A Model for Lithium Diffusion and Stress Generation in an Intercalation Storage Particle with Phase Change

Abstract

During the cycling of a lithium-ion battery, the active storage materials experience a volume change due to the intercalation process, often causing fracture, loss of contact among the active particles, and finally the degradation of the whole electrode. Here, we present a model for the lithium diffusion and stress generation in a particle of active material having a phase change. In our approach the driving force for diffusion is deduced from basic thermodynamics and statistical physics. The parameters of our model may be obtained from experimental measurements, or from ab-initio density functional theory calculations if the values are experimentally not accessible, as in the evaluation of new, as yet unsynthesized, computer-designed materials. We present results from simulations representing graphite known to experience phase-changes or staging. In some of our simulations, the particles are coupled to a battery simulator to apply conditions experienced in a functioning cell. We find that staging causes a significant increase in particle stress in comparison to when it is absent.

Electrochemical strain microscopy time spectroscopy: Model and experiment on LiMn2O4

“…X Li =3 is the isotropic approximation of the partial molar volume. 19 It is constant over the range of the intercalation and it is small enough in LiMn 2 O 4 to consider smallstrain theory (contrary to, e.g., silicon anodes 24 ). It is directly related to Vegard's tensor.…”

“…The present work is based on reusing the formal description of Bohn et al, 19 which is very similar to previous works done on ESM modeling, 3,10,20 and will also compare the influence of D eff on the ESM signal. The objective is to model the time evolution of lithium concentration, surface displacement, and the ESM signal below the tip during and after DC pulses.…”

“…This translates into irregularities in the Gibbs free energy evolution of the material upon change of lithium concentration, 18 leading to a phase growing into another one instead of having a smooth lithium concentration gradient across the particles. Bohn et al 19 developed a chemicalmechanical coupling model taking into account this irregularity by using an effective diffusion coefficient, denoted D eff and introduced in Section III A.…”

Simulation of Atomic Force Microscopy for investigating BaTiO3 and LiMn2O4 nanostructures based on Phase Field Approach

“…Since ferroelectrics have highly anisotropic properties, this model accounts for transversely isotropic symmetry using an invariant formulation. The polarization switching behavior under the electric field will be discussed with some numerical examples.In the simulation of ESM, we employ a constitutive model based on the work of Bohn et al [8] for the modeling of lithium manganese dioxide LiMn 2 O 4 (LMO). It simulates the deformation of the LMO particle according to an applied voltage and the evolution of lithium concentration after removing a DC pulse.…”

“…In the simulation of ESM, we employ a constitutive model based on the work of Bohn et al [8] for the modeling of lithium manganese dioxide LiMn 2 O 4 (LMO). It simulates the deformation of the LMO particle according to an applied voltage and the evolution of lithium concentration after removing a DC pulse.…”