Ab initio calculation of the voltage profile for LiC6
Introduction
Lithium-ion batteries [1], [2], [3] are the current and widely used rechargeable power source for portable electronics devices because of their high energy density. Previous theoretical studies [4], [5], [6], [7], [8] have modelled the energetics and corresponding cell voltage curves of the cathode materials. Aydinol et al. [5] calculated the average voltages for Li/LiMO2 and Li/LiCoX2 (M=Ti, V, Mn, Co, Ni, Cu, Zn, Al; X=O, S, Se) cells. An approximation made in these calculations is that the transformation from reactant to product is in two phases, so an average voltage can be defined [5]. Courtney et al. [6] used the ab initio pseudopotential plane-wave method and the approximation by Aydinol et al. [5] to calculate the average voltage for the anode material tin-oxide (in particular, lithium–tin, LixSny). Deiss et al. [4] calculated the energy density and cell voltages of LiC6/LiMoO2 (anode/cathode) and LiC6/NiO2 using the average voltage between the fully charged and the discharged states. Yamaki et al. [7] studied the contribution of the internal energy change to cathode voltage assuming that the cathode material (NiO2) is completely ionic and only the Coulombic potential was effective. Braithwaite et al. [8] used the ab initio pseudopotential plane-wave method and the finite difference approximation to calculate the variation of the cell potential with the degree of discharge. These calculations establish the value and reliability of DFT techniques in modelling the energetics of intercalation. It is the purpose of this communication to apply the same method to the problem of the anode intercalation reaction which has not previously been studied.
Section snippets
Li battery system
The basic cell structure of the lithium battery is of the typewhere LiX is a lithium salt (e.g. LiClO4), PC–EC is a mixed propylene carbonate (PC)–ethylene carbonate (EC) solvent and M is a transition metal (e.g. Ni, Mn or Co). The electrochemical process is as followswhere y is about 0.2 Faraday per mole and the cyclable charge x is around 0.5 [1]. The anode reaction can be summarised as:
In
Theoretical method
The total energy (Etot) code CASTEP [10] was used, which employs pseudopotentials to describe electron–ion interactions and represents the electronic wave-function using a plane-wave basis set [11]. The total energy is calculated within the framework of the local-density approximation (LDA) for the exchange-correlation energy. We chose LDA rather than the gradient generalized approximation (GGA) because the associated carbon pseudopotentials describe the interaction between graphite planes
Results
The total energy calculations for graphite, lithium metal and LiC6 are reported in Table 1. LiC6 contains six carbon atoms per unit cell and graphite contains four. Therefore, to obtain ΔE for the intercalation reaction, we write:
Using the values given in the Table 1, we obtain a value of −0.145 eV for ΔE. This result can be compared with experimental data of Avdeev et al. [9], who report a value of 0.145 eV (−13.9±1.2 kJ/mol) per Li for the intercalation
Acknowledgments
We would like to acknowledge the National Research Foundation (NRF) and Royal Society (UK) for financial support of the execution of this work. We are also grateful to the Materials Modelling Center for the availability of computational facilities at the University of the North.
References (17)
Solid State Ionics
(1994)- et al.
J. Power Sources
(2000) - et al.
J. Phys. Chem. Solids
(1996) - et al.
Solid State Commun.
(2002) - et al.
Prog. Batteries Sol. Cells
(1990) - Y. Nishi, in: M. Wakihara, O. Yamamoto (Eds.), Lithium Ion Batteries, Kodansha and Wiley-VCH, Tokyo (Japan), 1998,...
- et al.
J. Electrochem. Soc.
(1997) - et al.
Phys. Rev. B
(1997)