Modeling of coherent phase transformation and particle size effect in LiFePO4 cathode material and application to the charging/discharging process

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The effect of coherent strains which is involved during the fast charge/discharge processes and the influence of particle size reduction which improves the electrochemical performance of the cathode material are modelled in this study. An extension of the linear isotropic approximation for elastic energy stored in the coherent boundaries of an orthorhombic system is performed for the first time to calculate the coherent miscibility gaps of the LiFePO4-FePO4 cathode join. Noticeably, this approach is applicable for any thermodynamic models used for describing the equilibrium LiFePO4-FePO4 join. The coherent miscibility gaps corresponding to various crystallographic directions, which could explain the occurrence of a metastable phase, favorable phase boundaries during lithiation (delithiation), and the formation of dislocations or cracks via cycling, are presented. (100) is considered as the softest direction for coherence to form and the existence of (110) and (010) habit planes is also possible. Moreover, it is the first time that a model of particle size effect on both equilibrium and coherent olivine join is developed. Additionally, it is the first combined coherency-size type of calculation ever reported. The difference between the surface energies of the pure LiFePO4 and FePO4 and the excess surface energy of the olivine solid solution are the two important model parameters affecting the equilibrium and the coherent miscibility gaps. As the particle size decreases, the miscibility gaps shrink favoring the intermediate phase region between the two miscibility gaps. At nanoscale, coherent phase transformation seems to be more likely.