The Role of Coherency Strains on Phase Stability in Li[sub x]FePO[sub 4]: Needle Crystallites Minimize Coherency Strain and Overpotential

We investigate the role of coherency strains on the thermodynamics of two-phase coexistence during Li (de)intercalation of . We explicitly account for the anisotropy of the elastic moduli and analytically derive coupled chemical and mechanical equilibrium criteria for two-phase morphologies observed experimentally. Coherent two-phase equilibrium leads to a variable voltage profile of individual crystallites within the two-phase region as the dimensions of the crystallite parallel to the interface depend on the phase fractions of the coexisting phases. With a model free energy for , we illustrate the effect of coherency strains on the compositions of the coexisting phases and on the voltage profile. We also show how coherency strains can stabilize intermediate solid solutions at low temperatures if phase separation is restricted to Li diffusion along the -axis of olivine . A finite element analysis shows that long needlelike crystallites with the long axis parallel to the lattice vector of minimize coherency strain energy. Hence, needlelike crystallites of reduce the overpotential needed for Li insertion and removal and minimize mechanical damage, such as dislocation nucleation and crack formation, resulting from large coherency strain energies.