Journal of
Materials Chemistry A
PAPER
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Cite this: DOI: 10.1039/c6ta03595g
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Robust vanadium pentoxide electrodes for sodium
and calcium ion batteries: thermodynamic and
diffusion mechanical insights†
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Da Wang,a Hao Liu,b Joshua David Elliott,c Li-Min Liu*a and Woon-Ming Lau*ab
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It has long been a critical challenge to find suitable electrodes for rechargeable Na/Ca-ion batteries (NIBs/
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CIBs) with superior electrochemical performance. Vanadium pentoxides offer the prospect of serving as
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cathodes in the development of high-capacity NIBs and CIBs. Here the concentration-dependent
electrochemical characteristics of Na- and Ca-ions with a- and d-V2O5 are examined using density
functional theory with Hubbard U corrections. Multiple low energy configurations, stemming from the
different ionic concentrations, are identified to evaluate the stability of a- and d-V2O5 upon Na/Ca
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intercalation. It is computationally predicted that the a phase is more stable than the d phase during both
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Na and Ca intercalation processes. Additionally, the energy barriers for Ca diffusion in a-V2O5 at high
concentration are higher than that in d-V2O5 (0.975–1.825 eV compared to 0.735–1.385 eV), which
suggests that cycling V2O5 exclusively in the d phase may improve performance. More importantly, lower
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surface-to-bulk diffusion barriers of 0.498 and 0.846 eV are found for Na- and Ca-ion insertion at the
Received 29th April 2016
Accepted 12th July 2016
(010) surface, which account for the improved electrochemical properties found in nanostructured V2O5
compared to their bulk counterparts. Our results provide crucial insights into the thermodynamic and
DOI: 10.1039/c6ta03595g
electrochemical response of V2O5 to Na/Ca-ion intercalation, thus contributing to the design of high
www.rsc.org/MaterialsA
capacity NIBs/CIBs.
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Introduction
Lithium ion batteries (LIBs) have been the subject of intense
investigation due to their high energy density, high storage
capacity and good cycling performance.1,2 However, considering
the low natural occurrence of Li in the upper continental crust
(35 ppm), great concerns have been expressed over whether
the available lithium reserves in the earth are sufficient to meet
the ever-growing requirements for LIBs.3 Therefore, there is
a call for batteries based on more earth-abundant alkali metals
such as sodium. In comparison, sodium is cheaper, has a much
larger natural occurrence (28 300 ppm in the lithosphere and
10 320 ppm in seawater)4 and Na-ion batteries (NIBs) have the
second-lightest mass-to-charge ratio in the ranks of alkali
metals aer lithium. Furthermore, NIBs are desirable for use in
secondary batteries because of their lower reduction voltage
(2.71 V vs. standard hydrogen electrode) and greater extent of
a
Beijing Computational Science Research Center, Beijing 100084, China. E-mail: limin.
[email protected]; [email protected]; Tel: +86-10-82687086; +86-21-56331480
b
Chengdu Green Energy and Green Manufacturing Technology R&D Center, Chengdu
Development Center of Science and Technology of CAEP, Chengdu, Sichuan, 610207,
China
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c
Stephenson Institute for Renewable Energy & Department of Chemistry, University of
Liverpool, Liverpool, L69 7ZF, UK
† Electronic supplementary
10.1039/c6ta03595g
information
(ESI)
This journal is © The Royal Society of Chemistry 2016
available.
See
DOI:
chemical safety.5,6 What's more, the alkaline-earth metals such
as calcium can achieve a larger volumetric energy density (6.89
kW h L1) than Li metal (6.44 kW h L1) due to the increased
number of transferred electrons per ion. In spite of these
properties, improvements are still required for both of the
aforementioned nonconventional alkaline-earth-ion batteries if
they are to be integrated into real applications, and most of the
challenging problems involve the identication of promising
materials to work as electrodes as well as the optimum electrolyte for each system.
Layered materials with the van der Waals interlayer spacing
can effectively host alkali metals with a high charge/discharge
rate and minimum constructional distortion. In state-of-theart LIBs, graphite is the most widely used anode.7 However,
the larger Na- and Ca-ions (1.03/1.00 Å for Na+/Ca2+ vs. 0.76 Å for
Li+) exhibit highly inefficient intercalation into graphite.8 More
importantly, since Ca intercalation is accompanied by twice the
number of electrons, the larger electrostatic forces of the Ca2+
ions oen lead to a reduction of the rate of both intercalation
and diffusion processes. To address this problem, graphite-like
layered materials with a wide range of electron affinities for ions
and larger interlayer spacings are being studied as active electrodes for NIBs/CIBs. Among them, vanadium pentoxides
provide appealing prospects for use as advanced cathodes for
secondary batteries.9,10 As early as the 1970s, vanadium pentoxide was proposed as a promising cathode for LIBs.11 Since
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then, Li intercalation into V2O5 has been the subject of several
experimental12,13 and theoretical studies.14,15 Delmas et al.12
showed that a reversible electrochemical intercalation of more
than 1 mol of Li+ could be achieved in a V2O5 framework.
Lithium-ion technology has been investigated extensively for
the past 30 years, yet specic studies concerning the use of V2O5
for sodium-/calcium-based energy storage systems are limited.
West et al.16 reported the electrochemical intercalation of
sodium into a-V2O5 at 350 K using a polymer electrolyte.
Pereira-Ramos et al.17 investigated the electrochemical behavior
of a-V2O5 at 420 K in NaClO4 solutions in molten dimethyl
sulfone. X-ray diffraction experiments showed that NaxV2O5
bronzes exhibit morphological stability up to an alkali insertion
fraction of x ¼ 0.8. More recently, Muller-Bouvet et al.18 showed
a reversible electrochemical insertion of Na into V2O5 at room
temperature while also demonstrating superior capacities
(120 mA h g1) at C/10 rate using a 1 M NaClO4/PC electrolyte.
The combination of these promising electrochemical properties
motivates the continued development of V2O5 as a highperformance electrode for NIBs/CIBs. Although plenty of
studies have been carried out so far to explore the Li/Mg intercalation mechanism in V2O5, an atomistic-level understanding
of the Na/Ca charge/discharge process in this material is, to the
best of our knowledge, not yet available.
A growing number of studies suggest that the construction of
nano-structures could improve the electrochemical performance of both Na-ion19,20 and Mg-ion21–23 intercalation in V2O5
compared to their bulk counterparts. Nanoscale bilayer-V2O5
was reported to be able to maintain 85% of the initial capacity
aer 350 cycles, and its current density varies from 630 to 20 mA
g1.19 Some of the enhanced electrochemical properties can be
achieved by using defects or higher surface areas to produce
high capacities for the intercalation of alkali ions.19 Additionally, the short diffusion lengths in nano-dimensional materials
are also benecial for the rate-capability of electrodes.24 A recent
investigation by rst-principles calculations also showed that
the improvement in Mg intercalation in bilayered-V2O5 has
largely been attributed to solvent co-intercalation, which
shields the electrostatic charge of the Mg2+.22 Similarly,
improvements due to solvent co-intercalation have also been
reported for Ca-insertion in Prussian-blue analogues.25 On the
other hand, we should also note that the high surface area
occupation in nanostructures is likely to be detrimental because
of the undesirable reaction of the surfaces with the electrolyte.26,27 Until now, the essential basis for the contrasting
intercalation properties of bulk crystalline V2O5 and nanostructured V2O5 is not fully understood. To understand the
factors inuencing their electrochemical behavior, greater
knowledge of the diffusion pathways and activation energies
that govern ion diffusion at the surface and within the bulk are
needed at the atomic scale. This also leads to rapidly growing
interest in many nano-structural electrodes and the call for
exploration into the inuence of their interfaces and surfaces.28
In our study, we systematically investigate the structural
stability, intercalation voltages, electronic characteristics and
rate capability of Na/Ca-ion intercalation compounds with
a- and d-V2O5 using density functional theory calculations with
2 | J. Mater. Chem. A, 2016, xx, 1–10
Paper
Hubbard U corrections. We nd that the a phase is more stable
compared to the d phase during both Na and Ca intercalation
processes. Interestingly, a signicantly better mobility for Ca
was found in the d-CaV2O5 polymorph, suggesting a better rate
performance might be achieved by cycling Ca in the d phase.
More importantly, by explicitly calculating the surface-to-bulk
ion diffusion, lower barriers of 0.498 and 0.846 eV are found
for Na and Ca-ion insertion at the (010) surface that dominates
the equilibrium morphology. This is likely the reason for the
improved electrochemical properties found in nanodimensional V2O5 compared to their bulk counterparts. The
results presented here provide valuable insights into the
exploration of high-capacity V2O5 for potential NIB/CIB
applications.
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2 Computation methods
Our calculations are performed based on DFT calculations, as
implemented in the Vienna ab initio package (VASP).29,30 The
generalized gradient approximation of Perdew–Burke–Ernzerhof (GGA-PBE) is adopted for the exchange-correlation functional.31 We have employed the vdW-DF scheme32 for a better
description of the interactions between interlayers. The PBE+U
approach33 is employed to simulate atoms with strongly correlated 3d-electrons. A Hubbard U correction of 4.0 eV is added on
the vanadium d-electrons to obtain the energetic properties, as
reported by Scanlon et al.14 As previously indicated by Carrasco
et al.,34 the PBE+U obtains energetics better without the addition of van der Waals interactions. This is also conrmed by our
studies of Na/Ca-intercalated V2O5 systems (see ESI† for more
detail). Hence, PBE+U is used to compute the ground-state hull
of Na/Ca in a and d-V2O5. Moreover, the electron wave functions
were expanded by a plane wave cutoff of 500 eV. Using slabs of
238 atoms (V68O170), 280 atoms (V80O200) and 252 atoms
(V72O180), which have been cleaved with symmetric a-V2O5
(100), a-V2O5 (010) and d-V2O5 (100) surfaces and that have
vacuum separations of 15 Å, Na/Ca-ion migration from the
surface to the bulk-like slab center was studied by the CI-NEB
method35 as implemented in VASP. As we further check the
effect of U values on the migration properties in the V2O5
system, as shown in Fig. S5,† the results for different U (¼2.45,
3.1 and 4.0 eV) values are quite similar with relatively less
variation. Thus, the results on the diffusion properties of V2O5
are based on the PBE+vdW+U (¼2.45 eV) functional in our
study. Using the Monkhorst–Pack scheme, the k-space has been
sampled using 3 1 3, 2 2 1, 2 1 2 grid meshes. The
atomic relaxation threshold used for the total energy variation
was 105 eV and for the forces on each atom was 0.01 eV Å1.
The formation energy (DfEx) of MxV2O5 is calculated to nd
the most stable structure for each concentration:
DfEx ¼ E(MxV2O5) [xE(MV2O5) + (1 x)E(V2O5)]
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(1)
where E(MxV2O5) is the total energy of the conguration per
MxV2O5 f.u., E(MV2O5) and E(V2O5) are the energies of MV2O5
and V2O5, respectively. The magnitude of DfEx reects the
relative stability of MxV2O5 with respect to a fraction x of MV2O5
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and a fraction (1 x) of V2O5. Considering the following electrochemical reaction,
1
Mx1V2O5 + (x2 x1)Mn+ + n(x2 x1)e / Mx2V2O5
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Vavg ¼ 10
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EMx2 V2 O5 EMx1 V2 O5 ðx2 x1 ÞEM
nðx2 x1 Þe
(2)
where nDx refers to the number of electrons transferred. EMxV2O5
and EM indicate the total energy of M (¼Na, or Ca) insertion into
the structures and bulk M respectively. Using the methodology
of Obrovac et al.37 the volumetric energy density of a charged
V2O5 cathode material can be calculated as:
F
3f
(3)
U~ f ¼ Vavg
y
1 þ 3f
where F is the Faraday constant (26.802 A h mol1). Vavg is the
average potential of all a- and d-MxV2O5 (M ¼ Na, or Ca) phases
versus a hypothetical 0.75 V anode, and y is the volume occupied
per unit charge stored in MxV2O5 by Na (17.8 mL mol1) and Ca
(9.8 mL mol1).38 The real part, Resab(u) and imaginary part,
Imsab(u) of dielectric function are presented as:39
u
Im3ab ðuÞ
4p
u
½1 Re3ab ðuÞ
Imsab ðuÞ ¼
4p
Resab ðuÞ ¼
(4)
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The temperature-dependent Na diffusion rate (D) can be
evaluated by the Arrhenius equation:
Ea
(5)
D ¼ a2 n exp
kB T
where Ea, kB, n and a are the activation energy, Boltzmann
constant, attempt frequency (1013 s1)40 and hopping distance,
respectively.
3 Results
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the average intercalation voltage (Vavg)36 of NaxV2O5 and
CaxV2O5 can be determined by,
Ground state of MxV2O5 (x ¼ Na, Ca) congurations
The main difference between a (space group Pmmn) and d phase
(Cmcm) is a shiing of the alternating a-V2O5 layers in [100]
direction by “a/2” (Fig. 1). The Na/Ca-ions in both a and d phases are located in the middle of VO5 pyramids (along [100]) and
between two layers (along [010]). To understand the structural
evolution during the electrochemical process, the stability of
the a- and d-V2O5 crystal structures in the Na/Ca intercalation
process was explored rst. Notably, in graphite-like materials,
different stages are being observed during the alkali-ion intercalation process.41 This has also been experimentally conrmed
in graphitic carbon42,43 and has been investigated by theoretical
studies.44 It can be explained by considering the competition
between interlayer van der Waals interaction and ion–ion
Coulomb repulsion. If the energy required to expand the
interlayer separation is larger than the Coulomb repulsion
between ions, then ions are more favorably intercalated into
This journal is © The Royal Society of Chemistry 2016
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Fig. 1 Schematic illustration of the stage I and stage II arrangements of
Na/Ca storage in (a) a-V2O5 and (b) d-V2O5.
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a single gallery until it reaches a maximum capacity, and we
dene it as stage I. Another stage, where all galleries are occupied, we dene as stage-II. Diagrammatic schemes of the stage-I
and stage-II structures considered in our calculations are shown
in Fig. 1. Since the intercalation ordering would be variable for
different Na/Ca concentrations, some strategies were followed
to explore the structural evolution of a- and d-V2O5 in the
intercalation process, as can be seen in detail in the ESI.† As
a result, a total of 172 congurations were calculated to explore
the a- and d-Nax/CaxV2O5 ground state hull in our study, as
shown in Fig. S4.†
Fig. 2 shows the formation energies (DfEx dened in eqn (1))
of the various stable congurations of MxV2O5 across the entire
composition range. Also, the convex hulls of a- and d-MxV2O5
are shown as the blue and yellow solid lines in the gure. Based
on this analysis, we can identify some characteristics, rstly, the
a-phase V2O5 is 0.269 eV per formula unit more stable than the
d-phase (Table 1), consistent with the experiment results.45,46 In
addition, the formation energies of d-NaxV2O5 are positive and
higher than the a-phase across the entire range of compositions
considered (Fig. 2a), indicating their instability during the Na
insertion process. Also, a-CaV2O5 is about 0.207 eV per formula
unit more stable than d-CaV2O5, in agreement with other
theoretical studies47 and the fact that a-CaV2O5 can be synthesized experimentally.45,46
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Intercalation voltage and volumetric energy densities
To assess the suitability of layered V2O5 as a cathode material
for NIBs/CIBs, the theoretical intercalation voltages (Vavg, eqn
(2)) of NaxV2O5 and CaxV2O5 were calculated, as shown in Fig. 2,
and the basic energies and structural parameters of Na/Ca-ion
intercalated intermediates are reported in Table 1. The
average voltage for Na intercalation in the a-V2O5 host is 2.6 V
for 0 < x< 1, while the d-V2O5 phase is not accessible during the
whole Na intercalation process as demonstrated in the convex
hull. Notably, the higher voltages for a-V2O5 / Na0.167V2O5
(stage-I, 2.853 V) and Na0.167V2O5 / Na0.333V2O5 (stage-I, 2.698
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Fig. 2 The formation energies (DfEx) per formula unit and the voltages of a- and d-V2O5 are shown as a function of (a) Na and (b) Ca
concentration. The blue and yellow solid lines indicate the constructed convex hull of the a-phase and d-phase, respectively.
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Table 1 Optimized lattice parameters (a, b, c, a, b, g), volume change of the unit cell (3), average voltages (V) and formation energies (DfEx) for Na/
Ca-intercalated a- and d-V2O5
x
a (Å)
b (Å)
c (Å)
a ( )
b ( )
g ( )
3 (%)
Vavg (V)
DfEx (meV per f.u.)
a-V2O5
d-V2O5
3.606 (3.56b)48
3.643 (3.69)12
4.478 (4.36)
9.782 (9.97)
11.433 (11.51)
10.895 (11.02)
90 (90)
90 (90)
90 (90)
90 (90)
90 (90)
90 (90)
—
—
—
—
0
269
Na-ion intercalation
a-Na0.167V2O5
3.586
a-Na0.333V2O5
3.573
a-Na0.667V2O5
3.564
3.589 (3.61)48
a-NaV2O5
4.539
4.670
4.762
4.835 (4.80)
11.441
11.302
11.268
11.433 (11.315)
90
90
90
90 (90)
90
90
90
90 (90)
90
90
90
90 (90)
0.871
2.149
3.587
5.687
2.853
2.698
2.560
2.287
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92
71
0
Ca-ion intercalation
a-Ca0.333V2O5
3.582
a-Ca0.667V2O5
3.594
a-CaV2O5
3.585
4.546
4.618
4.755
11.524
11.498
11.504
90
90
90
90
90
90
90
90
90
1.646
3.368
6.223
3.263
3.017
2.248
644
819
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V) suggests a preference for forming stage-I structures during
the initial Na intercalation process. As the Na concentration
reaches Na0.333V2O5, further intercalation of Na into a single
layer would lead to a strong repulsive interaction between Naions, which is larger than the energy required to expand the
interlayer separation. In this case, the stage-II structures with
Na intercalation in all layers would be dominant in the
following: Na0.333V2O5 / Na0.667V2O5 (2.560 V) and Na0.667V2O5
/ NaV2O5 (2.287 V). In a similar way, by studying the maximum
capacity of Ca in a- and d-V2O5, a high intercalation voltage
(3.263 V) is found for stage-I a-V2O5 / stage-I Ca0.333V2O5. Aer
that, the second (stage-I Ca0.333V2O5 / stage-II Ca0.667V2O5)
and nal step (stage-II Ca0.667V2O5 / stage-II CaV2O5) with all
of the gallery being lled in the a-phase provide the average
voltage of 3.017 V and 2.248 V, respectively.
The volumetric energy densities (Ũ f, eqn (3)) and the extent of
the material expansion (3f) were examined to further evaluate the
behaviors of a- and d-MxV2O5 (M ¼ Na, or Ca) cathode materials.
4 | J. Mater. Chem. A, 2016, xx, 1–10
As shown in Fig. 3, the maximum volume expansions during the
Na-ion intercalation process are less than 6.0%. Moreover, the
d-phase exhibits a smaller volume expansion than the a-phase.
These results are consistent with the recent X-ray diffraction and
Raman spectroscopy studies, which indicated the relatively lowstrain structural behaviour of V2O5 during Na+ intercalation.18
The Ũ f reects the synergistic effect of the energy and structural
deformation in a special electrode. As shown in Fig. 3, a-NaxV2O5
yields a volumetric energy density of 128.826 W h L1 at a 5.673%
volume expansion, while d-NaxV2O5 can only provide 90.316 W h
L1 at 4.317%. Therefore, a-NaxV2O5 with a higher stability as
well as the suitable energy density has a great advantage. Also, in
the case of Ca intercalated in V2O5, the a-phase with a nal state
of a-CaV2O5 exhibits Ũ f of 241.403 W h L1 at a 6.237% volume
expansion which is marginally higher than the result obtained
for d-CaV2O5 (Ũ f ¼ 197.215 W h L1 at 3f ¼ 4.757%). This result
also conrms the great stability of the a-phase at the end of the
Ca-intercalation process as discussed above.
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Fig. 3 Volumetric energy density (W h L1) as a function of volume
expansion for a- and d-phase MxV2O5 (x ¼ Na and Ca). The inset shows
the volume expansion of the MxV2O5 phases as a function of Na (or Ca)
concentration.
3.3
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Electronic properties of Na/Ca-intercalated a- and d-V2O5
Generally, electrical conductivity is an essential factor for the
electrochemical properties of an electrode. Electrodes with
undesirable poor conductivity may not be appropriate for
specic battery applications. In our calculations, the imaginary
and real parts of the dielectric function are evaluated according
to eqn (4). The imaginary part of the dielectric function has
a direct response to the optical conductivity, which can be seen
as a generalization of the electrical conductivity that links the
current density to the electric eld for general frequencies.39
From the imaginary and real electrical conductivity shown
(Fig. 4a and c), the semi-conducting nature of a- and d-V2O5 can
be derived from the sharp peak at about 2.0 eV. However,
sodium/calcium intercalations cause a reduction of the band
Journal of Materials Chemistry A
gap in both a- and d-V2O5, where obvious Drude peaks appear
near the zero frequency (Fig. 4b and d).
To uncover the conductivity changes outlined above, the
partial electronic density of states (PDOS) of NaxV2O5/CaxV2O5
were calculated. It is well-known that the spin–orbit coupling
(SOC) effect can have a large impact on the calculated band gap
of strongly correlated systems. To address this, we have
analyzed the impact of SOC on the band structures of V2O5 (see
ESI† for more detail). The spin–orbit splitting predicted by the
PBE+U+SOC method is comparable in different V2O5 systems.
Thus, all the results on the electrochemical properties of
MxV2O5 (M ¼ Na, or Ca) are based on the PBE+U functional in
our study. As for the bulk a- and d-V2O5, the square pyramid
crystal eld splits the energies of the V-3d orbitals into the
ordering: dxz ¼ dyz < dxy < dz2 < dx2y2. The formal oxidation state
of V2O5 is 5+. The valence states lie between 7 and 1 eV,
derived from the bonding V-3 dyz, dxz and O-2p hybrid orbitals
(Fig. 5e), while the lower conduction bands successively contain
the unoccupied V-3 dxy, dz2, dx2y2 orbitals and the anti-bonding
V-3 dyz, dxz and O-2p hybrid orbitals. As a-V2O5 is fully intercalated by Na+, we make one key observation: the intercalation of
Na+ into the stoichiometric V2O5 results in a one-electron
transfer from Na-s to the conduction band minimum (CBM)
forming one V4+ ion, as revealed from the partially occupied,
localized V-3 dxy states in Fig. 5c and e. In this case, a drastic
reduction of band gap from 2.31 eV (a-V2O5) to 0.83 eV (NaV2O5)
is found, with the corresponding Fermi level shi of roughly
1.5 eV. Here the Fermi level was dened as the highest occupied
state of the system, and it was taken to be 0 eV. The band
energies of are obtained by aligning the energy of Kohn–Sham
states with respect to the vacuum level. Notably, the partial V
reduction from V5+ to V4+, as well as the Fermi level shiing for
Na-ion intercalation in V2O5 lms has also been observed using
X-ray photoelectron spectroscopy (XPS).13 In the case of bivalent
Ca-ion intercalation, all of the oxidation states of V ions are
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Fig. 4 The calculated imaginary (blue) and real (red) parts of the dielectric function for (a) a-V2O5, (b) d-V2O5, (c) a-NaV2O5 and (d) a-CaV2O5.
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Fig. 5 The partial density of states (PDOS) of (a) a-V2O5, (b) d-V2O5, (c) a-NaV2O5 and (d) d-CaV2O5. (e) Schematic of the band alignment
between V-3d and O-2p in a-V2O5 and d-V2O5. The band energies are obtained by aligning the orbital energies with respect to the vacuum level.
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reduced to +4, in which the V-3 dxy states are fully occupied at
the nal calcication state (a-CaV2O5), as depicted in Fig. 5d.
Eventually, a reduction of the band gap, from 2.56 eV (a-V2O5) to
1.09 eV (CaV2O5), is found. On the basis of these results, we
provide an intrinsic explanation of the evolution of the electronic structure of V2O5 during the electrochemical process, in
particular the large difference in the orbital occupations
between Na-intercalation and Ca-intercalation reactions.
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Surface-to-bulk diffusion properties
The ion diffusion properties are important for the rapid charge
and discharge performance and hence delivery of power by
LIBs. Earlier studies on the electrolyte–electrode combinations
in Mg-ion batteries49–51 have shown that ion transport in the
electrode could be impacted by complex surface phenomena
including ion desolvation and diffusion on the electrode
surface. There are marked improvements to the electrochemical
properties of nano-structured electrodes when compared to
their bulk counterparts.52–54 However, although the morphology
and surface energy of electrodes have previously been studied,55
explicit investigation of Na/Ca diffusion properties at the
surface/interface is, as far as we are aware, still lacking.
6 | J. Mater. Chem. A, 2016, xx, 1–10
In Fig. 6a and b we show different surfaces of the equilibrium crystal morphology of a- and d-V2O5 respectively. The two
most possible diffusion paths are highlighted: (1) diffusion
within the interlayer spacing, (010) plane and (2) diffusion
through different layers along the b direction (100) plane. The
prominence of the (010) surface is consistent with previous ab
initio56–58 and experimental work.59 Furthermore, the (100)
surface was calculated to have the lowest energy, aer (010),
among those surfaces providing access to the tunnel for a-axis
diffusion. It is likely that these are the surfaces through which
most Na/Ca-ions must diffuse into bulk crystals. Specically, we
have performed four sets of calculations: dilute Na concentration (x ¼ 0.025) in a-(100) (Fig. 6c), dilute Na/Ca concentration
(x ¼ 0.03) in a-(010) (Fig. 6d), high Ca concentration (x ¼ 0.97)
in a-(010) and d-(010) (Fig. 6e and Table 2).
These simulations reveal interesting characteristics, rstly,
the barriers of Na diffusion in the a-(010) plane (0.45–1.15 eV)
are lower than those in a-(100) (1.40–3.10 eV) (Table 2). Rong
et al.60 indicated that the migration barriers can be at most
650 meV for a nano-sized cathode particle to perform
adequate battery operation. Thus, the migration barriers for Na
in the a phase are still relatively high (1.131 eV). By further
calculating the diffusion constants (D, eqn (4)) in bulk a-(100)
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Fig. 6 The Na/Ca-ion surface-to-bulk diffusion barriers at the different surfaces, (a) a-phase and (b) d-phase. The diffusion paths and energy
barriers of (c) dilute Na-ion diffusion in the a (100) surface, (d) dilute Na/Ca-ion diffusion in the a (010) surface, (e) dilute and high Ca-ion diffusion
in the d (010) surface are shown along with the corresponding electrostatic potentials (blue dashed line). The black dashed line at the zero depth
indicates the surface of different phases. The purple, red, yellow and brown spheres indicate V, O, Na and Ca atoms, respectively.
plane, we nd that they are roughly 1030 times larger than those
observed in a-(010) at 300 K (Table 2). Ca2+ diffusion barriers in
a-(100) differ dramatically from that of Na+ (Fig. 6c). The larger
electrostatic forces associated with the divalent Ca2+ slow the
solid-state diffusion to a crawl. This is also the reason that there
is a more arduous search for suitable Ca-compatible electrodes
as well as electrolytes.
We have further explored the surface-to-bulk diffusion
properties of Na/Ca atoms in a- and d-V2O5. It is found that the
initial barrier for Na/Ca intercalation at both (100) and (010)
surfaces are much lower compared to diffusion in the bulk. For
example, in the a-(010) structure, the barriers for Na and Ca
atoms associated with diffusion from the outermost site of the
(010) surface to the inside are 0.498 and 0.846 eV, respectively,
as shown in Fig. 6d and Table 2. The activation barriers of Ca
diffusion in a-V2O5 are 1.643 eV and 1.827 eV for the dilute and
high concentrations, respectively, which is also consistent with
previous theoretical studies.47 We suggest that the lower diffusion barriers at the surface were controlled by two competing
factors: rstly, the broken bonds at the surface would lead to the
instability of the surface sites, which eventually results in lower
This journal is © The Royal Society of Chemistry 2016
activation barriers. On the other hand, the lacking V–O bonds
on the cleaved surface leads to the higher Na/Ca-intercalation
energy, which would also hinder the movement of these ions
into bulk sites. As shown in Table 2, the Na/Ca bonding energies
on the a-(010) surface sites are 1.478/2.689 eV, which is larger
than 0.698/1.243 eV in the bulk site. Similar trends were also
found in the cases of Na/Ca intercalation in a-(100) and d-(010).
From the discussions outlined above, the lower surface diffusion barrier is likely to favor ion intercalation into nanostructured samples of V2O5 and suggests a reason why
intercalation is enhanced upon moving to nanostructured
crystals. Indeed, the crucial differences in the Na/Ca mobility at
the surfaces and in the bulk play a key role in the intercalation
behaviors of bulk crystalline versus nano-structural systems for
many electrodes. In addition to the diffusion barriers obtained
from thermodynamic analyses, the electrostatic potential along
the diffusion path was also calculated (Fig. 6), which can be
derived from the sum of the Hartree and ionic potentials in the
ion deintercalation process. Fig. 6c–e show that a strong
correlation exists between the peak locations of the electrostatic
potential and the Na/Ca activation energy peaks could be seen
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Table 2 Calculated Na/Ca surface-to-bulk activation barriers (Ea),
bonding strengths, diffusion constants (D) and the diffusion distance
along paths (d) at the different surfaces of a- and d-phases
Bonding strengths
(eV per bond)
D (cm2 S1)
d (Å)
10
Na (a-010) dilute
1/2
0.498
2/3
1.122
3/4
1.137
Bulk
1.131
1.478
0.702
0.704
0.698
6.215 1011
2.098 1021
1.188 1021
1.477 1021
3.801
3.852
3.875
3.846
15
Na (a-100) dilute
1/2
1.424
2/3
2.849
3/4
3.073
Bulk
2.986
0.914
0.713
0.701
0.692
5.324 1021
6.362 1050
1.082 1053
3.072 1052
6.678
6.812
6.763
6.698
Ca (a-010) dilute
1/2
0.846
2/3
1.558
3/4
1.611
Bulk
1.643
2.689
1.224
1.241
1.243
8.918 1017
1.026 1028
1.312 1029
3.669 1030
3.815
3.914
3.902
3.832
Ca (a-010) high
1/2
0.976
2/3
1.825
3/4
1.822
Bulk
1.827
2.062
0.956
0.948
0.963
5.899 1019
3.310 1033
3.742 1033
2.916 1033
3.835
3.889
3.902
3.794
Ca (d-010) high
1/2
0.735
2/3
1.462
3/4
1.381
Bulk
1.373
1.983
1.295
1.171
1.159
1.021 1014
6.742 1027
1.505 1025
2.005 1025
4.769
4.956
4.887
4.833
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Path
Ea (eV)
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4 Conclusion
in both a- and d-V2O5. High potential and large oscillations of
electrostatic potential were found near the surface, which
makes the bonding stronger between Na/Ca atoms and V2O5. In
this regard, we draw the conclusion that the large oscillations of
electrostatic potential near the surface appear to be the major
determinant for the high intercalation energy at the surface.
Moreover, the diffusion barriers for high concentrations of
Ca in d-(010) (0.73–1.39 eV) are consistently much lower than
those in a-(010) (0.97–1.83 eV), as shown in Table 2. The
previous study on a variety of well-known Li-ion intercalation
host structures showed that the changes of the coordination
environment along the diffusion path can signicantly affect
the magnitude of ion diffusion barriers.60 In our work, the Ca in
the a phase is diffused between neighboring 8-coordinated sites
through a 3-coordinated transition-state. However, in the
d phase, Ca diffuses between neighboring 6-coordinated sites
through a 5-coordinated intermediate state and two 3-coordinated transition sites, resulting in a smaller coordination
change in the d phase than that in the a phase.47 Hence,
a signicant enhancement is observed for the mobility at high
Ca concentration in the d phase at room temperature (1025
cm2 S1 in bulk d-V2O5, compared to 1033 cm2 S1 in a-V2O5,
which is 8 orders of magnitude improvement in the diffusivity) (Table 2). It is worth noting that the lower coordination
8 | J. Mater. Chem. A, 2016, xx, 1–10
changes in the d phase gives rise to the smaller barriers, as
demonstrated in the previous study of Ca intercalation in V2O5
by Guatam et al.47 Further investigation of the Ca migration
properties at the dilute concentration (charged state) has been
carried out and the energy barrier was calculated to be 0.86 eV,
as shown in Fig. 6e. Prior computations by Gautam47 and Rong60
have reported lower (200 meV) barriers for Ca diffusion in
bulk d-V2O5, which is obviously smaller than our result of 0.86
eV. It should be noted that the previous work used the standard
GGA in their NEB calculation, while we used the GGA+U. In
order to check whether the functionals (GGA and GGA+U) can
affect the diffusion barrier, the migration behavior in V2O5 is
explored (see ESI† for more detail). The barrier of for Ca
migration in bulk d-V2O5 at the dilute concentration is 0.46 eV
(Fig. S5†) by GGA, which is quite close to the previous results of
0.2 eV.59,60 The difference may come the distinct images that
have been used for the NEB. Although the functional can affect
the diffusion barrier, all the calculated results suggest more
promising Ca migration in the d phase than that in the a phase.
To summarize, we have explored the possibility of using V2O5 as
NIB/CIB cathode materials by means of rst-principles calculations with Hubbard U corrections. The structural stability,
intercalation voltages, electronic characteristics and rate capability of Na/Ca-ion intercalation in a- and d-V2O5 compounds
were systematically examined. The a phase is computationally
predicted to be more stable than the d phase during both Na
and Ca intercalation processes. By explicit calculation of the
surface-to-bulk diffusion properties of a- and d-V2O5 systems,
lower barriers of 0.498 and 0.846 eV were found for both Na- and
Ca-ion intercalation at the (010) surface that dominates the
equilibrium morphology, which account for the improved rate
performance found in nano-dimensional V2O5 compared to
their bulk counterparts. With all these extraordinary characteristics, including the high stability for sodiation/calcication
and high Na/Ca-ion mobility, the V2O5, especially with the
construction of nanostructures should have great potential to
be applied as cathode materials for NIBs/CIBs.
Acknowledgements
This work was supported by the National Natural Science
Foundation of China (grant no. 51572016 and U1530401) and
the China Postdoctoral Science Foundation (grant no.
2016M590034). The computation supports from Tianhe-2JK
computing time award at the Beijing Computational Science
Research Center (CSRC) and the Special Program for Applied
Research on Super Computation of the NSFC-Guangdong Joint
Fund (the second phase) were also acknowledged.
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