Model for the Particle Size, Overpotential, and Strain Dependence of Phase Transition Pathways in Storage Electrodes: Application to Nanoscale Olivines

In the drive toward improved electrical energy storage for applications ranging from wireless devices to electric vehicles to grid stabilization, nanoscale materials are of growing interest as ion storage electrodes. Nanoscale olivines based on LiMPO4 (M = Fe, Mn, Co, Ni) are one class of compounds for which recent experimental developments reveal very different phase transition and solid-solubility behavior compared to larger particles. The olivines may be an exemplar for generalized behavior for which metastable crystalline or amorphous phases are produced under the large driving forces incurred during electrochemical reactions. Here we use a diffuse-interface thermodynamic model to assess the conditions under which amorphous phase transitions may occur in nanoscale LiMPO4 particles. There are three central conclusions. First, assuming as with similar solids that the amorphous phase has the lower surface energy, it is found that an initially crystalline phase may undergo amorphization during cycling when the particle size is below a critical value. Second, the effect of applied electrical overpotentials on the phase stability is evaluated for the first time, and is found to strongly influence the phase transition pathways of small particles. Third, the tendency to amorphize is significantly affected by the magnitude of the misfit strain between the lithiated and delithiated crystalline phases. It is shown that there exists a critical misfit strain above which the preferred transformation pathway is amorphization, regardless of the particle size. We use these results to interpret experimentally observed behavior of olivines, including data that up to now have been unexplained.