[Nanosized Insertion Materials for Li-Ion Batteries]Olivine LixFePO4

Olivine Li_xFePO₄

the question whether the nanosize improvements are caused by intrinsic changes in material properties or are simply due to the shorter diffusion distances through nanosized solid state

Explanations for the distribution of voltages (in literature are)

• (1) a reduction of the miscibility gap for smaller particle sizes due to strain, surface energy, and the (diffuse) interface energy 
• (2) a distribution of voltages due to a distribution in nanoparticle size

1.The solubility limits during the insertion reaction in LiFePO₄ have been (under intensive research) demonstrating narrow solid solution domains (x_α≈ 0 and x_β ≈ 1) in micrometer size particles at room temperature and a solid solution over the entire compositional range above 520 K

1.  extended solid- solution composition ranges in small particles, and a systematic decrease of the miscibility gap was suggested due to strain based on Vegard's law
2.  the diffuse interface, strain, and interface energy, all increasing the energy of the coherent interface between the coexisting phases
3.  in theory a coherent but compositional diffuse interface is able to destabilize the two-phase coexistence, predicting a size-dependent miscibility gap
4.  the diffuse interface also predicts the observed composition dependence of the miscibility gap, which is observed below particle sizes of 35 nm
5. in the nanoscale phases are not independently established but linked through their mutual interfaces and require Li transport between the two phases when the overall composition changes by (dis)charging

2.Surface free energies become increasingly important in affecting voltage profiles as electrode particles approach nanometer dimensions.