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Cite this: Phys. Chem. Chem. Phys., 2013,
15, 9075
b-MnO2 as a cathode material for lithium ion batteries
from first principles calculations†
Da Wang,ab Li-Min Liu,*b Shi-Jin Zhao,*a Bai-Hai Li,c Hao Liud and Xiu-Feng Langb
The search for excellent cathodes for lithium batteries is the main topic in order to meet the
requirements of low cost, high safety, and high capacity in many real applications. b-MnO2, as a potential
candidate, has attracted great attention because of its high stability and potential high capacity among
all the phases. Because of the complexity of b-MnO2, some fundamental questions at the atomic level
during the charge–discharge process, remain unclear. The lithiation process of b-MnO2 has been
systematically examined by first-principles calculations along with cluster expansion techniques. Five stable
configurations during the lithium intercalation process are firstly determined, and the electrochemical
voltages are from 3.47 to 2.77 eV, indicating the strongly correlated effects of the b-MnO2–LiMnO2
system. During the lithiation process, the changes in the lattice parameters are not symmetric. The
analysis of electronic structures shows that Mn ions are in the mixed valence states of Mn3+ and Mn4+
Received 28th January 2013,
Accepted 3rd April 2013
DOI: 10.1039/c3cp50392e
during the lithiation process, which results in Jahn–Teller distortion in Mn3+O6 octahedra. Such results
uncover the intrinsic origin of the asymmetric deformation during the charge–discharge process, resulting
in the irreversible capacity fading during cycling. From the analysis of the thermal reduction of delithiated
LixMnO2, the formation of oxygen is thermodynamically infeasible in the whole extraction process. Our
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results indicate that b-MnO2 has great potential as a cathode material for high capacity Li-ion batteries.
1. Introduction
Manganese dioxide (MDO) is a typical semiconductor material
and is believed to be a very promising electrode material due to
its easy preparation, low cost and low toxicity.1,2 It has been
widely used for commercial primary lithium batteries since the
mid-70s;3 however its development for secondary lithium batteries
has only been attempted in the early 80s.4,5 Most of the manganese
dioxides, such as a-MnO2, g-MnO2, and l-MnO2, can accommodate
significant lithium in their cavity, showing a large capacity as a
cathode material for lithium batteries.6–11 Among them, much
attention has been paid to b-MnO2 because the rutile structure of
b-MnO2 is a common phase of oxides (such as RuO2 and TiO2, etc.)
a
Key Laboratory of Microstructures and Institute of Materials Science,
Shanghai University, Shanghai 200072, China. E-mail: [email protected];
Tel: +86-21-56331480
b
Beijing Computational Science Research Center, Beijing 100084, China.
E-mail: [email protected]; Tel: +86-10-82687086
c
School of Energy Science and Engineering, University of Electronic Science &
Technology of China, Chengdu 611731, China
d
Chengdu Green Energy and Green Manufacturing Technology R&D Center,
Chengdu Development Center of Science and Technology, China Academy of
Engineering Physics, Chengdu, 610207, China
† Electronic supplementary information (ESI) available. See DOI: 10.1039/
c3cp50392e
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and has been widely used in electrochemistry and photochemistry.12,13 Furthermore, b-MnO2 is thermodynamically stable
and can be easily fabricated, which is widely prepared by thermal
decomposition of Mn(NO3)2,14,15 pyrolysis of MnOOH,16 and
hydrothermal reaction.17 However, some researchers worried that
(1 1) tunnels18 of b-MnO2 may be too narrow to accommodate
enough Li ions at room temperature. Some earlier studies19,20
showed that the amount of lithium chemically inserted into
crystallized b-MnO2 was less than Li/Mn = 0.3, it reaches near
Li/Mn = 1 only at temperatures above 50 1C or in poorly crystallized products.1,19,21 They suggested that b-MnO2 is not attractive
because of its poor ion insertion properties. Different from the
previous studies, the recent works show that nanocomposite
and mesoporous b-MnO2 exhibit high capacities, which can
even reach 320 mA h g1.15,22–26 Tang et al.24 prepared b-MnO2
by a method of thermal decomposition of Mn(NO3)2 mixed with
acetylene black. They suggested that a large amount of lithium
ions (Li/Mn = 1.15) are electrochemically inserted into the
b-MnO2 nanocrystals, which results in a pretty high capacity
of 320 mA h g1 at a cutoff voltage of 1.0 V. Jiao and Bruce15
studied Li intersection into mesoporous b-MnO2, and they
also found a high reversible storage (284 mA h g1), which
corresponds to Li0.92MnO2. Such experiments suggest that
the compact tunnel structure of b-MnO2 has the ability to
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accommodate the volume changes associated with charging
and discharging.
Such exemplary and complementary properties for both
storage and discharge rates suggest that different physicochemical
properties, such as particle size, surface area, morphology, etc. can
show hierarchical electrochemical properties in b-MnO2. In order to
improve the properties of b-MnO2 for advanced rechargeable
lithium batteries, it is greatly urgent to unveil intrinsic mechanisms
associated with storage and discharge of Li ions. Because the
charge–discharge process is complex, it is still rather difficult to
directly characterize the redox process and lithium diffusion at
the atomic level.27 Until now, many basic questions are still
unclear,2,19,25,28 such as, are lithium ions able to intercalate/
extract in the (1 1) tunnel? How does the structure evolve
during the whole electrochemical reaction process? What is the
intrinsic reason that leads to the structural distortions during
the lithiation process? This is difficult experimentally, and therefore, atomic scale first-principles calculations offer a unique
window of exploration into such materials. First-principles
calculations gradually play a key role in design and understanding
of the Li+ ion batteries which can provide deep insights into the
intrinsic origins at the atomic level.29–34 Recently, Ling and
Mizuno studied the insertion of Li and Li oxides into a-MnO2
through first-principles calculations. It was shown that the severe
deformation of structure is directly related to the ordered
reduction of Mn, which interprets well the experimentally
observed capacity fading. However, there are few first principles
studies on the charging/discharging mechanism of b-MnO2.
In this paper, b-MnO2, as a cathode material for intercalation/
extraction of lithium ions, has been systematically studied by
first-principles calculations combined with a cluster expansion
approach.35 The structural evolution of LixMnO2 (0 r x r 1) was
firstly determined, which shows that a total of 5 ground states
(MnO2, Li0.5MnO2, Li0.75MnO2, Li0.875MnO2, LiMnO2) exist during
the lithiation process. The calculated lithium intercalation
voltage is 3.47 V at the first stage and gradually stabilizes at
the potential plateau at B2.8 V in the following stage, which
agrees well with experimental results. The consistency between
the theoretical averaged potential and experimental measurements indicate the strongly correlated effects of the b-MnO2–
LiMnO2 system. The diffusion barrier of Li+ in the tunnel is
0.26 eV, which is comparable to other cathode materials. The
analysis of the electronic structures reveals that Mn ions are in
the mixed valence states of Mn3+ and Mn4+ during the lithiation
process from b-MnO2 to LiMnO2. While Jahn–Teller (JT) distortion
is not observed in Mn4+O6 octahedra, it is clearly seen in Mn3+O6
octahedra, in which the Mn–O bond lengths along the z-axis
direction are obviously elongated. Such distortion occurring in the
JT-active Mn3+ causes asymmetric deformation in the structure,
which should be responsible for the irreversible capacity fading
during cycling. Further studies of the stability of oxygen in
LixMnO2 (0 r x r 1) suggested that the decomposition reaction
along with oxygen liberation is not thermodynamically possible
during the whole lithiation process. Such results suggest that
b-MnO2 has great potential to be a decent cathode material for
high capacity lithium-ion batteries.
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2. Computational details
First-principles total energy calculations were performed using the
projector augmented wave (PAW) method36 and the generalized
gradient approximation (GGA) with a parameterized exchangecorrelation functional according to PBE,37 as implemented in the
VASP code.38 Valence electron configurations of the potentials were
taken as 1s2 2s1 for Li, 3d6 4s1 for Mn, and 2s2 2p4 for O. To check
the accuracy of the pseudopotential, one Mn pseudopotential with
3p as the semi-core was also tested, which gives the same lattice
constant and density of states (Fig. S1, ESI†) of b-MnO2. An energy
cutoff of 550 eV and appropriate k-point meshes are chosen so that
the total ground-state energies converge to within 3 meV per formula
unit. All atom coordinates and lattice vectors are fully relaxed for
each structure. The Gaussian smearing method with a smearing
width of 0.05 eV was used for the calculation of the density of states
(DOS). Spin-polarizations are included in all the calculations, and
pffiffiffi
pffiffiffi
the magnetic ordering is carefully considered. A 2 2 2 1
supercell is used in this study, unless otherwise stated.
Although b-MnO2 has been shown to exhibit an antiferromagnetic helical spin arrangement,39,40 an idealized collinear
arrangement was modeled in this study, as has been done in
previous studies.41,42 Lattice constant optimization was performed
for both anti-ferromagnetic (AFM) and ferromagnetic (FM) states of
b-MnO2. It is found that the total energies of the lithiated phase
with FM ordering are lower than those with AFM ordering
(see Table S1, ESI†). Thus, all results presented in the following,
are according to FM ordering.
b-MnO2 is a semiconductor, with a band gap in the range
0.1 to 1.0 eV.43–46 Standard DFT predicts a zero band gap for
b-MnO2 because pure DFT cannot fully cancel the self-interaction
error.42 A hybrid functional47 and the PBE + U approaches48 are
two typical approaches to overcome the shortcomings of DFT,
which can open band gaps of semiconductors. The hybrid
functional calculation is rather expensive, which is at least
20 times slower than the normal DFT one. In our calculations,
both hybrid and DFT + U approaches have been used. The
energies of structures generated with the ATAT program49 were
calculated by the PBE + U method. The Hubbard U value of Mn
atoms is chosen according to other Mn compounds reported in
literature,42,50–52 which shows that PBE + U can give a reasonable
prediction for the electronic structure of Mn compounds. All results
presented in this paper are calculated with U = 4.0 eV.42,50–52 To
check the accuracy of such settings of PBE + U, the relative energy
between MnO2 and LixMnO2 (DE = ELixMnO2 EMnO2) was calculated
with both HSE06 and PBE + U. As shown in Fig. S2 (ESI†), the
difference in the relative energy between U = 4.0 eV calculations
and those of HSE06 does not exceed 1.4%, which indicates that
U = 4.0 eV is reliable in this study.
3. Results and discussion
3.1
The crystal structure of b-MnO2
b-MnO2 has a regular rutile structure with the space group
P42/mnm,53 the metal atoms in the Wyckoff site 2(a) at
(0, 0, 0; 0.5, 0.5, 0.5) and the oxygen atoms in 4(f) at
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with PBE + U (HSE06). Each Mn atom is surrounded by 6 Mn–O
bonds, which form a MnO6 octahedron. Four of them are 1.922
(1.868) Å and the other two are 1.935 (1.883) Å calculated with
PBE + U (HSE06).
When one Li ion is inserted into the unit cell of b-MnO2, the
optimized polymorphs in Wyckoff site 4(c) at (0.5, 0, 0.5; 0, 0.5, 0.5)
lead to LiMnO2. The basic structure of b-MnO2 was unchanged
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[(u, u, 0); (u + 0.5, 0.5 u, 0.5)], as shown in Fig. 1(a). As
shown in Table 1, the calculated lattice parameters and bond
lengths with HSE06 are in agreement with available experimental values15,53 and other DFT studies,42,54,55 while PBE + U
overestimated the lattice constant, as observed in the previous
studies.42 b-MnO2 contains two different Mn–O bond lengths:
one is 1.922 (1.868) Å and the other is 1.935 (1.883) Å calculated
Fig. 1 (a) The crystal structure of b-MnO2, (b) The formation energies (Df Ex) of the various configurations calculated from first principles along with the corresponding
cluster expansion (CEs) fits as a function of Li content of the inverse LixMnO2. The Df Ex of 106 symmetry-inequivalent structures calculated from the CEs are also plotted
here, and the navy line is the constructed convex hull. Those with a formation energy larger than 250 meV per f.u. are not shown in the figure. (c) The Li/vacancy
configurations for the ground states of x = 0, 0.5, 0.75, 0.875, and 1, respectively. Each cavity corresponds to a MnO2 formula and the green balls indicate Li at the 3c
site. A–D correspond to different Li+ intercalation layers in Mn8O16, respectively.
Table 1 The calculated crystal lattice parameters (Å), bond angle (y), and bond lengths (Å) of Mn–O of LiMnO2 and MnO2, compared with available experimental
data. As for the bond length of Mn–O, the total number of each type of Mn–O per unit cell is shown as well, for example, 1.922 8 means that the total number of
Mn–O bond lengths with 1.922 Å is 8 within one unit cell
Mn2O4
a (Å)
b (Å)
c (Å)
a (y)
b (y)
g (y)
V (Å3)
LMn–O (Å)
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Li2Mn2O4
PBE + U
HSE06
Expt.53
PBE + U
HSE06
Expt.15
4.473
4.473
2.957
90
90
90
59.176
1.922 8,
1.935 4
4.362
4.362
2.861
90
90
90
54.436
1.868 8,
1.883 4
4.404
4.404
2.877
90
90
90
55.800
—
5.211
5.211
2.870
90
90
86.8
77.801
1.945 4, 1.981 4,
2.419 2, 2.268 2
5.072
5.072
2.801
90
90
86.7
72.056
1.938 4, 1.899 4,
2.347 2, 2.201 2
5.01
5.01
2.81
—
—
—
—
—
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after full intercalation of Li+ from b-MnO2 into LiMnO2.15,25 It
should be noted that insertion of lithium into b-MnO2 induces
a general expansion of the lattice parameters. Especially, the
Mn–O bonds tend to disunity with both the HSE06 and PBE + U
results. The four bonds with a length of 1.883 (1.935) Å for
b-MnO2 calculated with HSE06 (PBE + U) become two bonds
with a length of 2.347 (2.201) Å and two bonds with a length of
2.419 (2.268) Å for LiMnO2. Such disunity of Mn–O bonds will
greatly result in the distortion in the MnO2 octahedral lattice as
discussed later.
3.2
The ground-state of Li/vacancy configurations
To understand the structural evolution during the lithium
extraction–intercalation process, the stable crystal structure of
LixMnO2 in the process of lithium intercalation was firstly
explored. To explore the stable structure, the formation energy
for a given Li-vacancy arrangement with a composition of x in
LixMnO2 (Df Ex) is calculated with the following equation as:
Df Ex = E[LixMnO2] {xE[LiMnO2] + (1 x)E[MnO2]}
(1)
where E[LixMnO2] is the total energy of the configuration per
LixMnO2 f.u., E[LiMnO2] and E[MnO2] are the energies of
LiMnO2 and MnO2, respectively. The magnitude of Df Ex defined
in eqn (1) reflects the relative stability of LixMnO2 with respect
to a fraction x of LiMnO2 and a fraction (1 x) of MnO2.
For the intermediate LixMnO2, many different Li-vacancy
arrangements exist as a function of Li content in different sizes
of the unit cell. It is rather expensive to calculate all kinds of
configurations to determine the most stable one for each
composition. To solve this problem, a cluster expansion (CE)
approach, as implemented in the ATAT software package, was
used to search the stable configurations among a variety of
lithium-vacancy arrangements based on the DFT calculations.
The basic idea of CE is to expand the energies of a LixMnO2
(0 r x r 1) configuration into energy contributions of cluster
figures (single atoms, pairs, triples, etc.) based on a generalized
Ising Hamiltonian:56
X
X
EðsÞ ¼ J0 þ
Ji S^i ðsÞ þ
Jij S^i ðsÞS^j ðsÞ
i
þ
X
joi
Jijk S^i ðsÞS^j ðsÞS^k ðsÞ þ . . . ;
(2)
kojoi
The index i, j, and k run over all lithium intercalation sites, and
Sm (s) is +1 when it is occupied by Li and 1 if it is not. The first
two terms on the right-hand side of eqn (2) define the linear
dependence of the energy of LixMnO2 as a function of Li
composition x, while the third and fourth terms contain all
pair and three-body interactions, respectively. Every cluster
figure is associated with a coefficient Ja, that gives the energy
contribution of the specific cluster figure and is called the
effective cluster interactions (ECIs).57 In principal, the CE is
able to represent any LixMnO2 energy E(s) by an appropriate
selection of the values of Ja. The unknown Ja can be determined
by fitting them to the energies of some selected configurations
obtained through first principles calculations.
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In our simulations, the cross-validation (CV) score,58 which
is designed to evaluate the predictive ability of a cluster expansion,
is sufficiently small (29 meV per f.u.) to make sure the accuracy of
the calculations after the energies of up to 69 configurations
within quadruple-sized supercells were finally calculated from
first principles at different lithium compositions. The ECIs
coefficient obtained by fitting the energies of 69 configurations
to 175 configurations of LixMnO2, was parameterized for a
cluster expansion (CE) to evaluate the energy dependence of
the Li-vacancy configurations. Ultimately, three stable groundstate structures were determined by the calculated formation
energies using eqn (1), except the two end structures (MnO2
and LiMnO2). As shown in Fig. 1(b), the calculated formation
energies with the corresponding cluster expansions (red filled
triangles) and the original DFT + U values (green hollow
triangles) are rather consistent. The root-mean-square (rms)
error between the 69 PBE + U energies and the 175 cluster
expansion evaluated values is 18 meV per MnO2 formula unit,
which suggests the high reliability of our CE calculations. In
addition, the convex hull (navy line) connects all the lowest
energy phases, which suggests that a total of 5 ground states
(MnO2, Li0.5MnO2, Li0.75MnO2, Li0.875MnO2, LiMnO2) exist in the
whole intercalation process from MnO2 to LiMnO2.
The corresponding Li/vacancy configurations are illustrated
in Fig. 1(c). In order to better exhibit stable configuration of the
lithium insertion into b-MnO2, b-MnO2 with 8 formula units
can be divided into 4-layers (A–D), as shown in Fig. 1(c). During
the intercalation process, Li+ subsequently fills in the cavity of
each layer. At the initial stage from pristine b-MnO2 to
Li0.5MnO2, Lithium ions are firstly inserted into A and C layers.
By such filling, all inserted Li ions effectively avoid the electronic repulsion between different layers. In the following stage,
lithium ions intercalate alternately in the B and D layers until
the composition reaches Li0.75MnO2 which can achieve the
smallest electrostatic repulsion with neighboring lithium ions.
At the end of the Li+ intercalation, all these four layers (A–D) are
occupied, which corresponds to the composition LiMnO2.
3.3
Intercalation voltage and kinetics of lithium diffusion
To further investigate the electrochemical properties of b-MnO2,
the theoretical intercalation voltage59,60 of a Li/LiMnO2 cell was
calculated for each stable configuration. Considering the following
electrochemical reaction,
(x2 x1)Li+ + (x2 x1)e + Lix1MnO2 - Lix2MnO2
the average intercalation voltage, Vavg, can be determined by,
Vavg = DG/Dx
where Dx refers to the number of Li+ ions transferred, DG is
the difference in the Gibbs free energy for the intercalation
reaction. Considering the small changes in volume and
entropy, DG can be approximately calculated by the total energy
difference between the Lix2MnO2 and the sum of Lix1MnO2 and
bulk Li. The calculated average intercalation voltage corresponding
to each lithium intercalation stage is shown in Fig. 1(c). It is
show that the discharge profile for lithium intercalation is from
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3.47 V to 2.77 V. The experiment on the lithium intercalation23
shows that the voltage drops from B3.5 to B2.7 V. Further the
measured flat potential plateau in electrochemical experiments is
B2.8 V.15,23,25 Thus our calculated discharge profiles agree well
with the experimental results. The voltage of b-MnO2 from both our
calculations and other experiments indicate the strongly correlated
effects of the b-MnO2–LiMnO2 system, which is comparable to
other manganese family cathode materials.10,52,61,62
To achieve high power in rechargeable lithium ion batteries, it is
a requirement that Li+ diffusion in and out of the electrode material
is fast enough to supply the electric current in a short amount of
time. Lithium diffusion in the lithium intercalation channel is
an intrinsic property of the electrode material. In order to
know whether b-MnO2 can provide high power performance, it is
necessary to explore the kinetics of lithium diffusion in b-MnO2.
Although there are many possible diffusion paths in bulk
b-MnO2, it is primarily a one-dimensional (1D) channel along the
c-axis, which has been confirmed by many experiments.2,25,28 Large
anisotropy in Li ion diffusion has also been observed experimentally63 and from ab initio calculations64 in rutile TiO2. The diffusion
path of Li+ within the one-dimensional (1D) tunnels of b-MnO2 is
shown in Fig. 2(a). The typical diffusion pathway between two
neighboring lithium 4(c) sites along the c-axis is studied within the
LiMn16O32 system, and the energy barrier is calculated by the NEB
method.65 As shown in Fig. 2(b), the calculated energy barrier of Li
diffusion is 0.26 eV. In contrast, the pathway of Li within a-MnO2
is also through two adjacent position sites along the c-axis, and the
recent DFT calculation on the migration barrier of a single vacancy
in the a-MnO2 host is 0.47 eV.52 The calculated value for b-MnO2 is
even smaller than that of a-MnO2. Such results suggest that the
role of the (1 1) tunnel structure of b-MnO2 can facilitate the fast
transport and intercalation kinetics of lithium ions, resulting in a
high specific capacity even at a high charge–discharge current. It
should be noted that the absolute diffusion barriers may be
affected by the unitcell size, the different NEB method66 and the
exchange correlation functional, while the qualitative trend should
be the same.
3.4
Structural evolution of LixMnO2 (0 r x r 1)
As mentioned in Section 3.1, intercalating Li ions into b-MnO2
at a composition of x o 1.0 can induce the distortion of MnO6
octahedrons, which may play an important role in the severe
structural deformation of the compound. Several recent experiments on intercalating Li ions into b-MnO2 have observed that
the crystal structure expands remarkably during the delithiation–lithiation process.15,23,25 Jiao et al.15 reported that the
volume increases 26.5% during the discharge process, with
13.9% expansion along a and a slight contraction along c. At the
end of discharge, a expands from 4.40 to 5.01 Å, while c
contracts from 2.88 to 2.81 Å. In the meantime, no new phases
are observed during charge–discharge cycling, which suggests
that no irreversible structural change occurs, as demonstrated
by XRD25 and PXRD patterns.15 In fact, such a structural
distortion is also observed in the a-MnO2, l-MnO2 and polycrystalline LiMn2O4, which is explained by the Jahn–Teller
theorem,52,67–70 but there is still no clear explanation for
volume expansion in the b-MnO2 yet. On the other hand, the
capability of the LixMO2 (M = Mn, Co, Ni) compounds for
delithiation–lithiation, depends closely upon the deformation
behavior of the MO6 octahedron.52,71,72 It is, therefore,
greatly important to explore how the MnO6 octahedron deforms
during the process of delithiation–lithiation.
To unveil the intrinsic mechanism of volume change during
the intercalation of lithium ions into b-MnO2, the detailed
structural changes are examined. As shown in Fig. 3, the
intercalation of Li+ leads to obvious increases in lattice parameters
a and b and cell volume, while no more than a 3% change in
lattice parameter c (See Fig. S3, ESI†). Such results agree with the
experimental observation that there is no obvious change in the
c-axis.15,25 Different from the c-axis, the a- and b-axes change
remarkably during the intercalating process, which increase
19.5% and 12.9% from pristine b-MnO2 to LiMnO2.
In tetragonal symmetric b-MnO2, both lattice parameters a
and b are 12.337 Å. Interestingly, lattice parameters a and b do
not change symmetrically during the lithiation process. The
intercalation can be divided into two stages based on the strong
anisotropy of parameters a and b. The first stage (stage I) is
from pristine MnO2 to Li0.5MnO2, and at this stage a increases
rapidly from 12.337 to 14.641 Å, while b remains almost
unchanged (12.364 Å). After such a process, the crystal structure
changes from tetragonal to orthorhombic. The second stage
(stage II) corresponds to Li0.5MnO2 to LiMnO2. At this stage,
Fig. 2 Lithium diffusion process in bulk b-MnO2. (a) The Mn16O32 supercell used in our calculations with Li diffusion along the c axis. Only MnO6 octahedra and Li
atoms are plotted, with purple surfaces and green balls, respectively. (b) Calculated energy barriers with respect to the simulation steps shown in part a. A (100) slice
cut from part a are displayed in the inset, where the Li+ migration is represented by green circles.
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Fig. 3 The calculated crystal lattice parameters, a and b, (Å) and unit cell volume
pffiffiffi
pffiffiffi
2 2 2 1 super(Å3) for different compositions of LixMnO2 with HSE06. A
cell is used for such calculations.
b expands from 12.364 Å to 13.932 Å, and the crystal structure
remains orthorhombic.
To uncover the physical origin of the above mentioned
structural distortion, the electronic properties of LixMnO2 for
each stage are investigated. Firstly, the Bader atomic charges
were calculated for all the compositions.73 The results show
that the charge of Li+ is B+0.85 e for the whole delithiation,
indicating the strong ionicity of Li+. Different from that of Li,
the charge of Mn decreases from +1.88 e for b-MnO2 to +1.66 e
for LiMnO2. Accordingly, the charge of O is B1.10 e, which is
less than the classical oxidation state of O2. Such results
indicate the strong covalent interactions between the Mn and
O ions.
Furthermore, the detailed bond lengths (see Fig. 4) show
that Mn could be separated into two types by the different bond
lengths: ‘‘Mna’’ and ‘‘Mnb’’. For the bond lengths of Mna–O
within one MnaO6 octahedron in Fig. 4(a), no obvious elongation of bond length is observed, and their six Mn–O bonds can
be divided into four 1.883 Å and two 1.868 Å bonds, respectively. When the composition reaches Li0.5MnO2, the structural
situation is greatly changed in the MnbO6 octahedron. As
shown in Fig. 4(b), two of the six Mn–O bonds are greatly
enlarged from 1.883 to 2.692 and 2.010 Å along the z-axis
direction, respectively. The other four bonds within the
xy-plane are about 1.891 Å, close to that of b-MnO2. The charge
on Mna decreases from 1.88 to 1.74 e when Mna becomes Mnb.
At the same time, the charge and local atomic positions around
Mna in Li0.5MnO2 have no obvious change. That is to say, the
valence state of the remaining Mna in Li0.5MnO2 does not
change at this stage. When the composition becomes LiMnO2
(see Fig. 4(c)), the remaining Mna in Li0.5MnO2 (see Fig. 4(b))
changes the bond length of Mna–O from 1.907 to 2.200 Å,
leading to a further distortion of the MnbO6 octahedra. Meanwhile, the charge of the remaining Mna in Li0.5MnO2 changes
from 1.88 to 1.70 e, while Mnb stayed almost unchanged at this
stage (from 1.74 to 1.68 e). Such large structural distortions and
the charge change of the MnbO6 octahedron should be responsible for the great changes in the lattice constants and volume
expansion, as observed in the experiments.
3.5
Electronic properties and JT effect
To further reveal the reason for the structural distortion, the
total density of states (TDOS) and partial density of states
(PDOS) of LixMnO2 (x = 0, 0.5, 1) were analyzed by HSE06, as
plotted in Fig. 5. The total density of states suggests that
b-MnO2 is an insulator with a band gap of 0.20 eV. Previous
experimental work44 has shown the band gap in pyrolusite to be
in the range 0.08 to 0.25 eV based on activation energies for
semi-conduction, which agree well with the experimental work.
As for the bulk b-MnO2, the octahedral crystal field surrounding
each metal cation splits the energies of the 3d orbitals with t2g
symmetry from those with eg symmetry. The energy separation
between the t2g and eg levels is called the ligand-field splitting
(D0).74 The formal oxidation state of b-MnO2 is 4+. The t2g
majority states are occupied, whereas the eg majority states are
empty. As can be seen in Fig. 5(b), the calculated partial density
of states (PDOS) of b-MnO2 shows that the spin-up t2g bands are
occupied, while the spin-up eg band and all spin-down Mn-3d
Fig. 4 Local atomic positions around Mna and Mnb in (a) MnO2, (b)Li0.5MnO2 and (c) LiMnO2 calculated with the HSE06 functional. The green, purple, yellow and red
spheres are Li, Mna, Mnb and O atoms, respectively. Notations on each Mn atom indicate the Bader charge of corresponding Mn atoms. Bond lengths (Å) are for Mn–O
at different sites. Here, the n m format (e.g., 4 1.868) means that n Mn–O bonds at this site are in the length of m Å.
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Fig. 5 Total density of states (a) and partial density of states (b) of LixMnO2 (x = 0, 0.5, 1) for the most stable arrangements. The positive–negative directions in the yaxis represent the majority–minority spin directions. The density of states are aligned so that the Fermi energy is zero, and the projected density of states for Mna and
Mnb are illustrated by red and navy lines, respectively.
bands are empty. The oxidation state of Mn ions for b-MnO2 is
clearly +4 with an electronic configuration of t2g3eg0.
During the Li intercalating, at the first stage from pristine
MnO2 to Li0.5MnO2, Mna and Mnb ions in Li0.5MnO2 have quite
different characteristics (see Fig. S4, ESI†). The two eg bands of
Mnb split into a lower dz2 band and an upper dx2y2 band with a
gap (0.8 eV) between them, which reflects the obvious Jahn–
Teller distortion in crystal structures, and the oxidation states
of Mna has been changed from +4 to +3 with a high-spin d4
configuration (t2g3eg1). Distortion of the Mn3+O6 octahedral is
expected to happen and normally elongates bond lengths of
the related Mn–O along the z-axis. Such expansion reduces
repulsive interactions between the electron-occupied eg orbital
and oxide ions in the direction of the dz2 orbital, and thus it
stabilizes the dz2 orbital over the dx2y2 orbital. On the other
hand, the electronic configuration of Mna does not change in
this process. Such a large electronic structure difference
between Mna and Mnb should be the main reason for the
non-uniform expansion in a and b: about 18.7% expansion in
a and about 0.2% change in b at this stage (see Fig. 3). When
the MnO2 is fully intercalated by lithium, all of the oxidation
states of the Mn ions are reduced to +3. The Mn ions in
LixMnO2 are transformed from JT-inactive Mn4+ to JT-active
Mn3+ states with the Li intercalation composition from
Li0.5MnO2 to LiMnO2, which makes the lattice parameter b
increase about 12.7% and there is no obvious change in a. Such
results indict that JT effect should be responsible for the
asymmetric expansion of b-MnO2 during the lithiation process,
as observed in many previous experiments.15,23,25
3.6
The stability of oxygen in LixMnO2
Though b-MnO2 shows a potential application in practical
lithium batteries as described above, it is also a requirement
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that LixMnO2 has a high thermodynamic stability at a high
state of charge. Very often, the safety problem arises from the
interaction of the highly charged cathode with the electrolyte.
When a large amount of Mn4+ is present, these particularly
unstable oxidation states have the potential to reduce by
liberating oxygen, which may combust the electrolyte and even
cause fires at elevated temperatures. The intrinsic thermal
stability of b-MnO2 can be understood by the following decomposition reaction
y
Linx Mnn O2n ! Linx Mnn O2ny þ O2
(3)
2
The decomposition energy of the reaction is defined as
E o Linx Mnn O2ny þ y=2E ðO2 Þ E o ðLinx Mnn O2n Þ
DE ¼
y=2
(4)
where Eo refer to the total energy at 0 K and E*(O2) is the
calculated energy of an O2 molecule. Both Eo and E*(O2) are
calculated by GGA + U in our study. A (2 2 1) supercell is
used with one oxygen vacancy, where n is 8 in our system. The
low concentration reduces the interaction of vacancies between
periodic images so that the calculations correspond to the
onset of oxygen loss. Since the more electrons the O2 loses,
the stronger the tendency for it to be oxidized to O2. To locate
the lowest energy structure with the oxygen defect model, the
oxygen with the smallest Bader atomic charge is removed from
the cell of each ground state. The decomposition energy of
reaction (3) for each stage is shown in Fig. 6. Decomposition
energy of lithium extraction monotonically decreases as a
function of x, which indicates the downward trend in stability
of Li8xMn8O16 (1 Z x Z 0) with the decrease in x. The positive
DE means that the formation of oxygen is thermodynamically
infeasible. It can be seen that DE is always positive, thus the
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References
Fig. 6 The decomposition energy of reaction (3) for each ground state of
Li8xMn8O16 (x = 0, 0.5, 0.75, 0.875, 1).
decomposition is not thermodynamically possible. Such results
suggest that b-MnO2 has high stability, at least from the
energetic point of view.
4. Conclusions
The structural, electronic, and electrochemical properties of
b-MnO2 as cathode materials have been explored by firstprinciples calculations along with a cluster expansion technique.
Through systematical calculations, five stable Li configurations
for the intercalation process have been determined. The calculated intercalation voltages based on the stable configurations
are from 3.47 V to 2.77 V for LixMnO2, which agrees well with the
experimental result. A non-uniform structure expansion during
the lithiation process is observed, which results in a huge
structure distortion. The analysis of electronic structures and
valence bonds of LixMnO2 shows that multivalent Mn can exist
in different charge states (Mn3+ and Mn4+) simultaneously
within the crystal. Because of the existence of Mn3+, the
b-MnO2 exhibits JT effects during the charge–discharge process,
which plays a key role in the structure distortion. From the
analysis of the thermal reduction of delithiated LixMnO2, the
formation of oxygen is thermodynamically infeasible in
the whole extraction process. Such results not only help to
understand the intrinsic mechanism of the phenomenon
observed in the Li-ion battery experiments, but also suggest that
b-MnO2 has great potential to be a suitable cathode material for
lithium ion batteries.
Acknowledgements
This work was supported by the National Natural Science
Foundation of China (Nos. 51222212, and 50931003), the CAEP
foundation (Grant No. 2012B0302052), the MOST of China
(973 Project, Grant NO. 2011CB922200), the Ministry of
Science & Technology of China (Project 2012AA050704), and
Shu Guang Project (Grant No. 09SG36). The computations
support from Informalization Construction Project of Chinese
Academy of Sciences during the 11th Five-Year Plan Period
(No.INFO-115-B01) is also highly acknowledged.
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