Contribution of X-ray experiments and modeling to the understanding of the heterogeneous lithiation of graphite electrodes

Distributions of potential and lithium content inside lithium ion batteries highly affects their performance and durability. An increased heterogeneity of the lithium distribution is expected in thick electrodes with high energy densities or cycling at high currents. To optimize electrodes and cells designs, it is crucial to probe lithium concentration gradients across the depth of the electrode, but also to predict their occurrence and magnitude as a function of materials properties. Here, we follow the lithium distribution across a $80~\mu m$ thick porous graphite electrode using a $1~\mu m$ focused synchrotron X-ray beam. The sequential formation of the individual Li$_x$C$_6$ phases during lithium de-insertion is extracted from X-ray diffraction patterns, allowing the quantification of lithium concentration across the electrode thickness. Analyzing the evolution of heterogeneities as a function of time, we recover the striking features we predicted with a porous electrode model, including the succession of homogeneous and heterogeneous distributions of lithium. However, a clear difference is obtained at high stoichiometry, with a much more homogeneous distribution than initially predicted. Revisiting the interplay between transport and kinetic transfers limitations in the porous electrode model, we suggest that the kinetics of lithium (de)-insertion is highly reduced during the LiC$_6$/LiC$_{12}$ phase transition.