Structure, Defect Chemistry, and Lithium Transport Pathway of Lithium

Aug 30, 2012 - Computational modelling of inorganic solids. Elaine Ann Moore. Annual Reports Section "A" (Inorganic Chemistry) 2013 109, 421 ...
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Structure, Defect Chemistry, and Lithium Transport Pathway of Lithium Transition Metal Pyrophosphates (Li2MP2O7, M: Mn, Fe, and Co): Atomistic Simulation Study Sanghun Lee and Sung Soo Park* Corporate R&D Center, Samsung SDI Co. Ltd., Yongin, Gyunggido, 446-577, Republic of Korea S Supporting Information *

ABSTRACT: Lithium transition metal pyrophosphate materials (Li2MP2O7, M: Mn, Fe, and Co) have been proposed as promising novel cathode materials for lithium ion batteries. Using atomistic simulation with empirical potential parameters, which has been validated on various cathode materials by Islam et al. [Phil. Trans. R. Soc. A 2010, 368, 3255−3267], these new pyrophosphates are investigated to elucidate structure, defect chemistry, and Li+ ion transport pathway. The core−shell model with empirical force fields reproduces the experimental unit-cell parameters, and formation energies of intrinsic defects (Frenkel and antisite) are calculated. From migration energy calculation, it is found that the pyrophosphates without partial occupation have a 2D Li+ ion pathway. Meanwhile, under the condition of partial occupancies of Li and transition metal atoms, the diffusion pathway of Li+ ions is a 3D network. KEYWORDS: lithium ion battery, cathode materials, defect calculation, lithium ion migration, core−shell model

1. INTRODUCTION Since SONY’s first commercialization of the lithium ion battery (LIB),1 layered lithium transition metal oxides (LiMO2, M: transition metal, i.e., Co, Ni, Mn, etc.), which provide highly accessible Li+ ion diffusion pathways, have been widely used for cathode materials in LIBs for portable electronics. However, as the usage of LIBs has increased in other applications, such as electric vehicles (EVs), hybrid electric vehicles (HEVs), and energy storage systems (ESSs), concerns over safety and cost issues of LiMO2 have motivated development of new cathode materials. Several new materials including polyanions, such as phosphates,2 silicates,3 fluorophosphates,4,5 fluorosilicates,6 etc., have been possible candidates. In particular, olivine-structured orthophosphates, for example, LiFePO4, have been largely investigated for a decade and have gained a partial success in the commercial market.7−9 Recently, in order to reduce a drawback of low volumetric energy density of orthophosphates by increasing the number of lithium ions in a unit volume, an effort to synthesize a new type of pyrophosphates, i.e. Li2MP2O7, has been made. For the first time, Adam et al. succeeded in synthesis of Li2MnP2O7, even though there was no electrochemical data reported.10 Its crystal structure was identified as having a different structural framework to that of a known pyrophosphate, for example, LiFeP2O7, which is problematic due to its lack of lithium ions to be cycled and low voltage in the electrochemical reaction.11 Afterward, Nishimura et al. managed to synthesize the Fe version of Li2MnP2O7 and showed that it is a promising candidate for cathode materials for 3.5 V class LIBs.12 In a © 2012 American Chemical Society

study of mixed-metal phases (Li2MnxFe1−xP2O7), Zhou et al. found that the electrochemical capacity improves as the Fe concentration increases, and the electrochemical activity of the Fe phase is higher than that of the Mn phase in the common operating voltages (3−4 V).13 Moreover, employing neutron and X-ray diffractions, Kim et al. characterized the detailed atomistic structures of Li2FeP2O7 and Li2CoP2O7 and proposed that the Co version is also a promising cathode material for LIBs.14 However, despite these studies, information of Li2MP2O7 is limited compared to other cathode materials containing polyanions, for example, LiMPO4, and further investigation needs to be performed to understand these materials in detail. 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 calculations15,16 and classical atomistic simulations,16 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 comparatively a lot more atoms than the first-principles calculation.17−19 By employing energetics calculation with empirical potential parameters, Islam and coworkers successfully described the defect and transport Received: March 6, 2012 Revised: August 17, 2012 Published: August 30, 2012 3550

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properties of spinel manganates, 20 olivine-type phosphates,21−23 silicates,24,25 and tavorites.26 In addition, this methodology has recently been validated on the layered lithium mixed-metal oxides.19 The present work extends these studies of cathode materials with a comprehensive calculation on the energetics of intrinsic defects and Li+ ion migration in the pyrophosphate of Li2MP2O7 (M: Mn, Fe, and Co) materials.

2. SIMULATION METHODS All calculations were performed by the GULP code.27 To characterize structure and defect chemistry, the well-established modeling technique is employed19−28 and only a brief description will be given here. Interactions between ions in the crystalline Li2 MP2 O7 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 /rij 6 ⎝ ρ⎠

(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 P2O74− units to account for the bending interactions of O−P−O angles, as previously used in other studies of orthophosphates.21,22 It is given by Vijk(θijk) =

1 K (θijk − θ0)2 2

Figure 1. (a) Unit-cell structure of Li2MP2O7. (b) Views from ab (left) and ac (right) planes of supercell structure. Spheres represent Li+ ions, and polyhedrons are transition metals (deep blue and cyan) and phosphorus (pink) atoms. Crystallographically different sites are differentiated by their colors.

(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. To include the effects of electronic polarization, the core− shell model28,29 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

are 14 and 28 Å, i.e. regions I and II contain ∼2100 and ∼15 000 ions, respectively.

(3)

where r is the displacement between the core and the shell. To obtain the structural parameters of Li2MP2O7, calculations were performed on the cell with eight formula units (Figure 1). From the experimental study of X-ray diffraction,10 it is known that Li and Mn atoms in Li2MnP2O7 crystal occupy four and two different sites, respectively, with a full occupation. Fe- and Co-based pyrophosphates are isostructural to Li2MnP2O7, except for the partial occupancies of transition metal atoms in Li sites and Li atoms in transition metal sites. The defect energies were calculated by the Mott−Littleton method30 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. To determine the appropriate sizes of inner and outer spheres (rI and rII, respectively), the dependence of the defect energy on the radii of the spheres is investigated (Figure 2), where the rI ≥ 14 Å with rII ≥ 2rI is satisfied within ∼0.01 eV. In this work, rI and rII

Figure 2. Vacancy defect formation energy of Li1 of Li2MnP2O7 as a function of radii of region I (rI) and region II (rII).

3. SIMULATION RESULTS 3.1. Potential Parameters and Structural Modeling. For simplicity and comparison among three different pyrophosphates, the smaller occupancies of Li and transition metal atoms in Li2FeP2O7 and Li2CoP2O7 are neglected in this section and the partial occupancies are considered and discussed in a later section (3.4. Systems with Partial Occupancies of Li2FeP2O7 and Li2CoP2O7). In order to provide a good description by atomistic simulation, employing 3551

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suitable potential parameters is highly required. The interatomic interaction potential (Buckingham potential) parameters for Li+, Mn2+, Fe2+, Co2+, O2−, and P5+ were obtained by fitting to reproduce experimental structures. The initial values of Buckingham potential parameters were taken from Fisher et al.’s study of olivine-type phosphate materials.22 The core−shell interaction and O−P−O bending interaction parameters were employed as published in Fisher et al.’s work. The refined potential parameters in this work are slightly modified from the original values and listed in Table 1. To Table 1. Potential Parameters for Li2MP2O7 (M: Mn, Fe, and Co) Pyrophosphates (a) Buckingham Potential ρ (Å)

A (eV)

interaction

C (eV·Å6)

Li+···O2− Mn2+···O2− Fe2+···O2− Co2+···O2− P5+···O2− O2−···O2−

535.546 0.2906 2450.22 0.278 899.343 0.3106 1603.63 0.2859 975.496 0.35898 19251.5 0.149 (b) Core−Shell Interaction

interaction

Y(e) (shell charge)

k (eV·Å−2)

+

1.0 3.42 2.997 3.503 5.0 −2.96 (c) Three-Body Interaction

99999.0 95.0 19.26 110.5 99999.0 65.0

Li Mn2+ Fe2+ Co2+ P5+ O2− bond type O −P −O 2−

5+

2−

0.0 0.0 0.0 0.0 0.0 44.53

K (eV·rad−2)

θ0 (deg)

1.3226

109.47

determine the unit-cell parameters, the structures of Li2MP2O7 were optimized under the constant pressure conditions (0 Pa) with the P21/c symmetry constraint, and then both lattice parameters and ion positions were allowed to relax. The obtained unit-cell parameters are listed in Table 2 and show that they are highly comparable with the experimental values.10,14 As reported in the previous studies,10,12−14 these pyrophosphates have a 3D framework composed of MO5 square pyramids (M2) sharing edges with MO6 octahedra (M1), which are further interconnected through P2O7 groups. It results in two different quasi 2D networks (planes A and B in Figure 3) of Li+ ion paths. Li1, 3 and Li2, 4 (see Figure 1a) locate in planes B and A, respectively. Detailed results on Li+ ion migration in each diffusion path are shown in a later section (3.3. Li+ Ion Migration). 3.2. Intrinsic Defects. Understanding of defect chemistry in electrode materials is very crucial to improve electrochemical performaces.31,32 To determine Frenkel defect formation

Figure 3. (a) Supercell structure of Li2MP2O7. Two different quasi 2D networks of Li+ ions are located in planes A and B. Schematic illustration of possible Li+ ion migration paths with adjacent transition metals and P2O7 groups of planes (b) A and (c) B. Paths of dashed black arrows (named with prime notation) are equivalent to those of solid red ones.

Table 2. Calculated and Experimental Unit-Cell Parameters of Li2MP2O7 Li2MnP2O7

Li2FeP2O7

Li2CoP2O7

lattice parameter

calc

exp10

calc

exp14

calc

exp14

a (Å) b (Å) c (Å) β (deg)

11.2872 9.8004 9.8182 102.4092

11.1800 9.8289 9.9158 102.466

10.9844 9.6415 9.6703 101.8478

11.0192 9.7488 9.8057 101.569

11.0231 9.6509 9.7145 101.8021

10.9574 9.6921 9.7611 101.776

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defects, especially Li4/M2, are highly likely to occur compared to the Frenkel defects, which is consistent with the partial occupancies of Li2FeP2O7 and Li2CoP2O7 in Kim et al.’s experiment.14 Both the Li4 and M2 sites are similarly coordinated by five oxygen atoms. Compared to the olivinetype LiFePO4 (experimental antisite (Li/Fe) defect concentration: 3%33 and calculated energy for clustered pair of Li/Fe: 0.74 eV21), the antisite defects of Li/M in these pyrophosphate materials are highly favored at a high concentration level. Although the Li4/M2 defect in Li2MnP2O7 is also comparably favorable to those in the other relatives from our calculations, the partial occupancies in Li2MnP2O7 was not reported in the experimental study10 and it is further discussed in the Discussion section. 3.3. Li+ Ion Migration. We have systematically calculated the activation energy for diffusion, i.e. migration energy, of the Li+ ion by a simple vacancy hopping mechanism. These calculations were performed by the Mott−Littleton method. The position of the highest potential energy along the migration path corresponding to the migration energy, i.e. transition state position (stationary point with a single negative eigenvalue for the Hessian), is searched by rational functional optimization (RFO) method34 implemented in the GULP code. As shown in Figures 1a and 3, there are four different Li+ ion sites (Li2 and Li4 in plane A, Li1 and Li3 in plane B in Figure 3). From our calculations, the migration of Li+ ions along the direction of [1 0 0] was strongly prohibited (>3 eV); hence, we considered only the quasi 2D migration of Li+ ions in the bc plane (planes A and B) as shown in Figure 3. In Figures 4a, c, and e, the migration energies and distances between Li+ ions in plane A of three species, Li2MnP2O7, Li2FeP2O7, and Li2CoP2O7 are exhibited, revealing similar behaviors of Li+ ion migration. First, the migration energies for paths of Pa3 (0.64−0.74 eV), Pa4 (0.63−0.68 eV), and Pa5 (0.39−0.59 eV) comparable with those of olivine-type LiFePO4 (0.55 eV),21,22 tavorite-type LiFeSO4F (0.46 eV),26 and Li2FeSiO4 (0.91 eV)25 are obtained. In the cases of Pa1 and Pa2, of which migration energies are relatively high (Pa1: 3.03− 3.19 eV and Pa2: 2.04−3.03 eV), the Li+ ions at the transition states (TS) get close to a transition metal (TM). The distances between the TM and the Li+ ions of Pa1 and Pa2 for all three species are 2.6−2.8 Å while those of Pa3, Pa4, and Pa5 are above 3.2 Å. Meanwhile, the TS Li+ ion of Pa6 (migration energy: 1.14−2.17 eV) is not so close as those of Pa1 and Pa2; however, it is affected by two of four different TMs (see Figure 3b, there are two symmetric pathways in Pa6: 3.0 and 3.4 Å for Li2MnP2O7). Whereas, in the cases of Pa3, Pa4, and Pa5, only one TM locates close to the TS Li+ ion. Second, even though the direct moves in the direction of [0 0 1] (Pa1 and Pa2) are strongly prohibited, by combinations of the accessible moves (Pa3, Pa4, and Pa5), the Li+ ions in plane A can migrate through a continuous 2D pathway. Meanwhile, the Li+ ions in plane B also have diffusion paths of relatively low activation energies (Pb1: 0.46−0.77 eV. Pb2: 0.46−0.64 eV. Pb3: 0.31−0.41 eV. Pb6: 0.44−0.51 eV in Figures 4b, d, and f for Li2MnP2O7, Li2FeP2O7, and Li2CoP2O7, respectively). In the cases of Pb4 (2.34−2.58 eV) and Pb5 (2.69−3.26 eV), the TS Li+ ions get much closer to a TM (2.5−2.8 Å) than those of the other paths (>3.1 Å). Similarly to the plane A, by combination of Pb1 ∼ Pb3 and Pb6, they also have a continuous 2D migration pathway for Li+ ion conduction. More details about the highest (but accessible)

energies, point defect energies for vacancies and interstitials were calculated. These defects are expressed by Kröger−Vink notation: Li Frenkel X Li Li → V′Li + Li•i

(4)

M (Mn, Fe, and Co) Frenkel X MM → V″M + M•• i

(5)

Because the pyrophosphates have four different sites of Li and two different sites of transition metal atoms, the defect energies are dependent upon the positions of vacancies and interstitials. In Table 3, the smallest defect energy of each Table 3. Smallest Energy of Frenkel Defect in Li2MP2O7 energy (eV) defect

Li2MnP2O7

Li2FeP2O7

Li2CoP2O7

Li Frenkel M Frenkel

1.56 4.70

1.48 2.79

1.35 4.97

species is shown. Under the assumption of low concentration of Frenkel defects, the concentration is dependent on the defect formation energy, i.e. the enthalpy of formation of a Frenkel defect (ΔHF): ⎛ −ΔHF ⎞ c ≈ exp⎜ ⎟ ⎝ 2kBT ⎠

(6)

where kB and T are the Boltzmann constant and temperature, respectively. It is noticeable that all Frenkel defects are unfavorable in all three species and thus unlikely to occur in any significant concentration (10−12∼10−14 for Li and 10−24 ≫ for the transition metals at 300 K). In addition, we also investigated the Li/M antisite pair defects, which involve the exchange of a Li+ ion with a transition metal ion. Particularly, because the partial occupancies of Li (the fifth position of Li, originally occupied by transition metal, M2 in Figure 1a) and transition metal (the third position of transition metal, originally occupied by Li, Li4 in Figure 1a) atoms were reported,12,14 it is worthwhile calculating the Li/M defect energy to determine how favorably it occurs. The Li/M antisite defect is given by Li−M antisite X X Li Li + MM → M•Li + Li′M

(7)

In Table 4, the defect energies of eight combinations of Li/M antisite defects are shown. It is notable that the Li/M antisite Table 4. Li/M Antisite Defect Energy in Li2MP2O7 energy (eV) defect

Li2MnP2O7

Li2FeP2O7

Li2CoP2O7

Li1/M1 Li2/M1 Li3/M1 Li4/M1 Li1/M2 Li2/M2 Li3/M2 Li4/M2

1.19 1.01 0.92 0.70 0.68 0.53 0.71 0.17

0.54 0.28 0.45 0.30 0.33 0.14 0.34 0.11

0.70 0.64 0.65 0.53 0.50 0.35 0.49 0.18 3553

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Figure 4. Schematic illustration of distances between Li+ ions and Li+ ion migration energies. Planes (a) A and (b) B of Li2MnP2O7; planes (c) A and (d) B of Li2FeP2O7; planes (e) A and (f) B of Li2CoP2O7. The Li+ ion distances in angstroms are written in bold black, and the migration energies in electronvolts are written in blue and red. The migration energy is calculated from the relation of ΔE = E(transition state) − E(vacancy of Li). Vacancy formation energies of Li1 (Li2) and Li3 (Li4) are different because they occupy the energetically different Li sites.

respectively.14 Our main interest in these systems with partial occupancies is to see whether the Li5 site can mediate the Li diffusion. If it could do so, the 2D migration pathway in pyrophosphates without partial occupation would become a 3D network in those with partial occupation. We have focused only on the Fe and Co pyrophosphates because there have been no reports on the Mn version with partial occupation. In order to realize the systems with partial occupancies, we simply exchanged one of Li atoms on Li4 sites and one of transition metal atoms on M2 sites in the crystal unit cell

barrier for the Li+ ion diffusion are discussed in the later Discussion section. 3.4. Systems with Partial Occupancies of Li2FeP2O7 and Li2CoP2O7. As mentioned in the previous sections, the partial occupancies of Li (the fifth position of Li, Li5, originally occupied by transition metal, M2 in Figure 1a) and transition metal (the third position of transition metal, M3, originally occupied by Li, Li4 in Figure 1a) atoms were reported.12,14 The occupancies of Li5 and M3 are 0.15 (Li2CoP2O7) ∼ 0.18 (Li2FeP2O7) and 0.29 (Li2CoP2O7) ∼ 0.33 (Li2FeP2O7), 3554

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Table 5. Migration Energy of Li+ Ion Involving Li5 Site (To or From Li5 Site of Structure I in Figure 6) in Li2MP2O7 Having Partial Occupancies of Li and Transition Metal

containing 8Li2MP2O7 without the symmetry constraint of P21/c. As shown in Figure 5, four configurationally different

Li2FeP2O7

Li2CoP2O7

energy (ev) migration path (in Figure 6)

distance (Å)

A B C D E F G H

3.57 3.40 4.28 3.39 4.23 3.09 4.57 4.08

energy (ev)

to Li5

from Li5

distance (Å)

to Li5

from Li5

0.86 0.92 0.74 0.66 0.71 1.18 1.63 0.22

1.06 1.23 0.99 0.46 0.50 1.48 1.45 0.60

3.52 3.38 4.37 3.38 4.26 3.11 4.59 4.05

0.32 0.92 0.69 0.71 0.59 0.64 1.75 0.14

0.48 1.17 0.99 0.52 0.49 0.97 1.46 0.59

networks in the planes A and B are interconnected (see Figure 6 and Table 5). It is more effective than the 1- or 2D network in that it is well-secured even if the active material is coated by metal foil.

Figure 5. Partially occupied models of Li2MP2O7, which are considered in this work. In these models, Li5 and M3 atoms are sitting on the sites originally occupied by one of M2 atoms and one of Li4 atoms, respectively, in Figure 1a.

4. DISCUSSION In the experimental study of the Fe compound,12 only one Li+ per formula unit (Li2FeP2O7) is electrochemically removed from the compound. It is then interesting to examine which plane, A or B, is more likely to be delithiated. In our calculations, the order of vacancy energies of Li+ ions is Li1 ≈ Li3 ≈ Li4 (within 0.11 eV for all three compounds) < Li2 (higher by 0.4−0.5 eV); therefore, it is predicted that the Li+ ions are removed from both planes A (Li4) and B (Li1 and Li3) during delithiation. In order to obtain the exact final structure after the first Li delithation, we need to perform further investigations with different empirical parameters obtained by fitting to the structure of Li1MP2O7. It is interesting that there was no partial occupation observed in Adam et al.’s study10 of Li2MnP2O7 even though the calculated Li/Mn antisite defect energy, particularly, of Li4/ Mn2 is in the same order of magnitude as those of Li4/Fe2 and Li4/Co2 in this study. The synthetic temperature condition (∼600 °C) of Li2MnP2O7 in Adam et al.’s study10 was not different from those of Li2FeP2O7 in Nishimura et al.’s12 (∼600 °C) and Li2FeP2O7 and Li2CoP2O7 in Kim et al.’s14 (550−600 °C); hence, the entropic effect from the temperature condition can be ruled out as an origin of the discrepancy between experiments and calculations. Another possible source is a lack of this model. One of the most distinctive differences between Mn and the other transition metals is the electronic configuration. Therefore, if the crystallographic difference of the experimental observations between Li2MnP2O7 and the others is due to the difference in electronic structures, there is possibility that it would not be properly considered by this model in which the electronic structures are not reflected. However, we could not find any remarkable difference in geometries (i.e., electronic energies) of M2 and Li4 (both are very similarly close to square pyramidal structure); therefore, this cannot be an appropriate explanation. Meanwhile, although the experimental study of Li2MnP2O7 has not observed the partial occupancy,10 it may not completely exclude the possibility of antisite partial occupation. In other words, the results of few experiments (to our knowledge, the only one is Adam et al.’s10) are not enough to make a definite conclusion and it may be observed with different synthesis conditions and

structures were considered. In Table S1 (Supporting Information), the unit-cell parameters of Li2FeP2O7 and Li2CoP2O7 with partial occupation obtained by employing the potential parameters in Table 1 are shown. Note that they are nearly the same as those of pyrophosphates without partial occupation in Table 2. Migration energies of 7−8 diffusion paths involving the Li5 site (to or from Li5) for one structure (the diffusion paths of structure I are shown in Figure 6 and those of the other

Figure 6. Possible migration paths of Li+ ion on Li5 site of structures I.

structures II, III, and IV are shown in Figure S1 in the Supporting Information) were calculated and listed in Table 5 (for structure I) and Table S2 in Supporting Information (for structures II, III, and IV). In several cases, low migration energies (