[Nanosized Insertion Materials for Li-Ion Batteries] Discussion about size effects

Direct evidence of the impact of particle size on the thermodynamics of nanoinsertion materials is the change in the solubility limits

• In LiFePO₄ the reduction of the miscibility gap appears to result from the interface between the two end members, being the consequence either of strain, of interface energy or of the diffuse interface. The diffuse interface additionally explains the varying solubility limits that are observed with varying overall composition x in nano-Li_xFePO₄
• the presence of coexisting phases during (dis)charge: although the interfaces are directly observed in chemically lithiated materials, they are claimed to be absent under electrochemical conditions, keeping the two-phase transition mechanism

1. Because the constant voltage is indicative of the firstorder phase transition, the reduction of the composition domain where the voltage is constant, is associated with a reduction of the miscibility gap. However, this does not explain the curved shape of the voltage curve indicating a different distribution of chemical potentials in
2. Another eligible explanation is the distribution in particle sizes resulting in a distribution of voltages. Often the relative width in the particle size distribution is larger for smaller particle size.
3. A fundamental thermodynamic origin of the curved voltage profile is the smearing of the first-order phase transition as the result of configurational entropy. However, this effect can only be expected to become significant for systems smaller than ∼1000 atoms, which, considering 1000 Li atoms in LiFePO4, corresponds to systems smaller than∼4 nm. This appears consistent with the reported very small (approximately millivolt) hysteresis in equilibrium voltage curves due to this configurational entropy
4. A final factor is revealed by LTO in which the chemical potential, and hence the insertion voltage, is suggested to be different at the surface. Depending specifically on the orientation of the surface, the voltage can be expected to change gradually toward the bulk voltage over a distance of nanometers, as strengthened by our recent calculations of Li-ion storage at the oxygen-terminated surface of LTO