Structural, Electronic, and Li Migration Properties of RE-Doped (RE

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Structural, Electronic and Li Migration Properties of RE-Doped (RE = Ce, La) LiCoO for Li-Ion Batteries: A First-Principles Investigation 2

Fanghua Ning, Bo Xu, Jing Shi, Musheng Wu, Yinquan Hu, and Chuying Ouyang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b05091 • Publication Date (Web): 02 Aug 2016 Downloaded from http://pubs.acs.org on August 6, 2016

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The Journal of Physical Chemistry

Structural, Electronic and Li Migration Properties of RE-Doped (RE = Ce, La) LiCoO2 for Li-ion Batteries: A First-Principles Investigation Fanghua Ning, Bo Xu*, Jing Shi, Musheng Wu, Yinquan Hu, Chuying Ouyang Department of Physics, Laboratory of Computational Materials Physics, Jiangxi Normal University, Nanchang 330022, China *Corresponding author. E-mail: [email protected], Tel: +867918120370 Abstract: Rare earth elements, known for their large radius, high charge and strong self-polarization ability, are expected to bring improvements in Li-ion batteries. But some basic issues such as structural variation, the nature of the improved Li mobility and electronic conductivity in rare earth-doped electrode compounds are still unrevealed. In the present work, the structural, electronic and Li migration properties of Ce- and La-doped LiCoO2 cathode materials are systematically studied by using the first-principles calculations. The results show that after rare earth elements are doped the cell volume expands with local structure distortion around the substitution site. Meanwhile, the doped systems remain insulating characteristics with decreased band gap. The migration barriers vary considerably depending on different paths due to the competition between the increase of Li slab distance and the variation of potential energy surface caused by the doping of rare earth elements. The minimum activation barriers for Li motion decease significantly from 0.669 eV to 0.382 eV and to 0.239 eV upon Ce and La doping, respectively. Furthermore, Li ion migrations along the entire supercell are also studied.

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1. INTRODUCTION Lithium ion battery (LIB) has brought great changes to our modern life. We have greatly benefited from consumer electronics such as mobile devices 1 and electric vehicles (EVs) 2. The increasing requirements for batteries with high power and high energy density have promoted researches to enhance the performance of electrode materials. As one of the effective strategies, doping has made great improvements on battery performance, such as cycling performance. Appropriate doping can effectively inhibit structural variation of electrode materials during charge and discharge processes, thus improving the cycling performance of LIBs. Considering the large radius, high charge and strong self-polarization ability of rare earth (RE) ions, therefore, it naturally raises an interesting issue: whether RE-doping will bring dramatic changes to LIBs or not. In recent years, experimental studies have been made in RE-decorated electrode materials such as LiCoO2

3-5

,

LiMn2O4 6-14, LiFePO4 15-20, and LiNi1/3Co1/3Mn1/3O2 21-23, etc. For example, Yang and coworkers 6 reported that the lattice parameters increase due to the large radius of RE ions for the LiMn2-xRExO4 (x≤0.01, RE = Y, Nd, Gd, Ce) systems. The cycling performance of LIBs with these electrode materials is improved owing to the structural skeleton stabilization by RE-doping. Moreover, the Li motion is promoted due to the expanding of the three-dimensional (3D) migration channel. Likewise, Sun et al. 7 studied the LiMn2-xRExO4 (0≤x≤0.01, RE = La, Ce, Nd, Sm) electrode. It was found that the cycling ability and rate performance are improved significantly, compared to the pristine LiMn2O4. However, their results show that the lattice

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constants decrease, which is opposed to that of Yang’s results. Zhang et al.

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suggested that the reversible capacity as well as conductivity and Li+ migration rate could be drastically improved by substituting Li with La in LiFePO4. The samples of Li[Ni1/3Co1/3Mn1/3]1-xRexO2 (0≤x≤0.04, Re=La, Ce, Pr) exhibit higher discharge capability and better cycling performance.

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And the increase of charge transfer

resistance during cycling has been suppressed successfully by the doping of rare earth elements. In brief, rare earth-doped electrode compounds with good performance for LIBs can be synthesized successfully. However, some basic issues such as structural variation, the nature of the improved Li mobility and electronic conductivity are unclear so far. Taking LiMn2O4 for instance, majority of investigations show that the lattice parameters contract after RE-doping 7-10, 24, 25, while some others go against with it. 6, 26, 27 It is easy to accept that lattice expands after RE-doping due to the larger radius of RE ions. However, the contract of lattice parameters was explained by researchers as the stronger bond energy of RE-O bond. 10 This qualitative difference might be induced by various experiment conditions. Thus, atomic structures of RE-doped cathode materials are needed to be determined distinctly because atomic structure is closely related to the cycling performance of electrode. On the other hand, RE-doping improves the conductivity although these doped samples are semiconducting 10. This may be caused by the smaller band gap and impurity states, or the smaller polaron migration barrier 28. To reveal the true reason, the electronic structure and electronic dynamics are the key problems to be solved, while which are

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difficult for experimental observation. Finally, the increase of Li mobility is usually regards as the larger migration channel caused by large radius of RE ions 6. As we know, however, the local configurations around the RE ions are different from that of the original substituted transition metal (TM) ions, thus causing the variation of the potential energy surface. This variation may increase the migration barrier of Li ions, even changing the migration pathway. Obviously, using the expansion of the migration channel to explain the increase of Li mobility is too simple. Furthermore, previous report 29 indicates that the migration energy barrier along the constrained pathway is even likely to be decreased. The diffusion constant increases by 5 orders of magnitude for a 7% compressive strain on full delithiation state of LiMn2O4 (λ-MnO2). In a word, further study on the nature of the increased Li mobility is needed. The issues mentioned above are difficult to be settled by experimental approaches. To further study on these basic issues in LIB electrodes, therefore, the structural, electronic and Li migration properties of Ce- and La-doped LiCoO2 compounds (LiCo0.96Ce0.04O2 and LiCo0.96La0.04O2) are systematically studied by means of the first-principles calculations in the present work. Our results help to answer the questions for the RE-doped LiCoO2 system: (i) How does the cell volume vary? (ii) What is the electric conductivity? (iii) How does the migration behavior of Li ion vary? Therefore, our study reveals the microscopic influence mechanism of RE-doping on LIB electrode material LiCoO2.

2. COMPUTATIONAL DETAILS All calculations in the present study are performed by the Vienna Ab initio

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Simulation Package (VASP) 30 within the frame of density functional theory (DFT). The Kohn-Sham equations are solved within the projector augmented wave (PAW) method 31, while the electrons are described in generalized gradient approximation (GGA) with the Perdew and Wang (PW91) exchange-correlation functional

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.

Furthermore, in order to account for the strong onsite Coulomb repulsion among the Co-3d, Ce-4f, and La-5d electrons, GGA+U method is employed 33. The simplified rotationally invariant approach to the GGA+U is used. The U values of Co, Ce and La atoms are set to be 5.4, 6.0 and 8.2 eV, respectively, and the J values of Co, Ce and La atoms to be 0.5, 0.7 and 0.7 eV, respectively. The effective onsite Coulomb terms Ueff = U - J are chosen to be 4.9, 5.3 and 7.5 eV, respectively, which are based on previous references 34-36 and our tests. All calculations are performed in a 3 × 3 × 1 supercell, containing 27 LiCoO2 formula units (27 Li atoms, 27 Co atoms, and 54 O atoms). The doped LiCoO2 system is modeled by substituting one out of 27 Co ions with a Ce (La) ion. The Monkhorst-Pack scheme 37 with 3 × 3 × 2 k-point mesh is used for the integration in the irreducible Brillouin zone. The cutoff energy for the plane wave expansion is chosen to be 550 eV. The total energy is converged within 10−5 eV per formula unit. The lattice parameters and ionic positions are both relaxed. The final forces on all ions are less than 0.01 eV/Å. Spin-polarization is considered in all calculations. The calculation of density of states (DOS) is smeared by the Gaussian smearing method with a smearing width of 0.02 eV. The Li migration paths and energy barriers are obtained by using the nudged elastic band (NEB) method 38, 39.

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3. RESULTS AND DISCUSSION A. Atomic structure LiCoO2 belongs to the α-NaFeO2 type layered structure with space group R 3 m. Within this space group, Li, Co, and O atoms occupy the 3a, 3b, and 6c sites, respectively. The optimized lattice constants of the 3 × 3 × 1 supercell are 3a = 3b = 8.496 Å, and c = 14.182 Å, as is listed in Table 1, which are a bit larger than the experimental values4. The Ce (La)-doped LiCoO2 are modeled by substituting one out of 27 Co ions with a Ce (La) ion, forming Li(Co0.96Ce0.04)O2 and Li(Co0.96Ce0.04)O2 structures. The relaxed structures are shown in Fig. 1. The corresponding lattice constants are also given in Table 1. According to our calculations, the angles between lattice vectors remain unchanged after doping, which are α = β = 90°, γ = 120°. From Table 1, it can be observed that the lattice expands slightly after doping, regardless of Ce or La doping, which is likely induced by the large ion radius of Ce (La) ion compared to Co ion. In addition, our lattice parameters are basically in agreement with those of Li(Co0.95RE0.05)O2 reported by other experimental references 4, 5.

Figure 1. Schematic views of the optimized atomic structures of (a) Ce-doped LiCoO2 and (b) La-doped LiCoO2. 6


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Table 1. The relaxed lattice parameters of LiCoO2, Li(Co0.96Ce0.04)O2, and Li(Co0.96La0.04)O2. The calculated values correspond to the 3 × 3 × 1 LiCoO2 supercell, while experimental ones to the primitive cell. LiCoO2

LiCo0.96Ce0.04O2

LiCo0.96La0.04O2

LiCoO2

LiCo0.95Ce0.05O2

LiCo0.95La0.05O2

Cal.

Cal.

Cal.

Exp.4

Exp.4

Exp.4

a (Å)

8.496

8.576

8.575

2.8184

2.8322

2.8228

c (Å)

14.182

14.302

14.293

14.081

14.176

14.097

V (Å3)

886.567

910.955

910.169

96.866

98.476

97.279

Further local structures around the rare earth ions in Ce- and La-doped LiCoO2 are given in Table 2. The corresponding distances between Ce (La) and O ions are provided. For convenient comparison, the local structural information of Co ions in pure LiCoO2 is also given. When looking into the structures of pure LiCoO2, six Co-O bonds in CoO6 octahedron are equal to each other with length of 1.935 Å. After doping with Ce and La elements, it is found that the Ce-O and La-O bond lengths are larger than that of Co-O bond. In La-doped LiCoO2, the lengths of six La-O bonds in LaO6 octahedron are equal to 2.280 Å. In contrast, the Ce-O octahedron slightly distorts in the Ce-doped case. Six Ce-O bonds are divided into three groups with 2.189, 2.215 and 2.224 Å for each two. Interestingly, the local structure of the Co ion which is the nearest to Ce ion is also distorted in Ce-doped LiCoO2. Two Co-O bonds are the longest with length of 2.127 Å. The other four bond lengths are 2.030 and 2.062 Å respectively for each two. All of these Co-O bonds are larger than that in pure LiCoO2. In addition, the two longest Co-O bonds are linked with the two shortest Ce-O bonds, which is shown in Table 2. 7



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Table 2. Local structures around metal ions, distances between metal and O ions dM-O (M=Co, Ce, La), magnetic moments (MM) of metal ions, and electronic configurations for Co ions in LiCoO2 without and with RE doping. Co3+ in

Co2+ in

Ce4+ in

La3+ in

LiCoO2

LiCo0.96Ce0.04O2

LiCo0.96Ce0.04O2

LiCo0.96La0.04O2

Local structure around Co and RE ions

dM-O (M=Co, Ce, La) (Å)

1.935

1.935

2.030 2.030

2.189 2.189

2.280 2.280

1.935

1.935

2.062 2.062

2.215 2.215

2.280 2.280

1.935

1.935

2.127 2.127

2.224 2.224

2.280 2.280

0

3

0

0

(t2g↑)3(t2g↓)3

(t2g↑)3(eg↑)2(t2g↓)2 \

\

MM (µB)

Electronic configurations

B. Electronic structure

Figure 2. TDOS of (a) Ce-doped LiCoO2, (b) LiCoO2, and (c) La-doped LiCoO2. The Fermi levels (Ef) are set to be 0 eV.

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Figure 2 shows the total density of states (TDOS) of Li(Co0.96Ce0.04)O2, LiCoO2, and Li(Co0.96La0.04)O2 systems. In our calculations, pure LiCoO2 is a semiconductor with band gap of 2.6 eV. The Ce- and La-doped systems remain insulating characteristics except for the smaller band gaps that are 1.9 and 2.2 eV for LiCo0.96Ce0.04O2 and LiCo0.96La0.04O2 respectively. Despite the similarity, the difference between pure LiCoO2 and RE-doped LiCoO2 is observed near the Fermi level. One can see some edge states below the Fermi level for the RE-doped LiCoO2, which are marked by dotted circles (pink). To make further analysis, Figure 3 presents the energy bands that correspond to the impurity states, and the band-decomposed charge densities of the shown bands. The bands near the Fermi level for the Ce-doped LiCoO2 are spin-polarized. Two bands are occupied by spin-up states, while other two by spin-down states. Unlikely, the bands for the La-doped LiCO2 are non-spin-polarized. The band-decomposed charge densities give the evidence that the edge states are localized, regardless of Ce- or La-doped case. In the Ce-doped LiCoO2, the edge states are mainly contributed by the Co ion that is the nearest to Ce ion and the O atoms that are around the Co ion. However, the edge states almost come from the O atoms around La ion in the La-doped LiCoO2.

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Figure 3. Band structures and the band-decomposed charge densities for the edge states of Ce-doped LiCoO2 (a, c) and La-doped LiCoO2 (b, d). The Fermi levels (Ef) are set to be 0 eV.

In order to understand the nature of the edge states, we further analyze the electronic structures of the RE-doped systems. In our calculations, the valence shell of Ce is taken as 4f15d16s2. Obviously, the valence state of Ce is +4 in Li(Co0.96Ce0.04)O2 system, thus resulting in the non-magnetic state. This is confirmed by the magnetic moment of Ce ion, which is calculated to be 0 µB in Ce-doped LiCoO2, as is seen in Table 2. To keep the charge balance, one Co ion should change its valance state from +3 to +2. As there are 26 Co ions in Ce-doped LiCoO2, we calculate the total energies for the Co2+ ion locating at different sites. It is found that the case that the Co2+ ion locates at the nearest site to Ce ion has the lowest energy. Figure 1(a) shows the detailed position of the Co2+ ion. All the discussion in our study, therefore, are based on the structure in Fig. 1(a). For the Co2+ ion, the calculated magnetic moment is 3 µB, which is substantially larger than that of Co3+ ion, as is listed in Table 2. To make this clear, we plot the projected density of states (PDOS) of Co2+-3d orbitals in Li(Co0.96Ce0.04)O2 and Co3+-3d orbitals in pure LiCoO2, as is seen in Fig. 4. Figure 10


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4(b) shows that the Co3+ ion has non-spin-polarized PDOS, and possesses the (t2g↑)3(t2g↓)3 electronic configuration. The corresponding schematic view of energy level alignment could be found in the first column of Table 2. In contrast, the PDOS of Co2+-3d orbitals are spin-polarized, as is shown in Fig. 4(a). For Co2+ ion, five spin-up orbitals are all occupied, while three spin-down orbitals are empty. Obviously, the electronic configuration of Co2+ ion is (t2g↑)3(eg↑)2(t2g↓)2, which is shown in the second column of Table 2. Therefore, the magnetic moment of 3 µB is easy to be achieved according to the (t2g↑)3(eg↑)2(t2g↓)2 electronic configuration. Compared with the electronic configuration of Co3+ ion, spin-flip occurs for the Co2+ ion when adding one electron in it. It is the one extra electron and spin-flip that cause the weak interaction between Co2+ and O ions, which is suggested by the longer Co2+-O bond when compared to Co3+-O bond. Weak Co2+-O bonds lead to the energy rise of the related states, thus forming the edge states near the Fermi level in Fig. 3(a). For the La-doped case, La ion (valence shell of 5d16s2) remains La3+ non-magnetic state, the same valence state with Co3+. Hence, the calculated magnetic moment of La3+ ion is also 0 µB. Unlike the Ce-doped case, there is no Co3+ ion that changes its valence state. The band-decomposed charge densities, as is shown in Fig. 3(d), demonstrate that the edge states mainly come from the O atoms around La ion. Therefore, weak interaction between La and O ions could also be the reason for the edge states. It is noted that the weak interaction mentioned here refers to the Co-O interaction in pure system. To confirm this point, we replace the La ion by Co ion in the relaxed La-doped LiCoO2 system as a test. The only difference between this

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substituted structure and the pure one is the larger Co-O bonds in the former case. Obviously, the weaker interaction between the substituted Co ion and the neighboring O ions is formed. Then the electronic properties of the system without geometry relaxation are calculated. The electronic results (not shown here) show that the edge states still exist and mainly come from the O ions around the substituted Co ion. The difference is that the edge states are unoccupied, indicating that the interaction between Co ion and O ions are so weak that these O ions are unable to capture the electrons offered by the centre Co ion. This test supports the idea that the edge states are caused by the weak La-O interaction.

Figure 4. PDOS of (a) Co2+-3d orbitals in Ce-doped LiCoO2 and (b) Co3+-3d orbitals in undoped LiCoO2. The Fermi levels (Ef) are set to be 0 eV.

C. Migration of Li ion Since Li mobility in electrode compounds is a key aspect of the rate capability for rechargeable LIBs, a study on activation barriers for Li migration is essential to the Ce- and La-doped LiCoO2. In LiCoO2 compound, Li migration is constrained to a two-dimensional (2D) layer. The spacing between the oxygen layers around the migration path is critical to the Li motion. Ceder et al. 40 predicted that the activation

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barriers for Li migration vary considerably with Li slab distance, changing by more than 200% for a 4% change in Li slab distance. Our previous work 41 also found that tensile strain can promote the Li motion dramatically, especially along the c-axis. As a result, Li slab distance of the migrating Li ion should be mainly considered as the limiting factor of Li motion. In order to investigate the Li migration, we construct the mono-vacancy model by removing one single Li atom from the RE-doped LiCoO2. The Li migration energy profiles in Ce- and La-doped LiCoO2 from NEB calculations are given in Fig. 5(a) and Fig. 5(b). Various migration paths are considered in our calculations. The sites of the migrating Li ion within the Li layer that is adjacent to the RE-doped Co-O layer are shown in Fig. 5(c). Site 1 and 2 present the nearest sites to RE ions, while site 3 and 4 are the farthest ones. In addition, site 5 and 6 present the sites that are in another Li layer without the RE-doped Co-O layer near to it. Due to the introduction of a single Li vacancy, the valance state of one Co ion is changed in the doped LiCoO2 systems. For the Ce-doped LiCoO2, the Co2+ ion changes back to a Co3+ ion after removing one Li atom, thus resulting in the full Co3+ ions. In contrast, one Co3+ ion changes into a Co4+ ion in La-doped LiCoO2 when introducing one Li vacancy. The position of Co4+ ion has been tested. It is found that the Co4+ ion prefers to locate at the site near to La ion. It is the unsymmetrical position of Co4+ ion that causes the different energy between initial state and final state for the 1-2 and 3-4 migration paths, as is shown in Fig. 5(b). For the unsymmetrical energy profiles, the energy barriers are defined as the average barriers from different directions. The migration

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energy barriers (Ea) are listed in Table 3. In addition, the Li slab distance in Table 3 is defined as the average distance between the upper and lower O ions near the migrating Li ion along c-axis. According to Fig. 5 and Table 3, it is found that the migration energy profiles of the different migration paths are similar for the Ce-doped and La-doped LiCoO2. Except for the migration path 1-2, all of the migration energy barriers are essentially lower than that in pure LiCoO2, regardless of Ce- or La-doped LiCoO2, ranging from 0.382 eV to 0.621 eV for Li(Co0.96Ce0.04)O2 and from 0.239 eV to 0.562 eV for Li(Co0.96La0.04)O2. In addition, the migration barriers vary considerably with migration paths due to the different effect caused by the substitution ions. Since the path 5-6 is far away from the substitution ions, the effect of migration barriers by ion doing is slight. For the paths 3-4 and 2-3, the migration barriers are relatively lower compared to that of path 5-6. However, the situation of path 1-2 is somewhat different from other paths. The migration barrier of path 1-2 in the Ce-doped LiCoO2 (0.659 eV) is almost the same as that in pure one (0.669 eV), while higher (0.800 eV) in the La-doped LiCoO2. It is noted that the energy barrier of Li migration indicated in this work for pure LiCoO2 (0.669 eV) is substantially higher than the reference data (0.39 eV) found earlier by other reference 41. Actually, the reference data (0.39 eV) of migration barrier is based on a 2 × 2 × 1 supercell, while the migration barrier in the present work for pure LiCoO2 is calculated in a 3 × 3 × 1 supercell. Since the calculations for Li migration are based on the mono-vacancy model by removing one single Li atom

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from the LiCoO2 supercell, the Li vacancy concentrations (or the Li concentrations) are substantially different on account of the periodicity for the two different supercells. Previous studies 42,43 had shown that Li migration barriers within LixCoO2 depend strongly on the Li concentration with ranging from 0.23 eV to ~ 1.00 eV. Therefore, our result of Li migration barrier (0.669 eV) and the reference data (0.39 eV) are both reasonable. Generally, the migration barrier is related with the size of migration channel. Therefore, we examine the migration channel of Li ion, which is represented by the Li slab distance of the migrating Li, as is listed in Table 3. For path 5-6 the Li slab distances are 2.658 and 2.661 Å for Ce- and La-doped LiCoO2, respectively, which are slightly larger than that in pure LiCoO2 (2.656 Å). On contrary to this, the Li slab distances for other migration paths in the doped cases, namely paths 1-2, 2-3, and 3-4, are significantly larger than that in pure LiCoO2, which are 2.667 and 2.671 Å for Li(Co0.96Ce0.04)O2 and Li(Co0.96La0.04)O2, respectively. This is because these migration paths (1-2, 2-3, and 3-4) are adjacent to the RE-doped Co-O layer. Combining with the atomic structures, it is found that the increase of the Li slab distances for migration paths 1-2, 2-3, and 3-4 originates from the doping of RE ions. Larger migration channel always results in lower migration energy barrier. Therefore, the decrease of the migration barriers for paths 2-3 and 3-4 could be understood. Similarly, the migration barriers for path 5-6, regardless of Ce- or La-doped LiCoO2, are slightly lower than that in pure LiCoO2. However, the Li migration along path 1-2 is relatively complex. Since sites 1 and 2 are extremely close to the doped RE ions,

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around which the potential energy surfaces would change, the migration of Li ion from site 1 to 2 is actually affected by two factors. One is the size of the migration channel, and the other is the local potential energy surface. The competition of these two factors leads to the results of migration barriers along path 1-2 in the RE-doped LiCoO2.

Figure 5. Energy profiles of the Li ion migration in (a) Ce-doped LiCoO2 and (b) La-doped LiCoO2, (c) the corresponding migration paths.

Table 3. The Li slab distance (dO-O) of the corresponding path, the activation barrier and the corresponding diffusion constant (D). The diffusion constants are normalized to the times of the value of pure LiCoO2 (4.53×10-14 cm2/s). The Li slab distance is defined as the average distance between the upper and lower oxygen atoms near the migrating Li along c-axis. LiCoO2

Ce-doped LiCoO2 1-2

2-3

La-doped LiCoO2

Path

/

3-4

5-6

dO-O (Å)

2.656

Ea (eV)

0.669

0.659

0.382

0.511

0.621

0.800

0.239

0.524

0.562

D

1

1.47

6.63×104

4.51×102

6.40

6.30×10-3

1.67×107

2.73×102

62.7

2.667

1-2

2.658

2-3

3-4

2.671

16


5-6 2.661

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Since diffusivity is inversely proportional to the exponential of activation barrier, the barrier dropping will strongly improve the macroscopic rate of Li diffusion. The diffusion constant can be calculated by D = Г × l 2 according to the lattice-gas model 44

, where l is the hopping distance and approximately equal to one third of the lattice

constant a (here we choose l = 2.8 Å), and Г is the hopping rate. Within the hopping mechanism, Г is defined as Г = ν 0 exp ( - Ea / kBT ) , which can be obtained from transition state theory 45. The ν0 is the vibration frequency of the migrating Li ion, and the Ea is the migration energy barrier, kB and T are the Boltzmann constant and absolute temperature. Generally, the vibration frequency ν0 is in the same range of the phonon frequency, which can be calculated within a harmonic approximation. In this work, the phonon frequency is taken from our previous work 46. We choose 10 THz for the vibration frequency and a temperature of 300 K. The calculated diffusion constants are listed in Table 3. For convenient comparison, the diffusion constant of pure LiCoO2 is used for the reference, which is evaluated to be 4.53×10-14 cm2/s. According to Table 3, it is found that the maximum diffusion constant for the Ce-doped LiCoO2 increases by about 4 orders of magnitude, and the La-doped case even by 7 orders of magnitude, which can greatly enhance the rate capability of LIBs. The improvement of rate capability has also been found in other experimental study 3.

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Figure 6. (a) Three types of Li sites (marked with “I”, “II”, and “III”) within the Li layer that is adjacent to the RE-doped Co-O layer. The migration paths and the corresponding barriers for six kinds of Li migration paths in (b) Ce-doped LiCoO2 and (c) La-doped LiCoO2. All values of migration barrier are in unit of eV.

Furthermore, in order to obtain more information about Li ion migration along the entire supercell, we provide the migration barriers for Li migration within the Li layer that is adjacent to the RE-doped Co-O layer. As for Li migrations within the Li layer that are in other Li layer without the RE-doped Co-O layer near to it, the migration barriers are very close to each other, and similar to the case without rare earth elements. Therefore, we do not discuss here. For the nine Li sites within the Li layer that is adjacent to the RE-doped Co-O layer, we can classify them into three types on account of the symmetry, which are marked in Fig. 6(a) with “I”, “II”, and

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“III”, respectively. There are three equivalent Li sites for each type. As a result, the Li migration paths can be divided into six kinds, corresponding to the cases from “I” to “I”, “II” to “II”, “III” to “III”, “I” to “II”, “II” to “III” and “III” to “I”, respectively. Among them, the former three kinds correspond to the migrations between the same types of Li sites, while the later three kinds to those between the different types of Li sites. The calculated activation barriers for the six kinds of Li migration paths in Ce-doped and La-doped LiCoO2 are given in Fig. 6 (b) and (c), respectively. As is mentioned above, the activation barriers are defined as the average barriers from different directions. According to the obtained results, one can find that the activation barrier for the migration path from “I” to “II” is the lowest, regardless of Ce or La doping. Obviously, Li ion prefers migrating between “I” and “II” sites. Compared with other migration paths, Li migrations from “II” to “III” and “II” to “II” have relatively low activation barriers for both Ce- and La-doped LiCoO2. Therefore, there is a certain probability for Li migration between “II” and “III” or “II” and “II” sites.

4. SUMMARY In summary, we study the structures, electronic properties and Li migrations of the RE-doped (RE = Ce and La) LiCoO2 using the first-principles calculations within the frame of density functional theory. Structural optimization indicates that the lattice constants of the Ce- and La-doped LiCoO2 increase, which suggests the expansion of cell volume. Electronic structure calculations show that the doped compounds are semiconducting with the smaller band gap compared to the pure LiCoO2. In addition, some new edge states are observed, which are related to the doped RE ions. The

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migration barriers of Li ions vary considerably depending on the different paths. Basically, the migration energy barriers in the doped systems decrease to some extent due to the increase of the Li slab distance. However, the energy barrier of the migration path near the doped ions are close to, or even higher than that in pure case, resulting from the competition between the increase of Li slab distance and the variation of potential energy surface caused by the doping of rare earth elements. More importantly, the minimum migration barrier for Li motion deceases significantly from 0.669 eV to 0.382 eV (0.239 eV) upon Ce (La) doping, with the diffusion constant improved by 4 (7) orders of magnitude, which is beneficial to enhance the rate capability of LIBs. In addition, for the Li migration along the entire supercell, Li ion prefers migrating between “I” and “II” sites. At the same time, there is a certain probability for Li migration between “II” and “III” or “II” and “II” sites.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This work is supported by the Natural Science Foundation of China (Grand Nos. 11264014 and 11564016), the Natural Science foundation of Jiangxi Province (Grant Nos. 20152ACB21014, 20151BAB202006, and 20151BDH80033), and Foundation of Jiangxi Educational Committee (Grant No. GJJ14254). B. Xu is also supported by

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the oversea returned project from the Ministry of Education. F. H. Ning is supported by the Graduate Student Innovation Fund of Jiangxi Normal University. The computations were performed on TianHe-1(A) at the National Supercomputer Center in Tianjin.

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Calculations. Int. J. Electrochem. Sci. 2013, 8, 10549–10556.

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Table of Contents (TOC) Graphic

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Structural, Electronic, and Li Migration Properties of RE-Doped (RE

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