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Li$_xTM$O$_2$ (TM={Ni, Co, Mn}) are promising cathodes for Li-ion batteries,whose electrochemical cycling performance is strongly governed by crystalstructure and phase stability as a function of Li content at the atomisticscale. Here, we use Li$_x$CoO$_2$ (LCO) as a model system to benchmark ascale-bridging framework that combines density functional theory (DFT)calculations at the atomistic scale with phase field modeling at the continuumscale to understand the impact of phase stability on microstructure evolution.This scale bridging is accomplished by incorporating traditional statisticalmechanics methods with integrable deep neural networks, which allows formationenergies for specific atomic configurations to be coarse-grained andincorporated in a neural network description of the free energy of thematerial. The resulting realistic free energy functions enable atomisticallyinformed phase-field simulations. These computational results allow us to makeconnections to experimental work on LCO cathode degradation as a function oftemperature, morphology and particle size.

Li$_x$CoO$_2$ phase stability studied by machine learning-enabled scale  bridging between electronic structure, statistical mechanics and phase field  theories