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Structural, electronic and Li diffusion properties of LiFeSO4F
Solid State Ionics 181 (2010) 1209–1213
Contents lists available at ScienceDirect
Solid State Ionics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s s i
Structural, electronic and Li diffusion properties of LiFeSO4F Zhaojun Liu, Xuejie Huang ⁎ Beijing National Laboratory for Condensed Matter, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
a r t i c l e
i n f o
Article history: Received 12 February 2010 Received in revised form 18 April 2010 Accepted 22 June 2010 Keywords: LiFeSO4F Li-ion battery First-principles calculation Band gap Activation energy
a b s t r a c t The structural, electronic and Li diffusion properties of LiFeSO4F were analyzed by first-principles calculation under the DFT + U framework. The difference of the calculated lattice parameters and the reported data is within 3%. The redox potential of Fe2+/Fe3+ versus Li metal is 3.7 V, and phase separation of LiFeSO4F and FeSO4F is expected during Li extraction. Pure LiFeSO4F is an insulator with a band gap of 3.6 eV, while the band gap in the partially delithiated form Li1 − xFeSO4F is obviously smaller. A very low Li migration energy of 0.3 eV is required in the partially delithiated form Li1 − xFeSO4F, and the diffusion coefficient is estimated to be about 1.6 ⁎ 10−7 cm2 s−1. © 2010 Elsevier B.V. All rights reserved.
1. Introduction In 1997, Pahdi et al. proposed the polyanion compound LiFePO4 as a potential cathode material for Li-ion batteries [1,2], and it has attracted much of the research interest since then. Carbon coating and particle size reduction are effective to overcome its drawbacks of low intrinsic electronic and ionic conductivity [3–6]. The redox potential of Fe2+/Fe3+ versus Li in LiFePO4 is 3.45 V. A polyanion group XO4 with stronger electro-negativity is expected to lead to a higher Li intercalation potential due to the stronger inductive effect [7]. Recently, Recham et al. reported the reversible Li insertion/extraction in LiFeSO4F with a redox potential of 3.6 V [8]. LiFeSO4F has the same structure with LiMgSO4F. LiMgSO4F shows a considerable Li-ion conductivity with an activation energy of 0.93 eV [9], significantly lower than that of γ-Li3PO4 which has an activation energy of about 1.2 eV [10]. Due to the large cavities in its crystal structure, LiFeSO4F is likely to have a higher Li-ion conductivity compared with LiFePO4. First-principles calculation is an effective method to calculate the physical and chemical properties of the materials for Li-ion battery [11–15]. As for transition metal compounds, Local Density Approximation (LDA)/Generalized Gradient Approximation (GGA) calculations tend to delocalize the correlated 3d electrons and lead to obvious errors [15]. A DFT + U approach was well established in the 1990s. It reserves the high efficiency of the LDA/GGA method and an explicit treatment of the electron correlation with a Hubbard type model for the d electrons is included. The electronic structure [11], Li intercalation potential [12,15], phase diagram [13] and Li diffusion
⁎ Corresponding author. Fax: +86 10 82649046. E-mail address: [email protected] (X. Huang). 0167-2738/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2010.06.043
kinetics [14] for a few commonly used Li-ion battery materials have been calculated with the DFT + U method. Calculation results are in good agreement with experiment [16–18]. As for LiFePO4, Li diffusion kinetics [19,20], doping effect [14,21], electronic structure, and magnetic properties [11,22] have been intensively studied with first-principles calculations and the results agree well with the experimental data. Calculations on LiFeSO4F will help to understand its properties and benefit for its applications in battery.
2. Calculation method Calculations are performed within the GGA + U framework as implemented by the VASP program [23]. Electronic exchange correlation is treated with the Generalized Gradient Approximation. Projector augmented wave (PAW) pseudo-potentials are used [24]. Perdew– Wang 91 type GGA exchange correlation functional is adopted. For all calculations, an energy cutoff of 600 eV is used. A K-point mesh of 6x6x4 is used in a unit cell. For larger supercells, K-point mesh of similar density is adopted. The on-site interaction of 3d electron was treated with the rotationally invariant approach proposed by Dudarev et al. [25]. In this approach the total energy is only dependent on the effective interaction parameter Ueff = U − J and insensitive to the J parameter with fixed Ueff. The elastic band method was used to calculate the activation energy for Li diffusion [26]. At first, structures with Li ion at the starting point and end point of a diffusion process are fully relaxed. Then a series of images are linearly interpolated between the starting and the end structures. Images are allowed to relax perpendicular to the diffusion path, and elastic force was applied to ensure that all ions relax to the minimum energy path.
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Z. Liu, X. Huang / Solid State Ionics 181 (2010) 1209–1213
Table 1 Positional parameters of LiMgSO4F. Atom
Wyckoff position
Occupancy
Coordinates (x/a, y/b, z/c)
S Mg(1) Mg(2) F O(1) O(2) O(3) O(4) Li(1) Li(2)
2i 1b 1a 2i 2i 2i 2i 2i 2i 2i
1 1 1 1 1 1 1 1 0.5 0.5
(0.3316, 0.6354, 0.2515) (0, 0, 0.5) (0, 0, 0) (0.1102, 0.9176, 0.7554) (0.6178, 0.7456, 0.4045) (0.1263, 0.6561, 0.3602) (0.3177, 0.3525, 0.1448) (0.2711, 0.7722, 0.0973) (0.275, 0.643, 0.789) (0.253, 0.622, 0.713)
Table 2 Lattice parameter for LixMSO4 (M = Mg, Fe).
a b c
LiFeSO4F (calc)
LiFeSO4F (exp)
FeSO4F (calc)
FeSO4F (exp)
LiMgSO4F (calc)
LiMgSO4F (exp)
5.23 5.59 7.42
5.17 5.49 7.22
5.20 5.22 7.36
5.07 5.08 7.33
5.207 5.457 7.208
5.162 5.388 7.073
3. Crystal structure LiMgSO4F belongs to the P1 space group and its crystal structure is built up from corner sharing MgO4F2 octahedral chains along the c axis and SO4 tetrahedral which connects four MgO4F2 octahedrons [9]. This framework delimits cavities wherein Li is disordered between two halfoccupied positions. Table 1 lists the positional parameters of the structure. We take three typical Li configurations in a unit cell. Conf1 has two Li ions occupying the Li(1) site, conf2 has two Li ions occupying the Li(2) site and conf3 has one Li ion occupying a Li(1) site while the other one occupying a Li(2) site. Calculations show that conf1 has the lowest total energy, 49 meV and 27 meV lower than those of conf2 and conf3, respectively. Such a minor energy difference may lead to a disordered Li occupancy on the two distinct sites. The lattice parameters of LiMgSO4F calculated agree well with the experiment data, the overestimation is about 2%, as is shown in Table 2. GGA + U calculation tends to overestimate the bond length and thus the lattice parameters, calculations of other polyanion materials also give the same trend [7,12]. The same positional parameters as LiMgSO4F are adopted in the calculation of LiFeSO4F. Lattice parameters and internal coordinates of each atom fully relaxed. The total energy of conf1 is 60 meV and 30 meV lower compared with those of conf2 and conf3, respectively. Fig. 1 gives
Fig. 1. Schematic of the crystal structure of LiFeSO4F.
Fig. 2. The integrated differential spin density of Fe in LiFePO4 and LiFeSO4F.
the relaxed structure of LiFeSO4F. The calculated lattice parameters of LiFeSO4F and its delithiated form FeSO4F agree well with the reported data [8], with an error of 3%. Li extraction from LiFeSO4F leads to 6.6% shrinkage of the b value but very slight changes of a and c. 4. Electronic structure and phase separation during Li extraction For the Fe3d electrons, DFT + U calculation can well reproduce its electronic structure. For a given transition metal element, the U value is dependent on its oxidation state of the transition metal. In the olivine structure, the proper effective U values are 3.71 eV for LiFePO4 and 4.9 eV for FePO4. Calculation of the Li intercalation voltage requires the comparison of the total energy of LiFePO4 and FePO4. Calculations using an intermediate Ueff = 4.3 eV can well reproduce the electronic structure, Li intercalation voltage and phase diagram of LiFePO4 [11–13]. Fig. 2 gives the integrated differential spin density of Fe in LiFePO4 and LiFeSO4F with a U value of Ueff = 4.3 eV. The differential spin density is defined as N(up) − N(down) = ∫[ρ(↑) − ρ(↓)]dr. This eliminates the influences of other ions with no spin polarization. For ideal Fe2+ ion the spin configuration is t32g↑e2g↑t12g↓, and ∫[ρ(↑) − ρ(↓))]dr should be approximately 4. For ideal Fe3+, this value should be 5. The Fe–Fe distance is 3.87 Å in LiFePO4 and 3.71 Å in LiFeSO4F. As the differential spin density integration eliminates the charge of elements with no spin polarization, relatively large integration radius is adopted to take into account of all of the Fe3d electrons. A cutoff radius of 1.8 Å is appropriate to eliminate the influence of the adjacent Fe. The valence of Fe in LiFePO4 is 1.8+ while that in LiFeSO4F is 1.86+, indicating a slightly stronger inductive effect of the (SO4F)3− anion. Generally, larger U value should be adopted for the same element with higher valence, but the difference in U value required for such minor difference of the Fe valence can be neglected. The Li intercalation voltage can be calculated using the equation ΔG = −nEF, derived from the Nernst equation. In a solid phase the TΔS term contribution to ΔG is in the order of meV and the PΔV term contribution to ΔG is in the order of 10−3 meV respectively. Therefore, these terms can be neglected for calculating the voltage. Fig. 3 gives the U dependence of the Li intercalation voltage. At the Ueff value = 4.3 eV, the Li intercalation voltage is 3.7 eV. This value is 0.1 V larger than the measured one. This overestimation has happened also in the calculation of LiFePO4 [12]. Fig. 4 gives the calculated Density of States of LixFeSO4F. Pure LiFeSO4F is an insulator with a band gap of 3.6 eV. Its delithiated form FeSO4F has a band gap of 1.8 eV, which indicates also poor electronic conductor. In the case of Fe2+/Fe3+ coexisting phase (LixFeSO4F, 0 b x b 1), the band gap becomes significantly smaller as a result of the local distortion. Fig. 4d shows the band structure of Li0.5FeSO4F. At the Γ point, the gap is about
Z. Liu, X. Huang / Solid State Ionics 181 (2010) 1209–1213
Fig. 3. The relationship of the Ueff value and calculated Li intercalation potential.
1 eV. The direct gap at the Y and C point is about 0.8 eV. As a cathode material, Li deficiency forms easily by the electrochemical delithiation. The formation of a Li vacancy will introduce an electron hole, and electrons can hop in between Fe2+ and Fe3+. Its activation energy can be estimated as Eg/2 =0.4 eV. Due to the localization of the Fe3d electrons and the difference of Fe2+–O and Fe3+–O distance, electron transfer will cause the distortion of the local structure. A small polaron type conduction mechanism is expected. The activation energy for small polaron hopping can be analyzed using the Marcus theory [27]. The value
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of the activation energy could be estimated on the basis of adiabatic and non-adiabatic hopping. For adiabatic hopping, the adjacent ions can follow up the transfer of the electron. Maxich et al. used the elastic band method to simulate the adiabatic hopping process. This approach assumes that the move of ions is fast enough to follow the hopping of the electron. The calculated activation energy for small polaron hopping is 215 meV in LiFePO4 and 175 meV in FePO4. Maxich et al. tried to use the binding term of Li ion and small polaron to modify this value to fit the experimental data. We should note that when an electric field is applied, Li and electron move in the opposite direction, in the first several steps, the binding term is relatively larger. When the distance gets longer, the binding term will get smaller and can be neglected eventually. The calculated Ea for the first three steps in FePO4 are 280 meV, 175 meV and 180 meV. The calculated activation energy of 215 meV in LiFePO4 is much less than the value of the measured (0.6 eV) [3]. The activation energy can also be estimated using the non-adiabatic hopping, that is, when electron hopping occurs, the adjacent ions do not have enough time to follow the move of the electron. The activation energy is estimated as Eg/2 in this case. The band gap of Li7Fe8(PO4)8 is 0.8 eV, a band gap of 0.8 eV for LiFeSO4F hints that it has an electron conductivity comparable with that of LiFePO4. In the case of LiFePO4, phase separation of the LiFePO4 and FePO4 leads to a flat charge/discharge voltage curve [1]. We compare the total energy of LixFeSO4F and xLiFeSO4F + (1− x)FeSO4F to understand the phase transition behavior upon Li extraction. In the case of LixFeSO4F, there are different Li configurations. Configurations with the longest Li– Li distance are adopted in our calculation to represent the solid solution phase. Fig. 5 gives the formation energy calculated with different U values, the formation energy is defined as Eform = [E[Lix(FeSO4F)4] − xE[LiFeSO4F]− (1− x)E[FeSO4F]] / 4. A negative value of Eform indicates
Fig. 4. DOS of (a) LiFeSO4F, (b)FeSO4F, (c) Li0.5FeSO4F, and (d) band structure of Li0.5FeSO4 (spin down component).
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Z. Liu, X. Huang / Solid State Ionics 181 (2010) 1209–1213
Fig. 5. The relationship of Ueff value and formation energy of LixFeSO4F.
that a solid solution LixFeSO4F is energetically more favorable. A formation energy of 0.1 eV at x = 0.5 is required when Ueff = 4.3 eV. Phase separation of LiFeSO4F/FeSO4F is expected when Li is extracted from LiFeSO4F. However, due to the very small formation energy (0.1 eV/f.u.), the phase separation behavior could be tuned by changing of the particle size or temperature. This is consistent with the experimental results observed by X-ray diffraction [8]. 5. Kinetics for Li diffusion The ionic conductivity of LiFeSO4F is 4⁎10−6 S cm−1 at 147 °C, about 2⁎103 times larger than that of LiFePO4 [4,8]. The diffusion coefficient can be estimated from a microscopic model using the equation D=a2 ⁎ν⁎ exp(−Ea /kBT) [20,28]. Here a is the distance between the two sites for Li diffusion, ν is the attempt frequency, it is the same order magnitude of the phonon frequency. Once the activation energy Ea is known, the diffusion constant can be estimated by taking a typical value of 1013 Hz. For ideal crystal, the activation energy Ea =Ef/2+Em, here Ef is the Li vacancy formation energy and Em is the Li migration energy. For a cathode material, the phase Li1 − xFeSO4F forms after delithiation, and Li vacancy exists, the activation energy can be estimated by Ea =Em. However, for pure LiFeSO4F, the term Ef/2 cannot be neglected. The migration energy required for Li diffusion is calculated by the elastic band method. Fig. 6 gives also the energetically most favorable Li diffusion path (open circles in a curved line). A very low migration energy of 0.3 eV is
required for Li diffusion. Li diffusion along the c direction has a rather high activation energy ( 1.18 eV). Li diffusion along the a direction is less likely because the SO4 tetrahedron blocks the channel, while Li diffusion in the b direction is also less likely due to the long distance of 5.9 Å. Considering the lowest formation energy of an interstitial Li is 1.18 eV, Ea =Ef /2+Em, the activation energy for Li diffusion in pure LiFeSO4F is 0.89 eV. Alternating current measurement by Recham et al. shows that the conductivity in the measured temperature range is mainly ionic, and the measured activation energy is about 0.99 eV [8]. It is likely that the large cavities in the crystal structure allow the fast diffusion of Li ion. In the partially delithiated form Li1 − xFeSO4F, the estimated diffusion coefficient is 1.6⁎10−7 cm2 s−1, which is 104 higher than the calculated value of LiFePO4. The pre-factor A in D =Aexp(−Ea /kBT) could vary by several orders of magnitude [29]. It is also shown in our previous work on LiFePO4 that the calculated diffusion coefficient is 1.1⁎10−11 cm2 s−1, while the measured value is 10−13–10−14 cm2 s−1 [14]. Therefore, the above results mean that the diffusion of Li ion in Li1 − xFeSO4F is much faster that in LiFePO4.
6. Conclusion GGA+U calculation can reproduce the lattice parameter of LiFeSO4F with error less than 3%. The band gap of LiFeSO4F and FeSO4F is 3.6 eV and 1.8 eV, respectively. However, a small band gap in the partially delithiated phase Li1 − xFeSO4F facilitates a small polaron type conduction. Phase separation of LiFeSO4F and FeSO4F is expected during Li extraction, but it can be easily tuned due to the very low formation energy. From those calculations, it is seen that LiFeSO4F has much different physical properties with LiFePO4. The activation energy for Li diffusion is calculated to be 0.89 eV in pure LiFeSO4F, in well agreement with the experimentally measured value. However, in the partially delithiated form Li1 − xFeSO4F, a very low activation energy of 0.3 eV is obtained. It corresponds to a much higher Li diffusion coefficient. Extraordinary fast kinetics are expected if the phase separation of LiFeSO4F/FeSO4F can be suppressed by doping, particle size reduction, etc.
Acknowledgements This work is supported by the National High Technology Research and Development Program of China (863 Program) (Grant No. 2009AA033101). The calculations are finished at the Virtual Laboratory for Computational Chemistry, Computer NetWork Information Center, Chinese Academy of Sciences.
Fig. 6. Energetically most favorable Li diffusion path (open circles in a curved line) and corresponding energy profile.
Z. Liu, X. Huang / Solid State Ionics 181 (2010) 1209–1213
References [1] A.K. Padhi, K.S. Nanjundaswamy, J.B. Goodenough, J. Electrochem. Soc. 144 (1997) 1188. [2] A.K. Padhi, K.S. Nanjundaswamy, C. Masquelier, S. Okada, J.B. Goodenough, J. Electrochem. Soc. 144 (1997) 1609. [3] K. Zaghib, A. Mauger, J.B. Goodenough, F. Gendron, C.M. Julien, Chem. Mater. 19 (2007) 3740. [4] P.P. Prosini, M. Lisi, D. Zane, M. Pasquali, Solid State Ionics 148 (2002) 45. [5] M. Herstedt, M. Stjerndahl, A. Nyten, T. Gustafsson, H. Rensmo, H. Siegbahn, N. Ravet, M. Armand, J.O. Thomas, K. Edstrom, Electrochem. Solid-State Lett. 6 (2003) A202. [6] G. Kobayashi, S.I. Nishimura, M.S. Park, R. Kanno, M. Yashima, T. Ida, A. Yamada, Adv. Funct. Mater. 19 (2009) 395. [7] M.E. Arroyo-de Dompablo, M. Armand, J.M. Tarascon, U. Amador, Electrochem. Commun. 8 (2006) 1292. [8] N. Recham, J.N. Chotard, L. Dupont, C. Delacourt, W. Walker, M. Armand, J.M. Tarascon, Nat. Mater. 9 (2009) 68. [9] L. Sebastian, J. Gopalakrishnan, Y. Piffard, J. Mater. Chem. 12 (2002) 374. [10] A. Ivanov-Shitz, V. Kireev, O. Mel'nikov, L. Demianets, Crystallogr. Rep. 46 (2001) 864. [11] F. Zhou, K.S. Kang, T. Maxisch, G. Ceder, D. Morgan, Solid State Commun. 132 (2004) 181. [12] F. Zhou, M. Cococcioni, K. Kang, G. Ceder, Electrochem. Commun. 6 (2004) 1144. [13] F. Zhou, T. Maxisch, G. Ceder, Phys. Rev. Lett. 97 (2006) 155704.
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[14] Z.J. Liu, X.J. Huang, D.S. Wang, Solid State Commun. 147 (2008) 505. [15] F. Zhou, M. Cococcioni, C.A. Marianetti, D. Morgan, G. Ceder, Phys. Rev. B 70 (2004) 235121. [16] V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44 (1991) 943. [17] V.I. Anisimov, I.V. Solovyev, M.A. Korotin, M.T. Czyzyk, G.A. Sawatzky, Phys. Rev. B 48 (1993) 16929. [18] A.I. Liechtenstein, V.I. Anisimov, J. Zaanen, Phys. Rev. B 52 (1995) R5467. [19] C.Y. Ouyang, S.Q. Shi, Z.X. Wang, X.J. Huang, L.Q. Chen, Phys. Rev. B 69 (2004) 104303. [20] D. Morgan, A. Van der Ven, G. Ceder, Electrochem. Solid State Lett. 7 (2004) A30. [21] S. Shi, L. Liu, C. Ouyang, D.-s. Wang, Z. Wang, L. Chen, X. Huang, Phys. Rev. B 68 (2003) 195108. [22] S. Shi, C. Ouyang, Z. Xiong, L. Liu, Z. Wang, H. Li, D.-s. Wang, L. Chen, X. Huang, Phys. Rev. B 71 (2005) 144404. [23] G. Kresse, J. Furthmuler, Phys. Rev. B 54 (1996) 11169. [24] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [25] S.L. Dudarev, G.A. Botton, S.Y. Savrasov, C.J. Humphreys, A.P. Sutton, Phys. Rev. B 57 (1998) 1505. [26] G. Mills, H. Jonsson, G.K. Schenter, Surf. Sci. 324 (1995) 305. [27] R.A. Marcus, Rev. Mod. Phys. 65 (1993) 599. [28] E. Kaxiras, J. Erlebacher, Phys. Rev. Lett. 72 (1994) 1714. [29] W. Weppner, R.A. Huggins, J. Electrochem. Soc. 124 (1977) 1569.
Contents lists available at ScienceDirect
Solid State Ionics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s s i
Structural, electronic and Li diffusion properties of LiFeSO4F Zhaojun Liu, Xuejie Huang ⁎ Beijing National Laboratory for Condensed Matter, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
a r t i c l e
i n f o
Article history: Received 12 February 2010 Received in revised form 18 April 2010 Accepted 22 June 2010 Keywords: LiFeSO4F Li-ion battery First-principles calculation Band gap Activation energy
a b s t r a c t The structural, electronic and Li diffusion properties of LiFeSO4F were analyzed by first-principles calculation under the DFT + U framework. The difference of the calculated lattice parameters and the reported data is within 3%. The redox potential of Fe2+/Fe3+ versus Li metal is 3.7 V, and phase separation of LiFeSO4F and FeSO4F is expected during Li extraction. Pure LiFeSO4F is an insulator with a band gap of 3.6 eV, while the band gap in the partially delithiated form Li1 − xFeSO4F is obviously smaller. A very low Li migration energy of 0.3 eV is required in the partially delithiated form Li1 − xFeSO4F, and the diffusion coefficient is estimated to be about 1.6 ⁎ 10−7 cm2 s−1. © 2010 Elsevier B.V. All rights reserved.
1. Introduction In 1997, Pahdi et al. proposed the polyanion compound LiFePO4 as a potential cathode material for Li-ion batteries [1,2], and it has attracted much of the research interest since then. Carbon coating and particle size reduction are effective to overcome its drawbacks of low intrinsic electronic and ionic conductivity [3–6]. The redox potential of Fe2+/Fe3+ versus Li in LiFePO4 is 3.45 V. A polyanion group XO4 with stronger electro-negativity is expected to lead to a higher Li intercalation potential due to the stronger inductive effect [7]. Recently, Recham et al. reported the reversible Li insertion/extraction in LiFeSO4F with a redox potential of 3.6 V [8]. LiFeSO4F has the same structure with LiMgSO4F. LiMgSO4F shows a considerable Li-ion conductivity with an activation energy of 0.93 eV [9], significantly lower than that of γ-Li3PO4 which has an activation energy of about 1.2 eV [10]. Due to the large cavities in its crystal structure, LiFeSO4F is likely to have a higher Li-ion conductivity compared with LiFePO4. First-principles calculation is an effective method to calculate the physical and chemical properties of the materials for Li-ion battery [11–15]. As for transition metal compounds, Local Density Approximation (LDA)/Generalized Gradient Approximation (GGA) calculations tend to delocalize the correlated 3d electrons and lead to obvious errors [15]. A DFT + U approach was well established in the 1990s. It reserves the high efficiency of the LDA/GGA method and an explicit treatment of the electron correlation with a Hubbard type model for the d electrons is included. The electronic structure [11], Li intercalation potential [12,15], phase diagram [13] and Li diffusion
⁎ Corresponding author. Fax: +86 10 82649046. E-mail address: [email protected] (X. Huang). 0167-2738/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2010.06.043
kinetics [14] for a few commonly used Li-ion battery materials have been calculated with the DFT + U method. Calculation results are in good agreement with experiment [16–18]. As for LiFePO4, Li diffusion kinetics [19,20], doping effect [14,21], electronic structure, and magnetic properties [11,22] have been intensively studied with first-principles calculations and the results agree well with the experimental data. Calculations on LiFeSO4F will help to understand its properties and benefit for its applications in battery.
2. Calculation method Calculations are performed within the GGA + U framework as implemented by the VASP program [23]. Electronic exchange correlation is treated with the Generalized Gradient Approximation. Projector augmented wave (PAW) pseudo-potentials are used [24]. Perdew– Wang 91 type GGA exchange correlation functional is adopted. For all calculations, an energy cutoff of 600 eV is used. A K-point mesh of 6x6x4 is used in a unit cell. For larger supercells, K-point mesh of similar density is adopted. The on-site interaction of 3d electron was treated with the rotationally invariant approach proposed by Dudarev et al. [25]. In this approach the total energy is only dependent on the effective interaction parameter Ueff = U − J and insensitive to the J parameter with fixed Ueff. The elastic band method was used to calculate the activation energy for Li diffusion [26]. At first, structures with Li ion at the starting point and end point of a diffusion process are fully relaxed. Then a series of images are linearly interpolated between the starting and the end structures. Images are allowed to relax perpendicular to the diffusion path, and elastic force was applied to ensure that all ions relax to the minimum energy path.
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Z. Liu, X. Huang / Solid State Ionics 181 (2010) 1209–1213
Table 1 Positional parameters of LiMgSO4F. Atom
Wyckoff position
Occupancy
Coordinates (x/a, y/b, z/c)
S Mg(1) Mg(2) F O(1) O(2) O(3) O(4) Li(1) Li(2)
2i 1b 1a 2i 2i 2i 2i 2i 2i 2i
1 1 1 1 1 1 1 1 0.5 0.5
(0.3316, 0.6354, 0.2515) (0, 0, 0.5) (0, 0, 0) (0.1102, 0.9176, 0.7554) (0.6178, 0.7456, 0.4045) (0.1263, 0.6561, 0.3602) (0.3177, 0.3525, 0.1448) (0.2711, 0.7722, 0.0973) (0.275, 0.643, 0.789) (0.253, 0.622, 0.713)
Table 2 Lattice parameter for LixMSO4 (M = Mg, Fe).
a b c
LiFeSO4F (calc)
LiFeSO4F (exp)
FeSO4F (calc)
FeSO4F (exp)
LiMgSO4F (calc)
LiMgSO4F (exp)
5.23 5.59 7.42
5.17 5.49 7.22
5.20 5.22 7.36
5.07 5.08 7.33
5.207 5.457 7.208
5.162 5.388 7.073
3. Crystal structure LiMgSO4F belongs to the P1 space group and its crystal structure is built up from corner sharing MgO4F2 octahedral chains along the c axis and SO4 tetrahedral which connects four MgO4F2 octahedrons [9]. This framework delimits cavities wherein Li is disordered between two halfoccupied positions. Table 1 lists the positional parameters of the structure. We take three typical Li configurations in a unit cell. Conf1 has two Li ions occupying the Li(1) site, conf2 has two Li ions occupying the Li(2) site and conf3 has one Li ion occupying a Li(1) site while the other one occupying a Li(2) site. Calculations show that conf1 has the lowest total energy, 49 meV and 27 meV lower than those of conf2 and conf3, respectively. Such a minor energy difference may lead to a disordered Li occupancy on the two distinct sites. The lattice parameters of LiMgSO4F calculated agree well with the experiment data, the overestimation is about 2%, as is shown in Table 2. GGA + U calculation tends to overestimate the bond length and thus the lattice parameters, calculations of other polyanion materials also give the same trend [7,12]. The same positional parameters as LiMgSO4F are adopted in the calculation of LiFeSO4F. Lattice parameters and internal coordinates of each atom fully relaxed. The total energy of conf1 is 60 meV and 30 meV lower compared with those of conf2 and conf3, respectively. Fig. 1 gives
Fig. 1. Schematic of the crystal structure of LiFeSO4F.
Fig. 2. The integrated differential spin density of Fe in LiFePO4 and LiFeSO4F.
the relaxed structure of LiFeSO4F. The calculated lattice parameters of LiFeSO4F and its delithiated form FeSO4F agree well with the reported data [8], with an error of 3%. Li extraction from LiFeSO4F leads to 6.6% shrinkage of the b value but very slight changes of a and c. 4. Electronic structure and phase separation during Li extraction For the Fe3d electrons, DFT + U calculation can well reproduce its electronic structure. For a given transition metal element, the U value is dependent on its oxidation state of the transition metal. In the olivine structure, the proper effective U values are 3.71 eV for LiFePO4 and 4.9 eV for FePO4. Calculation of the Li intercalation voltage requires the comparison of the total energy of LiFePO4 and FePO4. Calculations using an intermediate Ueff = 4.3 eV can well reproduce the electronic structure, Li intercalation voltage and phase diagram of LiFePO4 [11–13]. Fig. 2 gives the integrated differential spin density of Fe in LiFePO4 and LiFeSO4F with a U value of Ueff = 4.3 eV. The differential spin density is defined as N(up) − N(down) = ∫[ρ(↑) − ρ(↓)]dr. This eliminates the influences of other ions with no spin polarization. For ideal Fe2+ ion the spin configuration is t32g↑e2g↑t12g↓, and ∫[ρ(↑) − ρ(↓))]dr should be approximately 4. For ideal Fe3+, this value should be 5. The Fe–Fe distance is 3.87 Å in LiFePO4 and 3.71 Å in LiFeSO4F. As the differential spin density integration eliminates the charge of elements with no spin polarization, relatively large integration radius is adopted to take into account of all of the Fe3d electrons. A cutoff radius of 1.8 Å is appropriate to eliminate the influence of the adjacent Fe. The valence of Fe in LiFePO4 is 1.8+ while that in LiFeSO4F is 1.86+, indicating a slightly stronger inductive effect of the (SO4F)3− anion. Generally, larger U value should be adopted for the same element with higher valence, but the difference in U value required for such minor difference of the Fe valence can be neglected. The Li intercalation voltage can be calculated using the equation ΔG = −nEF, derived from the Nernst equation. In a solid phase the TΔS term contribution to ΔG is in the order of meV and the PΔV term contribution to ΔG is in the order of 10−3 meV respectively. Therefore, these terms can be neglected for calculating the voltage. Fig. 3 gives the U dependence of the Li intercalation voltage. At the Ueff value = 4.3 eV, the Li intercalation voltage is 3.7 eV. This value is 0.1 V larger than the measured one. This overestimation has happened also in the calculation of LiFePO4 [12]. Fig. 4 gives the calculated Density of States of LixFeSO4F. Pure LiFeSO4F is an insulator with a band gap of 3.6 eV. Its delithiated form FeSO4F has a band gap of 1.8 eV, which indicates also poor electronic conductor. In the case of Fe2+/Fe3+ coexisting phase (LixFeSO4F, 0 b x b 1), the band gap becomes significantly smaller as a result of the local distortion. Fig. 4d shows the band structure of Li0.5FeSO4F. At the Γ point, the gap is about
Z. Liu, X. Huang / Solid State Ionics 181 (2010) 1209–1213
Fig. 3. The relationship of the Ueff value and calculated Li intercalation potential.
1 eV. The direct gap at the Y and C point is about 0.8 eV. As a cathode material, Li deficiency forms easily by the electrochemical delithiation. The formation of a Li vacancy will introduce an electron hole, and electrons can hop in between Fe2+ and Fe3+. Its activation energy can be estimated as Eg/2 =0.4 eV. Due to the localization of the Fe3d electrons and the difference of Fe2+–O and Fe3+–O distance, electron transfer will cause the distortion of the local structure. A small polaron type conduction mechanism is expected. The activation energy for small polaron hopping can be analyzed using the Marcus theory [27]. The value
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of the activation energy could be estimated on the basis of adiabatic and non-adiabatic hopping. For adiabatic hopping, the adjacent ions can follow up the transfer of the electron. Maxich et al. used the elastic band method to simulate the adiabatic hopping process. This approach assumes that the move of ions is fast enough to follow the hopping of the electron. The calculated activation energy for small polaron hopping is 215 meV in LiFePO4 and 175 meV in FePO4. Maxich et al. tried to use the binding term of Li ion and small polaron to modify this value to fit the experimental data. We should note that when an electric field is applied, Li and electron move in the opposite direction, in the first several steps, the binding term is relatively larger. When the distance gets longer, the binding term will get smaller and can be neglected eventually. The calculated Ea for the first three steps in FePO4 are 280 meV, 175 meV and 180 meV. The calculated activation energy of 215 meV in LiFePO4 is much less than the value of the measured (0.6 eV) [3]. The activation energy can also be estimated using the non-adiabatic hopping, that is, when electron hopping occurs, the adjacent ions do not have enough time to follow the move of the electron. The activation energy is estimated as Eg/2 in this case. The band gap of Li7Fe8(PO4)8 is 0.8 eV, a band gap of 0.8 eV for LiFeSO4F hints that it has an electron conductivity comparable with that of LiFePO4. In the case of LiFePO4, phase separation of the LiFePO4 and FePO4 leads to a flat charge/discharge voltage curve [1]. We compare the total energy of LixFeSO4F and xLiFeSO4F + (1− x)FeSO4F to understand the phase transition behavior upon Li extraction. In the case of LixFeSO4F, there are different Li configurations. Configurations with the longest Li– Li distance are adopted in our calculation to represent the solid solution phase. Fig. 5 gives the formation energy calculated with different U values, the formation energy is defined as Eform = [E[Lix(FeSO4F)4] − xE[LiFeSO4F]− (1− x)E[FeSO4F]] / 4. A negative value of Eform indicates
Fig. 4. DOS of (a) LiFeSO4F, (b)FeSO4F, (c) Li0.5FeSO4F, and (d) band structure of Li0.5FeSO4 (spin down component).
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Fig. 5. The relationship of Ueff value and formation energy of LixFeSO4F.
that a solid solution LixFeSO4F is energetically more favorable. A formation energy of 0.1 eV at x = 0.5 is required when Ueff = 4.3 eV. Phase separation of LiFeSO4F/FeSO4F is expected when Li is extracted from LiFeSO4F. However, due to the very small formation energy (0.1 eV/f.u.), the phase separation behavior could be tuned by changing of the particle size or temperature. This is consistent with the experimental results observed by X-ray diffraction [8]. 5. Kinetics for Li diffusion The ionic conductivity of LiFeSO4F is 4⁎10−6 S cm−1 at 147 °C, about 2⁎103 times larger than that of LiFePO4 [4,8]. The diffusion coefficient can be estimated from a microscopic model using the equation D=a2 ⁎ν⁎ exp(−Ea /kBT) [20,28]. Here a is the distance between the two sites for Li diffusion, ν is the attempt frequency, it is the same order magnitude of the phonon frequency. Once the activation energy Ea is known, the diffusion constant can be estimated by taking a typical value of 1013 Hz. For ideal crystal, the activation energy Ea =Ef/2+Em, here Ef is the Li vacancy formation energy and Em is the Li migration energy. For a cathode material, the phase Li1 − xFeSO4F forms after delithiation, and Li vacancy exists, the activation energy can be estimated by Ea =Em. However, for pure LiFeSO4F, the term Ef/2 cannot be neglected. The migration energy required for Li diffusion is calculated by the elastic band method. Fig. 6 gives also the energetically most favorable Li diffusion path (open circles in a curved line). A very low migration energy of 0.3 eV is
required for Li diffusion. Li diffusion along the c direction has a rather high activation energy ( 1.18 eV). Li diffusion along the a direction is less likely because the SO4 tetrahedron blocks the channel, while Li diffusion in the b direction is also less likely due to the long distance of 5.9 Å. Considering the lowest formation energy of an interstitial Li is 1.18 eV, Ea =Ef /2+Em, the activation energy for Li diffusion in pure LiFeSO4F is 0.89 eV. Alternating current measurement by Recham et al. shows that the conductivity in the measured temperature range is mainly ionic, and the measured activation energy is about 0.99 eV [8]. It is likely that the large cavities in the crystal structure allow the fast diffusion of Li ion. In the partially delithiated form Li1 − xFeSO4F, the estimated diffusion coefficient is 1.6⁎10−7 cm2 s−1, which is 104 higher than the calculated value of LiFePO4. The pre-factor A in D =Aexp(−Ea /kBT) could vary by several orders of magnitude [29]. It is also shown in our previous work on LiFePO4 that the calculated diffusion coefficient is 1.1⁎10−11 cm2 s−1, while the measured value is 10−13–10−14 cm2 s−1 [14]. Therefore, the above results mean that the diffusion of Li ion in Li1 − xFeSO4F is much faster that in LiFePO4.
6. Conclusion GGA+U calculation can reproduce the lattice parameter of LiFeSO4F with error less than 3%. The band gap of LiFeSO4F and FeSO4F is 3.6 eV and 1.8 eV, respectively. However, a small band gap in the partially delithiated phase Li1 − xFeSO4F facilitates a small polaron type conduction. Phase separation of LiFeSO4F and FeSO4F is expected during Li extraction, but it can be easily tuned due to the very low formation energy. From those calculations, it is seen that LiFeSO4F has much different physical properties with LiFePO4. The activation energy for Li diffusion is calculated to be 0.89 eV in pure LiFeSO4F, in well agreement with the experimentally measured value. However, in the partially delithiated form Li1 − xFeSO4F, a very low activation energy of 0.3 eV is obtained. It corresponds to a much higher Li diffusion coefficient. Extraordinary fast kinetics are expected if the phase separation of LiFeSO4F/FeSO4F can be suppressed by doping, particle size reduction, etc.
Acknowledgements This work is supported by the National High Technology Research and Development Program of China (863 Program) (Grant No. 2009AA033101). The calculations are finished at the Virtual Laboratory for Computational Chemistry, Computer NetWork Information Center, Chinese Academy of Sciences.
Fig. 6. Energetically most favorable Li diffusion path (open circles in a curved line) and corresponding energy profile.
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References [1] A.K. Padhi, K.S. Nanjundaswamy, J.B. Goodenough, J. Electrochem. Soc. 144 (1997) 1188. [2] A.K. Padhi, K.S. Nanjundaswamy, C. Masquelier, S. Okada, J.B. Goodenough, J. Electrochem. Soc. 144 (1997) 1609. [3] K. Zaghib, A. Mauger, J.B. Goodenough, F. Gendron, C.M. Julien, Chem. Mater. 19 (2007) 3740. [4] P.P. Prosini, M. Lisi, D. Zane, M. Pasquali, Solid State Ionics 148 (2002) 45. [5] M. Herstedt, M. Stjerndahl, A. Nyten, T. Gustafsson, H. Rensmo, H. Siegbahn, N. Ravet, M. Armand, J.O. Thomas, K. Edstrom, Electrochem. Solid-State Lett. 6 (2003) A202. [6] G. Kobayashi, S.I. Nishimura, M.S. Park, R. Kanno, M. Yashima, T. Ida, A. Yamada, Adv. Funct. Mater. 19 (2009) 395. [7] M.E. Arroyo-de Dompablo, M. Armand, J.M. Tarascon, U. Amador, Electrochem. Commun. 8 (2006) 1292. [8] N. Recham, J.N. Chotard, L. Dupont, C. Delacourt, W. Walker, M. Armand, J.M. Tarascon, Nat. Mater. 9 (2009) 68. [9] L. Sebastian, J. Gopalakrishnan, Y. Piffard, J. Mater. Chem. 12 (2002) 374. [10] A. Ivanov-Shitz, V. Kireev, O. Mel'nikov, L. Demianets, Crystallogr. Rep. 46 (2001) 864. [11] F. Zhou, K.S. Kang, T. Maxisch, G. Ceder, D. Morgan, Solid State Commun. 132 (2004) 181. [12] F. Zhou, M. Cococcioni, K. Kang, G. Ceder, Electrochem. Commun. 6 (2004) 1144. [13] F. Zhou, T. Maxisch, G. Ceder, Phys. Rev. Lett. 97 (2006) 155704.
1213
[14] Z.J. Liu, X.J. Huang, D.S. Wang, Solid State Commun. 147 (2008) 505. [15] F. Zhou, M. Cococcioni, C.A. Marianetti, D. Morgan, G. Ceder, Phys. Rev. B 70 (2004) 235121. [16] V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44 (1991) 943. [17] V.I. Anisimov, I.V. Solovyev, M.A. Korotin, M.T. Czyzyk, G.A. Sawatzky, Phys. Rev. B 48 (1993) 16929. [18] A.I. Liechtenstein, V.I. Anisimov, J. Zaanen, Phys. Rev. B 52 (1995) R5467. [19] C.Y. Ouyang, S.Q. Shi, Z.X. Wang, X.J. Huang, L.Q. Chen, Phys. Rev. B 69 (2004) 104303. [20] D. Morgan, A. Van der Ven, G. Ceder, Electrochem. Solid State Lett. 7 (2004) A30. [21] S. Shi, L. Liu, C. Ouyang, D.-s. Wang, Z. Wang, L. Chen, X. Huang, Phys. Rev. B 68 (2003) 195108. [22] S. Shi, C. Ouyang, Z. Xiong, L. Liu, Z. Wang, H. Li, D.-s. Wang, L. Chen, X. Huang, Phys. Rev. B 71 (2005) 144404. [23] G. Kresse, J. Furthmuler, Phys. Rev. B 54 (1996) 11169. [24] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [25] S.L. Dudarev, G.A. Botton, S.Y. Savrasov, C.J. Humphreys, A.P. Sutton, Phys. Rev. B 57 (1998) 1505. [26] G. Mills, H. Jonsson, G.K. Schenter, Surf. Sci. 324 (1995) 305. [27] R.A. Marcus, Rev. Mod. Phys. 65 (1993) 599. [28] E. Kaxiras, J. Erlebacher, Phys. Rev. Lett. 72 (1994) 1714. [29] W. Weppner, R.A. Huggins, J. Electrochem. Soc. 124 (1977) 1569.