Defect Formation Energy in Spinel LiNi0.5Mn1.5

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Defect Formation Energy in Spinel LiNi Mn O Using Ab Initio DFT Calculations Hiromasa Shiiba, Nobuyuki Zettsu, Masanobu Nakayama, Shuji Oishi, and Katsuya Teshima J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b01661 • Publication Date (Web): 01 Apr 2015 Downloaded from http://pubs.acs.org on April 5, 2015

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The Journal of Physical Chemistry

Defect Formation Energy in Spinel LiNi0.5Mn1.5O4-δ Using Ab Initio DFT Calculations Hiromasa Shiiba1,2, Nobuyuki Zettsu1,2,3, Masanobu Nakayama4,5, Shuji Oishi1, Katsuya Teshima1,2,3,* 1

Department of Environmental Science & Technology, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan 2

CREST, Japan Science and Technology Agency, 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan

3

Center for Energy and Environmental Science, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan

4

Department of Materials Science and Engineering, Nagoya Institute of Technology, Gokiso, Showa, Nagoya, Aichi466-8555, Japan 5

PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan

KEYWORDS : Lithium ion batteries, LiNi0.5Mn1.5O4, Ab initio DFT calculations, Oxygen defect

ABSTRACT: Defect formation energies based on an oxygen vacancy model and a metal-excess model in Ni/Mn ordered P4332 and disordered 3 LiNi0.5Mn1.5O4 (LNMO) were evaluated by using ab initio density functional theory (DFT) calculations. The defect formation energy for the metal excess model was lower than for the oxygen vacancy model in both P4332 and 3. This indicates that oxygen vacancy formation reactions are unlikely, although interstitial cation occupation at the octahedral vacancies occurred in both P4332 and 3 LNMO spinel compounds. In addition, the corresponding defect formation energy in 3 was lower than that in P4332, indicating that the amount of defects is sensitive to the cation ordering/disordering in the spinel framework. This agrees with the experimental results that show that only 3 tends to possess oxygen defects.

INTRODUCTION Rechargeable lithium ion batteries (LIBs) are important for addressing environmental concerns, such as global warming, and as power sources for hybrid electric vehicles and electric vehicles. In particular, spinel LiNi0.5Mn1.5O4 (LNMO) has attracted attention as a cathode material for lithium-ion batteries because it has a high voltage (~4.7 V), and thus a high energy density of 686 W h kg-1 compared with other candidates for cathode materials, such as LiCoO2 (518 W h kg-1), LiNiO2 (630 W h kg-1), LiMn2O4 (440 W h kg-1), LiFePO4 (495 W h kg-1), Li2FePO4F (414 W h kg-1), and Li(Ni1/3Mn1/3Co1/3)O2 (576 W h kg-1)1. In ideal (stoichiometric) LNMO, it has been suggested that all the Mn is present as Mn4+ and only a Ni2+/Ni4+ redox reaction occurs at 4.7 V vs Li+/Li during Li intercalation/de-intercalation2-15. The absence of Mn3+ prevents Jahn-Teller distortion and dissolution of Mn ions in the electrolyte solution16-19, which enables good cycling performance20, 21. Depending on the synthesis conditions, LNMO forms two different crystal structures: transition metal ordered space group of P4332 and disordered space group of 3 with both cubic symmetries22, 23. Ni occupies 4b sites and

Mn occupies 12d sites in P4332, whereas Ni and Mn occupies 16d sites randomly in 3. In addition, the disordered 3 structure is prone to containing oxygen deficiencies, such as LiNi0.5Mn1.5O4-δ, accompanying the reduction of Mn from Mn4+ to Mn3+. The voltage profile of P4332 exhibits a single flat plateau at 4.7 V corresponding to the Ni2+/Ni4+ redox reaction, whereas that of 3 exhibits a plateau at 4 V arising from the Mn3+/Mn4+ redox reaction in addition to that in the 4.7 V region. The flat voltage profile in P4332 indicates a region in which the two phases coexist during charge and discharge. Lee and Persson calculated theoretically that P4332 Li1xNi0.5Mn1.5O4 (0 ≤ x ≤ 1) has no intermediate phase by using ab initio density functional theory (DFT) with the cluster expansion method24, which agrees with the experimentally observed voltage profiles. In contrast, a small voltage step is experimentally observed in the 4.7 V region in 3 at x = 0.52, 10, 12. There could be two reasons for the appearance of this voltage step. The voltage step could be caused by separate Ni2+/Ni3+ and Ni3+/Ni4+ redox reactions7-15. It could also be caused by Li/vacancy ordering at x = 0.5, as suggested experimentally by Xia et al.2 and computationally by Lee and Persson24. Interestingly, the phase stability of the intermediate phase changes with the Ni/Mn configurations in 3. Uniform Ni/Mn con-

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figurations, which contain a uniform distribution of Ni forming the face-centered-cubic Ni sublattice24, have an intermediate phase at x = 0.5, resulting in a small voltage step at x = 0.5. This voltage step could stem from the Li/vacancy configurations. The reduction of the Mn oxidation state from +4 to +3 was often observed during the synthesis of the LiNi0.5Mn1.5O4 at high calcination temperature12, 22, 23, 25-28. Empirical evidences suggested that O2 elimination from the lattice mainly contributed to the reduction of the Mn4+. For instance, an annealing process at below 700 °C in air after the high-temperature calcination at 1000 oC recovered oxygen defects and promoted P4332 formation12, 22, 23, 25-28. According to these reports, oxygen defects can be a critical factor for controlling the crystal structure symmetry to obtain the Ni/Mn ordered P4332 and disordered 3 phases. Some theoretical studies have been carried out on oxygen-deficient LNMO29, 30. Xin et al. used ab initio DFT to show that the oxygen vacancy formation energy of 3 LNMO is lower than that of P4332 LNMO29. Recently, Sushko et al. calculated the effect of oxygen vacancies on the arrangement of Ni/Mn in LNMO by using ab initio DFT30. Oxygen vacancies prefer to occupy O sites with one or more neighboring Ni ions, and the energy difference between oxygen-deficient P4332 and 3 decreases compared with the corresponding stoichiometric phases30.

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point mesh were chosen so that the product of the number of k-points and the number of atoms in the unit cell was greater than 1000. A superstructure of 56 atoms in a cubic spinel lattice of 8LiNi0.5Mn1.5O4 was used in all the calculations. For the disordered 3 structure, we used the uniform Ni/Mn distribution calculated by Lee and Persson24, 43 , which exhibits the highest entropy. Therefore uniform Ni/Mn distribution is the most realistic representation of a completely disordered phase at high temperature (Fig. 1(b)). Below, we refer to this structural model as “pseudo3”, unless otherwise mentioned. Five hundred and twenty-four structures with different Ni/Mn arrangements were systematically prepared from the Li2Mn4O8 primitive cell by using the ATAT package44, 45. The Coulombic energy was calculated for all the structures with the Ewald method, and we confirmed that the most stable Ni/Mn arrangement was consistent with a uniform distribution. The difference of the total energies calculated by ab initio DFT calculations between the most stable Ni/Mn arrangement and the tenth most stable Ni/Mn arrangement is only 19 meV per atom, which is smaller than 25 meV of thermal allowance at 300 K. This result suggests that several Ni/Mn arrangements co-existed in average structure of real 3 type LNMO.

Here, we suggest a metal-excess defect formation model for LiNi0.5Mn1.5O4 instead of the oxygen vacancy formation model. Ammundsen et al. computationally calculated the energies for Li1+xMn2-xO4 with Mn vacancies and excess interstitial Li, and they confirmed that excess Li preferably occupies in Mn vacancy sites31, which agrees with experimentally determined structure32. Hosoya et al. reported that the density of spinel LiMn2O4-δ increased with increasing oxygen deficiency, δ, suggesting that the metal-excess model applied33. Hayashi et al. also proposed the metal excess defect model in LiMgyMn2-yO4-δ because the chemical diffusion coefficient of Li ions for nonstoichiometric LiMgyMn2-yO4-δ is smaller than that for stoichiometric LiMgyMn2-yO434. Theoretical calculations reported by Koyama et al. also support these findings35. Since real materials usually contain some defects, investigation of defect formation can be useful for the field of physical chemistry. In this study, we focus on the phase stability and local structure of the oxygen-deficient LNMO with both P4332 and 3 symmetry. To determine the preferential formation of the oxygen deficiency model in LNMO, we evaluate the defect formation energies for both the oxygen vacancy model and the metal-excess model using ab initio DFT calculations. METHOD The Vienna ab initio simulation package36, 37 was used with the generalized gradient approximation (GGAPBEsol) + U38 and projector-augmented wave methods39. For the GGA + U calculations, the U values for the dorbitals of Ni and Mn were set to 6.0 and 3.9 eV based on previous reports40-42. An energy cutoff of 500 eV and a k-

Fig. 1. Crystal structure of (a) P4332 and (b) pseudo3 LNMO evaluated by Coulomb energy calculations. Arrangement of Ni/Mn on the (111) plane (c) in P4332 and (d) in pseudo-3, and on the (11-1) plane (e) in P4332 and (f) in pseudo-3. Green spheres, grey octahedron, purple octahedron, and red spheres indicate Li, octahedral Ni, octahedral Mn, O, respectively. Relaxation of the crystal structure was allowed for the stoichiometric models, and the final energies of the optimized structural geometries were recalculated to correct


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for changes in the plane-wave basis during relaxation. The calculated lattice constants for P4332 and pseudo-3 were 8.178 and 8.188 Å, respectively. These values are in good agreement with experimental values of 8.16623 and 8.172 Å23. The average voltages for P4332 and pseudo3 were calculated to be 4.72 and 4.64 V, respectively, which also agree with experimental values of 4.74 and 4.77 V for P4332, and 4.69 and 4.75 V for pseudo-312. The voltage step at a Li composition of x = 0.5 is much smaller for the ordered P4332 than for the disordered 3, as reported by Kim et al.23, 46.

Nonstoichiometric defect formation energies were calculated for two oxygen-deficient models, the oxygen vacancy model and the metal-excess model. Defect formation energies per oxygen deficiency were compared for each deficient model, the same as calculated for LiMn2O4 by Koyama et al.35. Formation of a single oxygen deficiency for the oxygen vacancy and metal-excess models can be described by conventional Kröger-Vink notation as

O → V∙∙ 2e O

(1)

LiNi. Mn. O → Li∙ Ni∙∙ Mn∙∙∙∙ 8e

2O "

(2)

F

From eqn. (1), the defect formation energy, E , for the oxygen vacancy in the superstructure can be described as # $ % #Li& Ni Mn O ' #Li& Ni Mn O #O (3)

whereas, from eqn. (2), the defect formation energy for metal-excess can be described as #$ % #Li) Ni Mn O #Li& Ni Mn O ( + #Li& Ni Mn O ' 25#LiNi. Mn. O

#O

with 1 Ni and 2 Mn ions at 16d cation sites. However, disordered 3 LNMO can be expressed as {(Li)8a}tet{(Ni0.5)16d(Mn1.5)16d}oct(O4)32e, and thus the 3 lattice has single crystallographic oxygen sites, ideally. However, the present pseudo- 3 model (uniform Ni/Mn structure) contains two types of oxygen site (Fig. 2(b)) because of the limited cell size, and the coordination with the transition metals is the same as in the P4332 model, namely the O@Mn3 and O@Ni1Mn2 sites in the pseudo-3 model. Therefore, we evaluated all four possible oxygen vacancy formation energies (Table 1). The oxygen vacancy formation at O@Ni1Mn2 sites show the lowest formation energy of 3.71 and 3.63 eV in both P4332 and 3, respectively, than that at O@Mn3 sites. This is consistent with the computational study reported by Sushko et al. that showed that oxygen vacancies preferentially occupy sites near Ni30. In the present work, the difference between the vacancy formation energies between P4332 and pseudo-3 is only 0.08 eV.

(4)

In eqn.(2), the first, second, and third terms indicate Li, Ni, and Mn interstitial defects, respectively. The lattice parameters of the defect models were fixed and only the relaxation of the atomic position was allowed because of the low defect concentration. The energy correction for O2 molecules was used for all the calculations as reported by Wang et al.47.

Fig. 2. Oxygen site in (a) P4332 and (b) pseudo-3 LNMO. Table 1. Oxygen vacancy formation energies for P4332 and 3 LNMO. EF [eV] P4332

3

8c (Mn3)

4.66

4.14

24e (Ni1Mn2)

3.71

3.63

RESULTS AND DISCUSSION

2. METAL-EXCESS MODEL

1. OXYGEN VACANCY MODEL

Formation energies were evaluated for the metal-excess model in the spinel lattice, either for single interstitial Li, Ni, or Mn in octahedral vacancy 4a and 12d sites for P4332, or 16c sites for pseudo-3. Octahedral vacancy sites are surrounded by six NN transition metal sites. The octahedral 4a sites in P4332 are surrounded by one Ni and five Mn (Fig.3(a)), whereas 12d sites in P4332 by three Ni and three Mn (Fig.3(b)). In contrast, in pseudo-3 with a uniform Ni/Mn arrangement, there are two types of octahedral vacancy sites surrounded by six Mn ions (Mn6, Fig. 3(c)), and by two Ni and four Mn ions (Ni2Mn4, Fig. 3(d)).

Single oxygen vacancy formation energies are calculated for P4332 and 3 by using eqn. (3). Each atom in P4332 LNMO occupies {(Li)8c}tet{(Ni0.5)4b(Mn1.5)12d}oct(O)8c(O3)24e, where superscripts indicate Wyckoff notation, and subscripts tet and oct indicate tetrahedral and octahedral sites, respectively. All oxygens are bound to three nearest neighbor (NN) transition metals; the oxygen in 8c sites is coordinated with three NN Mn ions (O@Mn3), and that in 24c sites with one Ni and two Mn ions (O@Ni1Mn2) as shown in Fig. 2(a). Hereinafter, O@Bn indicates the oxygen site coordinated with nearest neighbor cations, Bn. For example, O@NiMn2 represents the oxygen sites coordinated



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Fig. 3. Arrangement of Ni/Mn near the octahedral vacancy site: (a) 4a site in P4332, (b) 12d site in P4332, (c) 16c(Mn6) site in pseudo-3, and (d) 16c(Ni2Mn4) site in pseudo-3. White spheres and black spheres indicate the 4a site and 12d site in P4332, and the 16c(Mn6) site and 16c(Ni2Mn4) site in pseudo-3, respectively. Figure 4(a)–(c) shows schematic drawings of a single interstitial metal ion at octahedral vacancies and the surrounding cationic arrangements, in which neighboring tetrahedral sites are occupied by Li+ (Model i1). However, the lattice may be unstable because the ionic distance between the interstitial octahedral site and NN tetrahedral Li sites is short: 1.72 and 1.79 Å at the 4a and 12d sites in P4332, and 1.68 and 1.81 Å at the Mn6 and Ni2Mn4 sites in pseudo-3, respectively. Therefore, we also considered two additional types of cationic arrangement models where neighboring tetrahedral Li ions migrate to another octahedral vacancy site. These were Model i2), in which one Li ion migrates (Fig. 4(d–f)), and Model i3), in which two Li ions migrate (Fig. 4(g–i)). We systematically considered all the possible cationic arrangements and it is listed in Table 2 and 3.

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Fig. 4. Configurations of cations and vacancy sites in P4332 interstitial metal defects: (a), (b), (c) a single interstitial metal ion at octahedral vacancies and surrounding cationic arrangements, in which neighboring tetrahedral sites are occupied by Li ions (Model i1). Neighboring tetrahedral Li ions migrate to another octahedral vacancy site as follows: (d), (e), (f) Model i2) migration of one Li ion, and (g), (h), (i) Model i3) migration of two Li ions. Table 2. Relative energies for Li, Ni, and Mn interstitial models in P4332 LNMO. Interstitial cation

Li

Model

Interstitial sites

Model i1-1

4a

Model i1-2

12d

Model i2-1

4a

12d

0.086

Model i2-2

12d

12d

0

Model i3-1

4a

12d, 12d

0.396

4a, 4a

0.593

4a, 12d

0.297

12d, 12d

0.202

Model i3-2 Model i3-3

12d


4a

Model i1-2

12d

Model i2-1

4a

Model i2-2 Ni


12d 4a


12d

Model i3-4 Mn

Model i1-1

4a

Model i1-2

12d


Octahedral vacancy sites occupied by Li ions N/A

N/A

Defect formation energy [eV (relative)] 0.434 0.211

0.613 0.137

12d

0.574

4a

0.094

12d

0.408

12d, 12d

0

4a, 4a

0.667

4a, 12d

0.351

12d, 12d

0.009

N/A

1.353 1.503

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The Journal of Physical Chemistry Model i2-1 Model i2-2 Model i2-3 Model i3-1

4a 12d 4a


12d

Model i3-4

12d

0.862

Model i3-3

16c(Ni2Mn4) 16c(Ni2Mn4), 16c(Ni2Mn4)

4a

0.562

12d

0.445

Model i3-4

12d, 12d

0

Model i1-1

16c(Mn6)

4a, 4a

0.533

Model i1-2

16c(Ni2Mn4)

4a, 12d

0.366

Model i2-1

16c(Mn6)

12d, 12d

0.338

Model i2-2 Model i2-3 Ni

Model i3-1

16c(Ni2Mn4) 16c(Mn6)


16c(Ni2Mn4)


16c(Mn6)

Model i1-2

16c(Ni2Mn4)

Model i2-1

16c(Mn6)

Model i2-2 Model i2-3 Mn Fig. 5. Configurations of cations and vacancy sites in pseudo-3 interstitial metal defects: (a), (b), (c) a single interstitial metal ion at octahedral vacancies and surrounding cationic arrangements, in which neighboring tetrahedral sites are occupied by Li ions (Model i1). Neighboring tetrahedral Li ions migrate to another octahedral vacancy site as follows: (d), (e), (f) Model i2) migration of one Li ion, and (g), (h), (i) Model i3) migration of two Li ions. Table 3. Relative energies for Li, Ni, and Mn interstitial models in pseudo-3 LNMO. Inte rstit ial cati on

Li

Interstitial sites

Model i1-1

16c(Mn6)

Model i1-2

16c(Ni2Mn4)

Model i2-1

16c(Mn6)

16c(Ni2Mn4)

0

Model i2-2

16c(Ni2Mn4)

16c(Ni2Mn4)

0.431

Model i3-1

16c(Mn6)

16c(Ni2Mn4), 16c(Ni2Mn4)

N/A

16c(Mn6), 16c(Mn6)

0.388

16c(Mn6),

0.118

Model i3-2

16c(Ni2Mn4)

Octahedral vacancy sites occupied by Li ions

Defect format ion energy [eV (relati ve)]

Model

0.109

N/A

0.345

Model i3-1

16c(Ni2Mn4) 16c(Mn6)

Model i3-2 Model i3-3 Model i3-4

16c(Ni2Mn4)

N/A

N/A 0.619 N/A

16c(Ni2Mn4)

0.083

16c(Mn6)

0.312

16c(Ni2Mn4)

1.198


0

16c(Mn6), 16c(Mn6)

0.317

16c(Mn6), 16c(Ni2Mn4)

0.028


0.746

N/A

1.917 N/A

16c(Ni2Mn4)

0.771

16c(Mn6)

N/A

16c(Ni2Mn4)

N/A


0.720

16c(Mn6), 16c(Mn6)

0

16c(Mn6), 16c(Ni2Mn4)

0.181


0.813

The calculated energies for Model i1)–i3) with interstitial Li, Ni, and Mn ions are listed in Table 2 and 3 for P4332 and pseudo-3, respectively. The lowest (most stable) energies are set as zero for each model. Model i1 is not the most stable structure among the metal interstitial models, indicating that the migration of tetrahedral Li ion to a neighboring octahedral vacancy is accompanied by doping with metal ions at interstitial sites. In P4332, for the Li excess model, the most stable cationic configuration is Model i2-2 (interstitial Li at 12d sites and one Li ion migrating to 12d sites), which is {(Li8c)7(Vac8c)1}tet{(Li12d)1(Li12d)1}oct{(Ni4b)4(Mn12d)12}octO32. For the Ni and Mn excess model it is Model i3-1 (interstitial Ni or Mn at 4a sites and two Li ions migrating to both 12d sites), which is {(Li8c)6(Vac8c)2}tet{(Ni4a)1(Li12d)2}oct{(Ni4b)4(Mn12d)12}octO32 and {(Li8c)6(Vac8c)2}tet{(Mn12d)1(Li12d)2}oct{(Ni4b)4(Mn12d)12}octO32, respectively. One Li+ in the tetrahedral 8c sites moves away to the octahedral vacancy sites in the Li excess model. The ionic distance between the excess metal and the NN tetrahedral Li sites is relatively short, which results in



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ionic repulsion between the excess Li+ and tetrahedral Li+. However, Li+ prefers to occupy tetrahedral sites, and thus two tetrahedral Li+ migrating to octahedral sites can be unstable, which is the same as for LiMn2O4, as reported by Koyama et al.35. However, two Li+ in the tetrahedral 8c sites move away to octahedral vacancy sites in the Ni excess and Mn excess models. This could be because the electrostatic repulsion of Ni2+ and Mn3+ is stronger than that of Li+; we confirmed that the ionic valence of interstitial Ni and Mn are +2 and +3 through the partial density of states (PDOS) and the total electron-spin difference for Ni and Mn ions. In pseudo-3, the most stable cationic configuration is the combination of Model i2-1, Model i3-1, and Model i3-2 with excess Li, Ni, and Mn ions, respectively. Compared with P4332, all of the metal-excess models have similar Li configurations; one tetrahedral Li+ moves away to the octahedral vacancy site in the Li excess model and the two tetrahedral Li+ move away to the octahedral vacancy sites in the Ni excess and Mn excess models. In P4332, the most stable interstitial model for Ni and Mn is the same (Model i3-1); however, in pseudo-3 the most stable interstitial model for Ni is Model i3-1 and that for Mn is Model i3-2. We found that the ionic valence of interstitial Mn for Model i3-1 in pseudo-3 is +2, whereas that for Model i3-2 in pseudo-3 is +3. In the Model i3-1, interstitial site is surrounded by six Mn4+, therefore interstitial Mn prefer to be lower ionic valence (Mn2+) to prevent repulsive interaction. On the other hand, in the Model i3-2, interstitial site is surrounded by four Mn4+ and two Ni2+, which is lower repulsive interaction as compared to Model i3-1. Thus interstitial Mn became Mn3+ with Jahn-Teller distortion. Mn2+ in the spinel lattice could be unstable because the ionic radius of Mn2+ (0.83 Å48) is larger than that of Mn3+ (0.645 Å48) and Ni2+ (0.69 Å48). This could be why Model i3-2 becomes more stable than Model i3-1 for interstitial Mn in pseudo-3. The total energies for Model i3-1 and i3-4 for interstitial Li, Model i1-2 for interstitial Ni, and Model i1-2, i2-2 and i2-3 for interstitial Mn in pseudo-3 were not available because the neighboring Li ions for these models migrated during structural relaxation, forming Model i1-1 and i12 for interstitial Li, Model i3-2 for interstitial Ni, and Model i3-2, i3-3 and i3-2 for interstitial Mn, respectively. This finding implies that these models are unstable because of the repulsive interaction between neighboring Li ions. Next, we consider interstitial Ni or Mn occupying the tetrahedral Li site, namely, NiLi or MnLi antisite defects (Fig. 6). There are two possible antisite Li positions: 4a sites (Model a1) and 12d sites (Model a2) in P4332; and 16c(Mn6) sites (Model a1) and 16c(Ni2Mn4) sites (Model a2) in pseudo-3. The antisite energy from the most stable configurations in P4332 (Model i3-1 for both interstitial Ni and Mn) to Model a1 and Model a2 is listed in Table 4, and that in pseudo-3 (Model i3-1 for interstitial Ni and Model i3-2 for interstitial Mn) to Model a1 and Model a2 is listed in Table 5. All the antisite energies were positive values; therefore, antisite defects are not stable defect models.

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Fig. 6. Configurations of cations for antisite defects: (a) schematic of antisite defects, and schematics of interstitial metal occupying tetrahedral 8a sites and antisite Li occupying (b) 4a sites (Model a1) and (c) 12d sites (Model a2) in P4332, and (d) 16c(Mn6) sites (Model a1) and (e) 16c(Ni2Mn4) sites (Model a2) in pseudo-3. Table 4. Antisite energies from the octahedral interstitial model (Fig. 4) to the tetrahedral interstitial model (Fig. 6) for P4332 LNMO. Space group

Interstitial model

EF [eV]

P4332

Model i2-2 (Li) + Model i3-1 (Ni) + Model i3-1 (Mn)

2.98

Model i2-1 (Li) + Model i3-1 (Ni) + Model i3-2 (Mn)

2.58

3

Table 5. Antisite energies from the octahedral interstitial model (Fig. 4.) to the tetrahedral interstitial model (Fig. 6) for pseudo-3 LNMO. Model

Model a1 Model a2 Model a1 Model a2

Antisite cation Ni

Mn

Antisite position

Li

Antisite [eV]

16c(Mn6)

0.818

16c(Ni2Mn4)

0.436

16c(Mn6)

1.870

16c(Ni2Mn4)

0.454

energy

Defect formation energies calculated with equation (4) and the most stable energies listed in Table 2 and 3 are shown in Table 6 for P4332 and pseudo-3. For P4332, the defect formation energy is 2.98 eV for the metal excess model in P4332, which is smaller than the oxygen


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vacancy formation energy of 3.71 eV (Table 1), indicating that the metal excess defect model can be the favorable oxygen deficiency model in P4332 LNMO. Similarly, the defect formation energy in pseudo- 3 is 2.58 eV, which is smaller than the oxygen vacancy formation energy of 3.63 eV. Accordingly, the oxygen vacancy formation reaction is unlikely, although interstitial cation occupation at the octahedral vacancies occurred in both P4332 and pseudo-3 LNMO spinel compounds. In addition, formation energy for the metal excess model in pseudo3 was about 0.4 eV smaller than that in P4332. This is consistent with experimental results that show only pseudo-3 possesses oxygen defects. The difference in defect formation energy between P4332 and pseudo-3 for the metal-excess model (0.40 eV) is larger than that for oxygen vacancy formation (0.08 eV). Stoichiometric P4332 is 0.10 eV f.u.-1 more stable than pseudo-3, whereas the energy difference between P4332 and 3 for interstitial Li, Ni, and Mn models decreased. Thus, 3 becomes more favorable than P4332 as the concentration of interstitial metal defects increases. This is in agreement with experimental results2, 23. This computational studies provide a plausible mechanism for the formation of 3 type LiNi0.5Mn1.5O4-δ. We found an introduction of interstitial metal to the vacancy sites triggered the reduction of Mn4+ to Mn3+ due to charge neutrality. Furthermore, this new findings strongly suggest that an introduction of interstitial Li+ to the vacancy sites will enhance the density of transportable Li+ because the vacancy site is positioned in Li+ diffusional pathway as well as enhance the density of conduction electron through the formation of Mn3+ ions, leading to develop the functionalized LiNi0.5Mn1.5O4-δ which provides an excellent high-power characteristics. Table 6. Defect formation energies for the metal-excess model for P4332 and 3 LNMO.

Model

Model a1 Model a2 Model a1 Model a2

Antisite cation Ni Mn

Antisite Li position

Antisite [eV]

4a

1.098

12d

0.649

4a

0.988

12d

0.469

energy

and pseudo-3 LNMO spinel compounds. In addition, the difference in the formation energy of around 0.40 eV for the metal excess model between P4332 and pseudo3 is relatively large, and the formation energy in pseudo-3 is smaller than that in P4332. This is in agreement with experimental results that show that only 3 possesses oxygen defects. This computational studies provide a plausible mechanism for the formation of 3 type LiNi0.5Mn1.5O4-δ. This new findings strongly suggest that an introduction of interstitial Li+ to the vacancy sites will enhance the density of transportable Li+ because the vacancy site is positioned in Li+ diffusional pathway as well as enhance the density of conduction electron through the formation of Mn3+ ions, leading to develop the functionalized LiNi0.5Mn1.5O4-δ which provides an excellent high-power characteristics.

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENT The present work was partially supported by JSPS KAKENHI Grant Number 26630331, Grant-in-Aid for Challenging Exploratory Research, JSPS; Japan Society for the Promotion of Science, Japan. H. S. and M. N. were grateful for financial support from Institute of Ceramics Research and Education (ICRE) in Nagoya Institute of Technology. The crystal struc49 ture figures were drawn with VESTA .

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CONCLUSIONS We have investigated the phase stability and local structure of oxygen-deficient LNMO with both P4332 and pseudo-3 symmetry by using ab initio DFT calculations. The defect formation energies for both the oxygen vacancy model and the metal-excess model were evaluated. The defect formation energies for the metal excess model of 2.98 eV for P4332 and 2.58 eV for pseudo-3 are smaller than that for the oxygen vacancy model of 3.71 eV for P4332 and 3.63 eV for 3. This indicates that the oxygen vacancy formation and interstitial cation occupation at the octahedral vacancies occurred for both P4332

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A Table of Contents graphic


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Defect Formation Energy in Spinel LiNi0.5Mn1.5

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