Multiphysics Simulations of Lithiation-Induced Stress in Li_1+xTi₂O₄ Electrode Particles

Abstract

Cubic spinel Li1+xTi2O4 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 Li1+xTi2O4 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.

Boosting Rechargeable Batteries R&D by Multiscale Modeling: Myth or Reality?

“…This latter observation has been ascribed to the associated breaking of the structural symmetry, which could be one of the reasons for the less stability of the compound as cathode material for LIBs. Following a computational study 118 already devoted to the same material, Jiang et al 119 focused their work on the spinel Li 1+ x Ti 2 O 4 by combining DFT calculations with statistical mechanics methods including cluster expansion/Metropolis MC and kMC. This complete investigation encompassed the prediction of lattice parameters, elastic coefficients, thermodynamic potentials, migration barriers, as well as Li diffusion coefficients.…”

“…Intermediate values of the composition correspond to the two-phase regions. Reproduced with permission from ref (119). Copyright 2016 American Chemical Society.…”

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

“…[56]: The diffusivity surrogate function and the predicted data are plotted in Figure 4, where the effective vibrational frequency ν * is reported to be on the order of 10 13 s −1 [56]. The mobility M is related to D by the equation M = x/(k B T ) [57]. The value of D is multiplied by 4 to approximate the diffusivity at 340 K and is divided by 4 for 260 K. The factor of 4 for every 40 K is based on the predicted diffusivity at 400 K being approximately 30 times the diffusivity at 300 K [56].…”

“…Additional phase field simulations show the effect of cycling of a Li x CoO 2 particle at 260, 300, and 340 K, as presented in Figure 15 [57]. The Li composition was initialized to 0.5, following the recommended lower limit of composition for LCO, below which large c-axis variations of the lattice cause enhanced degradation [67].…”

Variational system identification of the partial differential equations governing microstructure evolution in materials: Inference over sparse and spatially unrelated data

“…For context, we briefly discuss the role of pattern forming systems of equations in these phenomena. Pattern formation during phase transformations in materials physics can happen as the result of instability-induced bifurcations from a uniform composition [1,2,3], which was the original setting of the Cahn-Hilliard treatment. Following Alan Turing's seminal work on reaction-diffusion systems [4], a robust literature has developed on the application of nonlinear versions of this class of PDEs to model pattern formation in developmental biology [5,6,7,8,9,10,11,12,13].…”