool to
673 K with a rate of 2 K/h, followed by natural cooling to room
temperature. After thermal treatment, the sample mostly consists of
Li17Sn4 and excess lithium. In order to remove the excess lithium, the
opened Ta-ampule was transferred to an H-tube and washed several
times with liquid ammonia until the liquid ammonia only showed a
faint blue coloration, indicating just traces of elemental lithium being
left in the sample (exposed to ammonia for about 1 h). During this
operation Li17Sn4 decomposes to a so far unknown badly crystallized,
tin-richer product, leaving crystals of Li5Sn behind, which also
decompose upon extended treatment of more than 1 day in liquid
ammonia.

Single-crystal X-ray diffraction measurements were taken with a κ-
CCD Bruker-Nonius single-crystal diffractometer (Mo Kα radiation, λ
= 0.710 73 Å) and analyzed with the ShelX software package.27

Further details on the crystal structure investigation may be obtained
from the Fachinformationszentrum Karlsruhe, 76344 Eggenstein-
Leopoldshafen, Germany (fax: (+49)7247-808-666; e-mail:
crysdata@fiz-karlsruhe.de), on quoting the depository number CSD-
2099217.

Chemical analysis on O, N, and H was carried out on a LECO
ONH835 analyzer (LECO, St. Joseph, MI, USA), to confirm the
composition.

3. COMPUTATIONAL METHODOLOGY
3.1. Structure Enumeration. Previously, new stable or

metastable Li−Sn phases were explored by Mayo and Morris26

using random structure searching31,32 and by Sen and Johari25

based on evolutionary crystal structure prediction,33−35 both in
combination with ab initio calculations. In these studies, Mayo
and Morris26 predicted hexagonal P6/mmm Li5Sn, while Sen
and Johari25 predicted monoclinic C2/m Li5Sn. In contrast, as
detailed below in Section 4.1, the Li5Sn structure observed in
the present experiments obeys orthorhombic symmetry with
the space group Cmcm. However, all three structures
mentioned above consist of arrangements of Sn-centered
capped hexagonal prisms surrounded by Li atoms as shown in
Figure 2a. The difference among the structures lies only in the
arrangement of the Sn coordination polyhedra perpendicular
to the cap direction. Specifically, P6/mmm Li5Sn consists
exclusively of face-sharing Sn coordination polyhedra (Figure
2b). The Sn coordination polyhedra in C2/m and Cmcm Li5Sn,
in contrast, are both face- and edge-sharing (Figure 2c) but

Figure 1. (a) Chronology of experimental reports of lithium stannides. Note that only the bold compositions are backed by structure determination
and typically further investigations. For the other compositions no crystal structure data are available, composition assignments have been changed,
or the presence of the phase has been completely refuted over time. (b) Li mole fractions of the experimentally confirmed lithium stannides.

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arranged in different ways. For the cap direction, every unit
polyhedron shares the cap Li atoms with other polyhedra. As a
consequence, all three Li5Sn structures can be schematically
understood in a two-dimensional configuration space as
different arrangements of hexagons with two colors (Figure 3).
To investigate the thermodynamic stability of Li5Sn in detail,

we conducted ab initio simulations. Since various candidate
crystal structures were already examined in the previous works
of Mayo and Morris26 and of Sen and Johari,25 in the present
study we intensively focused on the Li5Sn structures consisting
of the Sn coordination polyhedra described above. We
however considered not only the above-mentioned three
Li5Sn structures but actually in total 108 arrangements of the
Sn coordination polyhedra determined using the structure
enumeration algorithm.36,37 We considered up to eight
hexagons in the unit cell in the two-dimensional configuration
space. We mostly utilized the implementation in ICET (ver.
1.3),38 but a few remarks are in order:

1. In the two-dimensional representation visualized in
Figure 3, arrangements need to be omitted if they are
equivalent to another arrangement via a color symmetry
operation, i.e., by flipping the two colors. A correspond-
ing symmetrization procedure was implemented by
ourselves.

2. The cell shapes created according to point 1 are not
immediately in the standardized representation. The
latter is however beneficial to improve numerical
stability of the DFT simulations. After enumeration,
we therefore further conducted a two-dimensional
Delaunay reduction.29,30 Since the standardization
implemented in ICET ver. 1.3 (Niggli reduction30,39)
applies only to three-dimensional cases, we implemented
a two-dimensional Delaunay reduction by ourselves.

In Figure 3 some of the thus obtained arrangements of Sn
coordination polyhedra are described. They include the
arrangements previously predicted by Mayo and Morris26

(#0) and by Sen and Jonari25 (#83). The arrangement found
in the present experiments is #7 (cf. Section 4.1), while the
arrangement showing the lowest energy at 0 K in the ab initio
simulations is #23 (cf. Section 4.4). Structures #1 and #41
show the highest and the second lowest energies, respectively,
at 0 K in the ab initio simulations.
Note that for some of the 108 structures, we could in

principle make smaller primitive cells by choosing a lattice

basis that mixes the axial and the basal directions. However, as
we have to determine very small energy differences (cf. Section
4.4), we prefer to keep computational consistency among all
investigated structures as much as possible. Therefore, for all
the 108 structures, we set one of the lattice vectors along the
cap direction and chose the other two lattice vectors
perpendicular to this cap-direction lattice vector. We further
applied the same number of k points along the cap direction
for all 108 structures.

3.2. Electronic Structure Calculations for the 108
Li5Sn Structures. For all 108 Li5Sn structures created
systematically by structure enumeration (Section 3.1),36,37

we conducted structure optimization. We employed the
projector augmented wave (PAW) method40 as implemented
in VASP41,42 in combination with the provided potentials.43

The reciprocal space was sampled by the Methfessel−Paxton
scheme44 with a smearing width of 0.2 eV.

Figure 2. (a) Sn-centered bicapped hexagonal prism composed of 14
Li atoms. The cap direction is shown by the gray arrow. Gray spheres
represent Sn atoms, and dark green and light green spheres represent
Li atoms at the cap and the prism positions, respectively. (b) Two
face-sharing Sn coordination polyhedra. (c) Two edge-sharing Sn
coordination polyhedra. The polyhedra in the different colors are on
different levels with respect to the cap direction (cf. Figure 3).
Visualization was performed using VESTA.28

Figure 3. Two-dimensional schematics for some of the 108
arrangements of the Sn coordination polyhedra investigated in the
present ab initio simulations. Each hexagon represents one Sn
coordination polyhedron, a bicapped hexagonal prism consisting of 14
Li atoms. Hexagons of the same color (either blue or orange) indicate
prisms lying on the same level and thus sharing their faces as shown in
Figure 2b. Orange hexagons are shifted with respect to the blue ones
along the direction perpendicular to the paper surface (i.e., along the
cap direction) by half of the prism height. Thus, neighboring blue and
orange hexagons represent edges sharing prisms as shown in Figure
2c. The parallelogram for each structure shows the projected unit cell
standardized by the two-dimensional Delaunay reduction.29,30

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To make sure that our results are robust and insensitive with
respect to the computational conditions, we tested five
different computational settings summarized in Table 1.

Specifically, we tested two cutoff energies (200 and 500 eV),
two k-space mesh densities, and two sets of PAW potentials
with different valence states. Further, in addition to the
generalized gradient approximation (GGA) in the Perdew−
Burke−Ernzerhof (PBE) form,45 we also employed the local
density approximation (LDA),46,47 the GGA in the Perdew−
Wang form (PW91),48 and the strongly constrained and
appropriately normed (SCAN) meta-GGA.49,50 As detailed in
Section 4.5, our conclusions are robust against these
computational settings. Thus, we utilized setting A from
Table 1 for further analysis of the 108 Li5Sn structures.
Total energies were converged to within 1 × 10−5 eV per

unit cell. Full structure relaxation was performed by optimizing
cell volume, cell shape, and internal atomic positions so that
the forces on atoms and the stress components on the unit cell
are less than 1.5 × 10−3 eV/Å and 1 × 10−2 eV/Å3,
respectively.
To compare the phase stability of the 108 Li5Sn structures

with respect to the two-phase state of the known equilibrium
phases, i.e., body-centered cubic (bcc) Li and F4̅3m
Li17Sn4,

19,20 we also simulated these latter two phases with
optimizing their structures. The same computational con-
ditions (setting A from Table 1) and the same convergence
criteria as above were applied. The energy difference of Li5Sn
referenced to the two-phase state was computed as

Δ = − +i
k
jjj

y
{
zzzE E E E(Li Sn)

1
8

(Li)
7
8

(Li Sn )5 17 4 (1)

where E(α) denotes the energy of phase α per atom.
To get insight on the dependence of the phase stability of

Li5Sn on pressure and thermal expansion, we computed the
energy−volume curves for the structures #0, #7, #23, and #83
at 13 fixed volumes within a range of 16−22 Å3/atom. At each
volume, both the cell shape and the internal atomic positions
were optimized. For the stress components, both the diagonal
terms (minus their mean values) and the off-diagonal terms
were optimized to be less than 5 × 10−5 eV/Å3. The structure
optimization was repeated several times to be consistent with
the given energy cutoff.

3.3. Cluster Expansion of the Sn Polyhedra Arrange-
ment. To analyze the impact of the arrangement of the Sn
coordination polyhedra on the energies of the 108 Li5Sn
structures, the cluster expansion (CE) method51−53 was
employed. While the CE method is typically applied to
describe atomic configurations on a given 3D crystal lattice, in
the present study we regard the Sn coordination polyhedra as
the fundamental objects of the CE, which live on a 2D lattice.
The two irreducible Sn coordination polyhedra along the Li
cap direction that arise for the edge-sharing situation (Figure
2c) are mapped onto two types of elements (blue and orange)
in the CE. They can be thought of as two distinct types of
atomic species in a usual CE. These two elements can be
arranged in different configurations via the CE on a two-
dimensional triangular lattice. Note that due to symmetry, only
the clusters involving even numbers of Sn coordination
polyhedra like doublet and quartet clusters contribute to the
energies, and there are no contributions of clusters with odd
numbers of polyhedra like singlet and triplet clusters; in the
schematics in Figure 3, this means that the color switching of
all the polygons does not affect the energies. Note also that,
unlike in typical CE applications, in the present study we
consider a fixed atomic composition of Li5Sn, with differences
only in the arrangement of the Sn coordination polyhedra. The
energy range for the effective cluster interactions (ECIs) and
for the fitting error is therefore much smaller than in typical
CE applications.
The ICET code38 was utilized for the CE analysis. The ECIs

for clusters with odd numbers of Sn coordination polyhedra
were restricted to be zero. The ECIs were determined based on
the least absolute shrinkage and selection operator (LASSO)
regression.54

3.4. Gibbs Energies for Structures #7 and #23. The
thermodynamic stability of Li5Sn at finite temperatures was
investigated for the two most relevant structures (Sn
coordination polyhedra arrangements), i.e., the experimentally
observed one (#7) and the energetically lowest one as
determined from theory (#23).
To this end, we employed the thermodynamic integration

using Langevin dynamics (TILD)55,56 method, i.e., the
combined application of thermodynamic integration,57−59

free energy perturbation (FEP) theory,57,60 and the Langevin
thermostat.61 Approaches based on the TILD concept can
predict various material properties such as defect formation
energies55,62−64 and melting points65,66 both accurately and
efficiently.
We decomposed the Helmholtz energy F(V, T) at

temperature T and at volume V for a given structure as

= +F V T E V F V T( , ) ( ) ( , )DFT
vib,el (2)

where EDFT is the conventional 0 K total energy of the system
obtained by DFT calculations and Fvib,el the contribution of
lattice vibrations and electronic excitations, including their
adiabatic coupling. The contribution Fvib,el was obtained based
on ab initio molecular dynamics (MD) in the finite-
temperature DFT extension by Mermin,67 where the Fermi−
Dirac distribution at the corresponding temperature was
applied to include the impact of electronic excitations. Note
that the impact of the coupling between lattice vibrations and
electronic excitations can be tens of meV/atom,68 and its
inclusion is therefore important for a high-accuracy prediction
of the Helmholtz energy.

Table 1. Ab Initio Computational Conditions Investigated in
the Present Studya

valence

XC cutoff (eV) k space Li Sn

A PBE 200 ≥16 128 2s 5s5p
B PBE 500 ≥16 128 2s 5s5p
C PBE 200 ≥21 600 2s 5s5p
D PBE 500 ≥16 128 1s2s 4d5s5p
E LDA 200 ≥16 128 2s 5s5p
F PW91 200 ≥16 128 2s 5s5p
G SCAN 200 ≥16 128 2s 5s5p

aThe columns “XC”, “cutoff”, “k space”, and “valence” refer to the
exchange−correlation functional, the energy cutoff for the plane
waves, the number of points per reciprocal atom sampled in the
reciprocal space, and the orbitals treated as valence for each element,
respectively. We also tested the energy cutoff of 700 eV (used by Sen
and Johari25) and found negligible differences from 500 eV.

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We computed Fvib,el(V, T) as

= + Δ + Δ→ →F F F Fvib,el vib,el
eh

vib,el
eh MTP

vib,el
MTP DFT

(3)

The first term in eq 3 is the contribution of lattice vibrations
to the Helmholtz energy, analytically computed based on an
effective harmonic (eh) potential69,70 (Appendix B.2 in the
Supporting Information) obtained from ab initio MD results
(Appendix B.1 in the Supporting Information). Using such a
potential can provide a better approximation of the Helmholtz
energy than the harmonic potential at 0 K71 and therefore
serve as a computationally better reference for the following
thermodynamic integration.
The second term (eh → MTP) in eq 3 amounts to the

difference between the Helmholtz energies of the system
governed by the effective harmonic potential and that by a
moment tensor potential (MTP),72−75 and it is computed by
thermodynamic integration. The MTP is a type of machine-
learning interatomic potential that can predict accurate
energies and atomic forces even for complex multicomponent
systems71,74,76 or systems with magnetic degrees of freedom.77

In this work, the MTP was obtained by fitting to ab initio MD
data (Appendix B.3 in the Supporting Information). Note that
the accuracy of the MTP can be further systematically
improved by using active learning techniques.73−75,77−79

The third term (MTP → DFT) in eq 3 is the difference
between the Helmholtz energies of the system governed by the
MTP and that by DFT and is computed by the first-order
approximation of the FEP theory.60 “Direct upsampling” was
performed from MTP runs at each (V, T), wherein 10 random
configurations were chosen and self-consistent DFT calcu-
lations were carried out to obtain the Helmholtz energy
difference. The DFT Helmholtz energy was obtained based on
the Fermi−Dirac distribution with the true electronic temper-
ature in the formalism of Mermin;67 that is, the contribution of
electronic excitation to the Helmholtz energy was also
considered here. The exchange−correlation functional, the
plane-wave cutoff energy, the mesh for the reciprocal-space
sampling, and the orbitals treated as valence states were the
same as those chosen for the 0 K structure optimization
(condition A in Table 1).
Each of the three terms in eq 3 was computed for seven

volumes between 16 and 19 Å3/atom and 12 temperatures
from 50 K up to 600 K. The highest temperature of 600 K was
set because, above 600 K, the MTP predicted a phase change
at higher temperatures in structures #7 and #23 (Appendix E
in the Supporting Information). These were then fitted to
polynomials with the terms of T, TV, T2, TV2, and T2V. The
three terms in eq 3 were then summed up to provide the entire
Helmholtz energy surface F(V, T) for a dense grid of
temperatures and volumes. Then, the Gibbs energy G(p, T),
where p is the pressure, was computed via a Legendre
transformation, which is shown in Section 4.8.

4. RESULTS AND DISCUSSION
4.1. Experimental Section. Li5Sn was obtained as

described in Section 2 in the form of gray crystals with no
recognizable shape and sizes of around 0.3 mm. The excess
lithium together with tin probably provides a melt functioning
as self-flux for enhanced crystal growth of the Li-rich
compounds.80 Li5Sn forms as a byproduct of Li17Sn4. During
treatment with liquid ammonia Li17Sn4 is apparently
decomposed in a reaction with ammonia to a badly crystallized

Li-poor product, indicating the redox activity of ammonia. This
was earlier observed in similar reactions of intermetallic phases,
for example, the oxidation of silicide or germanide Zintl ions to
new tetrel element modifications81−83 or to framework
clathrate structures by protic reactants as organic ammonium
ions, HCl, or water,84 to name only few. The Li5Sn crystals are
more kinetically stable against attack of ammonia and thus can
be isolated after brief exposure. However, upon extended
contact to liquid ammonia, these crystals also degrade. The
crystal structure contains mutually isolated tin atoms entirely
surrounded by lithium atoms, putting forward an interpretation
of Sn4− in a metallic Li matrix, in other words (Li+)5[Sn

4−]·e−,
as similarly discussed for Li17Sn4.

21 The results of the crystal
structure refinements leave little room for unnoticed deviations
from the derived composition. In order to exclude the presence
of unintended contamination by hydrogen or small amounts of
oxygen or nitrogen, a chemical analysis on these elements by
the hot gas extraction technique was carried out, resulting in
only negligible concentrations calculated to an overall
composition of Li5SnN0.0005O0.13H0.06. The small oxygen
contamination is typical for a highly air- and moisture-sensitive
compound and likely to originate in a brief air contact during
transfer of the only mechanically closed tin capsules from the
glovebox to the analyzer.
Table 2 shows the lattice parameters and the fractional

atomic coordinates of Li5Sn obtained from experiments.

Details of the structure refinement are found in Table 3.
Li5Sn crystallizes in the orthorhombic space group Cmcm with
only one crystallographic site for Sn and two for Li. Sn and
Li(1) with equal multiplicity (Wyckoff site 4c) are situated in
hexagonal prisms of Li(2) with four times larger multiplicity
(site 16h). These hexagonal prisms around Sn are capped by
two Li(1) and vice versa to yield 14-fold coordinations. The 11-
fold coordination of Li(2) atoms resembles an Edshammar
polyhedron, which occurs rather frequently in intermetallic

Table 2. Lattice Parameters and Fractional Atomic
Coordinates of Li5Sn in Cmcm (#7) from Experimental
Structure Determination at Room Temperature in
Comparison with Those Obtained from Ab Initio
Calculationsa

experimental ab initio

compound Li5Sn
crystal system orthorhombic
space group Cmcm (no. 63)
number of formula units Z 4
a (Å) 5.6638(4) 5.701
b (Å) 9.3417(8) 9.108
c (Å) 8.0477(6) 8.206
volume V (Å3) 425.80(6) 426.06
density ρcalc (g cm−3) 2.393 2.392
Li(1) 4c x 0 0

y 0.3984(12) 0.384 96
z 1/4 1/4

Li(2) 16h x 0.2492(8) 0.241 70
y 0.1193(5) 0.125 40
z 0.0756(7) 0.082 41

Sn 4c x 1/2 1/2
y 0.35493(3) 0.368 24
z 1/4 1/4

aDetails of the structure refinement are found in Table 3.

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compounds.85,86 All three occurring coordination polyhedra
are depicted in Figure 4. These are markedly different from

those occurring in Li17Sn4, which, as most previously
characterized binary Li-rich stannides, can be structurally
related to an ordered body-centered cubic packing of Li and
Sn, distorted by the different spatial requirements of both
metals.16 Tables 4 and 5 show the interatomic distances and
angles, respectively, of Li5Sn obtained from experiments. The
Sn−Li distances of 2.8609(16) Å for Li(1) and 2.972(5)−
3.172(5) Å for Li(2) are in the expected range as compared to
those obtained for Li17Sn4 with similar high coordination
numbers and probably the same electronic situation.19 The
shortest distance Sn−Li(1) is located in voids of a hexagonal
channel of Li(2). In order to maximize this distance, both Sn
and Li(1) are slightly displaced from the center of the
coordination polyhedron parallel to [010] in opposite
directions, resulting in the Li(1)−Sn−Li(1) angle of
163.7(4)° as depicted in Figure 4.
Figure 5a shows a section of the experimental crystal

structure of Li5Sn emphasizing the framework of vertex-, edge-,
and face-sharing bicapped hexagonal prisms around Sn. In this
structure, the polyhedra around Sn share the opposite capping

Li(1) vertices parallel to [100]. For polyhedra around Li(1)
this applies correspondingly, sharing opposite capping vertices
of Sn, resulting in parallel slightly kinked chains of alternating
Sn and Li(1) atoms within this direction located in a hexagonal
primitive channel of Li(2). The coordination polyhedra around
Sn are connected to eight other Sn coordination polyhedra in
the edge-sharing manner and to four further ones via
rectangular face-sharing within (100). This face-sharing leads
to zigzag chains parallel to [001].

4.2. Structural Comparison between Experiment and
Ab Initio for Cmcm Li5Sn. In Table 2, the structural
parameters of Cmcm Li5Sn (structure #7 in the enumeration)
obtained from the ab initio calculations at 0 K are compared
with those obtained from our experiments. The differences in
the lattice parameters lie in the range of 1% to 2%, which is a
typical range of deviation for the standard exchange−
correlation functionals (e.g., refs 87 and 88). Thus, the
comparison of the geometry of the specific Cmcm Li5Sn
structure provides a reasonable agreement with experiment in
terms of structural data.

4.3. Structural Characteristics of the Li5Sn Family.
The Cmcm structure observed in the experiments is different
from the structures previously reported in ab initio
investigations on Li5Sn.

25,26 However, as described in Section
3.1, the experimental and the previous ab initio structures can
be understood as different arrangements of the bicapped
hexagonal prisms with Sn at the center and with a frame of 14
Li atoms, among which 2 and 12 are on the cap and the prism
positions, respectively (cf. Figure 4a). Indeed, there exists a

Table 3. Selected Parameters in Experimental Structure
Determination of Li5Sn in Cmcm (#7) in Experiments

temperature T (K) 293
diffractometer κ-CCD Bruker-

Nonius
wavelength λ (Å) 0.710 73
monochromator graphite
2θmax (deg) 54.90
absorption coefficient μ (mm−1) 5.750
h, k, l −7 ≤ h ≤ 5

−12 ≤ k ≤ 12
−10 ≤ l ≤ 10

measured reflections 3979
unique reflections 291
Rint, Rσ 0.0476, 0.0177
refined parameters 19
goodness-of-fit on F2 (GoF) 1.181
R1, wR2 0.0154, 0.0384
extinction parameter 0.0030(8)
F(000) 260
largest peak, deepest hole in e− difference map (Å−3) 0.84, −0.36

Figure 4. Coordination polyhedra around (a) Sn, (b) Li(1), and (c)
Li(2) occurring in the experimentally observed Li5Sn structure with
the space group Cmcm (#7 in Figure 6). Gray, dark green, and light
green spheres represent Sn, Li(1), and Li(2), respectively. Note that
the alternative notations Li(cap) and Li(prism) are from the
viewpoint of the Sn coordination polyhedra and are used for the ab
initio analysis in Section 4.7.

Table 4. Interatomic Distances of Li5Sn in Cmcm (#7)a

distance (Å)

quantity experimental ab initio

Sn−Li(1) 2 2.8609(16) 2.854
Sn−Li(2) 4 2.972(5) 2.992

4 2.986(5) 3.056
4 3.172(5) 3.046

Li(1)−Li(2) 4 2.871(9) 2.976
4 2.986(5) 3.101
4 3.280(10) 3.062

Li(2)−Li(2) 1 2.539(9) 2.655
1 2.729(9) 2.644
1 2.806(11) 2.750
1 2.822(10) 2.756
1 2.841(10) 2.945

aQuantities are evaluated with focusing on the first atom.

Table 5. Interatomic Angles of Li5Sn in Cmcm (#7)a

angle (deg)

quantity experimental ab initio

Sn−Li(1)−Sn 1 163.7(4) 173.9
Li(1)−Sn−Li(1) 1 163.7(4) 173.9
Li(1)−Sn−Li(2) 2 56.6(2) 60.5

2 61.36(10) 63.2
2 68.4(2) 63.1
2 109.3(2) 114.3
2 117.15(10) 116.7
2 125.3(2) 122.1

aQuantities are evaluated with focusing on the pair of first and second
atoms. The angles of Sn−Li(1)−Sn and Li(1)−Sn−Li(1) are
symmetrically equivalent.

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large family of such structures that feature the capped
hexagonal prisms as the basic entity which can be systemati-
cally arranged by the technique of structure enumeration (cf.
Section 3.1). The Li coordination polyhedra are also similar
among all of these structures; the coordination polyhedra
around Li(cap) are always bicapped hexagonal prisms
consisting of two Sn and 12 Li(prism) atoms, like in Figure
4b, and the coordination polyhedra around Li(prism)
Edshammer polyhedra85,86 consisting of three Li(cap), five
Li(prism), and three Sn atoms like in Figure 4c, where only the
arrangements of Sn and Li differ among the structures. In order
to provide a comprehensive phase stability analysis, we thus
consider a large subset of Li5Sn structures from this family
(specifically 108 structures) with different arrangements of the
polyhedra generated by structure enumeration.
4.4. Phase Stability at 0 K. Figure 6 shows the ab initio

computed energies of the 108 Li5Sn structures at 0 K with
relaxed atomic positions and relaxed cell shape. Structure #23
is found to be energetically the most stable one among all the
structures. Structure #23 has a space group of Immm (No. 71)
and is different from those found in the previous ab initio

investigations, i.e., from the one found by Mayo and Morris
(#0, P6/mmm (No. 191), +10.6 meV/atom)26 and by Sen and
Johari (#83, C2/m (No. 12), +0.5 meV/atom).25 Structure
#23 is also distinct from the experimental structure (Cmcm
(No. 63)), which in Figure 6 corresponds to #7. At 0 K, the
experimental Li5Sn structure (#7) is higher in energy by +12.1
meV/atom than the computationally determined lowest-
energy structure (#23). Figure 5b shows the arrangement of
the Sn coordination polyhedra in structure #23. The lattice
parameters of structure #23 are a = 5.763 Å, b = 8.156 Å, and c
= 13.681 Å, and the fractional atomic coordinates are
summarized in Table 6.
One may notice that the energy differences among the three

lowest-energy structures (#23, #41, #83) vary only within 0.5
meV/atom. As detailed in Section 4.5, however, these energy
differences are very robust against detailed computational
conditions, and thus we can conclude with confidence that in
DFT at 0 K the structure #23 is the energetically most stable
phase with the composition of Li5Sn.
Figure 7 shows the computed energy−volume curves at 0 K

for some of the structures. Structure #23 is found to be

Figure 5. (a) Li5Sn with the space group Cmcm found in the present experiments. (b) Li5Sn with the space group Immm showing the lowest energy
at 0 K in the ab initio simulations. Li(1) (Li(cap)) atoms are shown in dark green, Li(2) (Li(prism)) atoms in light green, and Sn atoms in gray. Sn
coordination polyhedra in different colors (blue and orange) are connected in an edge-sharing manner (cf. Figure 3).

Figure 6. Comparison of ab initio computed energies of the 108 Li5Sn structures at 0 K at their optimized atomic positions. The energy of structure
#23, which shows the lowest value, is set as the reference.

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energetically the most stable one for most of the investigated
volumes, and structure #7, found in the present experiments, is
substantially higher in energy than structure #23. This implies
that, by the application of pressure, it is unlikely that the
experimentally observed structure #7 could be thermodynami-
cally stabilized over structure #23.
The just presented phase-stability analysis among the 108

Li5Sn structures reflects only the energetic competition at a
fixed composition of 83.3̅ at. % Li. To investigate whether
phase decomposition into a two-phase state is energetically
more favorable than the best Li5Sn structure (i.e., #23),
specifically a decomposition into the end-member phase bcc Li
and the known stable phase F4̅3m Li17Sn4, we have invoked eq
1. Indeed, we find that structure #23 of Li5Sn is 9.8 meV/atom
higher in energy than the two-phase state, which means that
structure #23 (as well as any of the other investigated Li5Sn
structures) does not correspond to an equilibrium state but to
a thermodynamically metastable phase at 0 K and under zero
pressure.
4.5. Robustness against Computational Conditions.

To make sure that our results are robust and insensitive to the
details of the computations despite the small energetic
differences, we tested various computational settings, including
different cutoff energies, different k-space mesh densities, PAW
potentials with different valence states, and various exchange−

correlation functionals (cf. Section 3.2 and specifically Table
1). Figure 8 shows the resulting energy comparison among
these computational settings in the form of correlation plots,
with the energy of structure #23 set as the reference. For all
investigated computational settings, structure #23 is clearly
found to be the energetically lowest one among the 108 Li5Sn
structures. In fact, all the energy differences among the 108
structures are very similar among the various computational
settings, as evidenced by the crosses lying closely to the
diagonal in the correlation plots. For the PBE calculations
(Figure 8a−c), we see a nearly perfect correlation, and even
between different exchange−correlation functionals we see a
good correlation (Figure 8d−f). These results substantially
strengthen our confidence in that the phase stability among the
108 investigated Li5Sn structures as obtained in the ab initio
calculations is reliable and that structure #23 can be
conclusively regarded as the energetically most stable one
among the 108 structures at 0 K on the DFT level.

4.6. Impact of the Arrangement of the Sn Coordina-
tion Polyhedra on Phase Stability. To understand how the
arrangement of the Sn coordination polyhedra is related to the
relative energies of the Li5Sn structures, we employ the CE
method (Section 3.3). Figure 9a shows the ECIs obtained
when the doublet and the quartet clusters, i.e., clusters made of
two and four Sn coordination polyhedra, are considered in the
expansion. The largest contribution to the energy comes from
the first three smallest doublet clusters, which are visualized in
Figure 9b. The absolute values of their ECIs decrease with the
increase of the maximum projected distance D between the
centers of the Sn coordination polyhedra within the clusters.
Further, a quartet cluster, which is also visualized in Figure 9b,
has an ECI whose absolute value is larger than 1 meV/atom.
This highlights the importance of this quartet cluster to be
included for an accurate energy prediction. In particular, the
quartet cluster is more important than the doublet cluster with
the projected distance ≈D D7 2.646 between the centers of
the Sn coordination polyhedra.
As found from Figure 9a, the first-nearest neighbor doublet

cluster shows a negative ECI, which means that the Sn
coordination polyhedra favor being connected with each other
in the face-sharing manner. It is, however, critical to realize that
there is a counteracting contribution from the second- and the
third-nearest neighbor doublet clusters as well as the above-
mentioned quartet cluster, which can stabilize Li5Sn structures
involving edge-sharing Sn coordination polyhedra in rather
sophisticated ways. In particular, the two doublet clusters with
positive ECIs favor configurations where the second and third
nearest-neighbor coordination polyhedra are shifted against
each other by one-half along the cap direction (i.e., they favor
orange-blue occupations).
We can quantify the importance of the various clusters by

the analysis of the root-mean-square error (RMSE) of the
energies predicted by the CEs including specific clusters, as
summarized in Table 7. In the extreme limit, when only the
first nearest-neighbor doublet cluster is included, we obtain an
RMSE of 2.702 meV/atom, which is large compared to the
relevant energy scale (≈16 meV/atom, cf. Figure 6). When
four doublet but no quartet clusters are included, the RMSE
reduces to 1.300 meV/atom. This value is still appreciable due
to the comparably small overall energetics. This statement is
better supported by the scatter observed in the correlation plot
in Figure 10a for the CE containing only doublet clusters. Even

Table 6. Fractional Atomic Coordinates for Structure #23
with the Space Group Immm As Obtained in the Ab Initio
Simulations with Setting A in Table 1

Wyckoff x y z

Li 16o 0.761 46 0.331 46 0.164 01
Li 8n 0.224 98 0.162 46 0
Li 4j 1/2 0 0.844 39
Li 2c 1/2 1/2 0
Sn 4i 1/2 1/2 0.319 55
Sn 2d 0 1/2 0

Figure 7. Ab initio computed energy−volume relations of Li5Sn at 0
K. The curves are obtained by fitting the energy−volume relations to
the Vinet equation of state.89,90 The minimum energy of the structure
#23 is set as the reference.

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Figure 8. Comparison among the various computational settings listed in Table 1 for the ab initio computed energies at 0 K of the 108 investigated
Li5Sn structures. The energy of structure #23 is set as the reference.

Figure 9. (a) ECIs obtained from the CE considering four doublet and 25 quartet clusters. The unit of the horizontal axis is the projected distance
between the nearest-neighbor Sn coordination polyhedra D. Some typical arrangements of the polyhedra in the specified clusters and how they
contribute to the energy are shown in the boxes. (b) Smallest doublet and quartet clusters. The clusters annotated by blue text show the largest
absolute values of ECIs.

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worse, such a CE fails to correctly predict the lowest-energy
structure (#23).
In contrast, when we add the above-discussed quartet cluster

with an ECI of +1.02 meV/atom (cf. Figure 9b) instead of the
fourth doublet cluster, the RMSE reduces down to 0.818 meV/
atom, which confirms the importance of this quartet cluster.
When the whole set of doublet and quartet clusters is
considered, the correlation is further significantly improved, as

indicated by the RMSE reducing down to 0.388 meV/atom. In
fact, it is essential to include the quartet clusters for correctly
predicting the lowest-energy structure #23, as demonstrated in
Figure 10b.

4.7. Sn−Li Distances and Their Relation to Energies.
Figure 11 displays the average distances from Sn to two types
of Li, i.e., Li(prism) and Li(cap), for all of the 108 Li5Sn
structures. As emphasized by the large gap between the two
gray-shaded regions, the average Sn−Li(prism) distance is
substantially larger than the Sn−Li(cap) distance for all
structures. This finding is nicely consistent with the observed
interatomic distances in the experimentally found Cmcm Li5Sn
structure (#7) (cf. Table 4). Indeed, we see a good quantitative
agreement between the theoretical prediction (orange dots in
Figure 11) and experiment (orange crosses) for structure #7.
Figure 12 shows various correlation plots among the relevant

energetic and geometric quantities for the 108 Li5Sn structures.
Between the average Sn−Li(cap) distance and the relative
energies (Figure 12a), there is a strong anticorrelation with a
Pearson coefficient of −0.942, which implies that longer Sn−
Li(cap) distances are energetically preferable. In relation with
the CE discussion in Section 4.6, we can state that the
structures lower in energy profit from an easier elongation of
the Sn−Li(cap) distance. The elongation of the Sn−Li(cap)
distance is mostly achieved by the elongation of the lattice
parameter along the cap direction, as demonstrated by the
strong positive correlation between them (Figure 12d).
Further, the off-centering of Sn in its coordination polyhedron
also contributes to an increase of the Sn−Li(cap) distance, as
found from the positive correlation between the Li(cap)−Sn−
Li(cap) angle and Sn−Li(cap) distance (Figure 12e).
There is also a positive correlation between the average Sn−

Li(prism) distance and the relative energies (Figure 12b) with
a Pearson coefficient of +0.698, which is however not as strong

Table 7. Dependence of the RMSE of the Energies
Predicted by the CE Method on the Numbers of Doublet
and the Quartet Clusters Included in the Expansiona

doublet quartet RMSE (meV/atom)

1 0 2.702
2 0 2.349
2 1 1.832
2 2 1.776
3 0 1.415
3 1 0.818
3 2 0.810
3 7 0.727
4 0 1.300
4 1 0.741
4 2 0.738
4 7 0.616
4 25 0.388

aStarting in the first row of the table with an expansion containing
only the strongest first nearest-neighbor doublet cluster (cf. doublet
cluster with 1D in Figure 9b), the following rows represent expansions
with successively more doublet and quartet clusters. For the rows with
the same number of doublet clusters, quartet clusters with successively
larger distances Dquartet are included, but only up to a Dquartet ≤ Ddoublet,
where Ddoublet is the maximum distance of the included doublet
cluster.

Figure 10. Comparison of ab initio computed energies at 0 K for the 108 Li5Sn structures with those obtained from the CE method. The energy of
structure #23 obtained from the ab initio calculation is set as the reference. (a) CE considering only the doublet clusters for the fitting. (b) CE
considered both the doublet and the quartet clusters for the fitting.

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as the anticorrelation between the average Sn−Li(cap)
distance and the relative energies (Figure 12a). The correlation
is primarily broken by a few streaks of data points (dashed gray
lines in Figure 12b), which can be identified with structures

involving linear ordering of face-sharing Sn coordination
polyhedra, as exemplified in Figure 12c. This implies a relation
between the Sn−Li(prism) distance and the type of
connection between the Sn coordination polyhedra. Figure

Figure 11. Comparison of the average Sn−Li distances for the 108 Li5Sn structures at 0 K at their optimized atomic positions. The crosses for
structure #7 indicate the values observed in our experiments at ambient temperature.

Figure 12. (a, b) Correlations of the ab initio computed energies at 0 K with (a) the average Sn−Li(cap) distances and (b) the average Sn−
Li(prism) distances for the 108 Li5Sn structures. Dashed gray lines are guides for the eyes. (c) Examples of linear face-sharing arrangement of Sn
coordination polyhedra in the same representation style as Figure 3. (d) Correlation between the lattice parameters along the cap direction and the
average Sn−Li(cap) distances. (e) Correlation between the average Li(cap)−Sn−Li(cap) angles and the average Sn−Li(cap) distances.

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13 shows the corresponding correlation plot between the
average Sn−Li(prism) distance and the average correlation

function of the first nearest-neighbor (1NN) doublet clusters,
which accounts for the number of face- and edge-sharing
polyhedra in the structure. There is a strong anticorrelation
between these properties, as indicated by the Pearson
coefficient of −0.953. That is, the more the 1NN polyhedra
are arranged in a face-sharing manner, the shorter the Sn−
Li(prism) distances are. As found in Section 4.6, however, it is
essential for an accurate energy prediction to take the doublet
clusters beyond the 1NN as well as the quartet clusters into
account.
4.8. Phase Stability for Li5Sn at Finite Temperatures.

Based on the detailed analysis in foregoing subsections, we can
confidently claim that, at 0 K and at the composition of Li5Sn,
ab initio predicts structure #23 with the space group of Immm
as the lowest-energy structure. Since this structure is different
from the experimentally found one (#7), the experimental
Cmcm Li5Sn phase is metastable and may therefore be realized
either by (1) thermodynamic stabilization at finite temperature
or (2) due to kinetic reasons during the experimental process.
To check the first possibility, i.e., whether the experimental
structure #7 could be stabilized at finite temperatures due to
lattice vibrations or electronic excitations, we further computed
the Gibbs energy at finite temperature based on ab initio
calculations. Specifically, we utilized the TILD approach55,56

with an intermediate MTP potential to get accurate Gibbs
energies at finite temperatures (Section 3.4) with considering
both lattice vibrations, including full anharmonicity, and
electronic excitations.
Figure 14 shows the computed Gibbs energies with respect

to the 0 K static energy of structure #23 as a function of
temperature for structures #7 (found in experiments) and #23
(ab initio lowest-energy state at 0 K found in the present
study). Even up to 600 K, i.e., slightly lower than the
temperature above which the initial phase is not stable
(Appendix E in the Supporting Information), the experimental

structure (#7) is found to be higher in Gibbs energy than
structure #23, although the difference of the Gibbs energies
becomes marginally smaller at higher temperatures. It should
be emphasized that the Gibbs energy in the present approach
considers full vibrational anharmonicity and the coupling
between the lattice vibrations and electronic excitations. This
implies that the experimental Cmcm Li5Sn structure is realized,
not due to thermodynamic stabilization but likely due to
kinetic reasons, e.g., due to the cooling process from the liquid
phase.

5. CONCLUSIONS
For the binary system Li−Sn, a new and to date the most
lithium-rich compound Li5Sn with the space group Cmcm was
obtained and structurally characterized. Knowledge of the
phase space is of pivotal importance for a deeper under-
standing of the electrode processes in the lithium−tin battery.
Formation of this particular lithium-rich compound would
enable an increase of the capacity. In accordance with two
independent recent predictions, the crystal structure is
composed of the identical coordination polyhedra (notably
bicapped hexagonal prisms around Sn and Li(1) and
Edshammer polyhedra around Li(2)) though differently
arranged.
Ab initio analyses, including thermodynamic integration

using Langevin dynamics in combination with moment tensor
potentials, have also been conducted to understand the
thermodynamic stability of the experimentally observed
Cmcm Li5Sn structure. Among the 108 Li5Sn structures
systematically derived using the structure enumeration
algorithm,36,37 including the Cmcm structure and those
predicted in previous studies, another new structure with the
space group type Immm has been found to be energetically the
most stable at 0 K. This computationally found Immm
structure is thermodynamically favorable even at finite
temperatures, indicating that the experimentally observed

Figure 13. Correlation of the Sn−Li(prism) distances and the average
correlation functions of the 1NN doublet clusters for the 108 Li5Sn
structures.

Figure 14. Computed Gibbs energies as a function of temperature of
the Li5Sn structures found in experiments (#7) and of ab initio lowest-
energy states at 0 K (#23) in the present study using MTP-assisted ab
initio thermodynamic integration with 288-atom supercell models.
The 0 K static energy of structure #23 is set as a reference.

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Cmcm Li5Sn is realized due to kinetics rather than
thermodynamics.

■ ASSOCIATED CONTENT

*sı Supporting Information
The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/jacs.1c10640.

Displacement parameters of experimentally found Cmcm
Li5Sn, further details of the computational conditions of
the Gibbs energies at finite temperatures, comparison of
the ab initio structural parameters of P6/mmm (#0) and
C2/m (#83) Li5Sn with previous publications, ab initio
structural stability of Cmcm (#7) and Immm (#23) Li5Sn
at finite temperatures using MTPs, density of states of
Cmcm (#7) Li5Sn (PDF)

Accession Codes
CCDC 2099217 contains the supplementary crystallographic
data for this paper. These data can be obtained free of charge
via www.ccdc.cam.ac.uk/data_request/cif, or by emailing
data_request@ccdc.cam.ac.uk, or by contacting The Cam-
bridge Crystallographic Data Centre, 12 Union Road,
Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

■ AUTHOR INFORMATION

Corresponding Author
Yuji Ikeda − Institute for Materials Science, University of
Stuttgart, 70569 Stuttgart, Germany; orcid.org/0000-
0001-9176-3270; Email: yuji.ikeda@imw.uni-stuttgart.de

Authors
Robert U. Stelzer − Institute of Inorganic Chemistry,
University of Stuttgart, 70569 Stuttgart, Germany

Prashanth Srinivasan − Institute for Materials Science,
University of Stuttgart, 70569 Stuttgart, Germany;
orcid.org/0000-0002-9199-4340

Tanja S. Lehmann − Institute of Inorganic Chemistry,
University of Stuttgart, 70569 Stuttgart, Germany

Blazej Grabowski − Institute for Materials Science, University
of Stuttgart, 70569 Stuttgart, Germany; orcid.org/0000-
0003-4281-5665

Rainer Niewa − Institute of Inorganic Chemistry, University of
Stuttgart, 70569 Stuttgart, Germany; orcid.org/0000-
0002-2633-7109

Complete contact information is available at:
https://pubs.acs.org/10.1021/jacs.1c10640

Notes
The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS
This project has received funding from the European Research
Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (grant agreement no.
865855). The authors also acknowledge support by the state of
Baden-Württemberg through bwHPC and the DFG through
grant no. INST 40/467-1 FUGG (JUSTUS cluster) and the
support by the Stuttgart Center for Simulation Science
(SimTech). P.S. would like to thank the Alexander von
Humboldt Foundation for their support through the Alexander
von Humboldt Postdoctoral Fellowship Program.

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