[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

 

[Nanosized Insertion Materials for Li-Ion Batteries]Spinel Li4Ti5O12

The disadvantage of a high voltage of∼1.55 V versus Li metal compared with anode materials like graphite is compensated by the material's safe operation, high rate capability, low cost, and excellent recyclability

 in micrometer sized Li_4+xTi₅O₁₂ two-phase separation is unstable above 80 K and domains of 16c occupation and 8a occupation intimately mix at a nanometer length scale. This appears as a solid solution for diffraction and the open circuit potential

 - The very low interface and strain energy imposed by the coexisting phases facilitates mixing of the two phases on a small scale. This leads to a solid solution electrochemical response at relative low temperatures (above 80 K)

(c) Li occupancy of the 8a (closed symbols) and 16c (open symbols) sublattices in spinel Li₄þxTi₅O₁₂. 

  - additional lithium incorporation was predicted to lead to a negative and therefore impossible to achieve intercalation potential - directly observation indicates an increased capacity at positive potential with decreasing particle size, exceeding Li7Ti5O12. Neutron diffraction proved simultaneous occupation of both 8a and 16c, which explains the additional capacity.Furthermore, the additional capacity was suggested to reside mainly near the surface, explaining the increasing capacity with decreasing particle size

 oxygen-terminated surface (oxygen-rich surfaces) would explain the relative high voltages of the first inserted capacity as well as the additional capacity at low potential that scales with the particle surface. However, too high surface lithium storage was found to result in irreversible capacity loss, most likely due to surface reconstruction, creating a thin layer of inactive material

[Nanosized Insertion Materials for Li-Ion Batteries]LixTiO2(Anatase, Rutile, TiO2(B), and Brookite)

Advantage: inherent safety and stability of titanium oxides  working at potentials around 1.5 V

• Nanosize
• Increased reaction areas
• Shortened Li diffusion paths
• Enhanced Li solubility and capacity

Voltage profiles of different particle sizes 

(b) Solubility limits in anatase LixTiO2 where α,β, and γ represent anatase, lithium-titanate, and LiTiO2 respectively. (α)+(β) and (α+β) refer to the situation that each particle either has phase α or β and that both phases coexist within one particle, respectively.

 * the thermodynamics of insertion in anatase is strongly affected by the crystal particle size
 * The increase of the surface area has profound impact on the storage properties

a particle size of 7 nm can completely be transformed toward tetragonal LiTiO₂. Down to ∼3 nm deep, the surface allows lithium storage exceeding the orthorhombic Li_∼0.5TiO₂ composition, which is responsible for the larger reversible (dis)charge capacities observed

the storage capacity increases with decreasing particle size, suggesting similar surface environment enhanced Li storage
 - The region where the voltage is constant reflects the first-order phase transition from Li-poor anatase Lix_a≈0.025TiO₂ to Li-rich lithium-titanate Lix_b≈0.5TiO₂
 - A remarkable observation is that the Li-ion solubility in the various phases depends systematically
on the crystal particle size, shifting the miscibility gap rather than decreasing it

• The 120 nm anatase crystals can host approximately Li/Ti = 0.03
• the 7 nm particles are able to host up to Li/Ti = 0.21 while maintaining the anatase structure.

The disappearance of the voltage plateau for smaller particle sizes has been related to these changing solubility limits

Another interesting observation is the different phase behavior in particle sizes above and below ∼80 nm referred to as (α +β) and (α) + (β)

•  Large particles appear to be able to host both phases within one crystallite
• small particles have either the Li-poor anatase or lithium-titanate phase

 - The origin of this was suggested to be the prevention of intraparticle coexisting phases and the associated phase boundary, that is, preventing the resulting energy penalty due to interface energy and strain
 - The absence of the interface rules out the interface energy effects on the solubility limits as discussed for LiFePO4

Upon nanosizing, all TiO2 polymorphs suffer from a substantial irreversible capacity loss on the first cycle that appears to scale with the surface area, compromising the use of nanostructured materials. Generally, the irreversible capacity loss is attributed to trapped lithium in the host structure or decomposition of the electrolyte and SEI formation. However, titanium oxide surfaces are wellknown for H2O and OH physisorption and chemisorption, forming strong Ti -O- H type bonds. We have shown that this explains the irreversible capacity loss by the formation of Ti -O- Li at the surface of amorphous TiO2 where Li+ exchanges with H+, which reduces the electrolyte

[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.