Bridging scales with Machine Learning: From first principles statistical mechanics to continuum phase field computations to study order–disorder transitions in LixCoO2

LixTMO2 (TM=Ni, Co, Mn) forms an important family of cathode materials for Li-ion batteries, whose performance is strongly governed by Li composition-dependent crystal structure and phase stability. Here, we use LixCoO2 (LCO) as a model system to benchmark a machine learning-enabled framework for bridging scales in materials physics. We focus on two scales: (a) assemblies of thousands of atoms described by density functional theory-informed statistical mechanics, and (b) continuum phase field models to study the dynamics of order–disorder transitions in LCO. Central to the scale bridging is the rigorous, quantitatively accurate, representation of the free energy density and chemical potentials of this material system by coarse-graining formation energies for specific atomic configurations. We develop active learning workflows to train recently developed integrable deep neural networks for such high-dimensional free energy density and chemical potential functions. The resulting, first principles-informed, machine learning-enabled, phase-field computations allow us to study LCO cathodes' order–disorder transitions in terms of temperature, microstructure, and charge cycling. We highlight several insights gained to the dynamics of the phase transitions, and that have been made possible by the quantitatively rigorous scale bridging. To the best of our knowledge, such a scale bridging framework has not been previously demonstrated for LCO, or for materials systems of comparable technological interest. This approach can be expanded to other materials systems and can incorporate additional physics to that studied here.