Application of Ab Initio Methods to Secondary Lithium Batteries
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chemical potential side). Meanwhile, to compensate charge neutrality in the host cathode, electrons flow through the external circuit. Charging of the battery is the reverse of this process. Rechargeability of the battery requires that this cycle can be performed several hundred times without loosing its capacity. This requires a cathode material where Li ions can easily be inserted and removed. In addition, the material must retain its structural integrity during this process and chemical reactions between electrode and electrolyte need to be prevented. edischarge charge V
Electrolyte
Anode
discharge
Li+
(Li) I- ihigh
Cathode (LixMO2 )
Li+ • charge Li 4
Li
low
Figure 1. Schematics of a rechargeable lithium battery. Li is accommodated in the cathode by intercalation into transition metal oxides such as LiCoO 2, LiNiO 2 and LiMn 20 4. LiCoO 2 and LiNiO 2 adapt the layered a-NaFeO 2 structure whereas LiMn 20 4 has a spinel structure. However, both LiNiO 2 and LiMn 20 4 suffer severe capacity loss during repeated recharging. For LiMn 20 4, cycling performance can be enhanced at the expense of capacity by substituting excess Li for Mn [7]. The open circuit voltage obtained from a lithium insertion reaction, is directly related to the difference in chemical potential of lithium in the anode and in the cathode [8]; cathodeanode ze where z is the number of electrons transferred and e is the electronic charge. If the anode is composed of pure metallic lithium, the anode chemical potential is constant and the variation of open cell voltage during the insertion process can be associated with changes of the lithium chemical potential in the cathodic host material. Although it is difficult to compute the lithium chemical potential in the cathode as a function of lithium content [9-11], the average potential can be determined more easily. By integrating Equation 1 between the end-of-charge composition (xi) and end-of-discharge composition (x2), the average open cell voltage can be found as, AGr S
(x2 - x,)zF
(2)
where F is the Faraday constant and AGr is the Gibbs free energy change (in Joules) in the reaction,
66
(x2
_x,) Li (anode) + Li] Host (cathode)
dishrge
Li,2 Host (cathode)
(3)
Assuming that the entropy and volume effects are negligible, AGr (-=AEr + PAVr - TASr) can be approximated by only the change in the internal energy (AEr) at 0 'K. AEr is approximately 3 to 4 eV, the term PAVr is of the order of 10.' eV and the entropy term is of the order of thermal energy, kBT (about 25X1 03 eV at room temperature). Therefore the above approximation is quite valid. Computing the variations in potential during the intercalation process can be done in a similar way. However, since ordered arrangements of Li and vacancies can occur during lithium removal [9-12], computing the variation in potential necessitates the information on structural changes in the host structure as the lithium content varies. This generally involves computing the energy of large supercells which can be tedious with accurate quantum mec
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