LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. During discharge, LiFePO4 material can undergo phase separation, between a highly and lowly lithiated form. Discharge of LiFePO4 crystals has traditionally been modelled by one-phase Stefan problems, which assume that phase separation occurs.
Recent work has been using phase-field models based on the Cahn-Hilliard equation, which only phase-separates when thermodynamically favourable. In the past year or two, this work has been having considerable impact in both theoretical and experimental electrochemistry.
Unfortunately, these models are very difficult to solve numerically and involve large, coupled systems of nonlinear PDEs across several different size scales that include a range of different physics and cannot be homogenised effectively.
This talk will give an overview of recent developments in modelling LiFePO4 and the sort of strategies used to solve these systems numerically.