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Multiscale modeling of the impact of dislocations on the electro-chemo-mechanical behavior of lithium-ion battery electrodes

Applicant Professorin Dr.-Ing. Bai-Xiang Xu, since 6/2020
Subject Area Mechanical Properties of Metallic Materials and their Microstructural Origins
Term from 2018 to 2021
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 398072825
 
Final Report Year 2023

Final Report Abstract

1. A chemo-mechanical phase-field model combined with a non-singular continuum dislocation theory was developed, where the dislocation was introduced in the model in the form of an eigenstrain distribution derived from a non-singular continuum dislocation model. The generalized configurational force theory for dislocations in mechanically coupled phase transformation problems was proposed. The model was numerically implemented in the finite element method based on a mixed formulation of the diffusion equation. The numerical models were benchmarked with comparison to analytical solutions, that are analytical solutions for the singular and nonsingular dislocation stress fields, equilibrium concentration field in the vicinity of an edge dislocation and the Peach-Koehler force. The model was applied to study the interaction of lithium ions and dislocations in battery materials. In particular, diffusion, mobility, and phase separation were studied in isotropic spinel LiMn2O4. The configurational mechanics was applied in formulating an energy based formation criterion of misfit dislocations to study the critical particle size for stable dislocations in two-phase anisotropic LiFePO4. 2. The chemo-mechanical model was applied to study the influence of the dislocation stress field on the diffusion of lithium ions. It was shown that the concentration increased in the tensile region and decreased in the compressive region and the enrichment or depletion of concentration was SOC dependent has shown a symmetry with respect to SOC = 0.5. The diffusion induced stress tends to reduce the stress field of the dislocation and was also found to be SOC dependent with a similar symmetry respective to the SOC. The potentiostatic and galvanostatic charging of a particle with a single dislocation was simulated showing an influence on the ion concentration distribution while the average charging rate was not influenced. The mobility in the vicinity of an edge dislocation was analyzed in terms of homogenization. The mobility around the dislocation core has shown obvious SOC dependence with a maximum at an SOC = 0.5, and the tensile and compressive sides of the region near the dislocation core introduced mobility heterogeneity. However, the average mobility was equivalent to a dislocation-free material, and the existence of the dislocation did not introduce apparent mobility anisotropy in the bulk material. Threedimensional simulations of the diffusion along the edge dislocation line were performed where different diffusion coefficients were considered inside the dislocation core region. The result has shown the formation of a fast diffusion path initiated on the tensile side of the edge dislocation core. Results for the diffusion model: concentration redistribution, SOC symmetry, DIS, charging: no influence on charging rate but on the ion distribution. Mobility and pipe diffusion. 3. The chemo-mechanical model for dislocated solids was then adopted to study the interaction between the diffusive ions and a dislocation in a phase separation model for isotropic LiMn2O4. The redistribution and the related diffusion-induced stress were found to be stronger for a smaller ̃ core width, where the core width ℎ = 1 resulted in concentrations close to c = 0 and c= 1. The phase separation with a dislocation was shown with its dependence on the SOC and the interaction parameter χ. For χ ≤ 2.5, the distribution of the high concentration and the low concentration phase followed the tensile and compressive side of the dislocation, respectively. The charging of a particle considering phase separation was shown with and without dislocation. It was found that the dislocation had a pinning effect when the interface is close to the dislocation. 4. Then the phase separation model was applied to study the stability of misfit dislocations in twophase LFP particles with anisotropic elasticity. First, the resulting driving forces F1 and the change of the system energy upon introduction of the dislocation into the material were studied in a single square-shaped two-phase particle. Three equilibrium positions with zero driving force on the dislocation were found, where the one in the center of the phase boundary was identified as a stable equilibrium position and the other two near the free surface as unstable equilibrium positions. The unstable equilibrium positions coincided with a maximum system energy change which determined the energy barrier to introduce misfit dislocations. For the assumed circumstances and given model parameters, a minimum particle size for stable misfit dislocations of Lc= 52.5 nm was found and defined as critical particle size. Different particle shapes were studied in the sense of an aspect ratio, where the shear stress σ̃_12 of the interface was found to increase with the aspect ratio thereby stabilizing the dislocation. Particles with an aspect ratio of a = 1.5 can be pointed out due to the largest predicted critical specific surface area. Concluding the critical particle size was analyzed in dependence of the position of the interface and the dislocation. In general, a deviation of the interface position from the center of the particle was found to destabilize the misfit dislocation, so that the critical particle size could be found with the interface in the particle center. 5. Conclusively, the effects of some essential model parameters on the stability prediction of misfit dislocations in two-phase LFP particles were discussed. First, the influence of the relaxation of the interface was studied by comparing the first timestep with the equilibrium state. In the first timestep, a larger critical particle size was predicted. Thus interface relaxation resulted in a significantly smaller critical particle size compared to a non-relaxed interface. The results obtained implementing an elasticity tensor as a function of the concentration in this work were compared to results implementing a constant stiffness tensor. It was found that the constant stiffness tensors only lead to small differences in the driving forces and prediction of the critical particle size in comparison to the phase-sensitive stiffness tensor. Finally, the influence of the description of the dislocation core on the results was studied. A larger critical particle size was predicted for a smaller core width. The driving forces on the dislocation were most strong close to the surface and were affected the most by the description of the dislocation core. Therefore this region, in combination with the dislocation core model, is most critical for an accurate prediction of the critical particle size.

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