  Cubic spinel Li$_{\rm 1+x}$Ti$_2$O$_4$ is a promising electrode material as
it exhibits a high lithium diffusivity and undergoes minimal changes in lattice
parameters during lithiation and delithiation, thereby ensuring favorable
cycleability. The present work is a multi-physics and multi-scale study of
Li$_{\rm 1+x}$Ti$_2$O$_4$ that combines first principles computations of
thermodynamic and kinetic properties with continuum scale modeling of
lithiation-delithiation kinetics. Density functional theory calculations and
statistical mechanics methods are used to calculate lattice parameters, elastic
coefficients, thermodynamic potentials, migration barriers and Li diffusion
coefficients. These quantities then inform a phase field framework to model the
coupled chemo-mechanical evolution of electrode particles. Several case studies
accounting for either homogeneous or heterogeneous nucleation are considered to
explore the temporal evolution of maximum principle stress values, which serve
to indicate stress localization and the potential for crack initiation, during
lithiation and delithiation.
