A first-principles study of bulk and
surface Sn-doped LiFePO4: The role of
intermediate valence component in the
multivalent doping
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Phys. Status Solidi B, 1700041 (2017) / DOI 10.1002/pssb.201700041
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basic solid state physics
Lianxi Hou1,2 and Guohua Tao*,1,2
1
2
School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen 518055, P.R. China
Shenzhen Key Laboratory of New Energy Materials by Design, Peking University, Shenzhen 518055, P.R. China
Received 17 January 2017, revised 28 April 2017, accepted 23 June 2017
Published online 18 July 2017
Keywords doping, electronic structure, LiFePO, multivalence, surface
* Corresponding
author: e-mail taogh@pkusz.edu.cn, Phone: 86-755-26035309, Fax: 86-755-26615595
Doping can be employed to enhance the electrical
conductivity and electrochemical performance of LiFePO4,
a promising material for Li-ion batteries. However, the
microscopic mechanism of doping is not fully understood. In
this study, ab initio density functional theory (DFT) with the
generalized gradient approximation (GGA) þ U calculations
was performed on both bulk and surface Sn-doped LiFePO4.
Our results indicate that surface doping is preferred over
bulk or subsurface doping because it shows a lower doping
energy and surface energy. The doping effect appears to be
local, and the effect of the Li vacancy (VLi) distribution was
examined. The multivalent Sn doping may facilitate the
formation of an Fe2þ/Fe3þ complex with the involvement of
an effective intermediate Sn3þ component, which complements the existing charge transfer model for LiFePO4. The
effective Sn3þ–Fe3þ/2VLi complex may exist on the
LiFePO4 surfaces, providing possible surface design
schemes to control charge transfer. The results suggest that
the Sn dopant could modulate band gap and local charge
transfer, and improve the electrochemical performance at the
last stage of the charging process with no capacity loss.
However, an optimized doping concentration may exist for
electrochemically inactive doping with an unfavorable
doping energy.
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1 Introduction As a promising cathode material of
lithium ion batteries [1–9], the olivine-type LiFePO4 has
been implemented in commercial electric automobiles.
Despite the many excellent properties of LiFePO4, such as
good thermal stability, environmental benignity and relatively low cost, one of its primary disadvantages is its low
intrinsic electronic conductivity (109 1010 S cm1) [10].
To improve the electrochemical performance of LiFePO4,
extensive research has focused on the development of
coatings [11–18] (such as carbon, metal, or metal oxides),
particle size minimization [2, 12, 19, 20], doping techniques [10, 21–35] and so on. Among these treatments, doping
may have advantages over the others in the enhancement of
the intrinsic electrical conductivity with no loss of energy
density due to introducing nonactive materials (C coating) or
void spaces (nanoparticle assembling). However, the effect
of doping on the electrochemical performance of LiFePO4
and its mechanism are controversial. An early study [10]
proposed that a variety of cation dopants could increase the
electrical conductivity of LiFePO4 by several orders of
magnitude. Later studies [13–15] demonstrated that high
conductivity might be attributed to the effect of carbon
coating or the formation of metal impurities. Theoretical
calculations [23–25] also indicated that aliovalent doping is
highly unfavorable, and isovalent doping at the Fe site would
have limited effect on the conductivity [22], while doping at
the Li site may improve the intrinsic electronic conductivity [21] at the expense of the detrimental Li ion diffusion. It
has been suggested [24, 36–38] that charge carrier transport
follows a polaronic hopping mechanism instead of delocalized band-like conduction. Therefore, the improvement of
LiFePO4 conductivity upon doping would be related to the
extrinsic impurities, such as small hole polarons and Li
vacancies [39].
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L. Hou and G. Tao: First-principles study of bulk and surface Sn-doped LiFePO4
In actual battery systems, surfaces, and interfaces
typically play an important role [8, 9, 40] in controlling the
structures, properties, and functions of the working
materials. Physical insights provided by theoretical studies
would be invaluable because molecular structures and
mechanisms are difficult to identify using experiments
alone. For example, Ceder and co-workers [41] calculated
the surface energy of the individual surfaces in crystalline
LiFePO4 using the density functional theory (DFT) method,
and they found that the (010) and (201) surfaces are the
lowest in energy, which may become preferential surfaces
for crystal growth. Similar results were also obtained by the
Chen Group from their first principles studies [42]. Based on
the atomic simulations, Islam and co-workers [43, 44] were
able to calculate the equilibrium growth morphology of
nanocrystalline LiFePO4 with the low energy surfaces
dominating, which appeared to agree with the experiments.
The Henkelman group evaluated the Li-ion diffusion
barriers in a variety of local environments in the bulk, on
the surface, and in defected systems of LiFePO4 and FePO4
using DFT calculations [45], and the authors claimed that
the surface diffusion of Li ions is much slower than that in
bulk, which may explain the wide range of experimental
measurements on Li diffusion coefficients and the difference between the theoretical predictions and experiments.
Moreover, Goodenough, Henkelman and coworkers [31]
suggested that the high barrier for the surface charge transfer
might be alleviated by the anion surface modification, which
improves the charge/discharge performance of the LiFePO4
cathode. Recently, the Zaghib group [46] successfully
realized an inexpensive hydrothermal synthesis of LiFePO4
nanoparticles, and a high electrochemical performance was
achieved since the Li–Fe anti-site defects preferably
aggregate on the surfaces of LiFePO4 and can be effectively
removed by calcium ions, which is consistent with previous
theoretical investigations [47].
Since the electrochemical performance of LiFePO4
could be controlled by surface effects, it would be
interesting to examine how doping on the surfaces could
contribute to the rational design of high performance
cathode materials compared with their bulk counterparts. In
this study, we perform ab initio DFT calculations on Sndoped LiFePO4 in the bulk and on the surfaces and
investigate the effect of Sn doping on the electronic
structures and microscopic environments, as well as the
underlying doping mechanism on the structure stability and
electrochemical performance. We selected tin because (1) it
is a multivalent element (Snþ2 and Snþ4) presenting a good
opportunity for systematic theoretical investigations, and (2)
LiFePO4 is a strong ionic material built on a rigid PO4
skeleton, while the Sn-O bond is weak. Thus, the effect of
the Coulomb interactions can be separated from otherwise
nonlocal distortions in the doping mechanism. Moreover,
recent experiments indicate that improved Liþ diffusion and
good electrochemical performance can be achieved in the
bulk Sn-doped LiFePO4 [28] and the Sn-coated LiFePO4/
C [29]. Even as an electrochemically inactive spectator
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cation, Sn may help stabilize the structure and reduce
the voltage decay in layered oxide cathode materials of
Li2Ru1-ySnyO3 [48, 49].
Specifically, we calculated the electronic structures and
doping energies of Sn-doped systems in the bulk and on the
(010) surface and compared the structural stability of a
variety of different doping configurations. The (010) surface
is chosen because it allows the channel entrance of the most
facile pathway for Li ion diffusion to be exposed to the
surface, which also appears as the most stable and prominent
surface compared with the other surfaces in previous
calculations [42] and experiments [43]. The Li vacancy
distribution was examined in the aliovalent doping of Sn4þ,
and the effect on the electrochemical performance,
connections to experiments, and insights into the new
cathode material design were discussed.
2 Computational details The olivine structure of
LiFePO4 (space group Pnma) [32] is formed via polyhedra
connected by common O atoms, as shown in Fig. 1. Liþ and
Fe2þ ions occupy the centers of the octahedra, and the P
atoms are located in the center of the PO4 tetrahedral
structure. To perform ab initio calculations, we constructed
a 1 2 3 supercell containing 24 formula units of the
compound (Fig. 1a and 1b). Pure bulk and stoichiometric
Sn-doped Li24Fe24xSnxP24O96 with x ¼ 1 (unless specified
otherwise) are considered, corresponding to a 4 mol%
isovalent doping of Sn2þ at the Fe site. This doping
concentration is close to that (3%) with the best
electrochemical performance among a series of doping
contents, namely, 1, 3, 5, and 7%, in experiments [28].
The electronic structure calculations were performed
using DFT [50, 51] of a generalized gradient approximation
(GGA) form following Perdew, Burke and Ernzerhof [52]
using the VASP (Vienna ab initio simulation package)
program [53, 54] with the plane-wave projector-augmented
wave (PAW) method [55, 56] applied. An energy cutoff of
520 eV and a 3 3 3 Monkhorst–Pack [57] mesh of kpoint sampling in the Brillouin zone were chosen to ensure
that the final forces were smaller than 0.01 eV Å 1 or that
the energy convergence of 105 was satisfied. It is well
known that local density approximation (LDA) and GGA
underestimate the band gap, especially for transition metals.
Therefore, the GGA þ U approach [58] was used to
consider the electron correlation of Fe d state electrons in
which the screened onsite coulomb term U and the exchange
term J can be grouped into a single effective parameter
Ueff ¼ U J [59]. The GGA þ U computations for LiFePO4
using a value of Ueff ¼ 4.3 eV based on the average Ueff for
Fe2þ (3.7 eV) and Fe3þ (4.9 eV) [60] may produce lattice
structures with a band gap of 3.7 eV and a Li intercalation
voltage relative to a Li metal anode (3.5 eV) that is in
excellent agreement with previous theoretical values
[36, 41, 60] and experimental measurements [1, 2, 36]
(for details, see the supplement). We used the Gaussian
smearing method [61] with a width of 0.2 eV to perform all
the k-point integrations, unless specified otherwise. All
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Figure 1 Crystal structures of LiFePO4 systems. (a) Unit cell containing four formula units of the compound, (b) 1 2 3 supercell,
(c) (010) surface structure of a 1 2 3 supercell slab. Li (green), Fe (golden), P (purple), and O (red).
calculations were spin-polarized, and the ferromagnetic
configuration was assumed.
The structure of the (010) surface was constructed using
the periodic slab model [41] (Fig. 1c) for a 1 2 3
supercell. A 15 Å vacuum layer was used to ensure that the
interactions between the periodic images of surfaces were
negligible, and a k-point setting of 3 1 3 was used. The
convergence was checked to ensure that the energy
difference was less than 1 meV atom1. In our study, the
lattice parameters of the supercell were kept fixed. The top
6 Å surface layers of the slab were allowed to fully relax,
and the final forces were smaller than 0.01 eV Å 1. The
doping configuration was established by replacing one or
two of the Fe atoms on the surface or in the subsurface with
tin atoms (Fig. 1c).
Because Sn is multivalent and both Sn2þ and Sn4þ ions
have been identified in Sn-doped LiFePO4 experimentally [28], we also examined the effect of Sn4þ doping and
co-doping of both types of ions. The Sn4þ-doped LiFePO4
was constructed by replacing one Fe2þ ion with one Sn4þ
ion while simultaneously removing two Li ions for the
charge compensation. To study the Sn2þ and Sn4þ co-doped
LiFePO4, one Sn2þ ion and one Sn4þ ion were introduced
into the system. The atomic illustrations were produced
using the VESTA program [62]. For the Sn4þ doping, there
are a number of combinations for the relative locations of
the Li vacancy sites and the doping site. Fig. 2 displays four
representative configurations for the Sn4þ/2VLi doped
system, from which we examine the effect of the Li
vacancy distribution in Sn4þ doping. The Li vacancies in
Fig. 2a are located on two Li sites closest to the Sn-doping
site in a nearby Li diffusion channel in the b direction
(labeled by the n1d model). In Fig. 2b, the Li vacancies are
set on two of the closest sites from different nearby b
channels (n2d model), and in Fig. 2c (f1d model) and
Fig. 2d (f2d model), the Li vacancies are located in one or
two b channels far from the doping site.
To compare the stability of Sn-doping in bulk and that
on surfaces, the doping energy Ed was evaluated. Here, we
consider the following reaction:
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LFP þ SnO ! LFPSn þ FeO:
ð1aÞ
where “LFP” and “LFP_Sn” denote pure and Sn-doped
LiFePO4 (bulk or surface structures), respectively. The
energy values of the metal oxide compounds were
calculated based on the corresponding molecular structures.
For the surface doping, we consider Sn4þ with an O atom on
the surface to balance the charge:
LFP þ SnO2 ! LFPSn½IVO þ FeO:
ð1bÞ
The surface energies can be defined as follows:
g down ¼
Es Eb
;
2S
ð2aÞ
where Es and Eb are the total energy of the surface structure
and that of the corresponding bulk structure, respectively,
and S is the surface area. Factor 2 is considered because the
surface has two sides. Note that here, the upper and lower
surfaces are different because we fix atoms on the bottom.
Therefore, we first fix all atoms on the slab, and the lower
surface energy was calculated using Eq. (2a). The upper
surface energy can then be evaluated by the following
modified equation:
g up ¼
Es 0 Eb
g down ;
S
ð2bÞ
0
where Es is the total energy of the relaxed surface structure.
3 Results and discussion
3.1 Bulk doping The crystal structure of LiFePO4
was first optimized, which allows both lattice parameters
and ion positions to fully relax. The lattice parameters of the
relaxed bulk LiFePO4 structure were a ¼ 10.432 Å ,
b ¼ 6.062 Å , c ¼ 4.742 Å , and V ¼ 299.88 Å 3, which agree
well with the experimentally determined values (Table S1)
and are in excellent agreement with previous
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Figure 2 Sn4þ doping with two Li vacancies
located in different sites. Arrows indicate the
Li locations of the vacancy sites: (a) close one
channel; (b) close two channels; (c) distant
one channel; and (d) distant two channels. Li
(green), Fe (gold), P (purple), O (red), and Sn
(blue).
calculations [60]. The optimized crystal structures of
LiFe23/24Sn1/24PO4 and FePO4 are also listed along with
the experimental values for comparison. The difference
between the calculated results and the experimental values is
less than 3%, and the change of crystal volume is
approximately 5% during the charge/discharge process.
The crystal volume increases by approximately 1% upon Sn
doping; in contrast, the volume of the octahedral structure at
the doping site increases by approximately 33% from 12.9 to
17.2 Å 3 (Table S2). Therefore, the doping of Sn2þ does not
significantly change the host lattice structure, except for the
local environment around Sn2þ. Since the radius of the Sn2þ
ion (0.93 Å ) is larger than the Fe2þ ion (0.76 Å ), crystal
distortion may be induced; however, the stable olivine
structure confines the distortion within the local space.
Upon Sn doping, new electronic states appear on the top
of the valence band (Sn2þ) and/or the bottom of the
conduction band (Sn4þ), leading to a decrease in band gap
from 3.74 eV (pure bulk) to 2.96, 2.06, and 1.50 eV for the
Sn2þ doped, Sn4þ doped and co-doped LiFePO4, respectively (see Fig. S1). Note that the electrical conductivity
may not appreciably increase upon the Sn doping since
the dispersion remains flat and is largely unchanged. For the
aliovalent doping (Sn4þ and Sn2þ/Sn4þ co-doping) in the
bulk LiFePO4, the calculated doping energies are higher
than those for the isovalent Sn2þ doping (Table S3), which
is consistent with previous observations [23–25].
The detailed electronic structures, that is, the density of
states (DOS) and partial density of states (PDOS) of pure
and Sn-doped LiFePO4, are displayed in Fig. 3. Compared
with the results for pure LiFePO4 (Fig. 3a), upon Sn2þ
doping, the new states near the Fermi level primarily consist
of the Sn_5s and the O_2p characteristics (Fig. 3b and
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Fig. S2 in the supplement), similar to an N-type doped
semiconductor. In contrast, for the Sn4þ doping, new states
appear below the conduction band, which primarily consist
of Sn_5s and O_2p characteristics (Fig. 3c), similar to a
P-type doped semiconductor. The co-doped structure, as
expected, appears as the superposition of Sn2þ and Sn4þ
doping (Fig. 3d), and the band structure of the LiFePO4
component appears insensitive to the Sn-doping.
To further examine the chemical nature of the doping
effect, we plotted the electron density-difference maps in
Fig. 4. It is evident that Fe–O and P–O form strong bonds in
pure LiFePO4 (Fig. 4a). Much weaker bonding is shown for
the doped Sn and O, and the electron donation from O
in the Sn4þ–O bond is clearly observed (Fig. 4b–d).
Therefore, the effect of doped tin on electron density is
localized and the P–O and Fe–O bondings appear largely
unchanged.
For the aliovalent doping, Li vacancies are introduced
for charge compensation. The results for the Sn4þ doping in
bulk indeed vary with different Li vacancy distributions,
however the effect is not significant. For example, the
calculated lattice parameters for all four models in Fig. 2 are
within 0.4% (Table S4), and the largest difference in the
total energy of the doped systems is approximately 1.06 eV
with the n2d model most stable and the f1d model most
unstable (Table S5). Moreover the electronic structures for
all four models are similar, (see for example Fig. S3).
In principle, there is another alternative configuration
for the Sn-doped system with two Li vacancies, that is, two
Fe2þ ions are replaced with Fe3þ, and Sn remains as Sn2þ or
as other intermediate complexes with electrons redistributed
between Fe and Sn. However, the calculated total energy of
the four models for the Sn3þ–Fe3þ/2VLi doping is
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Figure 3 DOS and PDOS of pure and Sndoped LiFePO4. (a) pure; (b) Sn2þ doped; (c)
Sn4þ doped; and (d) Sn2þ/Sn4þ co-doped. The
inset shows the PDOS of the Sn component in
the Sn-doped LiFePO4. The Fermi level is set
to zero in all DOS plots in this study.
approximately 0.5–1.3 eV higher than those for the
corresponding Sn4þ configurations, indicating that these
configurations are meta-stable So the Sn4þ doping in bulk
LiFePO4 tends to keep the Fe ion in the lower valence, that
is, Fe2þ; thus, the changes the doped system undergoes at
the last stage of the charging process should be determined.
To ensure charge neutrality, Sn could not be alone in the
fully charged FePO4. If Sn were divalent (or for any other
divalent element), then another Li ion would be required to
remain in the system for charge compensation, which leads
to the loss of reversible capacity. Since the Sn2þ ion is more
easily oxidized than Fe2þ, it is likely that Sn remains
tetravalent along with another Fe ion that is divalent [10];
therefore, there is no waste of Li ions. Furthermore, the
existence of the Fe2þ/Fe3þ pair facilitates charge transfer,
which is supported by the DFT calculations (see Fig. S4).
3.2 Surface doping Experimentally, both the Sn2þ
and Sn4þ components were detected in the bulk Sn-doped
LiFePO4 [28]. In principle the Sn doing may also occur on
the surfaces. Therefore, we consider surface doping here
too. The calculated doping energy increases as the doping
site moves from the surface (Ed 2.67 eV) to the subsurface
(Ed 3.96 eV), and the latter is very close to the doping
Figure 4 Electron density-difference maps
of pure and Sn-doped LiFePO4. (a) pure; (b)
Sn2þ doped; (c) Sn4þ doped; and (d) Sn2þ/
Sn4þ co-doped. Atoms shown are Fe (gold), P
(purple), O (red), and Sn (blue).
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energy for the bulk (Ed 4.15 eV, Table S3). This finding
indicates that surface doping by Sn2þ is energetically more
favorable than the bulk/subsurface doping, and the surface
effect is highly local. Similar results were obtained for the
Sn4þ doping. Interestingly the Sn4þ doping with an O atom
(Eq. (1b)) results in a relatively stable doped surface
(Ed 1.6 eV), which could make an appreciable contribution in experiments [28, 29]. The calculated lower and upper
surface energy values (Eq. (2a) and (2b)) were 1.04 and
0.62 J m2 for pure LiFePO4. For the Sn-doped system, the
upper surface energy increases from 0.46 to 0.60 J m2 as
the doping position moves from surface to subsurface,
approaching the value for the pure system. This result
confirms that the effect of Sn-doping is local and surface
doping is energetically more favorable. The band gap of
pure surface LiFePO4 was 2.42 eV, which is smaller than
that for bulk. Surface doping with Sn2þ or Sn4þ-O reduces
the band gap by 0–0.2 eV (Table S6). The Sn2þ/Sn4þ codoping in the surface system does not significantly change
the band gap with respect to the single valence doping.
The electronic structures of the pure and doped LiFePO4
surfaces were also investigated. Figure 5 shows the DOS
and the PDOS of the pure and Sn-doped (0 1 0) surface of
LiFePO4. In the bulk, Fe ions are six-fold coordinated by
oxygen. Once the surface is cut, the exposed Fe ions become
five-fold coordinated, leading to a broken symmetry of FeO6
octahedra. The energy level splitting of the Fe_3d orbitals
changes the distribution of electronic states near the Fermi
level, resulting in the coincidence of the DOS of Fe_3d with
the Sn components near band edges. From the PDOS in
Fig. 5b inset, both the s and p electrons of Sn contribute to a
greater extent to the DOS functions near band edges than
those in the doped bulk system, which implies a larger
hybridization of the s and p orbitals. Consequently, the
energy level has a small downshift relative to the Fermi level
compared with the counterpart in bulk (Fig. 3b inset).
Consistent with the doping energy analysis, the electronic
structure of subsurface doping (Fig. 5c) resembles that of
bulk doping, indicating that the surface effect is significantly
reduced below the topmost two layers, that is, the surface
and subsurface layers. The LiFePO4 surface subjected to
Sn4þ doping by replacing Fe2þ with Sn4þ and with an extra
O ion instead of two Li vacancies (Fig. 5d) resembles that
for the bulk doping (Fig. 3c), except that the Sn orbitals
become s-p hybridized.
For the Sn4þ doping on the surface, the Sn3þ–Fe3þ
configuration with two Li vacancies is another theoretical
possibility to accommodate the charge neutrality. In contrast
to the stability analysis of bulk doping, the energies of the
Sn3þ–Fe3þ/2VLi and the Sn4þ/2VLi configurations are
reduced, with the former being approximately 0.02 eV
lower than the latter (Table S3). The existence of Sn4þ or the
Sn3þ–Fe3þ combination can be clearly identified from the
DOS and PDOS plots of the doping system shown in Fig. 6.
Fig. 6a displays the DOS and PDOS of the Sn4þ-doped
(010) surface of LiFePO4, and the overall behavior
resembles that for the bulk doping system (Fig. S3a) and
that for the Sn4þ surface doping with a Sn-O bond (Fig. 5d),
with a small Sn component (Fig. 6a inset) appearing in the
middle of the band gap. The Sn3þ–Fe3þ/2VLi system
features Fe3þ orbitals in the gap, which lowers the band gap
substantially (Fig. 6b), similar to its bulk counterpart
(Fig. S3b). Again, the surface-doped Sn (Fig. 6b inset)
shows appreciable s–p hybridization in the bands near the
Fermi level, probably due to the low symmetric local
structures on the surfaces. Although both Sn3þ–Fe3þ/2VLi
and Sn4þ/2VLi seem likely to exist on surfaces during the
charge/discharge process, the former is preferable because it
Figure 5 DOS and PDOS of the pure and Sndoped (010) surface of LiFePO4. (a) pure
surface; (b) doped surface; (c) doped subsurface; (d) doped surface with O.
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Figure 6 DOS and PDOS of the Sn-doped (010) surface of
LiFePO4. (a) Sn4þ with 2 Li vacancies; (b) Sn3þ–Fe3þ with 2 Li
vacancies.
is compatible with the existence of the Fe3þ/Fe2þ small
polaron, without a substantial reduction in conductivity
(here, Sn holds one electron with an effective valence of
þ3), which ensures that the final discharge process (the
restoration of the last two Li ions in this case) proceeds more
favorably than that in the Sn4þ-doped system.
4 Discussion It would be informative to investigate
how the multivalent doping of Sn affects the structure and
charge transfer of the doped LiFePO4. Here, we examine the
effect of Sn doping on the O–O bonding taking the n1d
model for bulk as an example (see Fig. S5 and Table S7).
The shortest O–O bond in the Sn4þ-doped LiFePO4 is
2.407 Å in comparison with 2.471 Å in the pure system,
which is larger than that for the Fe3þ/VLi (2.389 Å ), and that
for the unstable Sn3þ–Fe3þ-doped LiFePO4 with two Li
vacancies (2.374 Å ). This implies that the relatively stable
Sn4þ doping (Fig. 7d) may help maintain the original bulk
structure in the presence of Li vacancies, since a shorter O-O
bond length seems associated with local structure distortions, which might lead to the O2 release. The results for
the other models in Fig. 2 representing different Li vacancy
distributions are similar (not shown).
Figure 7 displays the electron density maps of the
cutting slab of pure bulk (Fig. 7a), pure bulk with a Li
vacancy (Fig. 7b), the effective Sn3þ-doped (Fig. 7c), and
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Sn4þ-doped systems (Fig. 7d), corresponding to the
structures in Fig. S5. Fe3þ in the Sn3þ-doped system (Fe
11 in Fig. 7c) resembles Fe3þ in Fig 7b with a more extended
electron distribution than that of Fe2þ in pure bulk or in the
Sn4þ-doped system. In contrast, neither Sn3þ nor Sn4þ
shares much electron density with neighboring atoms, while
stronger Coulomb interactions are presented in the latter
case.
The Sn doping in bulk is energetically unfavorable,
although it may exist under nonequilibrium conditions
during the charge/discharge process. Practically, it would be
more interesting to consider surface doping. By construction, only three Li ions existed on the (010) surface of
LiFePO4 along the c direction near the edge of the
simulation box (Fig. 8). Therefore, when considering the
case of Sn doping with two Li vacancies, the vacancy
distribution is limited. However, we consider two representative configurations, as shown in Fig. 8a–d, with the Li
atoms on the middle upper edge removed (the remaining
ones are those on the lower layers and their images),
corresponding to the results in Fig. 6a and b, respectively.
Figure 8 displays the electron density maps of the doped
systems along with the corresponding electron density
difference between the doped and pure surface, and the
doping-induced charge redistribution around the Li (vacancy) sites and the metal site is clearly demonstrated. The
Sn4þ in Fig. 8a and b and the Fe3þ ion (Fe15) in Fig. 8c and
d can be identified by the PDOS. The charge occupancy on
these ions are 1.13 vs. 1.34 s electrons on Sn, and 6.07 versus
5.79 d electrons on Fe15 for the Sn4þ/2VLi and the Sn3þ–
Fe3þ/2VLi doping systems, respectively. In the presence of
Li vacancies, the O–O bond [O19–O18 (2.425 Å ) with O18
hidden behind] near Sn4þ and the O–O bonds near Sn3þ
[O19–O18 (2.440 Å )] or Fe3þ ions [O57–O58 (2.402 Å ,
O57 hidden)] shortened by approximately 0.03 0.07 Å
compared with those in the pure system.
Similar to the results for bulk doping, Fe3þ (Fe15) in the
3þ
Sn -doped system shows a more delocalized electron
density distribution than that of Fe2þ in the Sn4þ-doped
configuration, with Sn3þ occupying a larger low electron
density region than that occupied by Sn4þ. This difference is
consistent with the observation in the corresponding electron
density difference plot shown in Fig. 8b and d, that is, the
charge redistribution upon doping results in a higher electron
density (yellow regions) in the neighboring area around the
high valence ions Sn4þ in Fig. 8b and Fe3þ in Fig. 8d. The
transformation of these two doping configurations via a small
polaron-like charge transfer from Fe15 to Sn can be imagined,
which is presumably different from the Fe2þ/Fe3þ transfer. A
direct dynamics simulation could aid the understanding of the
detailed charge transfer mechanism in which nonequilibrium
conditions may play a key role. Note that even the phase
transformation during the lithiation/delithiation process is in
equilibrium [33]; the instant local dynamics could still be in
nonequilibrium. Further investigations on a larger surface
system also appear necessary to identify the boundary effect;
however, this is beyond the scope of this work.
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L. Hou and G. Tao: First-principles study of bulk and surface Sn-doped LiFePO4
Figure 7 Electron density maps of pure and
Sn-doped LiFePO4 in bulk. The a–b plane
projections of the cutting slab of the simulation box are shown including the doped atom
for clarity. The regions appear in green and
blue due to the cutting. (a) pure; (b) VLi; (c)
Sn3þ–Fe3þ/2VLi; and (d) Sn4þ/2VLi. The
color schemes are Li, green polyhedral; Fe:
gold; O: red; P: purple; and Sn: blue.
The DFT þ U method may produce meta-stable
structures by penalizing electron delocalization due to
self-interaction errors, thus preventing prediction of the true
ground state [63]. However, this meta-stability problem
appears negligible for d orbitals, and our system does not
include delocalized electrons introduced by the oxygen
vacancy. Indeed, the existence of meta-stable configurations
in LiFePO4 was suggested to be responsible for the
Figure 8 The electron density maps of
surface Sn-doped LiFePO4 with two Li
vacancies and electron density differences
between that and the pure (010) surface. The
cutting slabs are plotted including the surface.
(a-b) Sn4þ/2VLi and (c-d) Sn3þ–Fe3þ/2VLi.
(a) and (c) are electron density maps, and (b)
and (d) are the corresponding density differences. The color schemes are Li, green; Fe:
gold; O: red; P: purple polyhedral; and Sn:
blue. Isosurface: positive (yellow), and negative (light blue).
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Original
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Phys. Status Solidi B (2017)
formation of the nonequilibrium single-phase transformation pathway [64, 65] and dynamically accelerated
nonequilibrium Li ion diffusion [66]. According to the
previous analysis, Sn could remain in the tetravalent state
along with a divalent Fe ion in the fully charged FePO4.
However, Sn3þ/Fe3þ may be more favorable than Sn4þ/
Fe2þ in the fully discharged LiFePO4 and during the charge/
discharge process especially for surface doping. Here, the
multivalent Sn dopant acts as a buffer to accommodate both
LiFePO4 and FePO4, resulting in the Fe2þ/Fe3þ complex
with an effective intermediate Sn3þ component involved,
which may modulate the local charge transfer and improve
the conductivity. Therefore, our case study on Sn-doped
LiFePO4 is used to propose a plausible mechanism in which
an intermediate valence ion may be involved for the
aliovalent doping. This idea is different from the early
hypothesis in which only cation vacancy [10] or the donoracceptor co-doping of anions with the delocalized band-like
conduction [30] is considered.
The existence of Sn may help stabilize the O–O bond
during the charge/discharge process and improve the
electrochemical performance at the last stage of the
charging process by forming a Fe2þ/Fe3þ small polaron
while making full use of Li. However, high concentration
doping would be detrimental to charge transfer and would
cause instability since the Sn dopant itself is electrochemically inactive and the doping energy is positive; therefore,
an optimized doping concentration is expected [28].
Furthermore, our calculations were done only for the
(010) surface so far, and it would be definitely interesting to
examine the doping effect on other possible surfaces, which
may be done in future work.
In this work, we do not focus on the aliovalent doping
of Sn2þ at the Li site for the following reasons: first
previous theoretical studied indicate that the aliovalent
doping at the Li site is highly unfavorable, and second the
experimental measurement shows that the Li ion diffusion
increases upon the Sn doping at the low concentration
(<3%) and then decreases (>5%). If Sn were doped first
at the Li site, the initial increase in the Li ion diffusion
would not be observed. Indeed, we performed the simple
check on the case of the aliovalent doping of Sn2þ at
the Li site for several representative configurations (see
the supplement), that is the Li vacancy located at different
site with respect to the Sn dopant. The calculated doping
energy is about 0.8–1.5 eV (see Table S9) higher than that
of the isovalent doping at the Fe site, in excellent
agreement with previous studies [23–25]. Furthermore,
we also consider an effective isovalent doping of Sn in
combination with the Li–Fe antisite defect, that is first
replace one Fe by Sn and switch the position of Sn and one
Li. The calculated doping energy is 0.7–0.8 eV (Table S9)
higher than the normal isovalent Sn doping at the Fe site,
for representative antisite defect models [67]. Even
though dynamically the Li–Sn antisite defect may
temporally exist, chances are good that it would quickly
recombine.
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(9 of 11) 1700041
5 Conclusions First-principle DFT calculations were
performed on tin-doped LiFePO4 in both bulk and surface
systems. The doping effect on the structural stability and the
electronic structure was investigated. The low doping
energy and surface energy indicate that surface doping is
preferred over bulk or subsurface doping. According to our
calculations, the Sn4þ–O dopant may exist in experimental
samples. New states are introduced above the valence band
or below the conduction band for the Sn2þ and Sn4þ doping,
respectively, and the band gap decreases from 3.74 to
2.96 eV (Sn2þ) or 2.06 eV (Sn4þ) in the bulk. Interestingly,
co-doping of Sn2þ and Sn4þ ions may alter the electronic
structures by forming a microscopic p–n pair, resulting in a
further reduction in the band gap. The microscopic donoracceptor doping by multivalent ions shares the same
idea [30] of co-doping multiple ions, which may be useful
for doping engineering of electronic structures to improve
the electrochemical performance of doped LiFePO4. For
surface systems, tin doping reduces the band gap by
approximately 0–0.2 eV. The doping effect appears to be
local so that subsurface doping resembles bulk doping. The
Sn4þ doping on the surface by replacing Fe2þ with Sn4þ and
with an extra O ion gives similar results to those for bulk
doping, except for more s–p hybrid Sn orbitals.
When the system is fully discharged, Sn2þ doping is
preferred. As Li vacancy exists, the situation becomes more
complicated. In the bulk, the Sn3þ–Fe3þ/2VLi complex
appears relatively unstable, and it may transform into Sn4þ/
2VLi or Sn2þ with the vacancies refilled by external Li ions.
Since bulk doping is energetically unfavorable, the Sn
dopant may migrate from the bulk to the surfaces. In
contrast, the Sn3þ–Fe3þ/2VLi complex on the surface
appears to be conductive and has a similar level of stability
as the Sn4þ/2VLi compound, at least for the doping
configurations studied here, for which the Li vacancies
may form or recover easily. Therefore multivalent element
doping could result in the formation of the Fe2þ/Fe3þ
complex with the involvement of an effective intermediate
Sn3þ ion, which may complement the small polaron transfer
model for transition metal oxides such as LiFePO4. Our
results indicate that the local structure and charge transfer
could be modulated by the dopant, and the doping-induced
charge redistribution demonstrates the possibility of surface
design by multivalent doping. Although here we focus on
the Sn doping case, the idea of the intermediate valence
component modulation may also find its applications in the
multivalent doping of other elements in energy materials
such as LiFePO4.
Supporting Information Additional supporting
information may be found in the online version of this
article at the publisher’s web-site.
Acknowledgements We acknowledge the support from
Peking University Shenzhen Graduate School, Shenzhen Science
and Technology Innovation Council (JCYJ20120829170028565
and ZDSY20130331145131323), Guangdong Science and
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L. Hou and G. Tao: First-principles study of bulk and surface Sn-doped LiFePO4
Technology Department (2013N080), National Natural Science
Foundation of China (51471005), and National Supercomputing
Center in Shenzhen (Shenzhen Cloud Computing Center). We
thank Prof. Hong Jiang for providing helpful comments and Prof.
Ian MacLachlan for his assistance proofreading the manuscript.
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