Atomistic Simulation Study of Mixed-Metal Oxide ... - ACS Publications

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Atomistic Simulation Study of Mixed-Metal Oxide (LiNi1/3Co1/3Mn1/3O2) Cathode Material for Lithium Ion Battery Sanghun Lee and Sung Soo Park* Corporate R&D Center, Samsung SDI Co. Ltd., Yongin, Gyunggido, 446-577, Republic of Korea ABSTRACT: Using atomistic simulation with empirical potential parameters, a layered metal oxide (LiNi1/3Co1/3Mn1/3O2) as cathode material for lithium ion battery is investigated in terms of energetics and dynamics. Structural characteristics, defect chemistry, and doping effects are determined by atomistic energetics calculation, which has been developed by Islam et al., while dynamics properties are characterized by molecular dynamics simulation. The core− shell model with empirical force fields reproduced the unit-cell parameters, which are well matched with the experimental data. With regard to the intrinsic defects, the calculated results indicate that the antisite defect, in which Li+ and Ni2+ exchange positions, is most favorable. In the isovalent doped systems, the solution energy increases with increasing disparity in size between dopant and host ion. In addition, it is found that ions become more mobile due to growing thermal motions with increasing temperature and the local mobility is anisotropic. tion,34 structure, thermal stability, and transport properties of various cathode materials have been extensively investigated. In particular, the classical atomistic simulation including molecular dynamics (MD) has a benefit of accessibility to relatively many atoms over the first-principles calculation. By employing energetics calculation with empirical potential parameters, Islam and co-workers successfully described the defect and transport properties of spinel manganates,35 olivine-type phosphates,36−38 silicates,39,40 and tavorites.41 Based on MD simulation with the same force field parameters, Zhang et al. explained structural and transport properties of LiFePO4.42,43 In addition, Adams showed the effect of structural disorder of LiFePO4 on lithium diffusion pathway and ionic conductivity from MD simulation44,45 with the bond valence force fields.46 For studying energetics, we employed Islam et al.’s wellestablished methodology and force field parameters.36−41 As mentioned above, many types of cathode materials have been covered in their pioneering works; however, the methodology and force field parameters have not been validated on the layered metal oxide materials, which substantially differ from the materials in the previous studies with respect to the structure and composition. Hence, the need to test whether their models work for the layered metal oxide materials for LIB cathodes provides an additional motivation of the present work with the intrinsic interest of the structure, defect chemistry, and dynamics properties of the layered LiNi1/3Co1/3Mn1/3O2. To our knowledge, the study of classical atomistic simulation on LiNixCoyMn1−x−yO2 has not been reported.

1. INTRODUCTION Layered lithium transition metal oxides (LiMO2, M: Co, Ni, and Mn) are the most successful cathode materials for lithium ion batteries (LIBs). Among these layered cathode materials, which offer a highly accessible lithium diffusion pathway, LiCoO2 has been most commonly used since SONY’s first commercialization.1 Many efforts to replace Co with alternative transition metals, for example, LiNiO22−5 or LiMnO2,6−11 have been made for the past two decades because of several drawbacks of LiCoO2, such as cost, environmental risk, and so on. Unfortunately, these materials also exhibit significant shortcomings; i.e., LiNiO2 is known to be difficult to synthesize and suffers from poor cyclability12,13 and LiMnO2 undergoes crystallographic phase transformation to spinel structure during charge/discharge cycling.6,14 On the other hand, simultaneous partial replacements of Co by Ni and Mn have been introduced and shown electrochemically improved performances in the viewpoint of stable cyclablility, thermal stability, and capacity.5,15−25 Even though the electrochemical behavior of LiNixCoyMn1−x−yO2 is dependent upon various factors, for example, structure, composition, synthesis method, and operation voltage range,25−31 this material not only is being currently widely used in LIB but also still has room for improvement. Regarding further information such as properties, preparation, performances, and prospects of LiNixCoyMn1−x−yO2, the reader is directed to the review by Wang et al.32 Meanwhile, to understand the features influencing the electrochemical behavior of electrode materials, it is valuable to characterize the structure, underlying defect, and transport properties at the atomic level with molecular simulation. From first-principles calculation33,34 and classical atomistic simula© 2012 American Chemical Society

Received: December 19, 2011 Revised: February 6, 2012 Published: February 18, 2012 6484

dx.doi.org/10.1021/jp2122467 | J. Phys. Chem. C 2012, 116, 6484−6489

The Journal of Physical Chemistry C

Article

Figure 1. Suppercell structure (27 formula units) of LiNi1/3Co1/3Mn1/3O2 for energetics calculation. Views from (a) a−b plane and (b) a−c plane. (c) Representation of the Mott−Littleton method for defect modeling. (d) Suppercell structure (108 formula units) of LiNi1/3Co1/3Mn1/3O2 for MD simulation.

2. SIMULATION METHODS All calculations were performed by the GULP module47 in Materials Studio 5.5 package.48 To characterize structure and defect chemistry, a well-established modeling technique is employed,36−41,49 and only a brief description will be given here. Interactions between ions in the crystalline LiNi1/3Co1/3Mn1/3O2 are composed of long-range Coulombic and short-range nonbonded interaction components. The short-range interactions were modeled using the Buckingham potential function given by ⎛ rij ⎞ Vij(rij) = A exp⎜ − ⎟ − C /rij6 ⎝ ρ⎠ (1)

Mn in the crystal are +2, +3, and +4, respectively. All energetics calculations were performed on supercell with 27 formula units and the Ni, Co, and Mn are alternatively arranged along the a and b directions (Figure 1a and b). The defect energies were calculated by the Mott−Littleton method51 implemented in the GULP code. This method is to partition the crystal lattice surrounding defect into two spherical regions. In the inner sphere (region I), the ions are strongly displaced by the presence of the defect so that the interactions are treated explicitly and the ions are allowed to fully relax. In contrast, the ions in the outer region (region II) are treated implicitly as a dielectric continuum (Figure 1c). In the similar calculation of uranium dioxide, Read and Jackson investigated the dependence of the energy on the size of these regions to determine the most appropriate cutoffs. They found that the radius of inner sphere above 11 Å is sufficient and the optimal value for outer sphere is double the radius of the inner sphere.52 In this work, the radii for the inner and outer spheres are 14 and 28 Å; i.e., regions I and II contain ∼2700 and ∼19 000 ions, respectively. To promote understanding structural and dynamics properties of LiNi1/3Co1/3Mn1/3O2, MD simulations were performed. From the optimized structure (27 formula units), the initial structure for MD (108 formula units) was produced by multiplying by 2 × 2 in the a and b directions (Figure 1d). The simulations were performed at 500, 1000, and 2000 K with NVT ensemble (fixed number of particles, volume, and

where rij is the distance between atoms i and j and A, ρ, and C are the empirical parameters. To include the effects of electronic polarization, the core−shell model49,50 was employed, which has proven to be effective in simulating the dielectric properties of ceramic oxides. In this model, a massless shell of an atom with a partial charge Y is coupled to the core with charge q − Y, where q is the formal charge, by a spring with force constant k. Then, the core−shell energy is given by

V=

k 2 r 2

(2)

where r is the displacement between the core and the shell. It was assumed that the charges of transition metals Ni, Co, and 6485



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temperature) and Nosé−Hoover thermostat.53,54 The Ewald sum method was applied for charge calculation under the periodic boundary condition. Before obtaining average properties in our interests for 100 ps, an equilibration run of 10 ps was preceded with the time step of 1 fs.

calculated. These defects are expressed by Kröger−Vink notation:

3. RESULTS AND DISCUSSION 3.1. Potential Parameters and Structural Modeling. In order to give a good description by atomistic simulation, employing suitable potential parameters is highly required. The interatomic and core−shell interaction potentials for Li+, Ni2+, Co3+, and O2− were obtained from Fisher et al.’s study of olivine-type phosphate materials,37 and we confirmed that the parameters reproduced experimental unit-cell parameters of LiO2, NiO, and LiCoO2. For Mn4+, we modified the parameters from Ammundsen et al.’s study of LiMn2O435 and reproduced experimental unit-cell parameters of λ-MnO2.55 The refined potential parameters used in this work are listed in Table 1. The

Li ···O Ni2+···O2− Co3+···O2− Mn4+···O2− O2+···O2‑

k (eV·Å−2)

1.0 3.344 2.04 4.0 −2.96

9999.0 93.7 196.3 95.0 65.0

Li Ni2+ Co3+ Mn4+ O2−

a

c

2.862 2.864 2.892

14.227 14.233 14.251

this work

2.868

14.213

4 2 2 2 2

× × × × ×

2.05 2.07 2.04 2.05 2.06

X O Frenkel: OO → V •• O + O″i

(7)

→ V″″Mn + 2V •• O + MnO2

(8)

Co−O

4 2 2 4

× × × ×

1.95 1.96 1.92 1.93

(10)

(11)

In addition, we also calculated antisite pair defects, which involve the exchange of a metal ion with another metal ion of different species. It is necessary to investigate this type of defect since adverse effects of antisite defect on electrochemical performances have been observed in the layered structure of LiNiO258 and LiNi0.5Mn0.5O2.59 The antisite defects are given by X X Li−Ni antisite: Li Li + Ni Ni → Ni•Li + Li′Ni

(12)

X X Li−Co antisite: Li Li + CoCo → Co•• Li + Li″Co

(13)

X X Li−Mn antisite: Li Li + Mn Mn → Mn••• Li + Li′″Mn (14)

Additionally, antisite events between transition metals, which seem inappropriate to be called defects, can occur and are given by X X Ni−Co antisite: Ni Ni + CoCo → Co•Ni + Ni′Co

(15)

X X Co−Mn antisite: CoCo + Mn Mn → Mn•Co + Co′Mn (16) X X Mn−Ni antisite: Mn Mn + Ni Ni → Ni″Mn + Mn•• Ni (17)

bond lengths Ni−O

(6)

X X MnO2 Schottky: Mn Mn + 2OO

Table 2. Calculated and Experimental Structural Parameters of LiNi1/3Co1/3Mn1/3O2

experiment56 experiment57 ab inito5

X Mn Frenkel: Mn Mn → V″″Mn + Mn•••• i

X X NiO Schottky: Ni Ni + OO → V″Ni + V •• O + NiO

structure of LiNi1/3Co1/3Mn1/3O2 was optimized under the constant pressure conditions (0 Pa), and then both lattice parameters and ion positions were allowed to relax. The obtained unit-cell parameters and bond lengths are compared with the experimental values56,57 and ab initio calculations16 in Table 2 and show that they are highly comparable. 3.2. Intrinsic Defects. To determine Frenkel and Schottkytype defect formation energies, point defect energies for vacancies and interstitials and relevant lattice energies were

unit-cell parameters

(5)

X X Li2O Schottky: 2Li Li + OO → 2V′Li + V •• O + Li2O

0.0 0.0 0.0 0.0 65.0

Y (e) (shell charge)

+

X Co Frenkel: CoCo → V′″Co + Co••• i

+ 2V •• O + LiNi1/3Co1/3Mn1/3O2

C (eV·Å6)

632.1018 0.2906 1582.50 0.2882 1329.82 0.3087 1397.63 0.3211 22764.3 0.149 (b) Core−Shell Interaction

interaction

(4)

(9)

ρ (Å)

A (eV)

2−

X Ni Frenkel: Ni Ni → V″Ni + Ni•• i

1 X 1 X 1 X Ni Ni + CoCo + Mn Mn 3 3 3 1 1 1 X + 2OO → V′Li + V″Ni + V′″Co + V″″Mn 3 3 3

(a) Buckingham Potential +

(3)

X full Schottky: Li Li +

Table 1. Parameters of Buckingham Potential and Core− Shell Interaction for LiNi1/3Co1/3Mn1/3O2 interaction

X Li Frenkel: Li Li → V′Li + Li•i

The calculated defect formation energies are listed in Table 3. The results indicate that formation of defects is generally unfavorable. In particular, the defects involving Mn except for Co−Mn antisite defect are highly unfavorable due to strong Mn−O Coulombic interaction; thus, they would hardly occur compared to the other types of defects. The most favorable defect is the Li−Ni antisite defect (0.84 eV), and there will be a small portion of defects at even at low temperatures depending on the synthesis conditions. In addition, the transition metals

Mn−O

6 × 1.94 2 × 1.85 4 × 1.86

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Table 3. Energies of Intrinsic Defects in LiNi1/3Co1/3Mn1/3O2 defect

energy (eV)

Li Frenkel Ni Frenkel Co Frenkel Mn Frenkel LiNi1/3Co1/3Mn1/3O2 Schottky Li2O Schottky NiO Schottky LiNi antisite LiCo antisite LiMn antisite NiCo antisite CoMn antisite MnNi antisite

3.73 7.33 11.76 15.33 18.10 9.20 7.77 0.84 4.06 8.56 1.04 1.08 4.09

Figure 2. Solution energies vs Δr (differences of ionic sizes between doped and host ions).

is one of our future works. As shown in Figure 2, it is noticeable that the solution energy increases with increasing disparity in size between doped and host ions. 3.4. MD Simulation. In the layered structure of lithium metal oxides, it is believed that Li+ diffusion takes place in the Li layer by hopping from octahedral to octahedral site through intermediate tetrahedral sites.66 If we know a possible Li+ migration pathway, the activation energy (Ea) of Li migration can be calculated by the defect modeling method. The calculated Ea is 0.56−0.63 eV depending upon the environments of migrating Li+. However, because there is no vacant Li site in our MD model, the Li+ migration would hardly occur on a accessible time scale by MD simulation. In our MD simulation, the Li+ migration was not observed even at very high temperature (2000 K) up to 1 ns. Hence, in this work, we focus on thermal motions of ions within a lattice unit. In Figure 3, the radial distribution function (RDF) of Li−O at different temperatures is shown. This plot shows a series of

are also interchangeable due to relatively low defect formation energies of Ni−Co (1.04 eV) and Co−Mn (1.08 eV) antisites. 3.3. Dopant Substitution. Results that doping with cations (such as Mo, Mg, Fe, Sn, Ti, etc.) improves the performance of LIB have been reported.27,60−65 From calculation of energetics of doped systems, a useful guide to the selection of proper dopants can be provided.37 The calculation method for doping energy is the same as that for defect energy, and the potential parameters for dopant metal ions were obtained from Fisher et al.’s study.37 Due to the need for charge compensation, aliovalent substitution is more complicated than isovalent substitution and its mechanism has not been clearly established. In Fisher et al’s study, the aliovalent substitutions are strongly unstable compared with the isovalent ones in LiMPO4 (M: Fe, Mn, Co, and Ni). In this study, only isovalent dopants are considered for simplicity as in the following equations monovalent ion:

1 1 X X M(I)2 O + Li Li → Li2O + M(I)Li , 2 2

M(I): Na, K, and Rb

(18)

X X divalent ion: M(II)O + Ni Ni → NiO + M(II)Ni ,

M(II): Mg, Ca, Sr, and Ba

trivalent ion:

(19)

1 1 X Li2O + M(III)2 O3 + CoCo 2 2

X → LiCoO2 + M(III)Co ,

M(III): Al, Ga, Sc, Y, and La

Figure 3. Radial distribution functions of Li−O at various temperatures.

(20)

X tetravalent ion: M(IV)O2 + Mn Mn → MnO2 X + M(IV)Mn ,

M(I): Ti and Zr

well-defined peaks corresponding to successive nearestneighbor distances, which is typical behavior for crystalline solids. As temperature increases, the peaks become broad due to thermal motions. The RDFs of Li−Ni, Co, and Mn are shown in Figure 4. The temperature dependence is similar to that of RDF of Li−O. Meanwhile, the intensity of the first peak is of the order Mn > Co > Ni, which indicates that the order of binding strength between Li+ and the transition metals is also Mn > Co > Ni. This suggests that Li+ near Ni2+ are preferentially delithiated from the electrode during the discharge process, which is consistent with experimental studies of in situ X-ray absorption spectroscopy during electrochemical cycling.67−69

(21)

Solution energies of dopant species are plotted as functions of difference of sizes between doped and host ions in Figure 2. Na+ and K+ doping for Li+ and Ga3+ doping for Co3+ were found to be strongly favorable (i.e., negative solution energies), whereas tetravalent ions (Ti4+ and Zr4+) for Mn4+ are highly unfavorable. Recently, Kam and Doeff reported that aliovalent substitution of Ti4+ for Co3+ improves discharge capacity and cycling performance, in which they suggested cosubstitution of Li+ with Ti4+ as a charge compensation mechanism.65 In this regard, the aliovalent substitution is worth investigating, and it 6487



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increasing temperature and the local mobility is anisotropic depending on the layered structure. In addition, the order of binding strength between Li+ and transition metals was found to be Mn > Co > Ni.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

Figure 4. Radial distributions functions of Li−Ni, −Co, and −Mn at 500 and 2000 K.

REFERENCES

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+

In Figure 5, the mean square displacements (MSDs) of Li at various temperatures are shown. This plot shows the anisotropy

Figure 5. Mean square displacements of Li+ at various temperatures.

of Li+ mobility; i.e., Li+s are more mobile in the directions of x and y than the z direction. As temperature increases, the higher mobility is exhibited. In crystalline solids, atoms are strongly bound to their positions, and the ions can move farther away from their lattice positions at higher temperatures.42 In this regard, the LiNi1/3Co1/3Mn1/3O2 in this model is considered to be a little less thermally stable than the LiFePO4,42 but much more stable than the LiMn2O4.70

4. CONCLUSION Employing classical atomistic simulation, the energetics, structural properties, defect chemistry, dopant effect, and dynamics behaviors of the layered cathode material, LiNi1/3Co1/3Mn1/3O2, are characterized. The experimentally observed crystal structures were successfully reproduced by empirical potential parameters of the core−shell model. The most favorable intrinsic defect is found to be the Li−Ni antisite defect (0.84 eV). Due to relatively low antisite energies of Ni− Co (1.04 eV) and Co−Mn (1.08 eV), the configuration of synthesized LiNi1/3Co1/3Mn1/3O2 would be highly dependent on the synthesis condition. Various isovalent doped systems, i.e., Na+ and K+ doping for Li+ and Ga3+ doping for Co3+, respectively, were found to be energetically favorable (negative solution energies). As disparity in size between doped and host ions increases, the solution energy also increases. Because there is no vacant Li site in our MD model, we could not observe lithium cation’s hopping event even at very high temperature during MD simulation; instead, we focused on thermal behaviors at various temperatures. It was found that ions become more mobile due to growing thermal motions with 6488



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