[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.

[Nanosized Insertion Materials for Li-Ion Batteries]Introduction: Energy Storage in Li-Ion

Electrochemical storage is attractive, having very high storage efficiencies typically exceeding 90%, as well as relatively high energy densities

Schematic principle of a Li-ion battery

Only Li ions can flow through the electrolyte, and the charge compensation electrons have
to follow the Li ions via the external circuit, which can be used to power an application

By application of a higher electrical potential than the spontaneous equilibrium open circuit polarization, the process can be reversed. High energy density requires a large specific capacity of ions in both electrodes and a large difference in chemical potential. High power requires both electrons and Li ions to be highly mobile throughout the electrode materials and electrolyte

 - Recent research has focused on nanosizing of electrode materials holding the promise of larger (dis)charge rates because it reduces the length of the rate-limiting diffusion pathway of Li-ions and electrons through the electrode material.

• The downside of the large surface area of nanostructured materials is the relative instability of nanomaterials promoting electrode dissolution and the increased reactivity toward electrolytes at voltages below 1 V vs Li/Li+, which may adversely affect the Li-ion battery performance
• Another potential disadvantage is the less dense packing leading to lower volumetric energy densities. Among the materials that benefit from the possibilities of nanosizing are the relatively stable transition metal oxides and phosphates operating well within the stability window of the electrolyte

Voltage profiles of different particle sizes for LixFePO4, anatase LixTiO2, and spinel Lix+4Ti5O12

The structural impact of nanosizing in the various insertion materials determined by neutron diffraction. (a) Calculated solubility limits in olivine LixFePO4 based on the diffuse interface in excellent agreement with the diffraction data. (b) Solubility limits in anatase LixTiO2where α,β, and γ represent anatase, lithium-titanate, and LiTiO2respectively. (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. (c) Li occupancy of the 8a (closed symbols) and 16c (open symbols) sublattices in spinel Li4+xTi5O12.

The fundamental question is: are these changes simply due to the more abundant surface area and the trivial shorter diffusion distances, or does nanosizing additionally alter critical materials properties such as defect chemistry and thermodynamics in a nontrivial way?

Cathode Materials for Li-Ion Batteries

Table 1. Electrochemical characteristics of the three classes of insertion compounds.

Framework	Compound	Specific capacity a (mAh g−1)	Average potential (V vs. Li0/Li+)
Layered	LiCoO2	272 (140)	4.2
	LiNi1/3Mn1/3Co1/3O2	272 (200)	4.0
Spinel	LiMn2O4	148 (120)	4.1
	LiMn3/2Ni1/2O4	148 (120)	4.7
Olivine	LiFePO4	170 (160)	3.45
	LiFe1/2Mn1/2PO4	170 (160)	3.4/4.1

a: Value in parenthesis indicates the practical specific capacity of electrode. 
I.The Cell Potential (Goodenough Diagram) 

−eV_oc = μ_Li(C) −μ_Li(A) = ∆μ_e + ∆μ_Li⁺

the chemical potential of the exchanged Li-atoms in anode (A) and cathode (C) is conceptually divided to the involved occupation of sites by Li⁺-ions and the valence electronic density of states (DOS) by electrons

Schematic diagram showing the electronic density of states and Fermi energies for an oxide-based electrode (Li_xNi_0.5−yMn_1.5−yCr_2yO₄ spinel material). The Li permeable solid electrolyte interface (SEI) layer formed on the electrode surface preserves the overall reversible reaction.

 - Successive redox couples are separated by an on-site effective Coulomb correlation energy U that can be large when augmented by either a crystal-field splitting or an intra-atomic exchange splitting. However,  when the Fermi energy E_FC of the cathode material approaches the top of the anion p bands of the host, the p-d covalent mixing may transform the correlated d electrons at E_FC into band electrons occupying one-electron states

 - In the absence of a crystal-field splitting of the d orbitals at E_FC, which is the case for Ni(IV) to Ni(II), the one-electron states are not separated by any on-site energy U and there is no step in the voltage of the battery. E_FC is moved from one formal valence state to another upon the reduction or oxidation of the host.
II.Crystal Structure and Electronic Properties

Crystal structure of the three lithium-insertion compounds in which the Li⁺ ions are mobile through the 2-D (layered), 3-D (spinel) and 1-D (olivine) frameworks

1.Layered Compounds

Li[M]O₂ (M = Co, Ni) oxides are isostructural to the layered α-NaFeO₂ (space group R3m, No. 166) with the oxygen ions close-packed in a cubic arrangement and the TM and Li ions occupying the octahedral sites of alternating layers with an ABCABC… stacking sequence called “O3-type” structure

A.Li_xCoO₂ (LCO)

• In LiCoO₂, the cobalt is trivalent in the electronic configuration (t_2g)⁶(e_g)⁰, i.e., in the  low-spin state (S = 0)
• However, LCO adopts the rhombohedral symmetry in the high temperature form, with Li in 3a, Ni in 3b and O in 6c sites 
• Note that the low-temperature form (LT-LCO) adopts the spinel lattice with the cubic symmetry (S.G. Fd3m) 

A lithium ordering and stacking sequences leading to an equivalent environment for all Co ions is preferred in order to achieve a maximum of charge delocalisation and to minimize the energy

 - In Li_xCoO₂, no coupling between Co:e_g and Li:2s states occurs and the lowest-energy is reached in the interplanar stacking that leads to as many equivalent Co sites as possible [In Li_0.5CoO₂, Co tends to have an intermediate oxidation state of +3.5 that induces a transition to a monoclinic structure]
 - LiCoO₂ suffers from the dissolution of the metal ion in the electrolyte that induces oxygen release, which becomes more important upon increasing the temperature. Thus, surface modification by metal-oxide coating such as ZrO₂, Al₂O₃, TiO₂, etc. was demonstrated being an effective strategy to avoid the cathode  breakdown
B.Li_1−zNi_1+zO₂ (LNO)
LiNiO₂ (LNO) is isostructural with LiCoO₂ and has the O3-type-oxygen packing (advantage: high lithium chemical potential provides a high cell voltage)
 - LNO suffers from a few drawbacks:

•  (i) difficulty to synthesize LiNiO₂ with all the nickel ions in the Ni³⁺ valence state and distributed in a perfectly ordered phase without a mixing of Li⁺ and Ni³⁺ ions in the lithium plane; 
•  (ii) Jahn-Teller distortion (tetragonal structural distortion) associated with the low spin Ni³⁺:d⁷ (t_2g⁶e_g¹) ion.
•  (iii) Irreversible phase transitions occurring during the charge-discharge process.
•  (iv) Exothermic release of oxygen at elevated temperatures and safety concerns in the charged state 

Solution: mixed LiNi_1−yCo_yO₂ phases allow overcoming the main drawbacks exhibited by both LiCoO₂ and LiNiO₂ oxides
 2.LiMn₂O₄ (LMO) 
LiMn₂O₄ belongs to the A[B₂]O₄ spinel-type structure and crystallizes in the Fd3m space group (O_h⁷ factor group) with the cubic lattice parameter a = 8.239 Å 

The cubic spinel LiMn₂O₄ structure is described with the Mn and Li cations on the 16d and 8a sites, respectively, and the oxygen ions located on the 32e sites form a nearly ideal cubic close-packed (ccp) sublattice. Lithium ions occupy tetrahedral sites, which share common faces with four neighboring empty octahedral sites at the 16c position

This lattice offers a three-dimensional network of transport paths 16c-8a-16c through which lithium ions diffuse during insertion/deinsertion reactions 
3.LiNi_0.5Mn_1.5O₄ (LNM)
Substitution of 25% Ni for Mn in LiMn₂O₄ spinel has been chosen because this composition implies that Mn is in the 4+ valence, thus avoiding the Jahn-Teller (JT) distortion associated to Mn³⁺.
=>the electrochemical activity is only due to the oxidation/reduction of Ni²⁺ ions leading transfer of 2e⁻ per Ni ion

• the face-centred spinel (S.G. Fd3m) named as “disordered spinel”
• the simple cubic phase (S.G. P₄332) named as “ordered spinel” 

The cation distribution in the P₄332 symmetry is then Li on 8c, Ni on 4b, Mn on 12d, and O(1) and O(2) oxygen ions occupy the 24e and 8c Wyckoff positions, respectively. The net result is thus a significant optimisation of space occupation leading to a reduced unit cell volume. It has been pointed out that phase-pure LNM is difficult to synthesize because impurities such as NiO and/or Li_yNi_1−yO usually exist . The partial replacement of Ni and Mn by Cr in LiNi_0.5−yMn_1.5−yCr_2yO₄ is an effective way to alleviate the problem of oxygen loss generating Mn³⁺ ions in the LNM framework and a voltage plateau at ca. 4 V vs. Li⁰/Li⁺. Thus, it has been demonstrated that the Cr-doping stabilizes the lattice without impacting the capacity significantly, but it decreases the energy density
4. Olivine LiFePO₄ (LFP)

 LFP crystallizes in the orthorhombic system (Pnma space group,  No. 62). It consists of a distorted hexagonal close-packed (hcp) oxygen framework containing Li and Fe located in half the octahedral sites and P ions in one-eighth of the tetrahedral sites. The FeO₆ octahedra, however, are distorted, lowering the regular octahedral O_h to the C_s symmetry

[[[The LiFePO₄ structure consists in three non-equivalent O sites. Most of the atoms of the olivine structure occupy the 4c Wyckoff position except O(3) which lies in the general 8d position and Li⁺ ions occupying only the 4a Wyckoff position (M₁ site on an inversion center). The Fe magnetic ions are in the divalent Fe²⁺ state and occupy only the 4c Wyckoff position (M₂ site in a mirror plane), i.e., the center of the FeO₆ units. As a consequence, Fe is distributed so as to form FeO₆ octahedra isolated from each other in TeOc₂ layers perpendicular to the (001)-hexagonal direction [22]. In addition, the lattice has a strong two-dimensional character, since above a TeOc₂ layer comes another one vertical to the previous one, to build (100) layers of FeO₆ octahedra sharing corners, and mixed layers of LiO₆ octahedra and PO₄ octahedra. The lithium iron phosphate material differs from the primary mineral triphylite Li(Mn,Fe)PO₄ by the fact that triphylite is only rich in iron, with some manganese ions also in the M₂ site [32]. However, while the triphylite is a naturally occurring mineral, LiFePO₄ is an artificial product]]]

Comparison of the energy vs. density of states showing the relative Fermi level of the Co^4+/3+ redox couple for LiCoO₂, the Ni^4+/3+ redox couple for LiNi_0.8Co_0.2O₂, the Mn^4+/3+ redox couple for LiMn₂O₄ and the Ni^3+/2+ redox couple for LiNiPO₄

The stabilization of the higher oxidation state is essential to maximize the cell voltage and the energy density. The location of O:2p energy and a larger raising of the Mⁿ⁺:d energies due to a larger Madelung energy make the higher valent states accessible in oxides. That is why transition-metal oxide hosts were pursued as positive electrode candidates for Li-ion secondary batteries. 

III.Electrochemical Properties and Phase Diagram

1.Lithium Cobaltate (LCO)

 

Charge-discharge curves Li_xCoO₂ at C/24 rate in the range 3.6–4.85 V vs. Li⁰/Li⁺. The sequence of the several phases is indicated as x varies from 1.0–0.05. 

Parameter: Charge-discharge curves Li_xCoO₂ at C/24 rate in the range 3.6–4.85 V vs. Li⁰/Li⁺

=> x varies from 1.0–0.05 

 - LiCoO₂ has shown degradation and fatigue during electrochemical cycling.

 - the valence band (VB) is mainly unchanged with a slight shift of the top of the VB to lower binding energies, which implies a shift of E_FC that provokes the removal of d-electrons due to the change of the oxidation state from Co³⁺ to Co⁴⁺.

• For 1.0 ≥ x ≥ 0.5, the DOS nearly does not change and the charge compensation with Li extraction leads to a removal of electrons from the Co:3d t_2g derived states with the Fermi level moving downwards
• For x < 0.5, a clear increase in hybridisation occurs between the Co:3d and O:2p states associated with a reduction of the  (CoO₆)-slab distances evidenced by the reduction of the c-axis lattice parameter 

=> the charge compensation of the delithiation leads to a removal of electrons from Co-O:d-p hybrid states, which translates to a partial oxidation of the O²⁻ ions

 2. Lithium Manganese Spinel (LMO) 

The spinel LiMn₂O₄ has a strong edge-shared [Mn₂]O₄ octahedral lattice and exhibits good structural stability during the charge-discharge process. LiMn₂O₄ spinels have shown a lack of robustness in their cycle life and irreversible loss of capacity that becomes rapid at elevated temperatures 

 - Li⁺ ions are extracted from the tetrahedral sites of the Li_xMn₂O₄ spinel structure at approximately 4 V in a two-stage process, separated by only 150 mV  at a composition Li_0.5Mn₂O₄

Voltage profile of a Li//LiMn₂O₄ cell discharged at C/24 rate with LMO material synthesized at 700 °C (left).Variation of the lattice parameters as a function of the Li content x during the charge/discharge in LMO cathode (right). 

A.Charge

Lithium insertion into LMO occurs at approximately 3 V. During this process, Li⁺ ions are inserted into the octahedral 16c sites of the spinel structure. Since the 16c octahedra share faces with the 8a tetrahedra, electrostatic interactions between the Li⁺ ions on these two sets of sites cause an immediate displacement of the tetrahedral-site Li⁺ ions into neighboring vacant 16c octahedral sites. The reaction results in a first-order transition to Li₂Mn₂O₄ with a stoichiometric rock-salt composition on the surface of the electrode particle.

B.Discharge

a reaction front of Li₂Mn₂O₄ moves progressively from the surface of the LiMn₂O₄ particle into the bulk. At 3 V, the Li insertion is accompanied by a severe Jahn-Teller distortion as a result of an increased concentration of Mn³⁺:d⁴ ions in the Mn₂O₄ spine1 lattice, which reduces the crystal symmetry from cubic (c/a = 1.0) to tetragonal symmetry (c/a = 1.16) that results in a 16% increase in the c/a ratio detrimental to the electrochemical cycling

. The decrease of the Li ion diffusion coefficient is involved as another contribution to the capacity fade, which is caused by the passive film formation on the active material surface

 - Several reasons have been proposed for the capacity loss of Li//Li_xMn₂O₄ cells in the 4-V  region:

• The major drawback is the disproportionation of Mn³⁺ at the particle surface in the presence of trace amounts of protons (acid attack) into Mn²⁺ and Mn⁴⁺   [  2Mn3+(solid) → Mn4+(solid) + Mn2+(solution)    ] resulting in a leaching out of Mn²⁺ ions from the positive electrode framework into the electrolyte 
• The instability of the delithiated spinel structure by oxygen loss in organic electrolyte solvents in the end of the charge.  
•  The onset of a Jahn-Teller effect at the end of discharge (particularly at high current density). Under dynamic, non-equilibrium conditions above 3 V, it has been proposed that some crystallites can be more lithiated than others, thereby driving the composition of the electrode surface into a Mn³⁺-rich Li_1+xMn₂O₄ region

Solution: 

• The appropriate method to reduce capacity fade of LMO is surface coating of the particles to prevent the Mn²⁺ dissolution by a thin layer of inorganic material such as Al₂O₃, zirconia, MgO, Li₂O-B₂O₃ glass, AlF₃ [improve the elevated temperature storage properties of LMN spinels] 
• choose chemical composition such that Mn remains inactive in the 4+ valence state; this is the case for LiNi_1/3Mn_1/3Co_1/3O₂ and LiNi_1/2Mn_3/2O₄

 - Additional Li could be inserted into the empty octahedral holes of the spinel framework at a potential  of ~3 V vs. Li⁰/Li⁺ accompanied by a structural change from cubic to tetragonal symmetry due to the Jahn-Teller distortion associated with the high-spin Mn³⁺ (t_2g³e_g¹) ions inducing a huge volume change and severe capacity fade

LiMn₂O₄ is a small-polaron semiconductor, electronic conduction occurring via hopping of electrons between e_g orbitals on adjacent Mn³⁺/Mn⁴⁺ cations. Thus, the gradual removal of Li⁺ ions from the structure during deintercalation should result in a decrease in the number of mobile electrons throughout the whole solid 

3.Lithium Mn-Ni-Co Oxides

  - The layered LiNi_yMn_yCo_1−2yO₂ (NMC) compounds with a hexagonal single-phase α-NaFeO₂-type structure have received great attention as 4V-electrode materials to replace LiCoO₂ in Li-ion batteries, owing to its better stability during cycling even at elevated temperature, higher reversible capacity and milder thermal stability at charged state 

 - The main problem that still needs to be solved for such applications of NMC is the cation mixing between nickel and lithium ions, since the ionic radius of Ni²⁺ (0.69 Å) is close to that of Li⁺ (0.76 Å)

Introduction to Li-ion batteries - Part 1

I.Introduction
 - Two type are well-known for their two-phase structure: olivine LiFePO₄ + spinel Li₄Ti₅O₁₂ 
 - In comparison to olivine LiFePO₄, spinel Li₄Ti₅O₁₂ possesses a ‘zero strain’ property and performs Li-site switching during the phase transition, which lead to a different phase structure

For the two-phase reactions, the two-phase interface will limit the diffusion of Li-ions, so the electrochemical kinetics will be dependent on the phasetransition mechanism. Although this mechanism is inherent to the electrode materials, it can be substantially influenced by nanosizing the crystallites, due to the reduced miscibility gap and the increased specific surface

 - Olivine LiFePO₄: most promising cathode materials [low toxicity, low cost and high safety]
 - Spinel Li₄Ti₅O₁₂: anode materials [excellent cycle ability, high rate capability, and better safety compared with carbon anodes]
II.Olivine LiFePO₄

1.Phase diagram 

Li_xFePO₄ could be described as a mixture of the Fe3+/Fe2+ mixed-valent intermediate Li_αFePO₄ and Li_1-βFePO₄ phases, where α = 0.05 and 1-β = 0.89 for particles with a mean size of 100 nm

(a) Open-circuit voltage versus x in LixFePO4 at 258C, where vertical lines are the monophase/biphase boundary estimated from Rietveld refinement results of neutron-diffraction data. (b) Phase distribution diagrams of LixFePO4 (0 < x < 1) established from temperature-controlled XRD data

 - the formation of a solid solution is almost entirely driven by electronic rather than ionic configurational entropy in the LixFePO4, where the electronic entropy arises as electrons or holes are localized

 - However, the electron delocalization would occur at an elevated temperature in the solid solution of LixFePO4, due to rapid hopping of the small polarons

2.Two-phase structure

(a) HRTEM image of the disordered region between two phases in a thin Li0.5FePO4crystal, with Fourier transforms of the indicated areas. (b) STEM high-angle annular dark field (HAADF) image of the chemically delithiated sample Li0.45FePO4with the analysis line and the 3D representation of EELS spectra recorded along that line. (c) Full field TXM image of a selected crystal in a sample with nominal composition Li0.74FePO4collected at 7080 eV, and the corresponding chemical phase map obtained by linear combination (LC) fitting of XANES data at each pixel. 

 - a disordered region between two crystalline domains is induced by the stress fields accompanying the lattice parameter mismatch

Transmission X-ray  microscopy  (TXM)  coupled  with  X-ray  absorption  near  edge spectroscopy  (XANES)  to  produce  the  chemical  composition maps  for  a  partially  delithiated  sample  of  Li0.74FePO4

• X-ray photoelectron spectroscopy (XPS): investigated the redox processes of nanosized carbon-coated LiFePO4

 - A continuous evolution of the Fe3+/Fe2+ ratio at the surface of the particles excellently agrees with the Li content of the entire electrode upon charge and discharge.

• soft  X-ray  absorption  spectroscopy  (XAS): studied  the  phase  transformation  and  (de)lithiation  effect on  the  electronic  structure  of  LixFePO4

3.Phase transition models

the  phase-transition  models  are  usually  established  on  the  basis  of  the  strong  anisotropy  of  Li-ion  diffusion

• maximum  entropy  method  (MEM): visualized  the one-dimensional  curved  Li-ion  diffusion  path  along  the  bPnmaaxis  of LixFePO4

 - the LiFePO4 nanoplates  with  crystal  orientation  along  the  ac  facet  show a  better  rate  performance  than  that  along  the  bc  facet  

 - the  size  effect  in  defective  LiFePO4 as  the  defects would  block  the  Li  migration  in  the  one-dimensional  channel

(a)  3D  distribution  of  Li  nuclear  as  blue  contours  calculated  by  the  MEM  using  NPD  data  measured  for  Li0.6FePO4at  620  K,  where  the  brown  octahedral represent  FeO6 and  the  purple  tetrahedral  represent  PO4 units.  (b)  Schematic  view of  the  ‘domino-cascade’  mechanism  for  the  Li  deintercalation/intercalation  mechanism  in  a  LiFePO4crystallite. (c)  Schematic  of  the  shrinking-core  model  to  describe  the  juxtaposition  of  phases  in  the  LiFePO4electrode.(d)  The  hybrid  phase-transition  model  as  a  combination  of  the  domino-cascade  model  and  the core-shell  model  to  describe  the  micro-particle  of  olivine  LixFePO4

•   For  the  LixFePO4 nanoparticles: the  phase  transition  is  considerably  faster  than  the nucleation  process => proposed  the ‘dominocascade’  mechanism  for  the  Li deintercalation/intercalation  in  a LixFePO4 crystallite [the  interfacial  zone  moves  rapidly,  like  a  wave,  through  the  crystallite  in  the  a direction]. The  two-phase  configuration  would  mainly  be  determined  by  the  poor  kinetics  of  Li-ion  diffusion  in  the  Li2O  solid electrolyte,  instead  of  the  strong  anisotropy  of  olivine  LiFePO4
• For  the  big  or  the  secondary  particles: the  two-phase  configuration  is  not  only  determined  by  the  anisotropy  of  olivine  LiFePO4, but  also  the  kinetics  inside  the  particles

‘core-shell’  model :  explain  the  asymmetric  behavior  and the  path-dependence  during  the  electrochemical  processes  of LixFePO4 electrodes
 - the  nucleation  and  growth of  a  new  phase  governed  the  electrode  kinetics  under  a  small
potential  step  applied  to  large  particles
4.Many-particle electrodes

(a)  Two  possible  scenarios  of  new  phase  formation  in  a  many-particle  system. (b)  &  (c)  Hysteretic  behavior  generated  by  an  electrode  with  10  and  1000  storage  particles.  (d)  PED phase  map  acquired  within  the  partially  charged  sample  as  Li0.25FePO4 and  (e)  the  corresponding  orientation  map,  where  color  coding  is  given  below  each image.  (f)  State-of-charge  mapping  obtained  via  scanning  transmission  X-ray microscopy  for  LixFePO4electrode  powder  dispersed  by  sonication.  Outlined  in  white  are  particles  in  which  two  phases  coexist  within  the  same  particle.

 - the  individual  particles  were  charged  oneby-one  rather  than  all  of  the  particles  simultaneously

 - a  saw-like chemical  potential  profile  for  few  particles  and  the  smoothed potential  for  many  particles as Firgure b [this  phenomenon  is  due  to  the  non-monotone  relation between  the  chemical  potential  and  the  Li  mole  fraction  of  a single  particle]
 - precession  electron  diffraction  (PED) : obtained LiFePO4and  FePO4 phase  mapping  at  the  nanometer-scale  on  a large  number  of  particles  of  sizes  between  50  and  300  nm  in  a
partially  charged  cathode as Firgure d & e

the  rate  of  initiating  the  phase  transformation  in  a particle  is  much  slower  than  the  rate  of  completing  the  phase transformation 

5.Strain accomodation

(a)  Free  energy  including  coherency  strain  energy  for  two-phase coexistence  for  the  various  morphologies  as  homogeneous,  incoherent  twophase  mixture,  the  periodic  two-phase  morphology  I  and  II. (b)  Simulated Li0.5FePO4 microstructures:  Phase  boundaries  align  along  (1  0  1)  planes  to minimize  elastic  coherency  strain  (left)  and  loss  of  coherency  in  the  (0  0  1) direction  causes  the  stripes  to  form  along  (1  0  0)  planes  (right).  (c) Diffraction  patterns  of  Li0.5FePO4(black)  and  Li0.5Fe0.85V0.1PO4(red),  insert shows  magnified  (2  0  0)  diffraction  peaks  of  triphylite  and  heterosite phases