Understanding Cation-Disordered Cathode Materials Based on Percolation Theory and Ligand Field Theory
Authors: Lee Jinhyuk , Seo Dong-Hwa , Urban Alexander , Ceder Gerbrand 
Published: February 2020

Throughout the history of Li-ion batteries, cathode materials with high energy density have been sought from well-ordered oxide compounds in which lithium and other cations occupy distinct sites within an oxygen FCC framework.[1,2] In contrast, cation-disordered materials have received only a limited attention as cathodes because lithium diffusion tends to be limited by their structure, resulting in poor cycling performance.[3] However, recent studies have shown that cation-disordered materials can in fact deliver higher energy densities than the ordered materials once enough excess lithium (x > 0.1 in Li1+xTM1-xO2, TM: transition metal) is introduced to their structure, opening a new search space for high energy density Li-ion cathodes.[4,5]
The understanding of disordered cathodes was first made with percolation theory which links the composition of a compound to the population of Li diffusion channels with low barriers.[4,5] In rocksalt-type oxides, Li diffusion takes place between two octahedral sites through a face-sharing tetrahedral site. Li+ ion in this tetrahedral site in the activate state in diffusion, whose electrostatic energy largely determines the diffusion barrier. Hence, (i) the oxidation states of species in the face-sharing octahedral sites and (ii) the tetrahedron height, along which the activated Li+ ion relaxes away the strong electrostatic repulsion from face-sharing octahedral species, largely determine the activity of a Li diffusion channel. [4] In the disordered rocksalt structure with small tetrahedron heights, it was found that only the diffusion channel through which an activated Li+ ion shares faces with no transition metal ions (0-TM channels) has low Li diffusion barriers. However, for the 0-TM channel to dominate macroscopic Li diffusion, the channel must be percolating in a crystal structure, such that every Li hopping occurs through the channel. Percolation theory predicts that Li excess introduces such 0-TM percolation, and hence Li-excess disordered cathodes should allow for facile Li diffusion.(Fig. 1a)[4] Consistent to the theory, recently developed cation-disordered Li-excess cathodes (e.g. Li1.211Mo0.467Cr0.3O2, Li1.3Mn0.4Nb0.3O2) deliver high capacity and energy density with facile Li diffusion.[4,6]
However, percolation theory alone cannot completely guide the design of high capacity disordered cathodes because it does not take redox process into account. While percolation theory predicts higher Li-excess contents should lead to better disordered cathodes, higher Li excess necessarily leads to lower transition metal contents hence their redox capacity.[7] Therefore, unless transition metals can exchange multiple electrons or oxygen redox can reversibly occur, the electron-storage capacity should decrease with Li excess, which is unwanted.
In this presentation, we explain how lithium excess can affect both Li diffusion and redox process in disordered cathodes using percolation theory and ligand field theory, respectively.(Fig. 1b, 1c)[4,8] Based on this understanding, we will show that Li diffusion and redox process in the materials are highly correlated hence need to be considered simultaneously. We further demonstrate how such complete understanding can be used to explain the performance of recently developed high capacity disordered cathodes (e.g. Li-Ni-Ti-Mo oxides) and to design improved disordered cathode materials.[7,8]
References
[1] K. Kang, Y. S. Meng, J. Bréger, C. P. Grey, G. Ceder, Science 311, 977–980 (2006).
[2] M. M. Thackeray, P. J. Johnson, L. A. De Picciotto, P. G. Bruce, J. B. Goodenough, Mater. Res. Bull.19, 179–187 (1984).
[3] M. N. Obrovac, O. Mao, J. R. Dahn, Solid State Ion.112, 9–19 (1998).
[4] J. Lee, A. Urban, X. Li, D. Su, G. Hautier, G. Ceder, Science 343, 519–522 (2014).
[5] A. Urban, J. Lee, G. Ceder, Adv. Energy Mater.4, 1400478 (2014).
[6] N. Yabuuchi et al., PNAS 112, 7650–7655 (2015).
[7] J. Lee, D.-H. Seo, M. Balasubramania, N. Twu, X. Li, G. Ceder, Energy Environ. Sci.8, 3255 (2015).
[8] D.-H. Seo‡, J. Lee‡, A. Urban, R. Malik, SY. Kang, G. Ceder, Nature Chem., in press (2016) (‡ equal contribution)

Figure 1