An energy-based stability analysis of misfit dislocations in two-phase electrode particles: A planar model and implications for LiFePO4

Abstract

It is well known that cycling induced capacity fading in phase transforming intercalation materials is critically linked to the severity of misfit strain between the phases which could result in the emergence of a variety of defects in the material. Here, adopting a planar model and making use of a well-established energy-based framework, we examine stability of a misfit dislocation lying at the phase boundary within a two-phase electrode particle. Within this framework, the stability criterion emerges as a result of competition between the work that must be done against the image forces with the work that is supplied by the phase transformation induced stresses, as the dislocation is pulled from free surface of the solid toward interior. A numerical model accounting for anisotropy of both misfit strain between the phases and elastic properties of the solid is developed. The model is in particular applied to the electrode particles of LiFePO4, a highly promising cathode material for lithium-ion battery applications in which misfit dislocations as a result of phase transformation have also been experimentally observed. The analysis is revealing of size effects on the stability of a misfit dislocation in the electrode particle. Most notably, it is shown that below a critical particle size, no misfit dislocation at the interphase can remain stable within the particle as it becomes energetically more favorable for the dislocation to be driven out of the particle through absorption by the free surfaces. Numerical estimates of the critical size are presented and discussed with reference to available experiments. Through providing a guideline for suppressing misfit dislocations, results of this work could have potentially important implications for disabling a wide range of dislocation-based fatigue mechanisms which could otherwise become active and result in capacity fading upon a large number of cycles.