Article pubs.acs.org/JPCC
Atomistic Simulation Study of Monoclinic Li3V2(PO4)3 as a Cathode Material for Lithium Ion Battery: Structure, Defect Chemistry, Lithium Ion Transport Pathway, and Dynamics Sanghun Lee* and Sung Soo Park* Corporate R&D Center, Samsung SDI Co. Ltd., Yongin, Gyunggido 446-577, Republic of Korea
ABSTRACT: By use of energetics calculation and classical molecular dynamics simulation, the structural characteristics, defect chemistry, Li+ ion migration, and dynamics properties of monoclinic Li3V2(PO4)3, which is one of the promising candidates for lithium ion battery cathode materials, are investigated. The empirical potential parameters reproduce experimentally determined unit-cell parameters with good agreement. It is expected that intrinsic defects such as Frenkel and antisite defects would rarely form due to their high formation energy. Migration energy calculation shows that the Li+ ion mobility is fairly high and strongly anisotropic. From molecular dynamics simulation, diffusion coefficients at various temperatures and activation energies of Li+ ion diffusion process are calculated. In addition, the anisotropic mobility of Li+ ions is confirmed by molecular dynamics simulation.
1. INTRODUCTION Layered lithium transition metal oxides (LiMO2, M = Co, Ni, and Mn) have been commonly used as cathode materials for lithium ion batteries (LIBs) due to their easy mass producibility as well as outstanding performance. However, because LiMO2 materials have several drawbacks including cost and environmental risk, many efforts to develop new cathode materials such as phosphates,1 silicates,2 fluorophosphates,3,4 fluorosilicates,5 etc., have been made. In particular, the olivine-structured orthophosphates, for example, LiFePO4, have been largely investigated for a decade and have gained a partial success in the commercial market.6−8 However, orthophosphates have several shortcomings such as low discharge voltage, low energy density, low tap density, poor electronic conductivity, and rate capacity; therefore, Li3V2(PO4)3 has emerged as a potential candidate of cathode materials due to its improved safety properties, higher Li diffusion coefficient, higher discharge voltage, and higher energy density.9−12 Li3V2(PO4) 3 exists in two different phases, i.e., the thermodynamically more stable monoclinic form13 and the rhombohedral form, which is well-known as NASICON (sodium superionic conductor) type structure.14 Their structural difference causes very different voltage-composition behaviors. The rhombohedral form exhibits one plateau from one two-phase transition between Li 3 V 2 (PO 4 ) 3 and © XXXX American Chemical Society
Li1V2(PO4)3, which corresponds to extraction of two Li atoms,15 whereas the monoclinic form, in which all three Li atoms are mobile, shows more complex behavior from the series of two-phase transitions during Li extraction.9,16,17 Because the monoclinic form has several advantages of high capacity and easy synthesis over the rhombohedral one, the former has intensive attention to be employed as a cathode material for LIBs. Although the monoclinic Li3V2(PO4)3 has the low electronic conductivity (2 × 10−8 S cm−1)17 to limit the wide application, several practical trials to overcome the restriction have been made by addition of conductive materials,9,18−32 doping or substitution of metal ions (Al,33−35 Mn,36 Na,37,38 Mg,39−41 Co,42 Fe,43 Cr,44 Ti,45 Nb,46 etc.), and structural modifications (mesoporous47 and macroporous48 materials, nanorod,49 platelike shape,50 core−shell,51,52 thin film,53 MgO coating,54 etc.). In addition, development of novel synthetic methodologies of the monoclinic Li3V2(PO4)3 has been intensively focused. By various synthetic strategies such as carbothermal reduction process,19 sol−gel synthesis,20−23 solidstate synthesis,24−26 ultrasonic spray pyrolysis,27 hydrothermal method,28 wet coordination method,29 and glass ceramic Received: June 21, 2012 Revised: October 8, 2012
A
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Figure 1. (a) Unit-cell structure of the monoclinic Li3V2(PO4)3 for energetics calculations. Views from bc plane (left) and ac plane (right). (b) Supercell structure for MD simulation.
process,55 relatively high operation voltage of 3.5−4.5 V and large capacity have been achieved. In the meantime, for understanding of the Li+ ion dynamics in the monoclinic Li3V2(PO4)3, Cahill et al. performed Li NMR measurements.56,57 From their 7Li NMR study, the activation energy of the Li+ ion hopping process was estimated to be 0.73−0.83 eV.56 Moreover, they observed that the three craystallo-
graphically distinct Li+ ions show the difference in mobility, and the order of mobility is correlated to the structural characteristics of the material.57 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 B
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Figure 2. Structures of monoclinic Li3V2(PO4)3 (left), Li2V2(PO4)3 (center), and Li1V2(PO4)3 (right) obtained after geometry optimization, which correspond to experimentally determined structures in ref 17.
first-principles calculation58,59 and classical atomistic simulation,59 the structure, thermal stability, and transport properties of various cathode materials have been extensively investigated. In particular, the classical atomistic simulation has a benefit of accessibility to a lot more atoms than the first-principles calculation. By performing energetics calculation with empirical potential parameters, Islam and co-workers successfully described the defect and transport properties of spinel manganates,60 olivine-type phosphates,61−63 silicates,64,65 and tavorites.66 In addition, this methodology has recently been validated on the layered lithium mixed-metal oxides67 and pyrophosphates.68 The present work extends these studies of cathode materials with a comprehensive calculation on the structure, dynamics, and Li+ ion migration in the monoclinic Li3V2(PO4)3.
calculations were performed on a unit cell of 4 formula units (Figure 1a). The defect energies were calculated by the Mott−Littleton method71 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. The radii for the inner and outer spheres are 14 and 28 Å, i.e., regions I and II contain ∼2 000 and ∼14 000 ions, respectively. To promote understanding of the structural and dynamics properties of the monoclinic Li3V2(PO4)3, molecular dynamics (MD) simulations were performed. From the optimized unitcell structure (4 formula units), initial structure for MD (32 formula units) was produced by multiplying by 2 × 2 × 2 in all directions (Figure 1b). The simulations were performed at various temperatures (500, 750, 1000, 1250, 1500, 1750, and 2000 K) with the NVT ensemble (fixed number of particles, volume, and temperature) and the Nosé-Hoover thermostat. The Ewald sum method was applied for charge calculation under the periodic boundary condition. Before obtaining average properties in our interests for 500 ps, an equilibration run of 10 ps was preceded with the time step of 1 fs.
2. SIMULATION METHODS All calculations were performed by the GULP module69 in Materials Studio 6.0 package.70 To characterize structure and defect chemistry, a well-established modeling technique is employed,61−68 and only a brief description will be given here. Interactions between ions in the crystalline monoclinic Li3V2(PO4)3 are composed of long-range Coulombic and short-range nonbonded interaction components. The shortrange interactions were modeled using the Buckingham potential function given by ⎛ rij ⎞ C Vij(rij) = A exp⎜ − ⎟ − 6 ⎝ ρ ⎠ rij
3. RESULTS AND DISCUSSION 3.1. Potential Parameters and Structural Modeling. To provide a good description by classical atomistic simulation, suitable potential parameters are highly required. The interatomic interaction potential (Buckingham potential) parameters for Li+, Vx+ (x = 3, 3.5, and 4 depending on the state of lithiation), O2−, and P5+ were obtained by fitting to reproduce experimentally determined structures of the monoclinic Li 3 V 2 (PO 4 ) 3 , Li 2 V 2 (PO 4 ) 3 , and Li 1 V 2 (PO 4 ) 3 (Figure 2) and are listed in Table 1. The partially lithiated structures of Li2V2(PO4)3 and Li1V2(PO4)3 are corresponding to the structures experimentally characterized during the electrochemical extraction of Li+ ions.17 The O−P−O bending interaction parameters were employed as published in other studies of orthophosphates.61,62 To determine the unit-cell parameters, the structures of the monoclinic Li3V2(PO4)3, Li2V2(PO4)3, and Li1V2(PO4)3 were optimized under the
(1)
where rij is the distance between atoms i and j, and A, ρ, and C are the empirical parameters. Additionally, the three-body interaction term was included for the PO43− units to account for the bending interactions of O−P−O angles, as previously used in other studies of orthophosphates.61,62 It is given by Vijk(θijk) =
1 K (θijk − θ0)2 2
(2)
where K, θijk, and θ0 are the force constant, bond angle of O(i)−P(j)−O(k) unit, and its equilibrium value, respectively. It was assumed that the charges of V in the crystal are +3, +3.5, and +4 depending on the state of lithiation. A fitting procedure to obtain parameters of Buckingham potential and energetics C
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of Li1 or Li2, during electrochemical cycling. Meanwhile, for Li1V2(PO4)3, energies of the two possible structures (Figure 3b) are almost identical within 10−5 eV/(4 formula units). During the electrochemical extraction of Li+ ions, observed Li+ ions in the Li1V2(PO4)3 structure were occupied only at the Li2 sites.17 During the reinsertion of Li+ ions, however, both the Li1 and Li2 sites were partially occupied in the structure of Li1V2(PO4)3.17 In their study, Yin et al. argued that this difference in lithium occupancy between the phases of Li1V2(PO4)3 on the extraction and reinsertion is manifested in structural effect, i.e., the differences of unit-cell parameters and positions of negatively charged framework (V2(PO4)3x−) between Li 2 V 2 (PO 4 ) 3 and V 2 (PO 4 ) 3 . The Li sites of LixV2(PO4)3 during electrochemical cycling is determined by not only thermodynamic but also kinetic factors, and our calculations are consistent with this observation. 3.2. Intrinsic Defects. To determine metal Frenkel defect formation energies, point defect energies for vacancies and interstitials were calculated. These defects are expressed by Kröger−Vink notation
Table 1. Parameters of Buckingham Potential for Li3V2(PO4)3, Li2V2(PO4)3, and Li1V2(PO4)3 interaction
A (eV)
ρ (Å)
C (eV·Å6)
Li ···O P5+···O2− O2−···O2− V3+···O2− (for Li3V2(PO4)3) V3.5+···O2− (for Li2V2(PO4)3) V4+···O2− (for Li1V2(PO4)3)
636.4052 811.9450 111749.2 1516.8064 1607.733 599.3754
0.2906 0.3590 0.149 0.3117 0.3161 0.3935
0.0 0.0 10.0 0.0 0.0 0.0
+
2−
constant pressure conditions (0 Pa) with the P21/n symmetry constraint. Both lattice parameters and ion positions were allowed to relax. As shown in Table 2, the calculated unit-cell Table 2. Structural Parameters and Selected Interatomic Distances of Li−O of Li3V2(PO4)3, Li2V2(PO4)3, and Li1V2(PO4)3 Li3V2(PO4)3 a (Å) b (Å) c (Å) β (deg) Li1−O (1) (Å) Li1−O (2) (Å) Li1−O (3) (Å) Li1−O (4) (Å) Li2−O (1) (Å) Li2−O (2) (Å) Li2−O (3) (Å) Li2−O (4) (Å) Li2−O (5) (Å) Li3−O (1) (Å) Li3−O (2) (Å) Li3−O (3) (Å) Li3−O (4) (Å) Li3−O (5) (Å) a
Li2V2(PO4)3
Li1V2(PO4)3
exptla
calcd
exptl
calcd
exptl
calcd
8.606 8.591 12.036 90.61 1.88
8.601 8.651 11.992 90.61 2.05
8.457 8.621 11.896 90.24 1.85
8.452 8.653 11.864 89.99 2.10
8.301 8.518 11.653 89.60
8.296 8.484 11.664 89.61
1.99
2.11
1.95
2.19
1.96
2.14
2.08
2.13
2.02
2.09
2.00
2.11
1.94
2.08
1.90
2.13
2.01
2.15
2.08
2.60
1.90
2.10
2.46
2.92
2.00
2.08
2.09
2.19
1.89
2.12
2.73
2.27
2.00
2.11
2.00
2.26
2.13
2.13
2.02
2.13
2.39
2.33
2.08
2.38
2.07
2.32
1.84
2.03
2.02
2.01
Li Frenkel: Li ×Li → Va/Li + Li•i
(3)
••• V Frenkel: V×V → Va/// V + Vi
(4)
where Va represents a vacant site. In addition, we also calculated an antisite pair defect, which involves the exchange of a Li+ ion with a V3+ ion. The antisite defects are given by // Li−V antisite: Li ×Li + V×V → V •• Li + Li V
(5)
The lowest Frenkel defect energies of Li and V and antisite defect energy of Li/V are 2.00, 21.5, and 4.02 eV, respectively. The results indicate that the formation of any type of intrinsic defect is strongly unfavorable. In particular, it is predicted that even the antisite pair defect, which has relatively low formation energy (0.7−1.3 eV) for LiMPO4 (M = Fe, Ni, Co, and Mn),61,62 would not easily form. 3.3. Li Migration. We have systematically calculated the activation energy for diffusion, i.e., migration energy, of the Li+ ion in the monoclinic Li3V2(PO4)3 by a simple vacancy hopping mechanism. These calculations were performed by the Mott− Littleton method.71 The position of the highest potential energy along the migration path corresponding to the migration energy, i.e., the transition state position (the stationary point with a single negative eigenvalue for the Hessian), is searched by rational functional optimization (RFO) method72 implemented in the GULP code. In Figure 4, the possible migration paths of the monoclinic Li3V2(PO4)3 are exhibited. As shown in Table 3, the low migration energies (
