Predicting the domain and nature of instabilities in charging and discharging Li batteries

A pattern of sequential group-by-group charging or discharging, of Li batteries with phase-separation thermodynamics, was detected by numerical simulations and justified by several experiments published in literature. The present work is the first to quantitatively predict the main characteristics of the sequential symmetry breaking (SB) events, such as the average Li concentration and the fraction of the Li-poor part at the SB transition times. Using a reduced two-zone (Li-poor and Li-rich) model, that ignores gradients in the liquid phase potential (ϕl), we derive an approximate solution predicting the effect of non-uniformity in initial conditions or in imposed parameter (collectively referred to as 'noise') on the characteristics. We show that gradients in ϕl, although extremely small, operate like noise leading to break-up of the homogeneous solution. A bifurcation map, showing the lowest current boundary that ensures a homogeneous lithiation/ delithiation as a function of noise level, is constructed.