ARTICLE pubs.acs.org/JPCC
Hybrid Density Functional Calculations and Molecular Dynamics Study of Lithium Fluorosulphate, A Cathode Material for Lithium-Ion Batteries Muhammad Ramzan,*,† Sebastien Lebegue,‡ Tae W. Kang,§ and Rajeev Ahuja|| †
Condensed Matter Theory Group, Department of Physics and Astronomy, Box 516, Uppsala University, SE-751 20 Uppsala, Sweden Laboratoire de Cristallographie, Resonance Magnetique et Modelisations (CRM2, UMR CNRS 7036) Institut Jean Barriol, Nancy Universite BP 239, Boulevard des Aiguillettes 54506 Vandoeuvre-les-Nancy, France § Quantum Functional Semiconductor Research Center, Dongguk University, Seoul 100-715, Republic of Korea Applied Materials Physics, Department of Materials and Engineering, Royal Institute of Technology (KTH), SE-100 44 Stockholm, Sweden
)
‡
ABSTRACT: In this paper, we use hybrid density functional theory to calculate the electronic structure of lithium fluorosulphate (LiFeSO4F), which has been found recently to be an excellent cathode material for lithium-ion batteries by Recham et al. (Nat. Mater. 2010, 9, 68). We calculate the average intercalation voltage of the corresponding battery, and we also analyze the electron charge distribution through Bader's analysis. Our results are in good agreement with the available experimental values. Then we studied the Li-diffusion in lithium fluorosulphate with ab initio molecular dynamics and found it to be three-dimensional.
’ INTRODUCTION The search for new and renewable energy resources is a popular demand of our time, as it is considered that the present fossil-fuel provisions are going to deplete.1,2 Global warming and environmental pollution also require some alternate green energy sources and the replacement of the present oil-based supplies with electric equipment.1,2 However, to ensure a proper continuation of this supply, the development of better energy storage systems is the key issue. Different kinds of batteries have been developed to meet these requirements.3,4 Rechargeable lithium ion batteries are a possibility to store this energy, having high energy density and output voltage among the best in known rechargeable devices.5-7 In particular, olivine (LiFePO4) is considered as a potential candidate, which has been studied thoroughly,8-15 but the development of the corresponding technology is now limited due to the one-dimensional Li-ion transport in olivine.16-19 In the search of new promising materials, Ellis et al.20 have presented Li2FePO4F and Na2FePO4F as potential cathode materials for lithium ion batteries, which were further studied with density functional theory calculations.21-23 Recently, Recham et al.24 have presented LiFeSO4F as a possible positive electrode, showing very promising results, which were later on confirmed by ab initio calculations with the GGA þ U method.25 In the present work, we study the crystal and electronic structure of lithium fluorosulphate (LiFeSO4F) and of FeSO4F and calculate the average intercalation voltage of the correspondr 2011 American Chemical Society
ing battery on the basis of Heyd-Scuseria-Ernzerhof (HSE06) hybrid density functional calculations. Recently, Chevrier et al.26 have used this functional to calculate the redox reaction and formation energies of transition metal compounds of interest for Li-ion batteries. Then, we investigate the electron density distribution in the LiFeSO4F and FeSO4F crystals using Bader's analysis. Moreover, using ab initio molecular dynamics simulations, we study the transport properties of Li in LiFeSO4F. Finally, in the last section, we offer our conclusions.
’ METHODS AND COMPUTATIONAL DETAILS We have used the HSE06 functional27-29 to perform hybrid density functional calculations as implemented in the Vienna ab initio Simulation Package (VASP), using the PAW (projector augmented wave) method.30 Starting from the PBE0 funcand the tional31 that combines the PBE exchange term EPBE x together with HF exchange term EHF correlation term EPBE c x such that: PBE EPBE0 ¼ 1=4EHF þ EPBE x x þ 3=4Ex c
ð1Þ
Then the long-range HF exchange term is replaced by the longrange PBE exchange term to save computational time, which Received: November 6, 2010 Revised: December 13, 2010 Published: January 12, 2011 2600
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Table 1. Lattice Parameters, Volume of the Cell, and the Magnetic Order of Fe Moments of LiFeSO4F and FeSO4Fa compound LiFeSO4F
method
a (Å)
mag. order
V (Å3)
R (deg)
β (deg)
γ (deg)
AFM
5.18
5.52
7.32
185.37
106.45
107.67
97.98
GGA þ U
AFM
5.13
5.46
7.14
177.01
106.43
107.71
98.07
5.1747(3)
5.4943(3)
7.2224(3)
182.559(16)
106.522(3)
107.210(3)
97.791(3)
5.11
7.39
166.81
111.16
111.21
88.55
HSE06
AFM
5.12
GGA þ U
AFM
5.05
5.03
7.26
160.43
109.65
111.13
89.89
5.0735(2)
5.0816(3)
7.3363(4)
163.640(12)
110.975(4)
111.189(4)
88.157(3)
expt a
c (Å)
HSE06 expt
FeSO4F
b (Å)
The GGA þ U (AFM) results are from ref 25, and the experimental values are from ref 24.
Table 2. Fractional Coordinates of S, Fe, F, O, and Li of LiFeSO4F and FeSO4F compound LiFeSO4F
FeSO4F
element
site
x
y
z
S
2i
0.3213
0.6368
0.2468
Fe(1)
1b
0.0000
0.0000
0.5000
Fe(2)
1a
0.0000
0.0000
0.0000
F
2i
0.1211
0.9090
0.7545
O(1)
2i
0.5905
0.7628
0.4092
O(2)
2i
0.0934
0.6458
0.3275
O(3)
2i
0.3240
0.3632
0.1507
O(4) Li
2i 2i
0.2748 0.2722
0.7624 0.6364
0.0910 0.8002
S
2i
0.3796
0.6190
0.2499
Fe(1)
1b
0.0000
0.0000
0.5000
Fe(2)
1a
0.0000
0.0000
0.0000
F
2i
0.0807
0.9190
0.7499
O(1)
2i
0.6856
0.6843
0.3389
O(2)
2i
0.2668
0.7395
0.4146
O(3) O(4)
2i 2i
0.3176 0.2576
0.3124 0.7298
0.1617 0.0840
gives the HSE06 formulation: , SR ðμÞ þ 3=4EPBE, SR ðμÞ þ EPBE, LR ðμÞ þ EPBE EHSE ¼ 1=4EHF xc x x x c ð2Þ -1
where μ = 0.207 is a screening parameter. We have fully optimized the atomic geometries, and the remaining forces on each atom were less than a threshold value of 10-5 eV/Å. The Gaussian smearing method with a 0.2 eV smearing width was used for the Brillouin zone integration. We have used 8 8 6 k-points to sample the Brillouin zone, using the MonkhorstPack32 method to generate the k-points mesh. A plane-wave cutoff of 800 eV was found suitable to get a sufficient convergence. The detailed procedure for the computation of the intercalation voltage of the LiFeSO4F battery can be found elsewhere.33 Then, to study the diffusion of lithium in LiFeSO4F, we have performed ab initio molecular dynamics calculations with VASP.34,35 To keep the computational time to a reasonable value, we have used the PBE36 variant of the generalized gradient approximation (GGA) for the exchange-correlation functional. The Verlet algorithm is used to integrate the equation of motion, with a time step of 3 fs, during a time scale of 1.5 ps. The simulations were performed in the normal volume and temperature (NVT) ensemble, with a temperature of 1200 K. From this simulation, the corresponding mean-square displacements (MSDs) were calculated and analyzed.37 27
’ RESULTS AND DISCUSSION LiFeSO4F and FeSO4F have been reported to crystallize in a triclinic cell with the space group P1, possessing lattice parameters, a = 5.1747(3) Å, b = 5.4943(3) Å, c = 7.2224(3) Å, R = 106.522(3)°, β= 107.210(3)°, and γ = 97.791(3)° for LiFeSO4F and a = 5.0735(2) Å, b = 5.0816(3) Å, c = 7.3363(4) Å, R = 110.975(4)°, β= 111.189(4)°, and γ = 88.157(3)° for FeSO4F, respectively.24 The atomic coordinates in LiFeSO4F were given in the experimental paper24 (except the position of Li, for which two different sites are possible), but the atomic coordinates in FeSO4F were not provided. Later on, the detailed crystal structures of LiFeSO4F and FeSO4F were determined with the GGA þ U approximation for an antiferromagnetic (AFM) ordering of the Fe magnetic moments in the cell.25 Hence, we have used the available experimental24 and theoretical25 data for LiFeSO4F and FeSO4F to set up our calculations. In the present work, we have performed a full structure relaxation (atomic coordinates, volume, and shape of the cell), with the same AFM order, using the HSE06 functional. In Table 1, we provide the values of the structural parameters of the LiFeSO4F and FeSO4F compounds, calculated from the HSE06 hybrid functional, conventional DFT method (GGA þ U), as well as the available experimental values to compare the accuracy of the hybrid density functional (HSE06) and DFT þ U methods. From Table 1, it appears that while the DFT þ U method is underestimating the values of the structural parameters of LiFeSO4F and FeSO4F, the HSE06 hybrid functional is slightly overestimating them, although in both cases the agreement is quite good, although better in the case of LiFeSO4F with HSE06 than with the GGA þ U method. It is striking that, in both cases, the largest error concerns the c lattice parameter. It could be related to the delicate description of the magnetic interactions that happens in this direction or maybe to the particular shape of the crystal structure. In Table 2, we have listed the atomic positions of all of the atoms in the LiFeSO4F and FeSO4F structures, determined with the HSE06 functional. We observe that our calculated values of the fractional coordinates of LiFeSO4F, calculated with the HSE06 functional are in better agreement with the available experimental values than the results obtained from the GGA þ U method (see Table 2 in ref 25 and Table 2 in the experimental paper in ref 24). For FeSO4F, the corresponding experimental data, concerning the atomic coordinates, has not been published, but it is fair to assume that our results obtained with the HSE06 functional will be closer to the experiment than the ones obtained from GGA þ U. Also, to analyze more deeply our results, we are presenting the partial density of states (PDOS) of LiFeSO4F (left part of Figure 1) and FeSO4F (right part of Figure 1) at equilibrium 2601
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Figure 1. Partial density of states of different atoms computed with the HSE06 functional for an antiferromagnetic ordering of the Fe atoms. Left: LiFeSO4F. Right: FeSO4F. The Fermi level is put at 0 eV.
Table 3. Calculated Bader Atomic Charges (In Units of e) with HSE06 Functional for LiFeSO4F and FeSO4F atom
LiFeSO4F
FeSO4F
S
þ5.82
þ5.82
Fe
þ1.68
þ2.25
F
-0.87
-0.77
O(1) O(2)
-1.95 -1.87
-1.85 -1.78
O(3)
-1.89
-1.83
O(4)
-1.90
-1.85
Li
þ0.98
Table 4. Calculated Intercalation Voltages of LiFeSO4F Batterya composition LiFeSO4F/FeSO4F
method
voltage (volts)
HSE06
3.54
GGAþU
3.69
Expt
3.6
a
The GGA þ U value is from ref 25, and the experimental value is from ref 24.
volume, for an AFM order of the magnetic moments, computed with the HSE06 functional. Comparing the two PDOS plots, they show some significant differences, which are obviously linked to the removal of the Li ion. For instance, the peak at -1 eV in the PDOS of Fe in LiFeSO4F has totally disappeared in the corresponding Fe-PDOS of FeSO4F. As a consequence, the PDOS of S, O, and F are also significantly changed, due to a modified hybridization with the Fe ion. Both LiFeSO4F and FeSO4F appeared to be wide band gap insulators. The band gap values calculated by the total DOS are 3.1 and 2.8 eV with the HSE06 functional and 2.6 and 1.3 eV with GGA þ U for LiFeSO4F and FeSO4F, respectively. The electronic structure can also be analyzed with the help of Bader's theory of atoms in molecules,38-40 in particular to analyze the charge densities of LiFeSO4F and FeSO4F. Within this theory, each basin belonging to a given atom can be defined with the use of zero flux surfaces of the charge density. Then, the charge density is integrated over the whole basin to get the charge assigned to that particular atom. In Table 3, we are reporting the corresponding charges of our studied compounds. It appears that the state of the Fe atom changes significantly upon the desintercalation process, as we have
seen in the PDOS plots. In LiFeSO4F, the iron atom possesses a charge of þ1.68, which has been increased to a value of þ2.25 in FeSO4F, which corresponds to the change from FeII ion to FeIII ion. The other atoms follow the basic rules of chemistry: Li and S are electropositive, while O and F are electronegative. Then, we have calculated the intercalation voltage of the LiFeSO4F/FeSO4F battery and compare it to the result obtained with the GGA þ U approximation, as well as the experimental result, as shown in Table 4. In terms of intercalation voltage of the LiFeSO4F battery, both theoretical methods are equally suitable to reproduce the experimental result. However, the HSE06 hybrid functional performs better for the structural properties than the DFT þ U method, and more importantly, it does not suffer from the fact that the U parameter has to be adjusted. Therefore, we believe that the HSE06 functional can be used as an alternate or an even better method than the DFT þ U to study and predict the properties of materials for Li-ion batteries. Finally, we have performed ab initio molecular dynamics simulations on LiFeSO4F. In Figure 2, we present our calculated MSDs of all of the species in LiFeSO4F as a function of time. It appears clearly that, while the Li specie shows a diffusive behavior, the other species show only a limited diffusion and in fact correspond to oscillations around their initial positions. To study in detail the diffusion of Li, we have projected its MSD along the three Cartesian axes (second plot of Figure 2). Although the diffusion is not isotropic, it happens along the three directions, with the diffusion along the z direction being higher than along the x and y directions. This confirms that the ionic transport properties of LiFeSO4F are superior to the ones of LiFePO4, for which the transport is mainly one-dimensional.41
’ CONCLUSIONS To conclude, we have successfully reproduced the structural parameters of LiFeSO4F and FeSO4F compounds and the intercalation voltage of the corresponding LiFeSO4F battery with the use of HSE06 hybrid functional. We have also shown that the HSE06 performs well to reproduce the experimental crystal structures of LiFeSO4F and FeSO4F compounds and equally well with DFT þ U to reproduce the experimental intercalation voltage, without the need to adjust the U and J parameters of DFT þ U. We have also explained the electronic structure and charge distribution of LiFeSO4F and FeSO4F compounds on the basis of this hybrid density functional. Thus, the HSE06 functional is a suitable method to study LiFeSO4F and FeSO4F and more generally materials for Li-ion batteries. Furthermore, we 2602
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Figure 2. Up: mean square displacements of all of the species of LiFeSO4F computed by molecular dynamics calculations at 1200 Ks. Down: mean square displacement of Li in LiFeSO4F projected on each Cartesian axis.
have also performed molecular dynamics simulations to study the diffusion of lithium in LiFeSO4F and predict that it is threedimensional, which is a clear advantage over other cathode materials of interest for Li-ion batteries, such as LiFePO4. Finally, we expect that our work will initiate further experiments on the LiMSO4F family of compounds and eventually that it will help to design new materials for energy storage.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Phone: þ46184715850. Fax: þ46184715999.
’ ACKNOWLEDGMENT We would like to acknowledge STINT, Formas, and FUTURA for financial support. M.R. acknowledges financial support from Higher Education Commission of Pakistan. SNIC and UPPMAX have provided computing time for this project. S.L. acknowledges financial support from ANR PNANO Grant No. ANR-06-NANO-053-02 and computer time using HPC resources from GENCI-CCRT/CINES (Grant 2010-085106). This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2010-0000751) and Leading Foreign Research Institute Recruitment Program through NRF-MEST (No. 2010-00218). ’ REFERENCES (1) Kates, R. W.; Clark, W. C.; Correll, R.; Hall, J. M.; Jaeger, C. C.; Lowe, I. Science 2001, 292, 641–642.
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