Understanding Mn-Based Intercalation Cathodes from Thermodynamics and Kinetics

Abstract

A series of Mn-based intercalation compounds have been applied as the cathode materials of Li-ion batteries, such as LiMn₂O₄, LiNi_1−x−yCo_xMn_yO₂, etc. With open structures, intercalation compounds exhibit a wide variety of thermodynamic and kinetic properties depending on their crystal structures, host chemistries, etc. Understanding these materials from thermodynamic and kinetic points of view can facilitate the exploration of cathodes with better electrochemical performances. This article reviews the current available thermodynamic and kinetic knowledge on Mn-based intercalation compounds, including the thermal stability, structural intrinsic features, involved redox couples, phase transformations as well as the electrical and ionic conductivity.

1. Introduction

Lithium-ion batteries have contributed to the popularization of portable electronic products during past two decades, and now demonstrated great potential in the fields of electric vehicles, smart electrical grids, etc. Among various cathode materials, Mn-based intercalation compounds have received much attention owing to their high nature abundance, low price as well as the excellent performances in electrochemical energy storage and conversion. From the aspect of element, Mn plays an important role in intercalation cathodes. As a variable valency element, Mn may provide two-electron process to obtain higher capacity [1], and ions with different valence exhibit varied kinetic properties, influencing the cycling performance of electrode [2,3,4]. As one of the transition metal (TM) elements in active cathode materials, Mn can act as either the structural stabilizer such as in LiNi_1−x−yCo_xMn_yO₂ (NCM) [3] or the active center such as LiMn₂O₄. Especially, in Li-rich layered oxides, Li₂MnO₃ not only acts as a unit of structural stabilizer but also becomes a major contributor to the increased capacity after its activation process [5]. Therefore, it is necessary to discuss Mn-based intercalation cathodes.

Though most Mn-based cathodes have their advantages, several drawbacks still limit their application in high-energy storage devices. For example, Li-rich layered oxides exhibit high capacities, such as 250–300 mA h g⁻¹ [6], however, problems of the capacity decay, voltage fading and hysteresis became obstacles to its commercialization. These disadvantages are rooted in their crystal structures and chemistries, such as the Jahn-Teller (JT) effect caused by Mn³⁺, interactions between spin moments, disproportionation reactions of Mn³⁺, ion mobility, the dimensions of structure, etc.

There are few reviews of Mn-based intercalation cathodes from the thermodynamic and kinetic points of view. This article focuses on the understanding the electrochemical performances of Mn-based cathodes from these two aspects. Firstly, the thermodynamic-related aspects are discussed, including the thermal stability, structural features, redox couples as well as the phase transformations. Then, the kinetic behaviors are reviewed, including electrical and ionic conductivity and the motion of cations.

2. Thermodynamics

2.1. Before Electrochemical Cycles

2.1.1. Theoretical Capacity

The theoretical capacity of a given electrode material can be obtained by the following equation:

$$Q=\frac{n\times N_A}{M\times 3.6}$$

(1)

where Q is the theoretical specific capacity, mA h g⁻¹; M is the molar mass of the active material, g mol⁻¹; n represents the number of electrons involved in the reaction; and N_A is the Avogadro’s number.

Generally, practical capacity is lower than the theoretical value, due to the occurrence of oxygen loss or irreversible phase change at low lithium content and high voltage [7]. The theoretical and practical capacities of several Mn-based cathodes are listed in

Table 1. The specific capacity of several Mn-based cathodes.

Compounds	Theoretical Capacity (mA h g−1)	Experimental Capacity (mA h g−1)	References
Li(Ni1−x−yCoxMny)O2	~285	150~210	[5]
xLi2MnO3∙(1 − x)LiMO2	~280	250~300	[8,9]
LiMn2O4	148	120 (C/10)	[10]
LiNi0.5Mn1.5O4	147	146 (C/20)	[11]
Li4Mn2O5	492	355 (C/20)	[1]

.

2.1.2. Thermal Stability

Thermal stability is required to be concerned for the following two reasons: firstly, the safety. Most cathode materials, especially delithiated phases, go through an exothermic/endothermic process accompanied by oxygen release or phase changes during heat treatment [4]. In the presence of electrolyte, the highly exothermic reactions of electrolyte with oxygen make the total reaction exothermic, even if the oxygen-release reactions of the cathode are endothermic [12]. These reactions are believed to be serious safety risks. Secondly, the knowledge obtained from thermal behavior studies can provide useful information for predicting the structure evolution during long-term electrochemical cycling [4]. For example, the lithium-rich layered oxides go through a structure transformation from layered to spinel during electrochemical processes, which is already observed in the thermal decomposition process at the initial stage of heating [13,14]. Thermal stability of cathodes is affected by many factors, such as the structure instinct stability at a certain temperature [12], the strength of TM-O bond [15], crystal field stabilization energy [4,12], etc., which will be discussed in the following part.

• Layered Mn-based Oxides

For most layered cathode materials, oxygen-release at high temperatures is common. One example is LiNi_1−x−yCo_xMn_yO₂, which is intensively studied by Noh et al. [5]. All samples have weight loss under heating attributed to the oxygen release during phase transitions (from layered R$\overline{3}$m to spinel Fd3m). In addition, the onset temperatures shift to lower side with increasing Ni content, as a result of the reduced structural stability.

Another example is the better thermal stability of charged Li_xNi_1/3Co_1/3Mn_1/3O₂ than Li_xNi_0.8Co_0.15Al_0.05O₂ [16,17]. This can be explained as the different structural transformation during heating. In the case of Li_0.55(Ni_1/3Co_1/3Mn_1/3)O₂, the formation of a stable spinel phase causes less structural disorder, while, for Li_0.45(Ni_0.8Co_0.15Al_0.05)O₂, the formation of a thermodynamically unstable spinel phase exacerbates the release of oxygen [16].

From the above examples, one can see that oxygen evolution at high temperatures is unavoidable for charged oxides, which can be understood from a thermodynamic point of view: (1) cations with high valence state, such as Ni⁴⁺ and Co⁴⁺, have a strong reduction tendency; (2) the delithiated compounds become unstable as predicted in phase diagram; and (3) reaction that releases O₂ gas has a large positive entropy and can always occur at a high enough temperature [4,12].

Phase changes during heating are companied by the movement of transition metal (TM) ions, as a result, thermal stability of cathodes is significantly affected by the ease of TM migration, which will be discussed in Section 3.2.3. Using cations that prefer to occupy T_d sites can stabilize the structure at the initial stage of heating, and hence the overall thermal stability of materials can be improved [4].

• Spinel-type Mn-based Oxides

At high temperatures, the decomposition of LiMn₂O₄ follows the reaction below [12]:

$${\mathrm{LiMn}}_2{\mathrm{O}}_4\to {\mathrm{LiMnO}}_2+\frac{1}{3}{\mathrm{Mn}}_3{\mathrm{O}}_4+\frac{1}{3}{\mathrm{O}}_2$$

(2)

The reaction enthalpy is 0.984 eV per formula unit of LiMn₂O₄, which indicates a highly endothermic process. As a result, in contrast to Li_xNiO₂ and Li_xCoO₂, LiMn₂O₄ is thermodynamically stable at common conditions [12].

The cation-substituted spinel oxides LiM_xMn_2−xO₄ (M = Ni, Co, Fe, Cr, Mg, Al, Ti, Cu, Zn, etc.) have different thermal stability from LiMn₂O₄. Among all doped compounds, LiNi_0.5Mn_1.5O₄ is one of the most attractive materials with a flat voltage plateau at 4.7 V, which can either form the disordered phase (space group Fd$\overline{3}$m) or the ordered phase (space group P4₃32). The disordered phase exhibits slightly poor thermal stability than the ordered one [4], due to the formation of Ni-rich and Ni-poor domains in the disordered compound, leading to two Jahn–Teller-distorted tetragonal phases with different Ni-Mn ratios [18]. In addition, nickel doping reduces the decomposition temperature, since the Ni²⁺-O bond is weaker than the Mn⁴⁺-O bond, resulting in a lower activation energy barrier for thermal decomposition [15]. The effect of other dopants can also be explained by the nature of the substituent cations and the metal–oxygen bond strength [15,19].

In summary, the decomposition temperatures of several materials are listed in

Table 2. Decomposition temperatures of several Mn-based oxides.

Compounds	Onset Temperatures of Decomposition (°C)	Reference
Li0.45(Ni0.8Co0.15Al0.05)O2	190	[16]
Li0.55(Ni1/3Co1/3Mn1/3)O2	250	[16]
0.22Li2MnO3∙0.78Li(Mn0.143Ni0.429Co0.429)O2	275	[20]
LiNi0.5Mn1.5O4 (ordered)	300	[4]
LiNi0.5Mn1.5O4 (disordered)	240	[4]
LiMn2O4	600	[21]
LixMn2O4	152~200	[22]

.

2.1.3. Pristine Structures and Their Formation

The cycling performances of rechargeable Li-ion batteries also greatly depend on the structural integrity of the host materials during electrochemical processes [23]. Therefore, the structures of electrode materials are important.

Table 3. Several crystal structures of Mn-based cathodes.

Type	Compounds	Symmetry	Space Group	Reference
Layered	LiMnO2	orthorhombic	Pmmn	[24]
		Monoclinic	C2/m	[25]
	Li(Ni1−x−yCoxMny)O2	Hexagonal	R$\overline{3}$m	[26]
	LiMn2O3	monoclinic	C2/m	[27]
	xLi2MnO3∙(1 − x)LiMO2	Hexagonal & monoclinic	R$\overline{3}$m & C2/m	[27]
Spinel	LiMn2O4	Cubic	Fd$\overline{3}$m	[28]
	LiNi0.5Mn1.5O4	Cubic	Fd$\overline{3}$m	[18]
		Cubic	P4332	[18]

summarizes the structures of several Mn-based cathodes for Li-ion batteries.

• Layered Mn-based Oxides

The main structural characteristics of layered oxides are: they adopt the $\mathsf{\alpha }$-NaFeO₂ structure as prototype, and possess cubic closed oxygen stacking, with metal ions occupied the O_h sites orderly [29].

1. LiMnO₂

LiMnO₂ has two competing ordered-rocksalt structures: orthorhombic LiMnO₂ (o-LiMnO₂, Pmnm) and monoclinic LiMnO₂ (m-LiMnO₂, C2/m). O-LiMnO₂ has an ordered-rocksalt structure in which MnO₆ and LiO₆ octahedra are arranged in corrugated layers. M-LiMnO₂ has the cation ordering structure, in which Li ions are located in the layers of O_h sites between MnO₂ sheets [30].

If there is no JT effect, LiMnO₂ is expected to be stable in the α-NaFeO₂ structure (space group R$\overline{3}$m), like LiCoO₂ [31]. When the cooperative JT distortion is introduced by Mn³⁺ (t_2g³e_g¹), the symmetry is reduced to monoclinic (C2/m). M-LiMnO₂ is unstable compared to o-LiMnO₂, which is attributed to the collective distortion of octahedron in the corrugated-layer structure reducing the elastic energy and its 3d spin ordering caused by the interaction between these moments [24,32].

O-LiMnO₂ is generally synthesized by high-temperature methods [33], while undoped m-LiMnO₂ has only been prepared by metastable synthesis routes such as ion-exchange from NaMnO₂ and hydrothermal reaction [33]. However, doped LiMnO₂ has been produced in the monoclinic phase, such as the LiAl_xMn_1−xO₂, which is attributed to the non-JT effect of Al³⁺ [34].

The reasons of using different synthesis routs can be understood in terms of the relative sizes. The radius order of widely used cations in Li-ion batteries is: Li⁺ (0.76 Å) > Ni²⁺ (0.69 Å) > Mn³⁺ (0.65 Å) > Co³⁺~Ni³⁺~Mn⁴⁺ (0.54 Å). Larger difference between Li⁺ and metal ions is beneficial to the formation of 2D structure [29], as a result, LiCoO₂ and LiNiO₂ enable strictly 2D layered oxides, while Mn³⁺ requires larger Na⁺ (1.02 Å) to stabilize the layered structure, which then act as a precursor to obtain LiMnO₂ by ion exchange [29].

2. LiNi1_−x−yCo_xMn_yO₂

Chemical substitution at the metal site of layered LiMnO₂ has been intensively explored and several materials including two or three 3d metals were produced synthetically considering cost reduction, safety and energy density, such as LiNi_1/3Co_1/3Mn_1/3O₂, LiNi_0.5Co_0.2Mn_0.3O₂, LiNi_0.6Co_0.2Mn_0.3O₂, LiNi_0.8Co_0.1Mn_0.1O₂, etc. They can be considered as solid solutions between LiCoO₂, LiNiO₂ and LiMnO₂, isostructural with the pure LiCoO₂ [26]. However, the distribution of the Ni, Mn, and Co metal cations is controversial: (1) considering the distribution as complete random in the established model [35]; (2) confirming the formation of Ni²⁺ and Mn⁴⁺ clusters through neutron pair distribution function (PDF) analysis, ⁶Li magic angle spinning (MAS), nuclear magnetic resonance (NMR) spectroscopy, extended X-ray absorption fine structure (EXAFS) studies, and reverse Monte Carlo (RMC) calculations [36,37,38]; and (3) demonstrating long range ordering through calculations [39,40]. This may influence the oxidation state of Ni and Mn ions and electrochemical profile [37].

The oxidation states of the Ni, Co and Mn ions in LiNi_1−x−yCo_xMn_yO₂ are +2, +3 and +4, respectively [6]. This can be explained by the different ionization energies of TM ions in oxide framework [2]. Take Li(Ni_0.5Mn_0.5)O₂ as an example. Since Mn³⁺ is more susceptible to be oxidized than Ni²⁺ (Figure 1), to meet the neutral requirements, the predicted valences of Mn and Ni are +4 and +2, respectively [2].

3. Li₂MnO₃

Li₂MnO₃ exhibits an O3-type structure described in the monoclinic system (space group C2/m), and can be written in the normal layered stoichiometry as Li[Li_1/3Mn_2/3]O₂ [41]. The ordered distribution of the Mn⁴⁺/Li⁺ cations in the mixed [Li_1/3Mn_2/3]O₂ layer formed a honeycomb pattern in which lithium ions are surrounded by six metal ions [29].

Li₂MnO₃ was considered an electrochemically inactive material for a long time, since Mn⁴⁺ can hardly be oxidized further and the absence of free sites for extra lithium ions. However, it becomes electroactive when it is treated by acid [42] or charged to high potentials [27], which is attributed to the leaching of Li₂O from the rock salt phase as well as the H⁺/Li⁺ ion exchange. Considering Li₂MnO₃ is inactive in the range of 3~4 V and its (001) interlayer spacing is similar to the (003) spacing of layered LiMO₂ (4.7Å) [20], it is possible to use Li₂MnO₃ as a structural stabilizer in layered LiMO₂, leading to the formation of Li-rich layered oxide.

4. Li-rich Layered Oxide

Materials made of Ni, Co and Mn with Li in excess (also termed as Li-Rich NCM) were firstly introduced by Thackeray et al. in 1993 [43]. These compounds are often written as three different notations: xLi[Li_1/3Mn_2/3]O₂∙(1 − x)LiMO₂, xLi₂MnO₃∙(1 − x)LiMO₂ or Li_1+xM_1−xO₂ (M = Mn, Co, Ni, etc.) [6].

The structure of Li-Rich NCM can be considered as a solid solution or a nanocomposite of layered Li₂MnO₃ and LiMO₂. Perhaps the most wildly accepted statement [6] is the nanocomposite structure, in which the distribution of Li₂MnO₃-like and LiMO₂-like nanodomains is short-range ordered, but not a completely solid solution. The peaks in Li-rich layered oxide XRD pattern can be indexed to the R$\overline{3}$m space group, with some exceptions in the 20°~25° range attributed to C2/m space group [29].

Synthesis routs will influence the structure and electrochemical performance of Li-rich layered oxide. For example, materials synthesized by hydrothermal assisted method are more uniform than those synthesized by co-precipitation and sol-gel methods, and hence demonstrate much better performances [44]. Xiang et al. claimed that preparation temperature significantly affect the oxidation process of cathodes during first charge [45].

• Spinel-type Mn-based Oxides:

1. LiMn₂O₄

The cubic spinel LiMn₂O₄ has a cation distribution of (Li)_8a[Mn³⁺Mn⁴⁺]_16dO₄. The O ions located at the 32e sites form a cubic closest packed (ccp) structure, and the T_d 8a sites are occupied by Li ions and the O_h 16d sites are occupied by Mn ions [46]. MnO₆ octahedrons are connected to each other through edge-sharing and hence form a three-dimensional network for lithium diffusion.

LiMn₂O₄ can be easily synthesized in air from variety precursors, reflecting the stability of spinel structure in Li-Mn-O system. If Li ions are extracted from the layered phase, the stable domain will fall into the spinel phase (Figure 2a).[47] Though spinel phase is metastable with respect to the formation of β-MnO₂ (Figure 2b), this transformation requires the rearrangement of the oxygen layers, and thus spinel structure is stable under common conditions [12].

2. LiMn₂O₄-based High-voltage Spinel Compounds

For Li_xM_yMn_2−yO₄ (M = Ni, Co, Fe, Cr, Mg, Al, Ti, Cu, Zn, etc.), the introduction of alien cations will not compromise the spinel structure. There are two different structures in LiNi_0.5Mn_1.5O₄ related to the annealing history: disordered Fd$\overline{3}$m phase (Ni and Mn randomly occupy the 16d sites) and ordered P4₃32 phase (Ni and Mn is located in 4a and 12d sites, respectively) [48]. Annealing at 700 °C makes the structure transformed from Fd$\overline{3}$m to P4₃32, leading to the ordering of Ni and Mn ions [18].

2.2. During Electrochemical Cycles

2.2.1. Involved Redox Couples and Voltage Profiles

In the traditional cathodes, lattice oxygen mostly acts as a pillar to maintain the structure without participating redox processes. As lithium ions are extracted from the host material, charge neutrality requires changing the valence state of the TM or oxygen ions. The potential and possible involved redox couples depend on its electronic structure and chemistry, which can be predicted at a certain extent through theoretical computations.

According to the Nernst equation, the voltage of a cell can be expressed as [49,50,51]:

$$\mathrm{Voltage}=-\frac{{\mu }_{\mathrm{Li}}^{\mathrm{cathode}}-{\mu }_{\mathrm{Li}}^{\mathrm{anode}}}{ze}$$

(3)

where e is the charge of an electron, ${\mu }_{\mathrm{Li}}^{\mathrm{cathode}}$ and ${\mu }_{\mathrm{Li}}^{\mathrm{anode}}$ is the chemical potentials per Li atom of in the cathode and anode respectively, z is the valence of the ion, here z equals to 1.

In an intercalation system, since only the chemical potential and the amount of Li ions are changed during the charge/discharge processes, while the temperature and pressure remain constant, the Gibbs free energy can be written as:

$$dG={\mu }_{Li}d{N}_{Li} \left(\mathrm{constant\; temperature\; and\; pressure}\right)$$

(4)

where ${\mu }_{Li}$ is the chemical potential of Li, N_Li is the amount of Li, and G is the Gibbs free energy per Li_xMA formula unit (MA represents the host of electrode material).

For instance, consider the operating voltage of Li_xCoO₂ (0 < x < 1):

$$\mathrm{Voltage}=-\frac{{\mu }_{\mathrm{Li}}^{{\mathrm{Li}}_{\mathrm{x}}{\mathrm{CoO}}_2}-{\mu }_{\mathrm{Li}}^{\mathrm{anode}}}{e}=-\frac{\frac{dG}{d{N}_{Li}}-{\mu }_{\mathrm{Li}}^{\mathrm{anode}}}{e}\approx -\frac{G\left({\mathrm{Li}}_{\mathrm{y}}{\mathrm{CoO}}_2\right)-G\left({\mathrm{Li}}_{\mathrm{x}}{\mathrm{CoO}}_2\right)-{\mu }_{\mathrm{Li}}^{\mathrm{anode}}}{e\left(y-x\right)}$$

(5)

Li metal is usually used as the reference anode, and its chemical potential is ${\mu }_{\mathrm{Li}}^{\mathrm{anode}}$ = −1.9 eV. Any changes in structure or chemistry of electrode during electrochemical cycles will alter its Li-chemical potential and Gibbs free energy, and hence the voltage. From this point of view, voltage measurements can provide direct thermodynamic information [49].

• Redox Couples Related to Transition Metal Cations

The 3d transition metal oxides (3d TM) are generally selected as the host owing to their appropriate energy to match the O 2p orbitals and relatively smaller molar mass. If the voltage values of several fictitious batteries combined with different TM oxides and metal Li are calculated with the hypothesis that all TM ions have the same valence, then one can obtain the voltage decreased with the order Cu > Ni > Co > Fe > Mn > Cr > V > Ti [7]. This is mainly caused by the decreased d-levels of the late TM oxides [51]. Moreover, in most lithium manganese oxides, lithium insertion into O_h sites with simultaneous reduction of Mn(IV) to Mn(III) occurs at a voltage just above 3.0 V vs. Li. A higher voltage can be obtained if lithium is accommodated on T_d sites [52].

Several factors can influence the intercalation potential. Chen et al. [53] found that the intercalation potential is related to the electron affinity of transition metal cation, which is dominated by the combination of crystal-field splitting and the on-site d-d exchange interactions. Ceder et al. [51] claimed that the structural symmetry can affect the voltage. They believed that the transition metal is less important in determining the voltage than previously thought, and it should be considered much more as a means to stabilize the oxide structure since its d-bands are above the p-states of oxygen [51]. In addition, for polyanionic-type materials, the voltage can be tuned by XO₄ groups (such as substitution of PO₄ by SO₄), which can be attributed to the weakened or strengthened covalency of TM-O bonds determined by the inductive effect of XO₄ groups [54].

• Redox Couples Related Oxygen Anions

The fact that Li-Rich layered oxide can deliver excess capacity beyond the theoretical TM redox capacity at high voltage attracts great attention of researchers. This is attributed to the activation of oxide anions of the Li₂MnO₃-domain [20].

Rozier et al. [29] summarized the parameters influencing oxygen release from the behavior of Li₂Ni_0.5Te_0.5O₃, Li₂Ru_1−ySn_yO₃, Li₂Fe_0.5Sb_0.5O₃, Li₂Fe_0.28Te_0.5O₃ and Li₂IrO₃ systems, and conclude that if the highest voltage is lower than the value of the E⁰ (O²⁻/O²) redox couple (4.3 V), oxygen evolution will not occur, consistent with the statement of Saubanere et al. [55]

The mechanism of anionic redox is related to hybridization between the orbitals of TM ions and oxygen ions [56]. Seo et al. [57] proposed that the Li-O-Li configurations caused by the Li-excess environment around O contribute to the activation of anionic redox, since the extraction of labile electrons comes from unhybridized O 2p states in Li-O-Li configurations. Saubanere et al. [55] suggested an M-driven reductive coupling mechanism, in which the M-O covalency determined the possibility of reversible O oxidation. The strong overlapping of the M (nd)-O (sp) bands is explained as the driving force for the formation of (O²)ⁿ⁻ species. Luo et al. [58] demonstrated that O-(Mn⁴⁺/Li⁺) extract electrons more easier than O-(Ni⁴⁺/Co⁴⁺), owing to its more ionic and localized O 2p orbitals interactions. Saubanere et al. [55] claimed that the stronger 3d TM-O bonds comparing to 4d/5d TM-O bonds and no empty MO*-orbitals closing to the top of O-band make O₂ evolution easier in 3d TM system.

• Voltage Profiles

While the involved redox couples mirror the voltage values, the shape of voltage curves is determined by the electrochemical process. Voltage profiles can be speculated from Equation (5), as shown in Figure 3 [49]. In addition, if an electrode material forms solid solution in charge/discharge processes, its voltage profile exhibits a smooth sloping as occurring in LiNi_1/3Co_1/3Mn_1/3O₂, while, if a first-order phase transformation takes place, the profile will show a plateau as occurring in LiMn₂O₄.

2.2.2. Phase Changes during Cycling

Phase changes during cycling, especially long-term cycling, affect the performance of cathode material obviously. The attempt of the ideal host material, which can maintain its structure during the intercalation/deintercalation of lithium ions, sometimes fails, due to the varied chemical environment during electrochemical processes. However, the phase changes may be kinetically controlled, and hence some materials are relatively stable during cycling. The phase behavior of different materials varied widely, which will be discussed in this part.

• Layered LiMnO₂

The layered-to-spinel transformation is thermodynamically favored in both Li_xCoO₂ and Li_xMnO₂, however, LiCoO₂ does not undergo such a conversion. This suggests the transformation is related to kinetic factors [12]. When layered Li_0.5MnO₂ convert to spinel, one-fourth Mn ions move into the lithium layer corresponding to the 16d sites of spinel, while lithium ions migrate to T_d sites corresponding to the 8a positions of spinel.

Reed et al. [59] claimed a two-stage mechanism for the layered-to-spinel conversion. In the first stage, a fraction of Mn ions rapidly migrate to adjacent T_d sites in the lithium layer owing to the low activation barrier (0.2 eV) and the disproportionation reaction of Mn³⁺, accompanied by roughly an equal amount of lithium ions entering octahedral vacancies left by Mn, and hence forming “Li-Mn dumbbells”. In the second stage, the tetrahedral Mn ions and octahedral Li ions rearrange to form the final spinel phase. Vitins et al. [52] also suggested that the high mobility of Mn²⁺ leads to the random distribution of Mn cations, which can easily relax to the Mn distribution characteristic of spinels.

• Li(Ni_1−x−yCo_xMn_y)O₂:

In Li(Ni_1−x−yCo_xMn_y)O₂, with the increase in Mn content and decrease in Ni content, the reversible capacity decreased, whereas the structural stability improved (Figure 4) [5,6,60].

This might be attributed to the following reasons: (1) Ni ions act as the main active redox species (Ni²⁺/⁴⁺) but have poor thermal stability. The highly reactive Ni⁴⁺ can accelerate the side reactions with electrolyte, which cause a thick insulating solid-state electrolyte interface layer [61]. The migration of Ni²⁺ destroys active lithium sites, leading to a gradual capacity decline[61]; (2) Mn⁴⁺ ions provided significant structural stability attributed to its octahedral affinity and non-JT effect [3]; (3) Co offers increased electrical conductivity and lowered the cation mixing between Li and Ni, resulting in an excellent rate capability [5,62,63].

However, slight phase changes can still occur in Li(Ni_1/3Co_1/3Mn_1/3)O₂, as demonstrated by Yin et al. [26] who claimed that the phase of Li_x(Ni_1/3Co_1/3Mn_1/3)O₂ changes from O3 phase (R$\overline{3}$m) to the O1 (P$\overline{3}$m1) when charged to x = 0.3, as a result of minimizing the van der Waals gap interactions. When x > 0.3, small volume variation (1%) is observed and the structure is maintained, while, if x < 0.3, re-intercalation of lithium was relatively irreversible in the subsequent cycle accompanied by a large volume change (7.2%).

• Li-rich Oxides:

In the initial charge, Li-rich compounds present a staircase charge profile and an S-shape discharge profile. Afterwards, the S-shape voltage profile is preserved on subsequent charge/discharge cycles [29]. The initial charge curve consists of two regions: a sloping before 4.4 V and a plateau after 4.4 V. During the first part, Li is extracted with the oxidation of the TM ions. The second part consists of Li being removed accompanied by the reversible or irreversible oxidation of oxide ions [6].

In the first cycle, several phase changes occurred: (1) oxygen is evolved from the surface of the material [64], whereas the bulk oxygen is oxidized without oxygen loss [65]; (2) irreversible loss of O₂ results in O deficient layered materials [65,66]; and (3) the changed oxygen and charge environment induce the transition metal ions’ diffusion from surface to bulk, and hence result in a denser lattice [64]. Moreover, metal ions tend to occupy the neighboring O_h sites left by lithium ions as well as rearrange in the metal plane [67,68,69,70]. Though the exact structure of the defect phase is not completely clear, it is generally considered as a spinel-like phase [6,13,14].

Due to the severe phase changes in the first cycle, it can be anticipated that the realized reversible capacity during subsequent cycles is closely connected to the behavior in the first cycle. It has been reported that the reversible capacity is proportional to the length of the plateau region, which could be changed by doping [71]. Manthiram et al. [71] systematically studied how the doping ions affects the plateau length, and demonstrated that the plateau region decreases with the order Co > pristine > Fe > Al > Cr > Ga, attributed to the decreased metal–oxygen covalence. In addition, Lee et al. [72] suggested that the length of plateau region during the first charge significantly affect the voltage decay of Li-rich layered oxides.

It should be mentioned that the origin of plateau region is the phase conversion during cycling, and thus the formation of spinel-like phase leads to a series of phenomenon, such as voltage hysteresis, capacity and voltage fading. The voltage hysteresis, closely related to the Li₂MnO₃ component [73], is caused by the migration of TM ions into Li⁺ layers [74,75]. Since the movement is some extent irreversible, the inactive metal ions in Li-layer result in a capacity fading [74]. The phase transformation and the microstrain within particles [29,76] also attributed to the capacity decay. Though the mechanism of voltage fade is still controversial, the main statements are [6]: (1) Li was trapped in the dumbbell structures accompanied by the migration of TM ions; and (2) TM ions are trapped in Li-layer or tetrahedral sites.

Extensive work has been done to improve the performance of Li-rich layered oxides from these aspects: (1) inhibit the growth of the spinel-like phase [77,78]; (2) protect electrode from side reactions with the electrolyte [79]; (3) form composite materials [80,81]; and (4) reduce the oxygen partial pressure on the surface of material [82].

• LiMn₂O₄

In theory, LiMn₂O₄ can either be discharged or charged initially, and then cycled over a composition range of 0 ≤ x ≤ 2 in Li_xMn₂O₄. When Li_xMn₂O₄ is discharged in the range of 1< x <2, lithium ions are inserted to empty O_h 16c sites, accompanied by a large anisotropic volume change (6.5%) caused by the formation of tetragonally distorted Li₂Mn₂O₄ [27,28]. As a result, in practice, the cycle is generally limited in 0< x <1, in which lithium ions are intercalated/deintercalated from the T_d 8a sites, and the cubic structure is maintained. In fact, Li_xMn₂O₄ (0< x <1) is not thermodynamically stable at low lithium content. The excellent structural stability may be explained as follows: (1) when x ≈ 0, Mn ions are primarily in +4 valence state with low mobility; and (2) when x ≈ 1, there are insufficient Li vacancies for Mn rearrangement [2].

However, gradual capacity fading was still observed, especially at elevated temperature (>55 °C). This is attributed to the following reasons: (1) The dissolution of Mn²⁺, associated with Mn³⁺ disproportionation (Equation (6)) in the presence of acidic components of the LiPF₆/organic carbonate electrolyte solutions, destroys the spinel structure and the leaving Mn⁴⁺ which cannot be oxidized further [27,83]; (2) The two-phase structure in the high voltage region easily transformed to a one phase structure (e.g., a lithium-rich structure) accompanied by the dissolution of Mn and the loss of oxygen [83,84].

$$2{\mathrm{Mn}}^{3+}\left(\mathrm{solid}\right)\to {\mathrm{Mn}}^{4+}\left(\mathrm{solid}\right)+{\mathrm{Mn}}^{2+}\left(\mathrm{solution}\right)$$

(6)

• LiMn₂O₄-based High-voltage Spinel Compounds

To avoid the Jahn–Teller effect caused by Mn³⁺ and Mn dissolution, the oxidation state of Mn is increased by substituting Mn with lower valence metal ions, causing a series of compounds with a general formula of LiM_xMn_2−xO₄ (M = Ni, Co, Fe, Cr, Mg, Al, Ti, Cu, Zn, etc.). Those compounds can deliver capacities at around 5V, and thus the corrosion reaction between the cathode surface and electrolyte is one of the main problems [18]. In LiNi_0.5Mn_1.5O₄, the amounts of dissolved Mn and Ni increase with state of charge, temperature, and storage time [85]. Moreover, the phase change behavior of the ordered phase is different from that of disordered one, though they all go through three stages [86]. In the ordered phase, the change occurs earlier during discharge since a larger parameter variation [86].

3. Kinetics

Diffusion properties of electrode affect some of the key properties in Li-ion batteries, such as rate performance, cycling stability and practical capacity [87,88]. In the following part, the electrical and ionic conductivity will be discussed.

3.1. Electrical Conductivity

The intrinsic electrical conductivity originates from the electronic structure of the electrode materials, which can be derived via quantum mechanical calculation. From a quantum mechanics point of view, only electrons nearing the Fermi level can be involved in the electron movement, which is more meaningful than the classical free electron gas model [87]. Therefore, it is necessary to discuss the electronic structures of cathode materials.

In most Mn-based intercalation cathodes, the TM-O covalent interaction arises mainly from the Mn-3d and O-2p hybridization. However, the type of Li–O bond is controversial: some researchers believed that Li⁺ is fully ionized [89], while others claimed a weak covalent interaction arising from the Li-2p/O-2p hybridization [90]. In the process of lithium insertion, each lithium loses almost one electron, and most of these electrons transfer to surrounding O-2p orbitals [90] or the Mn-3d band [91]. When lithium atoms are extracted from cathodes, the electrons are removed from the TM orbits in most cases. For example, in LiCr_xMn_2−xO₄, the electrons are first removed from Mn e_g, followed by Cr t_2g orbital [91]. The electrical conductivity of a cathode material can be determined, in some degree, by its electron densities at the Fermi level, which can be obtained from [87]:

$$\sigma =\frac{1}{3}{e}^2{v}_F^2\tau N\left(E_F\right)$$

(7)

$$N\left(E_F\right)=2{\left(\frac{k_{B}T}{2\pi {\hslash }^2}\right)}^{\frac{3}{2}}{\left(m_e{m}_h\right)}^{\frac{3}{4}}\exp \left(-\frac{E_g}{2k_{B}T}\right)$$

(8)

where σ is the electrical conductivity, S cm⁻¹; e is the charge of an electron, 1.602 × 10⁻¹⁹ C; N(E_F) is the number of available electron, mol eV⁻¹; v_F is the Fermi velocity, cm s⁻¹; τ is the relaxation time, s; k_B is the Boltzmann constant, 1.38054 × 10⁻²³ J K⁻¹; T is the temperature, K; $\hslash$ is the reduced Planck’s constant, 1.055 × 10⁻³⁴ J s; m_e is the effective mass of an electron, kg; m_h is the effective mass of holes, kg; and E_g is the band gap, eV.

Take LiMn₂O₄ as an example. The Fermi energy level (E_f) of LiMn₂O₄ is located in the Mn t_2g band and the Mn e_g band lies above it. There is an energy gap of about 2 eV between the O-2p and the Mn-3d band, reflecting a semiconductor feature [90,92]. When doped with Cu, the electrical conductivity increased owing to the contribution of Cu e_g holes to charge transport [93,94]. The band gaps and electrical conductivities at room temperature of several cathodes are summarized in

Table 4. Electrical conductivities of several cathodes at room temperature.

Cathode Material	Band Gap (eV)	Electrical Conductivity (S cm−1)	References
orthorhombic-LiMnO2	~1.9	-	[95]
LiCoO2	0.5~2.7	~10−4	[87]
Li(Ni1/3Co1/3Mn1/3)O2	-	5.2 × 10−8	[5]
Li(Ni0.5Co0.2Mn0.3)O2	-	4.9 × 10−7	[5]
Li(Ni0.6Co0.2Mn0.2)O2	-	1.6 × 10−6	[5]
Li(Ni0.8Co0.1Mn0.1)O2	-	1.7 × 10−5	[5]
LiMn2O4	0.28~2.2	~10−6	[87]
LiMnPO4	3.8~4.0	~10−14	[96]

. However, there are no viable theories to quantitatively describe the conduction properties using band gap analysis yet [87].

3.2. Ion Diffusion

Comparing to the ionic conduction, electrical conduction is not a dominant factor for intercalation cathodes in most cases [49,87]. Diffusion processes of Li-ion include several aspects such as grain boundary diffusion, anode and electrolyte resistance as well as interfacial diffusion. Here, we only focus on the lithium ion conductivity in Mn-based intercalation cathodes. In addition, the migration of cations will also be discussed.

3.2.1. Ion Transport Mechanisms

There are two concepts in describing the motion of Li-ions: ion diffusion coefficient D_i (or diffusivity) and ionic conductivity σ_i.

The diffusion coefficient of ions D_i (cm² s⁻¹) represents the ease of ions passing through Media under a concentration gradient, the definition of which is [49]:

$$-j_i=D_i\nabla c_i$$

(9)

where j_i is the ionic flux, mol cm⁻² s⁻¹; and $\nabla$c_i is the concentration gradient.

The ionic conductivity σ_i (s cm⁻¹) represents the motion of Li⁺ under external electrical potential, the definition of which is [87]:

$${\sigma }_i=j/\xi$$

(10)

where j is the current density, A cm⁻²; and ξ is the electric field, V cm⁻¹.

Both diffusivity and ionic conductivity are used to describe the motion of Li⁺. Generally, diffusion coefficient in electrode materials is hard to measure experimentally, whereas ionic conductivity is easier to measure, and thus the former could be deduced from measuring ionic conductivity [87]:

$${\sigma }_i=\frac{q_i^2{c}_i}{k_{B}T}{D}_i$$

(11)

where σ_i is the ionic conductivity, S cm⁻¹; q_i is numbers of holes, cm^-3; c_i is concentration of i, mol cm³; k_B is the Boltzmann constant, 1.38054 × 10⁻²³ J K⁻¹; T is the temperature, K; and D_i is the diffusivity of ions, cm² s⁻¹.

The generic diffusion mechanism for solid phase is a good start to understand the diffusion behavior in electrodes. Several diffusion mechanisms in solids are listed in

Table 5. Diffusion mechanisms in solids [97].

Mechanisms	Descriptions	Examples
Direct interstitial	An interstitial solid solution can diffuse by jumping from one interstitial site to one of its neighboring sites.	The diffusion of small foreign atoms such as H, C, N, and O in metals.
Collective	Simultaneous motion of several atoms in a chain-like or caterpillar-like fashion.	The motion of alkali ions in ion-conducting oxide glasses.
Vacancy	An atom jumps into a neighboring vacancy, making a series of exchanges with vacancies.	The diffusion of substitutional solutes and of matrix atoms in metals.
Divacancy	When a binding energy exists, which tends to create agglomerates of vacancies, diffusion occur via aggregates of vacancies.	The diffusion of Li+ in LiCoO2.
Indirect interstitial	A lattice atom is knocked out by a neighboring interstitial atom from its lattice positions under irradiating/ heating, and then deposited in the lattice as a self-interstitial.	Radiation-induced diffusion.
Interstitial-substitutional exchange	Some solute atoms may be dissolved on both interstitial and substitutional sites of a host crystal.	The diffusion of Au, Pt, Zn in silicon.

[97].

For intercalation cathode, Li-ions diffuse mainly by an interstitial or vacancy mechanism [87], the jump diffusion coefficient of which could be expressed as [49,87,98]:

$$D_i=a_l^2\Gamma$$

(12)

$$\Gamma =v^0\exp \left(-\frac{\mathsf{\Delta }G}{k_{B}T}\right)$$

(13)

where a_l is the jump length, $\Gamma$ is the hopping rate (or frequency), v⁰ is an effective vibrational frequency (or attempt frequency) and $\Delta$G is the activation barrier for the hop which can be determined by the nudged elastic band method.

From Equation (12), the diffusion coefficient is determined by jump rates and jump distance [97,99], which is affected by bonding potential and defects. As a result, it is important to consider crystal structure and surrounding potential carefully [87], which will be discussed in the next part.

3.2.2. Li⁺ Diffusion in Different Structures

The ion diffusion topology of lithium cathode can be divided in terms of the dimensionality, for example, 1D in olivine LiFePO₄ (Figure 5c), 2D in layered LiCoO₂ (Figure 5a) and 3D in spinel LiMn₂O₄ (Figure 5b). The dimensionality of diffusion has a considerable impact on macroscopic conductivity in a material [100].

• 1D Olivine:

The planes of Li chains in the olivine structure may form ion conducting 2D layers, analogous to layered LiMO₂ (M = Co, Mn, Ni, etc.). However, the Li ions within the chains are only 3.0 Å apart, whereas the distances between the chains are at least 4.7 Å. The large interchain distances, as well as the complex energy landscape between chains, make interchain Li hopping difficult and favor the adoption of [010]_Pnma axis as 1D tunnels [99]. Islam et al. [99] suggested a nonlinear, curved trajectory between adjacent Li sites. The diffusion coefficient D is 10⁻¹³~10⁻¹² cm² s⁻¹ for LiFe_1−xMn_xPO₄ [101].

• 2D Layered LiMO₂:

In layered transition metal oxides, such as Li_x (Ni_1/3Co_1/3Mn_1/3) O₂ and LiMnO₂, the least hindered hop path between neighboring O_h sites is along a curved path that passes through an adjacent T_d site (o–t–o migration), since the direct migration through the O-O edge shared by the O_h sites is too high in energy (Figure 6a) [49,102]. The energy of an intermediate T_d site is determined by its coordinated extent with neighboring cations. In the layered host, the intermediate T_d site shares a face with an octahedron which contains a transition metal, resulting in a strong repulsion [49]. However, when hopping into a divacancy, the repulsion is absent and hence the migration barrier is smaller. Therefore, lithium diffusion is predominantly mediated by a divacancy mechanism in layered oxides [49]. Since the diffusion channel passes through one adjacent TM ion, it is generally noted as a 1-TM channel. Moreover, all lithium sites in stoichiometric layered materials are equivalent, and thus form a 2D network. The diffusion coefficient is 10⁻¹³~10 ⁻⁷ cm² s⁻¹ for LixCoO₂ [99].

The two dominant factors affecting diffusion coefficient are: the size of T_d site determined by the c-lattice parameter, and the electrostatic repulsion between Li and neighboring transition metal ions [103]. The chemical diffusion coefficient has a strong concentration dependency, which decreases as Li ions are removed, owing to the increase in effective valence of TM ions and the contraction of the lattice parameter [49,98]. For example, the activation barrier in Li_xCoO₂ increases by more than 300 meV as x is reduced from 1 to 0 [98]. Other factors such as cation doping can be interpreted in terms of the size and electrostatic effect. Electronic effects can also affect the migration barriers when JT cations are involved.

Other factors arise from the wide compositions and complex structure in layered-LiMO₂ (M = Ni, Co, Mn, Al, etc.) system. In alloyed layered compounds such as Li_x (Ni_1−y−zCo_yMn_z)O₂, additional complexity is introduced by the different electron affinities of TM ions. For instance, in Li (Ni_0.5Mn_0.5) O₂, in which Ni and Mn are in +2 and +4 valence state, respectively, the diffusion barrier passed by Ni²⁺ ions is lower than that passed by Mn⁴⁺ ions. Venkatraman et al. [104] demonstrated that cation disorder in Ni-rich LiNi_1−x−yCo_xMn_yO₂ materials significantly decreases the lithium extraction rate through chemical extraction experiment, consistent with the study of Urban et al.[105] It can be interpreted by the smaller slab distances. However, the disordered materials with excess lithium are reported to possess facile lithium diffusion, which can be attributed to the formation of 0-TM channels in the presence of excess lithium environment [104].

• 3D Spinel:

Spinel structure is usually considered as quick ionic conductor. In LiMn₂O₄, Li ions migrate by hopping straightly from one 8a site to another 8a site through the intermediate 16c site (8a-16c-8a) [46]. Each face of the 8a site is shared with a 16c site, forming a 3D diffusion path inside the structure. A single vacancy mechanism is adopted since the intermediate O_h sites have no coordinated metal ions sites (Figure 6b).

Different dopants significantly affect the lithium diffusion coefficient [94]. Yang et al. suggested that doping of the spinel with other transition metals, particularly with Cu, can further reduce the barrier for Li migration, which may be attributed to the appropriate cation arrangement [94]. Nakayama et al. claimed that partially replace Mn with Co can improve the lithium conductivity owing to the charge disproportionation of Co^3.5+ [46]. For LiNi_0.5Mn_1.5O₄, the disordered phase has higher ionic conductivity, due to its reduced repulsive interactions among lithium ions caused by the randomly distributed Mn ions [106], and less intergrain stress as a result of the one-phase reaction upon charging [107]. In addition, local charge distribution may also influence lithium diffusion in LiMn₂O₄. Xu et al. demonstrated that Mn⁴⁺ can facilitate ion conduction [50].

In summary, Li-ion battery cathodes generally exhibit Li⁺ diffusivities in the range of 10⁻¹⁶ to 10⁻⁸ cm² s⁻¹ at room temperature (

Table 6. Lithium diffusion coefficients of layered and spinel Mn-based oxides.

Category	Materials	Diffusivity (cm2 s−1)	Preparation Methods	Measurement Techniques	References
Layered	Li[Ni0.5Co0.2Mn0.3]O2	~1 × 10−8	Atomic layer deposition (ALD)	CV	[108]
	Li0.99Al0.01Ni0.5Co0.2Mn0.3O2	2.41 × 10−11	Solid-state reaction	EIS	[109]
	Al2O3-coated Li[Ni0.5 Co0.2Mn0.3]O2	~0.5 × 10−8	ALD	CV	[108]
	ZrO2-coated Li[Ni0.5 Co0.2Mn0.3]O2	1.5~2.5 × 10−8	ALD	CV	[108]
	MgO-coated Li[Ni0.5 Co0.2Mn0.3]O2	3~4 × 10−8	ALD	CV	[108]
	Li1.2Ni0.13Co0.13Mn0.54O2	~10−16	Pulse laser deposition (PLD) method	DART−ESM	[110]
	Hollow hierarchical microspheres Li1.2Ni0.13Co0.13Mn0.54O2	1.34 × 10−15	Molten salt method	EIS	[111]
	Li1.17Ni0.23Mn0.58Mg0.02O2	2.10 × 10−15	Co-precipitation method	EIS	[112]
	Graphene@CNTs-modified Li1.165Ni0.167Co0.167 Mn0.501O2	~10−9	Ultrasonic-assisted co-precipitation method	CV	[113]
	Carbon-coated Li1.2Co0.4Mn0.4O2	10−12~10−9	Self-combustion reaction (SCR)	GITT	[114]
Spinel	LiNi0.5Mn1.5O4(ordered)	~5 × 10−10	Acquired from corporation	GITT	[106]
	LiNi0.5Mn1.5O4 (ordered)	10−9~10−8	-	Theoretical studies	[115]
	thin film LiNi0.5Mn1.5O4 (ordered)	10−12~10−10	Electrostatic spray deposition technique	EIS	[116]
	LiNi0.5Mn1.5O4 (ordered)	1.252 × 10−14	Co-precipitation method	EIS	[107]
	thin film LiNi0.5Mn1.5O4 (ordered)	10−12~10−10	PLD	PITT	[117]
	LiNi0.5Mn1.5O4 (disordered)	~10−9	Acquired from corporation	GITT	[106]
	thin film LiNi0.5Mn1.5O4-δ (disordered)	10−12~10−10	PLD	PITT	[118]
	LiNi0.25Cu0.25Mn1.5O4	10−14~10−13	Sol-gel method	PITT	[94]
	LiNi0.45Cu0.05Mn1.5O4	~10−9	Sol–gel method	GITT	[119]
	LiNi0.45Co0.1Mn1.45O4	8 × 10−12~7 × 10−10	PVP-combustion method	PITT	[120]
	LiNi0.5Mn1.5O4/Li7La3Zr2O12 composite cathode	1.83 × 10−10	Spray drying method	CV	[121]
	SiO2-Coated LiNi0.5Mn1.5O4 (ordered)	1.437 × 10−14	Co-precipitation method	EIS	[107]
	Polyimide-Coated LiNi0.5Mn1.5O4 (ordered)	1.154 × 10−14	Co-precipitation method	EIS	[107]

CV: cyclic voltammetry; EIS: electrochemical impedance spectroscopy; DART-ESM: dual AC resonance tracking-electrochemical strain microscopy; GITT: galvanostatic intermittent titration; PITT: potentiostatic intermittent titration technique.

), affected by their structural dimensionality, preparation method and measurement techniques.

3.2.3. The Mobility of Cations

The mobility of cations is closely related to the phase change during cycling. For example, the layered-to-spinel transformation is energetically favored for almost all 3d transition metal layered oxides, which requires the rearrangement of metal ions since all the structures share the same cubic closed-packed (ccp) oxide framework [2]. However, the transform rate varies for each 3d metal, reflecting a kinetic factor in the transformation. Another example is the voltage hysteresis of Li-rich layered oxides which is caused by the migration of TM ions from TM-layers to Li-layers [73,74]. Therefore, it is necessary to discuss the mobility of cations.

Take the migration of Mn as an example, which occurs in the layered-/orthorhombic-LiMnO₂ and Li-rich layered oxides. Reed et al. [2] pointed out that the valence and electronic structure play significant roles in determining the mobility of Mn, rather than the size effects, which can be understood by the ligand-field theory (LFT). Since the low-energy pathway for TM ion migration between O_h sites is octahedral-tetrahedral-octahedral (O_h → T_d → O_h), the change of ligand-field stabilization energy (LFSE) for TM ion movement between O_h and T_d coordination will determine the transformation resistance [2,4]. Mn⁴⁺ (3d³) is the most stable valence in O_h coordination, due to the increased energy when migrate from O_h (t_2g³) site to T_d (e²t₂¹) site (Figure 7a). Mn³⁺ has a reduced O_h affinity comparing to Mn⁴⁺ and less T_d preference than Mn²⁺, and thus $\mathsf{\Delta }{\mathrm{LFSE}}_{\mathrm{otc}\to \mathrm{tet}}$ has slightly positive value. However, the mobility is accelerated by the energetically favored charge disproportionation of Mn_oct³⁺ (t_2g³e_g¹), in which an additional electron transfers from the e_g orbital to the T_d Mn t₂ orbital (Figure 7b). Besides, other factors influencing the migration of Mn ions include [2]: (1) the d-orbital barycenter which is sensitive to cationic ordering; (2) the number of empty T_d sites determined by Li content; and (3) the amount of Mn²⁺ depending on the average degree of Mn oxidation. Considering that Mn⁴⁺ is the most stable in O_h coordination comparing to Mn²⁺ and Mn³⁺, it might be desirable for Mn to be electrochemically cycled near +4 valence state. However, oxidize Mn above +4 is difficult and may decompose to release O₂ [2]. When O₂ release occurred, such as in Li₂MnO₃, the valence of Mn ions may be reduced as a result of the changed oxygen charge densities [14], and thus the mobility of Mn ions is changed.

For the other 3d TM ions, their 3d orbitals have similar ligand-field spitting in O_h or T_d sites, and the magnitude of the splitting is determined by the extent of overlap between TM d and oxygen p states. Through similar calculation, Reed et al. [2] found that Ti⁴⁺ can easily move between O_h and T_d coordination attributed to its empty d band; for Cr^x+ (x = 3~4), Co^y+ (y = 3~4) and Ni^z+ (z = 3~4), a strong preference for O_h coordination is shown. Moreover, in the charged oxide cathodes, the mobility of metal cations decreases in the order Ni⁴⁺ > Co^x+ (3.5 < x < 4) > Mn⁴⁺ [4].

4. Conclusions

Mn-based cathodes are being pursued as cathodes for next generation Li-ion batteries, due to their native advantages of high abundance, inexpensive price, acceptable activity, and low toxicity. This report has provided a brief account of thermodynamic and kinetic understanding on Mn-based intercalation cathode materials. Generally, for Mn-based cathodes, the Jahn-Teller effect caused by Mn³⁺ (t_2g³e_g¹), the disproportionation reaction of Mn³⁺, the mobility of Mn ions in different valence states (Mn²⁺ > Mn³⁺ > Mn⁴⁺), and the structural features significantly influence their behavior in electrochemical processes. Besides, thermodynamic and kinetic factors should be considered equally in relatively structural stability, phase transformations, electrical and ionic conductivity, etc. These insights are valuable in the design of new cathode materials for the next generation Li-ion batteries.