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

Materials Science;Machine Learning;Computational Physics