Thermophysical Properties of LiFePO₄: DFT+U Computations Combined with a Thermodynamically Self-Consistent (TSC) Method

Introduction LiFePO 4 (LFP) was proposed by Padhi et al. 1 in 1997 as a promising cathode material for Li-ion batteries and very soon became the center of attention for researchers and industries in energy fields. Nowadays, it is commercialized and available in mass production through different methods. A lot of improvements in terms of material and production process have been achieved since its nascence. Nevertheless, our thermodynamic knowledge about LFP is limited to handful experimental works 2 on heat capacity and few computational studies 3 to estimate elastic properties at ground state condition. Enlarging our knowledge about thermophysical properties of LFP such as elastic properties, Debye temperature, heat capacity and also thermal expansion at higher temperatures is a crucial key to expand the thermodynamic information, and consequently to answer the arising questions about phase equilibrium in production process. Methodology Here, we present the abovementioned thermophysical properties of LFP in a wide range of temperature by Density Functional Theory (DFT) and a new Thermodynamically Self-Consistent ( TSC) method 4 . The TSC method is, in summary, an extension of the quasi-harmonic approximation (QHA) satisfying the Maxwell relations and thus ensuring thermodynamic consistency. For future, we assay the effect of vacancy and also elemental substitution on thermophysical and electrochemical properties of LFP. Computational Details. We use Vienna ab initio Simulation Package (VASP) 5 to address our aim. Projected Augmented Wave (PAW) approach 6 and the General Gradient Approximation (GGA) of Perdew, Burke and Ernzerhof (PBE) 7 are used to represent the electron-ion core and electron-electron interactions, respectively. The Hubbard U correction to the GGA (GGA+U) equal to 5.3 eV for Fe in oxide systems is employed to address a correct band structure and binding energies. Our results indicate that, a cut-off energy of 520 eV and 3×4×5 Γ-centered k-points grid in first Brillouin zone with a Gaussian smearing parameter σ of 0.02 eV ensure the accuracy in energy of the system to be more than 0.01 meV. Acknowledgement. The authors would like to thank the Natural Science and Engineering Research Council of Canada (NSERC) for the financial support awarded to this project as part of the Automotive Partnership Canada (APC) program. References 1. Padhi, A. K.; Nanjundaswamy, K. S.; Goodenough, J. B., Phospho‐olivines as Positive‐Electrode Materials for Rechargeable Lithium Batteries. Journal of The Electrochemical Society 1997, 144 (4), 1188-1194. 2. (a) Loos, S.; Gruner, D.; Abdel-Hafiez, M.; Seidel, J.; Hüttl, R.; Wolter, A. U. B.; Bohmhammel, K.; Mertens, F., Heat capacity (Cp) and entropy of olivine-type LiFePO4 in the temperature range (2 to 773) K. The Journal of Chemical Thermodynamics 2015, 85 (0), 77-85; (b) Nanda, J.; Martha, S. K.; Porter, W. D.; Wang, H.; Dudney, N. J.; Radin, M. D.; Siegel, D. J., Thermophysical properties of LiFePO4 cathodes with carbonized pitch coatings and organic binders: Experiments and first-principles modeling. Journal of Power Sources 2014, 251 (0), 8-13. 3. (a) Maxisch, T.; Ceder, G., Elastic properties of olivine LixFePO4 from first principles. Physical Review B 2006, 73 (17), 174112; (b) Shang, S. L.; Wang, Y.; Mei, Z. G.; Hui, X. D.; Liu, Z. K., Lattice dynamics, thermodynamics, and bonding strength of lithium-ion battery materials LiMPO4 (M = Mn, Fe, Co, and Ni): a comparative first-principles study. Journal of Materials Chemistry 2012, 22 (3), 1142-1149. 4. (a) Seifitokaldani, A.; Gheribi, A. E., Thermodynamically self-consistent method to predict thermophysical properties of ionic oxides. Computational Materials Science 2015, 108, Part A (0), 17-26; (b) Gheribi, A. E.; Seifitokaldani, A.; Wu, P.; Chartrand, P., An ab initio method for the prediction of the lattice thermal transport properties of oxide systems: Case study of Li2O and K2O. Journal of Applied Physics 2015, 118 (14), 145101. 5. Kresse, G.; Hafner, J., Ab initio molecular dynamics for liquid metals. Physical Review B 1993, 47 (1), 558-561. 6. Blöchl, P. E., Projector augmented-wave method. Physical Review B 1994, 50 (24), 17953-17979. 7. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]. Physical Review Letters 1997, 78 (7), 1396-1396.

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