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Batteries based on multivalent ions such as magnesium have been attracting considerable attention due to their potential for high energy densities, but their low ion mobility remains an obstacle. Herein, ionic conductivity in spinel host materials, which represent a promising class of cathode and solid‐electrolyte materials in batteries, is addressed. Based on periodic density functional theory calculations, the important parameters that determine the mobility and insertion of ions are identified. In particular, the critical role that trigonal distortions of the spinel structure play for the ion mobility is highlighted. It is shown that it is the competition between coordination and bond length that governs the Mg site preference in spinel compounds upon trigonal distortions. This can only be understood by also taking covalent interactions into account. This reveals that purely ionic concepts are not sufficient to understand mobility in crystalline battery materials. Furthermore, the calculations suggest that anionic redox plays a much more important role in sulfide and selenide spinels than in oxide spinels. The findings shed light on the fundamentional mechanisms underlying ionic conductivity in solid hosts and thus may contribute to improvement of ion transport in battery electrodes. Ion mobility in electrodes and electrolytes is a critical performance parameter for batteries. Herein, using first‐principles electronic structure calculations, the factors underlying the migration and site preference of ions in spinel chalcogenides are determined. It is demonstrated that a purely ionic picture of the interaction in crystalline battery materials falls short of providing a complete understanding of ionic conductivity.
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Mechanism of Magnesium Transport in Spinel
Chalcogenides
Mohsen Sotoudeh, Manuel Dillenz, and Axel Groß*
1. Introduction
The development of Li-ion batteries (LIBs) had a major impact on
the widespread use of portable electronic devices. However, there
are safety and abundance issues associated with LIBs
[1,2]
that moti-
vate the search for alternative battery chemistries.
[3,4]
As a promising
alternative, magnesium has been proposed
[58]
as an active element
with a much higher earth abundance of 13.9% compared to
7104%ofLi.TheionicradiiofMg
2þ,
0.86 Å, and Liþ, 0.90 Å, are rather similar,
[1]
but Mg has the advantage of being a bivalent
ion, which leads to a higher volumetric capac-
ity of Mg metal anodes compared to Li,
3833 mAh cm3versus 2062 mAh cm3,
and also to a low reduction potential of
2.37 V versus the standard hydrogen elec-
trode (SHE) compared to 3.05 V of
Li.
[9,10]
Furthermore, Mg-ion batteries
(MIBs) exhibit a low tendency for dendrite
formation
[1115]
and a high melting point.
A high multivalent ionic conductivity of
110 mS cm1has been achieved in MIBs
at high temperatures.
[16,17]
However, a
major problem for MIBs lies in the slug-
gish kinetics during intercalation at room
temperature.
[2,18]
It should be noted that
the design of chemically stable electrodes
with high ionic conductivity is highly
desirable,
[2,1923]
as a low ionic mobility can
severely limit the performance of batteries.
To address the slow migration of Mg ions
in cathode materials at low temperatures,
Chevrel phases and layered and spinel TiS2structures have been
studied in detail.
[24]
A Mg-ion migration barrier of about
550 meV was found in cubic Ti2S4using galvanostatic intermittent
titration technique measurements. Note that typically maximum
migration barriers of 525 meV for micron-sized particles and
650 meV for nanosized particles are assumed to be compatible
with an adequate battery operation.
[25]
Studies on the sulde and
selenide spinel frameworks indicate low-energy barriers for Mg-
ion diffusion comparable to those of LIBs.
[26]
In contrast, oxide
spinel cathode materials exhibit high migration barriers for Mg
ions, which are caused by the relatively strong Coulombic attraction
between the guest Mg2þand host oxygen lattice,
[23]
which leads to a
lower ion mobility. The smaller electronegativity of sulfur and sele-
nium lattices enlarges the lattice constant of these materials and
thus also their ion mobility as typically diffusion barriers become
smaller for larger lattice constants. Nevertheless, the increase of
the ion mobility through the lowering of diffusion barriers is also
accompanied by lower Mg insertion energies into the spinel struc-
tures, which lowers the voltage
[27,28]
and thus causes a reduction of
the energy densities of chalcogenide materials.
Recently, MgSc2Se4has been found to be a super ionic con-
ductor exhibiting a high Mg-ion conductivity of 0.1 mS cm1at
room temperature.
[26]
This high ion mobility not only makes
MgSc2Se4a promising cathode material for MIBs, but also sug-
gests that it could be used as a solid electrolyte. However, solid
M. Sotoudeh, M. Dillenz, A. Groß
Institute of Theoretical Chemistry
Ulm University
Albert-Einstein-Allee 11, Ulm 89081, Germany
E-mail: axel.gross@uni-ulm.de
A. Groß
Electrochemical Energy Storage
Helmholtz Institute Ulm (HIU)
Helmholtzstraße 11, Ulm 89069, Germany
The ORCID identication number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/aesr.202100113.
© 2021 The Authors. Advanced Energy and Sustainability Research pub-
lished by Wiley-VCH GmbH. This is an open access article under the terms
of the Creative Commons Attribution License, which permits use,
distribution and reproduction in any medium, provided the original
work is properly cited.
DOI: 10.1002/aesr.202100113
Batteries based on multivalent ions such as magnesium have been attracting
considerable attention due to their potential for high energy densities, but their
low ion mobility remains an obstacle. Herein, ionic conductivity in spinel host
materials, which represent a promising class of cathode and solid-electrolyte
materials in batteries, is addressed. Based on periodic density functional theory
calculations, the important parameters that determine the mobility and insertion
of ions are identied. In particular, the critical role that trigonal distortions of the
spinel structure play for the ion mobility is highlighted. It is shown that it is the
competition between coordination and bond length that governs the Mg site
preference in spinel compounds upon trigonal distortions. This can only be
understood by also taking covalent interactions into account. This reveals that
purely ionic concepts are not sufcient to understand mobility in crystalline
battery materials. Furthermore, the calculations suggest that anionic redox plays
a much more important role in sulde and selenide spinels than in oxide spinels.
The ndings shed light on the fundamentional mechanisms underlying ionic
conductivity in solid hosts and thus may contribute to improvement of ion
transport in battery electrodes.
RESEARCH ARTICLE
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electrolytes need to exhibit a very low electronic conductivity,
whereas MgSc2Se4is also a good electron conductor.
Doping MgSc2Se4by Ti and Ce leading to Ti4þand Ce4þ
impurities, respectively, has been considered a means to lower
and neutralize the electronic conductivity.
[22]
Still, a high electron
conductivity has been observed in these materials, which has
been related to the presence of defects or phase deforma-
tion.
[26,29]
Furthermore, it has been shown that for chalcogenide
spinels containing lanthanoids the Mg mobility increases with
the size of the lanthanoids.
[30]
Note that spinel structures including transition metal ions
such as Ti, Mn, Fe, and Co exhibit magnetic properties due to
the lling of the 3dshell which cause signicant distortions
of the crystal lattice, namely, trigonal distortion, as shown later.
Such trigonal distortions have hardly been considered in deter-
mining the transport properties of sulde and selenide spinels
yet. However, there is ample evidence for the existence of trigo-
nal distortions in oxide spinels,
[3133]
rendering their existence in
chalcogenide spinels very likely. As the physical and chemical
properties of these compounds strongly depend on the delec-
trons, it is important to understand the role of electrons in
the ionic ordering, lattice distortion, and magnetic properties.
Specically, there are no convincing explanations with respect
to the factors that determine the spatial distribution of the cations
over the tetrahedral or octahedral sites and also with regard to the
dependence of the activation barriers for migration on the doping
level.
[34,35]
Studies on concerted migration
[36]
and the impact of
the structural framework on the ionic conductivity
[37]
were con-
ducted to analyze the factors determining the energy barriers for
migration. However, there are still open questions regarding the
cation ordering within the lattice and ion mobility in the various
concentrations.
In this article we report rst-principles electronic structure
calculations addressing the Mg-ion mobility in MgB2X4spinel
structures. As mentioned previously, such spinels have been
considered as both electrode and solid electrolyte materials,
depending on their electronic conductivity and insertion
energy. Still, a high ion mobility is critical for the battery per-
formance both in electrodes and in solid electrolytes. Although
we particularly focus on the electronic properties determining
ion migration in these materials, we mostly disregard here
whether the considered spinels are better suited as electrodes
or solid electrolytes, as we are convinced that the principles
underlying low ion mobilities in these materials are indepen-
dent from whether they are eventually used as electrodes or
solid electrolytes. We nd a strong dependence of the stability
of the octahedral versus tetrahedral sites on the ion concentra-
tion,whichweexplainbyanoctahedraldistortionandthecor-
responding changes in the lattice constants. Based on
geometric considerations, we identify the ratio of distances
in the octahedron and tetrahedron k64 as a descriptor for
the stability of the cations within the octahedral and tetrahe-
dral sites in the spinel lattice. In addition, we show that a
purely ionic interaction picture is insufcient to capture the
physics and chemistry behind the ionic migration and site
preference. These insights also provide a framework for
proposing promising spinel materials with high ion mobility
based on fundamental material properties.
2. Computational Details
First-principles calculations are conducted in the framework of
density-functional theory (DFT)
[38,39]
to determine the properties
of MgB2X4(B ¼Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Y, Al and X ¼S, Se)
spinels with regard to Mg migration. Exchange-correlation
effects are approximated within the generalized gradient approx-
imation (GGA) using the PerdewBurkeErnzerhof (PBE)
functional.
[40]
The calculations are performed using the projector
augmented wave (PAW)
[41]
method as implemented in the
Vienna Ab-initio Simulation Package.
[4244]
The nudged elastic
band (NEB)
[45]
method is used to determine Mg-ion migration
barriers. A 2 22 supercell of the primitive spinel cell is
constructed for the NEB calculations, including 56 atoms. The
total energy is evaluated with a 2 22 k-point mesh. A plane
wave cutoff of 520 eV is chosen in the expansion of the wave
functions, and total energies are converged within 1 10
5
eV
per supercell. The NEB calculations have only been performed
for spinel structures with transition metals with empty dorbitals.
For these systems, the pure PBE approach is sufcient to yield
reliable electronic and structural properties, except for the exact
size of the band gap. Thus, we also avoid the well-known prob-
lems in obtaining converged NEB results when using GGA þU
approaches or hybrid functionals. The electronic properties of
spinels with transition metals that have partially lled dbands
have been obtained with the HeydScuseriaErnzerhof HSE06
functional
[46]
to correctly account for the electron correlation.
We also checked whether van der Waals interactions play a role,
but we found no signicant effects upon including van der Waals
dispersion corrections, so we did not further consider them in
our study.
Mg-ion migration in the chalcogenides has been studied in the
low (one Mg vacancy per supercell) and high (one Mg atom
inside the supercell) vacancy limit. The structures were fully
relaxed until the forces on the atoms were converged within
0.05 eV Å
1
. The NEB calculations have been conducted with
four distinct images between the tetrahedral and octahedral sites
to evaluate the Mg-ion migration trajectory. To minimize the
interaction between the migrating Mg ions across periodic
boundaries, a distance of 10 Å between them is chosen.
The Mg intercalation energy Einter in the spinel structure with
respect to a metallic magnesium anode is given by
EinterðMgÞ¼EðMgxþyB2X4ÞðEðMgyB2X4ÞþxEðMgÞÞ (1)
where EðMgyB2X4Þis the total energy of the spinel with a Mg
concentration yin the unit cell, and EðMgÞis the cohesive energy
of Mg bulk in the metal phase. The corresponding open circuit
voltage (VOC) is then given by
VOC ¼Einter
zF (2)
where Fis the Faraday constant and zcorresponds to the elemen-
tary charges that are transferred upon the discharging reaction
with z¼2 for MIBs. When Einter is expressed in electronvolts,
VOC in volts is simply given by Einter=2 for MIBs.
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3. Results and Discussion
Among the complex transition-metal (B) oxides and chalcoge-
nides, spinel structures with the composition Mg2þB3þ
2X2
4cor-
respond to the most promising Mg-ion conductors.
[29,47,48]
The
spinel structure shown in Figure 1 consists of a face-centered
cubic lattice of X anions (X ¼O, S, Se) with two kinds of inter-
stices between the sites of the fcc lattice: tetrahedral interstices
MgX4and octahedral interstices BX6. The BX6octahedra form a
network of edge-sharing chains, while the Mg ions are located in
the tetrahedrally vacant spaces of X ions, forming the MgX4
units. The B sublattice of the spinel structure is known as the
pyrochlore lattice with strong geometrical frustration effects.
The Mg sublattice forms a diamond lattice. As far as the elec-
tronic structures of the transition metal spinels are concerned,
the dorbitals split into the high-lying doubly degenerate eg
and low-lying triply degenerate t2gorbitals caused by the crystal
eld splitting of the regular BX6octahedron.
Note that it is well known that spinel oxides tend to exhibit a
strong JahnTeller distortion upon lithium insertion, which
leads to a reduction of the crystal symmetry from cubic to tetrag-
onal symmetry. For example, the lithiation of the LiMn2O4spinel
to Li2.2Mn2O4is accompanied by a tetragonal distortion charac-
terized by a c=aratio of c=a¼1.16.
[49,50]
On the other hand,
increasing the average oxidation state of manganese in these
lithium manganospinels from 3.5þto 4þsuppresses the
JahnTeller distortion connected at the same time with a transition
from antiferromagnetic to ferromagnetic behavior.
[51]
In our calcu-
lations of the sulde and selenide spinels, we carefully looked for
possible JahnTeller distortions, but could not detect any. We attri-
bute this to the predominant ferromagnetic order of these spinels,
which makes them much more conducting than oxides due to the
enhanced pdhybridization. Note furthermore that spinel oxides
are also prone to spin inversion and that sulde spinels such as
MgIn2S4have been shown to exhibit an inverted spinel structure.
[52]
However, to the best of our knowledge the number of sulde and
selenide spinels with an inverted structure is still limited. For exam-
ple, it has been carefully veried that MgSc2Se4does not exhibit
inversion.
[26]
We also attribute this to the higher conductivity of
sulde and selenide spinels associated with more delocalized elec-
tronic states, which suppresses high-spin states and thus strong
ligand-eld stabilization, which would favor spinel inversion.
However, spinel structures often exhibit a trigonal distortion
of the octahedra that corresponds to a displacement of the X ions
along the ½111direction and changes the Ohoctahedral symme-
try to a D3hoctahedral symmetry but keeps the overall octahedral
shape unchanged (see Figure 2a).
[53]
The trigonal distortion can
be characterized by a uanion parameter
[54]
that reects the dis-
placement of the X ions along the ½111direction in units of the
lattice constant a. Sickafus et al.
[54]
showed that this parameter
can be expressed through the effective radii r(Mg) and r(B) of the
Mg and metal cations, respectively, according to
Figure 1. a) Rock-salt, b) zinc-blende, and c) spinel structure. The spinel lattice is an ordered mixture of the zinc-blende and rock-salt structure. The A
species (yellow) of AB
2
X
4
occupy the tetrahedral sites, while the B species (blue) only occupy octahedral sites. The red spheres denote the oxide and
chalcogenide anions such as O2,S
2, and Se2.
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u¼0.3876 rðBÞ
rðMgÞ

0.07054 (3)
Interestingly, the effective radius of the X anions does not
enter this expression, which means that the size of these anions
obviously does not affect the trigonal distortions. For a value of
u¼3
8, an ideal spinel structure without any trigonal distortion
results. u>3
8is associated with a trigonal distortion of the octa-
hedra through which the tetrahedrons are enlarged at the
expense of the octahedrons, whereas it is the other way around
for u<3
8. The trigonal distortion of the octahedron further
divides the threefold degenerate t2gstates into a lower a1gstate
and a twofold degenerate e0gstate, as shown in Figure 2a. It
should be noted that the representation of the a1gstate is
1
ffiffi3
pðxy þyz þzxÞ, pointing toward the center of the B-lattice tet-
rahedron. The e0gstates are different from the doubly degenerate
egstates and they are perpendicular to the a1gstate. At low tem-
peratures,
[31]
alternatively a tetragonal distortion often occurs,
which splits the threefold degenerate t2gstates into a higher
xy state and the twofold degenerate yz=zx lower states. The
tetragonal distortion divides the doubly degenerate egstates as
well into x2y2and 3z2r2states. Note, however, that the split-
ting of the t2gstates shown in Figure 2a is exaggerated; the cal-
culated splitting is much smaller. Therefore we will in the
following still refer to these two groups of states by calling them
egand t2gstates for the sake of convenience.
Apart from the additional crystal eld splitting, the trigonal
distortions also modify the bonding distances, as mentioned
in the previous paragraph. This can be quantied by explicitly
looking at the MgX distances dðcn4Þand dðcn6Þin the tetrahe-
dral and octahedral sites, respectively. In the original spinel
structures with the Mg ion in a tetrahedral site and the octahedral
vacancy being empty, these distances can be expressed as a func-
tion of the anion parameter uas
[54]
dðcn4Þ¼ðu1
4Þaffiffi
3
p
dðcn6Þ¼ 2ðu3
8Þ2þðu1
8Þ2

1=2a(4)
Using Equation (4), the ratio k64 between the bond lengths in
the octahedral and the tetrahedral sites is given by
k64 ¼dðcn6Þ
dðcn4Þ¼ð2ðu3
8Þ2þðu1
8Þ2Þ1=2a
ðu1
4Þaffiffi
3
p¼
u¼0.375 2
ffiffi
3
p(5)
Here we indicated that in the perfect crystal with u¼3=8¼
0.375 the ratio is k64 ¼2=ffiffi
3
p1.15, which means that in this
structure the MgX bond length in the octahedral sites is 1.15
times larger than the tetrahedral bond length.
In Figure 2b, we have plotted the ratio k64 as a function of the
anion parameter ufor a number of ternary Mg spinels. The upper
black circles correspond to the values for the Mg ion in a tetrahe-
dral site and the octahedral vacancy being empty. It is obvious that
k64 decreases approximately linearly with uin the small consid-
ered interval of uvalues which are larger than the value of 0.375
for the ideal structure; i.e., for all considered spinels the size of
the tetrahedra is enlarged at the expense of the octahedron.
Furthermore, it is important to note that in the presence of the
Mg ions in the octahedral vacancy, k64, is further reduced, as
shown by the blue symbols in Figure 2b. Therefore, due to
the explicit interaction of Mg cations with the surrounding chal-
cogenide anions, the size of the octahedrons further shrinks with
respect to the tetrahedron. The dependence of k64 on uis in gen-
eral still linear, but there are outliers. This is particularly obvious
for MgMn2S4, where the presence of Mn apparently leads to a
signicant compression of the occupied octahedron.
Interestingly enough, the size of the trigonal distortions is not
(a) (b)
Figure 2. a) Illustration of the transition from an undistorted octahedron cage with a Ohoctahedral symmetry to a trigonally distorted cage with a D3h
octahedral symmetry and the associated further crystal eld splitting of the dstates. b) Dependence of the ratio k64 on the anion parameter ucharacteriz-
ing the trigonal distortion for S spinels. The black dots denote the results for the original spinel structures with the Mg ion in a tetrahedral site and the
octahedral vacancy being empty, and the black line corresponds to the analytical expression Equation (5). The blue diamonds are determined for the
relaxed spinels with the octahedral site occupied by a Mg cation. The blue line is a linear regression of these results. Note that the results for V and Al lie on
top of each other for both considered cases.
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exactly ordered according to d-state occupation but rather accord-
ing to decreasing crystal ionic radii as listed by Shannon,
[55]
sug-
gesting that the change in these radii acts as one of the main
driving forces for the trigonal distortions.
We now focus on the Mg mobility in the ternary spinel struc-
tures. The Mg-ion migration occurs between two tetrahedral sites
via the migration across the face-sharing octahedral void, which
is shown in Figure 3a. The transition state for the Mg migration
is located in the triangular face between the octahedral and tet-
rahedral sites. The magnitude of the activation energy Eais inu-
enced by the anion species and the size of the triangle. Oxide
cathode materials typically exhibit sluggish Mg2þmigration
kinetics and also limited cycle life. One way to reduce the mag-
nitude of the Mg2þmigration barriers is using the concept of
hardness/softness of ions,
[26,56]
which can be related to the polar-
izability of the ions
[57]
or the covalency of the interaction.
[58]
Using softeranions than oxygen, namely, S, Se, or Te, leads
to a weaker Coulombic attraction and a larger lattice constant,
which also increases the distance between the guest Mg2þand
the host lattice, thus enhancing ion mobility. Note that in fact
the degree of covalency can be quantied by the square of the
difference in the electronegativities of the migration cation
and the anion of the host lattice.
[59]
However, an increase in
the ion mobility is typically associated with a reduction of energy
density because low diffusion barriers are usually accompanied
by small intercalation energies.
Figure 3b shows the calculated Mg2þmigration barriers of
some selected sulde spinels. All compounds represent
Mg-ion migration energy smaller than 0.7 eV, conrming the rel-
atively good Mg2þconductivity in these spinel structures.
MgTi2S4is identied as a suitable Mg-ion conductor; however,
this compound is found to be unstable in the spinel structure and
to exhibit electronic conductivity.
[60]
Sulde spinels enhance the
pdhybridization compared to oxides and tend to be more con-
ducting. The various transition metal ions with d1d10 congu-
rations lead to magnetic structures that are caused by the strong
Coulomb repulsion within the dorbitals.
[61]
In addition, smaller
crystal ionic radii of the transition metals lead to decreased
atomic distances and add more trigonal distortion to the system,
as shown in Figure 2b. This obviously increases the Mg migra-
tion barriers. Hence, transition metals with occupied dorbitals in
general reduce the Mg-ion conductivity depending on the partic-
ular orbital character. Transition metal ions such as Sc with
empty dorbitals, in contrast, lead to small migration barriers.
In particular, the MgSc2S4spinel compound represents a balance
between small Mg2þmigration energies and sufcient structural
stability. Thus, in the following we will only focus on MgB2X4
compounds with empty dorbitals which are characterized by
high Mg-ion mobility according to our calculations. It is interest-
ing to note that an analogous trend has been found in a recent
computational study of Mg migration in lanthanoid chalcogenide
spinels.
[30]
In these systems, apparently the height of the Mg
migration barriers increases with higher f-state occupancy.
To elucidate the inuence of the electronic structure on the
properties of the spinels, we plotted in Figure 4 the density of
states (DOS) of MgB2X4spinels with B ¼Sc and Y and X ¼S
and Se that can be realized experimentally.
[62,63]
Note that these
spinel structures also exhibit trigonal distortions, but they are
smaller than those for the spinels with later d-band metals, as
shown in Figure 2b. In Sc and Y, the dorbitals are empty, which
leads to unoccupied t2g(green) and eg(yellow) manifolds. In both
compounds, with Sc and Y cations, respectively, the valence
bands are dominated by S- and Se-pbands, respectively, in
the energy range from 4 to 0 eV. For both systems, the DOS
of the t2gand egstates are rather broad and overlap with each
other. The main effect of replacing S ions by Se ions is a reduc-
tion of the bandgap by about 0.5 eV and a smaller ligand eld
splitting between antibonding egand nonbonding t2gstates. In
the valence band shown in Figure 4, d-derived states appear,
although Y and Sc in principle have no occupied dstates in
the conduction band. These states originate from the hybridiza-
tion between the dstates of the transition metal and the chalco-
genide pbands,
[64]
but they do not dominate the behavior of the
valence band.
Due to the absence of dvalence states in Sc and Y, these ele-
ments are not easy to oxidize or to reduce upon intercalation.
Hence, the chalcogenide anions need to be involved in the asso-
ciated redox processes. In fact, this anion-based redox chemistry
(anionic redox) has recently drawn quite some attention with
respect to the increase in the energy density of Li-, Na- and
Mg-ion batteries.
[6567]
To elucidate this anionic redox, we per-
formed a Bader charge analysis
[68]
and calculated charge density
(a) (b)
Figure 3. a) Illustration of single-ion migration from the tetrahedral site to the octahedral void and then to the next tetrahedral site. The chalcogenide
atoms such as S and Se are shown by the red spheres; the migrating Mg ions are presented by the spheres inside the tetrahedrons and the octahedron.
b) Calculated Mg migration barriers for several transition metal ions in the sulde spinels.
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differences
[69]
for MgSc2S4. Details of this charge analysis can be
found in the Supporting Information. Specically, we considered
the insertion of Mg into an octahedral site of the host Sc2S4lat-
tice at a low concentration resulting in a Mg0.125Sc2S4structure.
We nd that this insertion leads to a reduction of the sulfur
atoms reected by a change of the S Bader charge from
0.86eto 1.08e(see Figure S2, Supporting Information),
whereas Sc hardly participates in the reduction process. This con-
rms previous ndings that the classical description of the redox
process is no longer valid when the Fermi level becomes close to
the S/Se-pband.
[65]
In fact, even for spinel transition metals containing a nite
number of delectrons anionic redox can occur, as our calcula-
tions for MgCr2S4show. Upon Mg insertion into the Cr2S4host
lattice at a high Mg concentration, the S atoms become reduced
from a Bader charge of 1.02eto 1.30e, which is much stronger
than the accompanying reduction of the Cr atoms. In contrast, in
MgCr2O4both the Cr dand O porbitals participate in a compa-
rable fashion in the redox process according to our calculations
(see the Supporting Information). This indicates that in sulde
and selenide spinels the anionic redox should be much more
dominant than in oxide spinels, which can be traced back to
the much lower electronegativity of the chalcogenides S and
Se compared to oxygen.
Table 1 lists calculated properties of the considered spinel sys-
tems. These include structural properties of Mg(Sc/Y)
2
(S/Se)
4
spinels, the Mg migration barrier, the Mg intercalation energy,
and the open-circuit voltage in the high and low Mg concentra-
tion limit, and the volume change upon Mg intercalation. Based
on the calculations, MgY2Se4is a favorable candidate due to the
combination of a small migration barrier, a sufciently large
open-circuit voltage, and a small volume change. MgSc2Se4
and MgY2S4are also characterized by parameters that make
them suitable as Mg-ion conductors. However, the performance
of MgY2S4is deteriorated, despite a high open-circuit voltage
VOC, by an unfavorable volume expansion of almost 5% upon
Mg-ion removal. At rst sight, this volume expansion upon
removal of some atoms is surprising. Therefore, we also consid-
ered the volume change ΔV=Vupon Mg-ion removal for a num-
ber of spinel oxides. Interestingly enough, we nd a further
enhanced tendency toward volume expansion in these oxides
compared to the suldes. Obviously, there is competition
between volume reduction due to the removal of atoms and vol-
ume expansion as a consequence of the increased anion repul-
sion upon reducing the number of Mg cations, and this repulsion
increases with the hardness of the anions.
To further assess the ion mobility in these spinel structures,
the energies along the Mg migration paths for MgSc2S=SeðÞ
4and
MgY2S=Se
ðÞ
4for high and low concentrations of Mg ions are
plotted in Figure 5. Note that in the high Mg-ion concentration
limit, there are seven Mg ions in the 2 22 supercell located
in the tetrahedral sites, one of which is migrating, whereas in the
low Mg-ion concentration limit, there is only one Mg ion in the
supercell, which is also the migrating ion. The Mg-ion migration
barriers of MgY2S4(360 meV), MgY2Se4(361 meV), and
MgSc2Se4(375 meV) in the high Mg concentration limit are
rather small, leading to a high Mg mobility which is comparable
to Liþin fast Li conductors. This suggests that S and Se spinel
structures together with Sc and Y cations can act as excellent Mg
conductors. Furthermore, the bandgaps of about 1.5 eV for the
selenides and of about 2 eV for the suldes should lead to a rela-
tively low electron conductivity. Therefore, in principle, these
materials might as well be considered promising candidates
for solid electrolytes in Mg-ion batteries because of their high
Mg-ion mobility. However, experiments still found a high elec-
tron conductivity in these compounds,
[22]
probably due to the
presence of defects or phase deformations,
[26,29]
hindering their
use as solid electrolytes, but thus making them suitable as elec-
trode materials with high ion mobility.
In the low-Mg-concentration limit, the Mg-ion migration bar-
riers in the S and Se spinels are increased compared to the
Figure 4. Density of states for MgSc2S4, MgSc2Se4, MgY2S4, and
MgY2Se4from top to bottom. The total DOS is given in gray. The projected
DOS are shown in red for S and Se, in green for t2g, and in yellow for egd
orbitals. The energy zero is set to the top of the valence band.
Table 1. MgX, BX, BB, and MgMg bond lengths in angstroms for spinel compounds. B and X denote transition metal (Sc, Y) and anion (S, Se),
respectively. Calculated relative barrier energy Ea, intercalation energy Ehigh
inter (Elow
inter) (Equation (1)) for high (low) Mg concentration in electronvolts, and
corresponding open-circuit voltage Vhigh
OC (Vlow
OC ) in volts. The volume changes with respect to the structure without Mg are indicated by ΔV=V
Compound MgX [Å] BX [Å] BB [Å] MgMg [Å] Ea[eV] Ehigh
inter [eV] Vhigh
OC [V] Elow
inter [eV] Vlow
OC [V] ΔV=V[%]
MgSc2S42.464 2.593 3.784 4.634 0.415 5.149 2.574 5.165 2.582 10
MgSc2Se42.587 2.725 3.974 4.868 0.375 3.915 1.958 4.114 2.057 5
MgY2S42.510 2.740 3.949 4.836 0.360 5.508 2.754 5.561 2.780 þ4.8
MgY2Se42.624 2.868 4.131 5.059 0.361 4.329 2.165 4.432 2.216 2
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high-concentration limit, as shown in Figure 5. Furthermore, in
Mg0.125Sc2S=SeðÞ
4the Mg ion prefers the sixfold coordination
of the octahedral site, whereas in Mg0.125Y2S=SeðÞ
4the
Mg-ion prefers the fourfold coordination of the tetrahedral site.
Thus in the S and Se spinel structures together with Sc the most
favorable site for the Mg ion changes from the octahedral to the
tetrahedral site upon increasing the Mg concentration. This vary-
ing site preference, which is not the case for the Y cation, might
be detrimental for the performance of the Sc-containing cathodes
upon charge/discharge. In addition, the MgY2S=SeðÞ
4com-
pounds exhibit smaller relative volume changes upon the addi-
tion of Mg atoms than the MgSc2S=SeðÞ
4compounds, which
might be partly due to the fact Y has a larger crystal ionic radius
than Sc.
[55]
Up to now, we have concentrated on the electronic properties,
structural parameters, and Mg migration paths. Of particular
interest is that all Mg Sc=YðÞ
2S=SeðÞ
4compounds favor the tetra-
hedral sites for the Mg ions. However, in the low-Mg-
concentration limit, Mg ions prefer the octahedral site in the
Sc spinels. To analyze this behavior, we will rst concentrate
on the high-Mg-concentration limit. Interestingly, according to
our calculations Mg2þtends to occupy the octahedral sites in
the MgMn2S4spinel in the high-Mg-concentration limit. Here
we will show that it is the competition between coordination
and bond length induced by the trigonal distortion that governs
the Mg site preference in ternary spinel compounds MgB2X4
(B ¼Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Y, Al and X ¼S, Se).
To see this, we focus on the ratio k64 between the MgX bond
length in the occupied tetrahedral and octahedral sites, as shown
for some ternary spinels by the blue symbols in Figure 2b.
According to our calculations, for the MgAl2S4system character-
ized by a ratio of about k64 ¼1.08, the octahedral and tetrahedral
sites become energetically degenerate with regard to the Mg
occupation, as shown in Figure 6a. This can be explained by a
competition between bond length and coordination as a function
of the ratio k64. The octahedral site has the higher coordination
than the tetrahedral site, but obviously in the ideal structure the
elongation of the MgX bond length by 1.15 with respect to the
tetrahedral site makes the octahedral site energetically still less
favorable. However, for a decreasing ratio k64 the octahedral site
becomes increasingly more stable with respect to the tetrahedral
site. Note that the ratio k64 ¼1.08 is still larger than 1, but at this
value the larger bond length is compensated for by the higher
coordination of the octahedral site. For even smaller values of
k64, as for example in MgMn2S4with k64 ¼1.05, the octahedral
site is energetically more favorable, whereas for larger values of
k64, as in MgSc2S4with k64 ¼1.10, the tetrahedral site becomes
preferred (see Figure 6a).
A similar reasoning has recently been presented to under-
stand the Mg tetrahedral site preference in lanthanoid
0
0.1
0.2
0.3
0.4
0.5
0.6 (a)
Energy (eV)
MgSc2S4
MgSc2Se4
0
0.1
0.2
0.3
0.4
0.5
0.6
0 10 20 30 40 50
(b)
Energy (eV)
Reaction path length %
MgY2S4
MgY2Se4
(c)
Mg0.125Sc2S4
Mg0.125Sc2Se4
0 10 20 30 40 50
(d)
Reaction path length %
Mg0.125Y2S4
Mg0.125Y2Se4
Figure 5. The Mg2þmigration energy barriers (in electronvolts) as a function of the reaction path coordinate derived from periodic DFT calculations
combined with NEB for the single-ion migration from the tetrahedral site to the octahedral void corresponding to the S spinels (black) and the Se spinels
(blue) for low and high concentrations of Mg ions. The low-concentration limit has been realized by considering just one migrating Mg atom within the
222 supercell, whereas in the high-concentration limit we consider one additional migrating Mg atom within a 222 supercell with a
Mg0.875B2X4stoichiometry. Note that the full migration path in principle includes the further migration from the octahedral to the tetrahedral site,
but as the corresponding energies are symmetric with respect to the octahedral site, this part is omitted.
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chalcogenide spinels,
[30]
based on the concept that the preference
for coordination of a cation by an anion can be estimated by clas-
sic radii ratio rules. This argumentation about the competition
between bond length and coordination implicitly assumes that
the interaction is purely ionic between nonpolarizable atomic
charges so that the ionic interaction is additive. Let us make a
simple estimate about the stability of the tetrahedral Mg X4site
versus the octahedral Mg X6site assuming that only the direct
interaction between the Mg2þcation and the neighbouring chal-
cogenide X
2
anions contributes to the interaction. For nonpo-
larizable, spherically symmetric, and nonoverlapping charges,
the binding energies E(Mg X4) and E(Mg X6) in the tetrahe-
dral and the octahedral arrangement, respectively, are given by
EðMg X4Þ¼ 4QMg2þQx2
dðcn4Þ¼16
dðcn4Þ
EðMg X6Þ¼ 6QMg2þQx2
dðcn6Þ¼24
dðcn6Þ
(6)
where we have used cgs units for the sake of simplicity. For this
purely ionic interaction the binding energies are the same, i.e.,
EðMg X4Þ¼EðMg X6Þ), for the ratio of
kionic eq:
64 ¼dðcn6Þ
dðcn4Þ¼1.5 (7)
First of all note that this ratio of 1.5 is much larger than the
value of k64 ¼1.08 at which there is an equilibrium between the
tetrahedral site and octahedral site in MgAl2S4. In addition,
whether a spinel exhibits a tetrahedral or an octahedral site pref-
erence depends not only on the ratio k64, but also on the anion
parameter u. In Figure 6b, we again show the ratio k64 as a func-
tion of the anion parameter u, but now we also include some
additional data points for the low Mg-concentration limit.
In addition, we have inserted a dividing line given by
kdiv
64 ¼4.78ð12uÞ. In spinels above this line, the migrating
Mg ions prefer the tetrahedral site, whereas in those below this
line, the octahedral site is more stable. Thus for larger values of u,
the octahedral become more stable than the tetrahedral sites only
for smaller values of the ratio k64. In contrast, in the compounds
nearby the dividing line, such as Ti, the occupation of both the
tetrahedral and octahedral sites is energetically feasible, as also
conrmed experimentally.
[24]
To understand this trend, one should rst note that according
to Equation (4) both distances dðcn4Þand dðcn6Þbecome larger
with increasing uin the parameter range that is considered here.
However, for purely ionic interactions between nonpolarizable
spherically symmetric ions, the competition in the energetic
stability between two different structures does not depend on
the absolute distances, only on the ratio of distances,
[30,7072]
as reected in the simple estimate in Equation (7).
Consequently, these results can only be explained assuming that
the interaction is not purely ionic and that it falls off stronger
than 1=dwith distance d. Or, in other words, covalent interactions
contribute substantially to the stability of the Mg atoms in the voids.
Therefore, it follows that there is a simple criterion or descriptor
that allows one to identify whether covalent interactions play a
critical role in the relative stability of different structures: If
the relative stability depends not only on the ratio of distances
but also on the absolute value of these distances, then the inter-
action in these systems cannot be purely ionic.
The important role of covalent contributions in the interaction
within the spinels is also reected in the signicant width in the
DOS of the chalcogenide-derived states shown in Figure 4. For
covalent and metallic interactions, the strengths of single bonds
typically decrease with increasing coordination
[15]
based on bond-
order conservation arguments, so the single bond becomes
weaker for higher coordination. Furthermore, these interactions
0
0.2
0.4
0.6
(a) (b)
E
oct
E
tet
Energy (eV)
MgAl
2
S
4
(k
64
=1.08)
0
0.2
0.4
0.6
Energy (eV)
MgMn
2
S
4
(k
64
<1.08)
0
0.2
0.4
0.6
0 10 20 30 40 50
Energy (eV)
Reaction path len
g
th %
MgSc
2
S
4
(k
64
>1.08)
0.385 0.386 0.387 0.388 0.389
Anion parameter u
1.05
1.06
1.07
1.08
1.09
1.1
1.11
1.12
k64
Mg Ni S
MgB2S4
Y
Sc
Ti
Al Cr
Ni Fe Co
Mn
Mg Sc Se
Mg Sc S
Mg Y S
Mg Y2
Figure 6. a) Mg-ion migration barriers for spinel compounds with different trigonal distortions characterized by k64. b) The ratio k64 as a function of the
anion parameter ufor selected spinel compounds. Blue diamonds denote high-Mg-concentration compounds and red triangles low-Mg-concentration
compounds. The black line represents a dividing line between Mg tetrahedral and octahedral site preference.
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scale with the overlap between atomic orbitals, which falls off
exponentially for larger distances. Therefore, the ratio
k64 ¼dðcn6Þ=dðcn4Þneeds to become smaller for absolute larger
distances, i.e., for larger values of u, to make the octahedral more
stable than the tetrahedral site.
Our ndings provide a simple picture of the key parameter
underlying Mg-ion site preferences in spinel structures.
Similar to the Goldschmidt tolerance factor t,
[70]
which is used
to reect the variance in the stability of perovskites based only
on the ratio of the atomic radii of A, B, and X in ABX
3
,we
use a geometrical analysis to assess the relative stability of the
Mg2þsites in spinels. Our calculations and considerations of
the structure of the spinel compounds clearly indicate that it
is the ratio together with the absolute values of the MgX bond
lengths in the octahedral and tetrahedral sites that determines
the site preference and thus also the Mg mobility.
4. Conclusion
Based on periodic density functional theory calculations, we
have studied Mg ion mobility in spinel chalcogenides, which
are promising candidates for cathodes in MIBs. Overall, we nd
that trigonal distortions of the spinel structures play a critical
role for both the Mg site preference and the Mg migration bar-
riers. With respect to the transition metal used in the spinels, we
nd that an increasing d-band occupancy leads to smaller lattice
constants and larger trigonal distortions, which both lead to
larger migration barriers and thus decreasing diffusivities. In
addition, according to our calculations anionic redox upon
Mg insertion into the host lattice is more dominant in sulde
and selenide spinels than in oxide spinels. Therefore, we con-
centrated on spinel chalcogenide compounds with the early
d-band metals Sc and Y together with the soft-ion chalcogenides
S and Se.
Indeed, all these four considered spinels exhibit small diffu-
sion barriers of about 400 meV and smaller. In addition, these
materials allow open-circuit potentials with respect to metallic
Mg of about 2.5 V for the suldes and of about 2.0 V for the sele-
nides. This makes them theoretically well suited as cathode mate-
rials for MIBs. In contrast, the low diffusion barriers together
with the bandgap of about 1.5 eV for the selenides and of about
2 eV for the suldes limiting their electronic conductivity sug-
gests that these materials could also be used as solid electrolytes
in MIBs because of their high Mg-ion mobility.
In many spinel structures studied so far, the tetrahedral sites
exhibit a higher stability than the octahedral sites for Mg inser-
tion. Interestingly, we nd that in the Sc-based spinels this sta-
bility is reversed in the low-Mg-concentration limit. Our detailed
analysis reveals that the varying site preference is a consequence
of the competition between coordination and bond length
induced by trigonal distortions and absolute changes in the bond
distances demonstrating the important role of covalent contribu-
tions to the chemical interaction within the spinels. Thus, a
purely electrostatic interaction is inadequate for capturing all fac-
tors inuencing ion mobility and stability. In general, our results
and the analysis based on electronic and geometric factors pro-
vide a conceptual framework to understand fast ion conductivity
in spinel electrode materials, which will also be benecial for the
understanding and improvement of ion mobility in other mate-
rial classes.
Supporting Information
Supporting Information is available from the Wiley Online Library or from
the author.
Acknowledgements
M.S. thanks Sung Sakong and Mohnish Pandey for fruitful discussions.
The authors gratefully acknowledge nancial support from the Cluster
of Excellence POLiS (EXC-2154, project ID 390874152) of the Deutsche
Forschungsgemeinschaft (DFG) and computer time provided by the state
of Baden-Württemberg through bwHPC and the German Research
Foundation (DFG) through grant no INST 40/575-1 FUGG (JUSTUS 2
cluster).This work contributes to the research performed at CELEST
(Center for Electrochemical Energy Storage Ulm-Karlsruhe).
Conict of Interest
The authors declare no conict of interest.
Data Availability Statement
The data that support the ndings of this study are available from the
corresponding author upon reasonable request.
Keywords
density functional theory, ion conductivity, magnesium batteries, ternary
spinel chalcogenides
Received: June 1, 2021
Revised: July 9, 2021
Published online:
[1] J. Muldoon, C. B. Bucur, T. Gregory, Chem. Rev. 2014,114, 11683.
[2] P. Canepa, G. Sai Gautam, D. C. Hannah, R. Malik, M. Liu,
K. G. Gallagher, K. A. Persson, G. Ceder, Chem. Rev. 2017,117, 4287.
[3] G. A. Elia, K. Marquardt, K. Hoeppner, S. Fantini, R. Lin, E. Knipping,
W. Peters, J.-F. Drillet, S. Passerini, R. Hahn, Adv. Mater. 2016,28,
7564.
[4] M. Anji Reddy, M. Helen, A. Groß, M. Fichtner, H. Euchner, ACS
Energy Lett. 2018,3, 2851.
[5] T. D. Gregory, R. J. Hoffman, R. C. Winterton, J. Electrochem. Soc.
1990,137, 775.
[6] D. Aurbach, Z. Lu, A. Schechter, Y. Gofer, H. Gizbar, R. Turgeman,
Y. Cohen, M. Moshkovich, E. Levi, Nature 2000,407, 724.
[7] C. M. MacLaughlin, ACS Energy Lett. 2019,4, 572.
[8] R. Davidson, A. Verma, D. Santos, F. Hao, C. D. Fincher, D. Zhao,
V. Attari, P. Schoeld, J. Van Buskirk, A. Fraticelli-Cartagena,
T. E. G. Alivio, R. Arroyave, K. Xie, M. Pharr, P. P. Mukherjee,
S. Banerjee, Mater. Horiz. 2020,7, 843.
[9] N. Singh, T. S. Arthur, C. Ling, M. Matsui, F. Mizuno, Chem.
Commun. 2013,49, 149.
[10] Z. Zhao-Karger, M. E. Gil Bardaji, O. Fuhr, M. Fichtner, J. Mater.
Chem. A 2017,5, 10815.
www.advancedsciencenews.com www.advenergysustres.com
Adv. Energy Sustainability Res. 2021, 2100113 2100113 (9 of 10) © 2021 The Authors. Advanced Energy and Sustainability Research
published by Wiley-VCH GmbH
[11] D. Aurbach, Y. Cohen, M. Moshkovich, Electrochem. Solid-State Lett.
2001,4, A113.
[12] M. Matsui, J. Power Sources 2011,196, 7048.
[13] Q. S. Zhao, J. L. Wang, Electrochim. Acta 2011,56, 6530.
[14] M. Jäckle, A. Groß, J. Chem. Phys. 2014,141, 174710.
[15] M. Jäckle, K. Helmbrecht, M. Smits, D. Stottmeister, A. Groß, Energy
Environ. Sci. 2018,11, 3400.
[16] E. Levi, Y. Gofer, D. Aurbach, Chem. Mater. 2010,22, 860.
[17] Z. Zhao-Karger, R. Liu, W. Dai, Z. Li, T. Diemant, B. P. Vinayan,
C. Bonatto Minella, X. Yu, A. Manthiram, R. J. Behm, M. Ruben,
M. Fichtner, ACS Energy Lett. 2018,3, 2005.
[18] M. M. Huie, D. C. Bock, E. S. Takeuchi, A. C. Marschilok,
K. J. Takeuchi, Coord. Chem. Rev. 2015,287, 15.
[19] M. Walter, K. V. Kravchyk, M. Ibá˜nez, M. V. Kovalenko, Chem. Mater.
2015,27, 7452.
[20] C. B. Bucur, T. Gregory, A. G. Oliver, J. Muldoon, J. Phys. Chem. Lett.
2015,6, 3578.
[21] J. Bitenc, K. Pirnat, T. Banˇciˇc, M. Gaberšˇcek, B. Genorio, A. Randon-
Vitanova, R. Dominko, ChemSusChem 2015,8, 4128.
[22] L.-P. Wang, Z. Zhao-Karger, F. Klein, J. Chable, T. Braun, A. R. Schür,
C.-R. Wang, Y.-G. Guo, M. Fichtner, ChemSusChem 2019,12,
2286.
[23] T. Chen, G. Ceder, G. Sai Gautam, P. Canepa, Front. Chem. 2019,
724.
[24] X. Sun, P. Bonnick, V. Duffort, M. Liu, Z. Rong, K. A. Persson,
G. Ceder, L. F. Nazar, Energy Environ. Sci. 2016,9, 2273.
[25] Z. Rong, R. Malik, P. Canepa, G. Sai Gautam, M. Liu, A. Jain,
K. Persson, G. Ceder, Chem. Mater. 2015,27, 6016.
[26] P. Canepa, S.-H. Bo, G. Sai Gautam, B. Key, W. D. Richards, T. Shi,
Y. Tian, Y. Wang, J. Li, G. Ceder, Nat. Commun. 2017,8, 1759.
[27] M. S. Islam, C. A. J. Fisher, Chem. Soc. Rev. 2014,43, 185.
[28] A. Groß, Top. Curr. Chem. 2018,376, 17.
[29] P. Canepa, G. Sai Gautam, D. Broberg, S.-H. Bo, G. Ceder, Chem.
Mater. 2017,29, 9657.
[30] J. Koettgen, C. J. Bartel, G. Ceder, Chem. Commun. 2020,56, 1952.
[31] E. M. Wheeler, B. Lake, A. T. M. N. Islam, M. Reehuis, P. Steffens,
T. Guidi, A. H. Hill, Phys. Rev. B 2010,82, 140406.
[32] K. Matsuura, H. Sagayama, Y. Nii, N. D. Khanh, N. Abe, T. Arima,
Phys. Rev. B 2015,92, 035133.
[33] S. G. Menon, D. N. Hebbar, S. D. Kulkarni, K. Choudhari,
C. Santhosh, Mater. Res. Bull. 2017,86, 63.
[34] J. B. Goodenough, A. L. Loeb, Phys. Rev. 1955,98, 391.
[35] J. B. Goodenough, Energy Storage Mater. 2015,1, 158.
[36] X. He, Y. Zhu, Y. Mo, Nat. Commun. 2017,8, 15893.
[37] Y. Wang, W. D. Richards, S. P. Ong, L. J. Miara, J. C. Kim, Y. Mo,
G. Ceder, Nat. Mater. 2015,14, 1026.
[38] P. Hohenberg, W. Kohn, Phys. Rev. 1964,136, B864.
[39] W. Kohn, L. J. Sham, Phys. Rev. 1965,140, A1133.
[40] J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 1996,77, 3865.
[41] P. E. Blöchl, Phys. Rev. B 1994,50, 17953.
[42] G. Kresse, J. Hafner, Phys. Rev. B 1993,47, 558.
[43] G. Kresse, J. Furthmüller, Phys. Rev. B 1996,54, 11169.
[44] G. Kresse, D. Joubert, Phys. Rev. B 1999,59, 1758.
[45] D. Sheppard, R. Terrell, G. Henkelman, J. Chem. Phys. 2008,128,
134106.
[46] J. Heyd, G. E. Scuseria, M. Ernzerhof, J. Chem. Phys. 2003,118, 8207.
[47] C. Kim, P. J. Phillips, B. Key, T. Yi, D. Nordlund, Y.-S. Yu, R. D. Bayliss,
S.-D. Han, M. He, Z. Zhang, A. K. Burrell, R. F. Klie, J. Cabana, Adv.
Mater. 2015,27, 3377.
[48] J. Yin, A. B. Brady, E. S. Takeuchi, A. C. Marschilok, K. J. Takeuchi,
Chem. Commun. 2017,53, 3665.
[49] M. Thackeray, W. David, P. Bruce, J. Goodenough, Mater. Res. Bull.
1983,18, 461.
[50] M. M. Thackeray, A. de Kock, M. H. Rossouw, D. Liles, R. Bittihn,
D. Hoge, J. Electrochem. Soc. 1992,139, 363.
[51] C. Masquelier, M. Tabuchi, K. Ado, R. Kanno, Y. Kobayashi, Y. Maki,
O. Nakamura, J. B. Goodenough, J. Solid State Chem. 1996,123, 255.
[52] G. Sai Gautam, P. Canepa, A. Urban, S.-H. Bo, G. Ceder, Chem.
Mater. 2017,29, 7918.
[53] S. K. Banerjee, W. OReilly, T. Gibb, N. Greenwood, J. Phys. Chem.
Solids 1967,28, 1323.
[54] K. E. Sickafus, J. M. Wills, N. W. Grimes, J. Am. Ceram. Soc. 1999,82,
3279.
[55] R. D. Shannon, Acta Crystallogr. Sect. A: Found. Crystallogr. 1976,32,
751.
[56] A. Grimaud, W. T. Hong, Y. Shao-Horn, J. M. Tarascon, Nat. Mater.
2016,15, 121.
[57] J. Rungis, A. J. Mortlock, Philos. Mag. 1966,14, 821.
[58] J. Rouxel, Chem. Eur. J. 1996,2, 1053.
[59] M. Sotoudeh, A. Groß, Preprint, 2021, https://doi.org/10.21203/10.
21203/rs.3.rs309875/v2.
[60] A. Emly, A. Van der Ven, Inorg. Chem. 2015,54, 4394.
[61] C. Lacroix, P. Mendels, F. Mila, Introduction to Frustrated Magnetism:
Materials, Experiments, Theory, Springer Series in Solid-State Sciences,
Springer, Berlin 2011.
[62] M. Patrie, L. Domange, J. Flahaut, C. R. Hebd. Seances Acad. Sci. 1964,
258, 2585.
[63] M. Guittard, C. Souleau, H. Farsam, C. R. Hebd. Seances Acad. Sci.
1964,259, 2487.
[64] R. Asahi, Y. Taga, W. Mannstadt, A. J. Freeman, Phys. Rev. B 2000,61,
7459.
[65] M. Ben Yahia, J. Vergnet, M. Saubanère, M.-L. Doublet, Nat. Mater.
2019,18, 496.
[66] Z. Li, B. P. Vinayan, P. Jankowski, C. Njel, A. Roy, T. Vegge, J. Maibach,
J. M. G. Lastra, M. Fichtner, Z. Zhao-Karger, Angew. Chem. Int. Ed.
2020,59, 11483.
[67] N. Charles, Y. Yu, L. Giordano, R. Jung, F. Maglia, Y. Shao-Horn,
Chem. Mater. 2020,32, 5502.
[68] W. Tang, E. Sanville, G. Henkelman, J. Phys. Condens. Matter 2009,21,
084204.
[69] M. Dillenz, M. Sotoudeh, H. Euchner, A. Groß, Front. Energy Res.
2020,8, 584654.
[70] V. M. Goldschmidt, Naturwissenschaften 1926,14, 477.
[71] V. M. Goldschmidt, Trans. Faraday Soc. 1929,25, 253.
[72] V. Stevanovi´c, M. dAvezac, A. Zunger, Phys. Rev. Lett. 2010,105,
075501.
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... 29 However, we recently could show that the stability of ions in chalcogenide spinels can only be understood if deviations from a purely ionic interaction are taken into account. 50 It is essential to realize that the considered binary materials span the whole range of interaction characteristics between metallic and ionic bonding. Such bonding characteristics can in fact been classified in so-called Van Arkel−Ketelaar triangles, 51 in which compounds are placed according to the mean electronegativity χ mean (x axis) and the electronegativity difference Δχ(y axis) of the constituting elements. ...
... However, in a previous study 28 we found that the distance of the ions is the crucial parameter influencing the barrier heights, which can be represented by the sum r A + r X of their ionic radii. Furthermore, in another previous study 50 we have demonstrated that purely ionic concepts are not sufficient to understand the properties of nominally ionic crystals. Consequently, for the crucial new ingredient in the identification of a possible descriptor we propose to quantify the degree of the ionicity of the interaction through the square of the difference in the electronegativities of the migrating cation and the anion of the host lattice. ...
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Ion mobility is a critical performance parameter not only in electrochemical energy storage and conversion but also in other electrochemical devices. On the basis of first-principles electronic structure calculations, we have derived a descriptor for the ion mobility in battery electrodes and solid electrolytes. This descriptor is entirely composed of observables that are easily accessible: ionic radii, oxidation states, and the Pauling electronegativities of the involved species. Within a particular class of materials, the migration barriers are connected to this descriptor through linear scaling relations upon the variation of either the cation chemistry of the charge carriers or the anion chemistry of the host lattice. The validity of these scaling relations indicates that a purely ionic view falls short of capturing all factors influencing ion mobility in solids. The identification of these scaling relations has the potential to significantly accelerate the discovery of materials with desired mobility properties.
... The electrolyte provides the medium through which ions present in the battery migrate and reach the electrodes. In fact, the ion mobility in the electrolyte can be a critical factor in the performance of a battery [59]. The solvation strength of ions such as Li + and LiO 2 in the three electrolytes studied here may influence their transportation in the electrolyte. ...
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Density functional theory calculations together with ab initio molecular dynamics (AIMD) simulations have been used to study the solvation, diffusion and transformation of Li+ and LiO2 upon O2 reduction in three organic electrolytes. These processes are critical for the performance of Li-air batteries. Apart from studying the structure of the solvation shells in detail, AIMD simulations have been used to derive the diffusivity and together with the Blue Moon ensemble approach to explore LiO2 formation from Li+ and O2- and the subsequent disproportionation of 2LiO2 into Li2O2 + O2. By comparing the results of the simulations to gas phase calculations the impact of electrolytes on these reactions is assessed which turns out to be more pronounced for the ionic species involved in these reactions.
... A promising research field with great potential for improvement are multivalent ion batteries, in particular due to their high volumetric capacities as compared to lithium. [6][7][8] However, of course there are also certain drawbacks: Multivalent batteries suffer from mobility issues due to the higher ionic charge 5,[9][10][11][12] and also typically exhibit lower operating voltages than LIBs. 7 Additionally, new battery chemistries typically also require the identification and/or development of suitable electrolytes and electrode materials. ...
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While the Mo 6 S 8 chevrel phase is frequently used as cathode material in Mg–ion batteries, theoretical studies on this material are comparatively scarce. The particular structure of the Mo 6 S 8 phase, with rather loosely connected cluster entities, points to the important role of dispersion forces in this material. However, so far this aspect has been completely neglected in the discussion of Mo 6 S 8 as cathode material for mono– and multivalent–ion batteries. In this work we therefore have studied the impact of dispersion forces on stability and kinetics of Mo 6 S 8 intercalation compounds. For this purpose, a series of charge carriers (Li, Na, K, Mg, Ca, Zn, Al) has been investigated. Interestingly, dispersion forces are observed to only slightly affect the lattice spacing of the chevrel phase, nevertheless having a significant impact on insertion voltage and in particular on the charge carrier mobility in the material. Moreover, upon varying the charge carriers in the chevrel phase, their diffusion barriers are observed to scale linearly with the ion size, almost independent of the charge of the considered ions. This indicates a rather unique and geometry dominated diffusion mechanism in the chevrel phase. The consequences of these findings for the ion mobility in the chevrel phase will be carefully discussed.
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Periodic density functional theory calculations have been performed to study the migration of various charge carriers in spinel‐type MgSc2Se4. This compound exhibits low barriers for Mg ion diffusion, making it a potential candidate for solid electrolytes in Mg-ion batteries. In order to elucidate the decisive factors for the ion mobility in spinel-type phases, the diffusion barriers of other mono- and multivalent ions (Li⁺, Na⁺, K⁺, Cs⁺, Zn²⁺, Ca²⁺, and Al³⁺) in the MgSc2Se4 framework have been determined as well. This allows for disentangling structural and chemical factors, showing that the ion mobility is not solely governed by size and charge of the diffusing ions. Finally, our results suggest that charge redistribution and rehybridization caused by the migration of the multivalent ions increase the resulting migration barriers.
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