Single crystal layered oxides as cathode materials for next-generation lithium-ion batteries

Rapid climate change and the increasing frequency of natural disasters are increasingly attributed to global warming, which is a result of the industrial era and the growing consumption of fossil fuels. One strategy proposed to mitigate the adverse anthropogenic impact on the environment is the transition from internal combustion engine vehicles to electric vehicles. Despite the ongoing debates about the actual efficiency of this switching for decreasing the CO₂ emissions (measured in kg of CO₂ per km travelled), which depends on the nature of the electricity source (coal, gas, nuclear power, renewable energy) used to manufacture and charge electric vehicles,[1] these vehicles are being used more and more often as part of global efforts to reduce the carbon footprint. This imposes increasing demands on the next generation of lithium-ion batteries (LIBs), which are currently the most promising rechargeable power source for electric vehicles. Currently, LIBs have achieved specific energies of approximately 300 W h kg^–1 at the cell level, which is adequate for electric vehicles with a driving range of up to 600 km.[2][3] However, for vehicles with longer driving ranges, further increase in the energy density of LIBs is required.[4][5]

It is well known that the energy and power characteristics of LIBs are mainly limited by the positive electrode (cathode) material, which is the most expensive component of the battery. Therefore, to overcome the technological restrictions and design a new generation of LIBs with specific energy above 300 Wh kg^–1, it is necessary to develop cathode materials with enhanced electrochemical capacity. The layered oxides LiNi_xMn_yCo_zO₂ (x + y + z = 1, х≥0.6, so-called Ni-rich NMC)^* are considered to be excellent candidates for modern LIBs owing to their high discharge capacity (≥180 mA h g^–1),[6][7] which can be improvedby increasing the nickel content in NMC. However, cathode materials with a high nickel content (x > 0.8), while possessing markedly higher electrochemical capacity, are severely limited in practical applications due to pronounced capacity loss during electrochemical cycling and to low thermal stability, which poses a threat to the safe operation of the battery.[8]

The problem of electrochemical capacity degradation is related, first of all, to microstructural features of cathode materials based on NMC layered oxides. Cathode materials that are currently used in commercial LIBs are mainly based on particles (polycrystalline, PC-NMC, below referred to as polycrystalline NMC) that represent spherical agglomerates of 5 – 15 μm composed of randomly oriented primary particlesof < 0.5 μm (Fig. 1а).[7][9]

Fig. 1

SEM images of PC-NMC (а) and SC-NMC (b) materials. Author’s figure taken from the archive to a publication.⁹

The charge/discharge process in NMC includes a few phase transitions accompanied by a sharp decrease in the distance between the transition metal layers in the layered structure.[7][10-12] The sharp change in the interlayer spacing causes deformation of the crystal lattice, giving rise to mechanical stress within the electrode structure and, finally, results in a loss of mechanical integrity (cracking) of the agglomerates consisting of primary grains, thus accelerating the material degradation. These adverse consequences become even more grave in the case of Ni-rich NMC for which more than 80 – 90% of lithium can be extracted during electrochemical cycling. In this case, anisotropic expansion/contraction of the crystallographic unit cell during charge/discharge process results in the formation of microcracks not only at the level of agglomerates, but also at the level of primary particles, which results in a rapiddecrease in the LIB capacity.[13][14]

Apart from the polycrystalline morphology, NMC can be obtained as separate non-agglomerated primary particles of ≥1 µm in size (Fig. 1b) (single-crystal, SC-NMC, or monolithic particles;[15-17] here referred to as single-crystal NMC). However, these particles are not perfect single crystals but rather large crystalline grains devoid of internal grain boundaries characteristic of agglomerated structures. The absence of grain boundaries provides these materials with higher stability during electrochemical cycling due to lower mechanical stress concentrations and a reduced tendency for cracking.[9][18-21] Furthermore, single-crystal NMC of a particular morphology can exhibit a higher tap density than their polycrystalline counterparts; this increases the active material loading per unit area of the electrode, thus increasing the energy density of LIBs, and thereby enhancing safety and mitigating capacity fading owing to the reduced electrode–electrolyte interfacial area.[22-24]

Owing to these advantages, single-crystal Ni-rich NMC are attracting considerable attention among both researchers and industry professionals.[25] Analysis of the trends in the publication activity (Fig. 2) revealed a 7 – 10% annual increase in the number of papers on this subject. This trend is apparently due to both commercial interests of major industry players (such as Tesla Motors[26] and LG Chem[27][28]) and continuing efforts of researchers to improve the performance characteristics of SC-NMC materials.

Fig. 2

Data on the annual number of publications retrieved by the search for the terms ‘single crystal NMC’ and ‘single crystal NCM’ in Google Scholar over the last seven years from 2020 to 2026. The number of publications was extrapolated on the basis of data for the first four months of 2026.

Despite the annual increase in the number of original studies and reviews dealing with SC-NMC (see Fig. 2), these studies are mainly focused on comparison of the electrochemical properties of single-crystal and polycrystalline materials and on the search for the optimal method for the synthesis of SC-NMC. The issue of the rational design of the particle morphology for SC-NMC is usually addressed only occasionally in the context of the influence of synthesis temperature or the flux composition in the case where the molten salt (flux growth) method is used for the synthesis. Unlike most review publications available to date,[21][29][30] the present review is focused on analysis of the methods for controlling the morphology of SC-NMC in the context of thermodynamics and kinetics of crystallization processes. Particular attention is devoted to the effect of the SC-NMC morphology on the electrochemical properties, in particular on the bulk lithium diffusion and on the differences between the diffusion characteristics of single-crystal and polycrystalline materials. In addition, the review addresses various types of lattice defects in SC-NMC, the mechanisms of defect formation, and the influence of defects on the mechanical and electrochemical properties and also discusses the strategies for enhancing the electrochemical performance of these materials.

* In the scientific literature dealing with layered oxides based on lithium and transition metals (Ni, Mn, Co), the designations NMC and NCM are used interchangeably, with Ni being traditionally listed first. It is important to note that the formulations with the nickel mole fraction x≥0.6 are classified as nickel-rich ones, whereas materials with x = 0.3 – 0.6 are regarded as containing a moderate proportion of nickel.

An advantage of SC-NMC is the possibility of rational design of the particle shape and size by using various methods and by varying the synthesis conditions. Experimental studies clearly demonstrate that the SC-NMC morphology is determined by a combination of thermodynamic and kinetic factors that depend on the chosen synthesis method and conditions: temperature, atmosphere, starting reactants, and additives.[31] Thermodynamic and kinetic factors are competing, effective control of particle morphology requires understanding which factor plays a key role in determining the crystal faceting. In the case of thermodynamic control, the shape of the particles formed during the synthesis corresponds to the minimum surface energy (E_surf), whereas in the case of kinetic control, the synthesis proceeds along the path with the lowest energy barrier (E_a) and results in the formation of particles with a greater surface energy (Fig. 3). In the following Sections, the thermodynamic and kinetic factors that determine the SC-NMC morphology are examined in detail.

Fig. 3

Energy diagram illustrating the choice between thermodynamically (black) and kinetically (red) controlled products. E_a is the activation energy for the formation of a product of a specified shape, ΔG° is the Gibbs free energy difference between the reactant and the product, Esurf is the surface energy of a product particle. The reactant is a critical-size nucleus and the product is the particle formed upon the synthesis.

Ni-rich NMC possesses a layered structure with rhombohedral symmetry (space group R3^–m, α-NaFeO₂ structural type) composed of two interpenetrating distorted close-packed FCC sublattices, one consisting of oxygen anions and the other containing Li and transition metal (M) cations in alternating (111) planes of the parent FCC structure (Fig. 4).

Fig. 4

Crystal structure of a layered lithium and transition metal (M) oxide.

The equilibrium shape of a particle formed under particular synthesis conditions can be predicted using the Wulff shape construction method.[32][33] This method makes it possible to determine faceting of a crystal with a fixed volume corresponding to the minimum surface energy based on the crystal symmetry and energies of the main crystallographic planes involved in the formation of the particle facets (surface energies). Thus, to determine the equilibrium shape of a particle, it is necessary to know the set of main surfaces and the corresponding surface energies, which are usually calculated using density functional theory (DFT).[34]

The LiMO₂ layered oxides comprise two types of surfaces, nonpolar and polar ones. The nonpolar surfaces are characterized by the Miller indices (104), (110), and (100), while the Miller indices of the polar surfaces are (012), (003), (101), and (111) (Table 1).[35] The surfaces with other Miller indices possess high energy and are not observed experimentally. This subdivision corresponds to the Tasker classification,[36][37] in which the nonpolar surfaces have a zero charge and a zero magnetic moment, while the polar surfaces, in turn, may have a non-zero charge or a non-zero magnetic moment.

Table 1

\[ \]

Main crystallographic facets of the LiMO₂ crystals with a layered structure (space group R3^–m). An example of description of images given in Table 1 is shown in Fig. 5.

(1)

The DFT calculations of the surface energy involves the use of special model cells (slabs) containing a bulk phase with two symmetrical surfaces and a vacuum layer (Fig. 5).

Fig. 5

Model slab used to calculate the surface energy.

In general terms, the surface energy is defined as the difference between the energy of a slab with two free surfaces and the energy of an equiatomic bulk cell divided by twice the slab surface area A:

(1)

Slabs with symmetric nonpolar surfaces retain their stoichiometric composition, while for polar surfaces, the composition deviates from the stoichiometry. Therefore, the following relation is used to calculate the energy of a polar surface:

(2)

where μ_i is the chemical potential of an atom of type i, and n_i is the number of atoms of type i. The chemical potentials of elements are determined from the thermodynamic equilibrium condition for the particle surface and bulk. For example, the condition of equilibrium for LiNiO₂ is written as

(3)

Thus, according to this condition, the energy of a polar surface depends on two independent chemical potentials, μ(Li) and μ(O). Usually, the energy of a lithium metal atom in a BCC lattice is taken as the standard lithium chemical potential μ⁰(Li), while the standard oxygen chemical potential μ⁰(O) is the energy of an oxygen molecule with a correction of 1.36 eV, associated with the error of calculation of the molecular binding energy using the PBE exchange-correlation functional.[38] The chemical potentials μ(Li) and μ(O) corresponding to the synthesis conditions are found from the phase diagrams for the Li – M – O systems plotted in the Δμ(Li) and Δμ(O) coordinates using DFT data for the full set of phases in each system (Fig. 6).[37][39][40]

Fig. 6

Phase diagrams of the Li – Ni – O (a) and Li – Co – O (b) systems plotted in the Δμ(Li) and Δμ(O) coordinates on the basis of the DFT data. Change in the oxygen chemical potential vs. temperature (c) and partial oxygen pressure (d).

The change in the oxygen chemical potential Δμ(O) depends on the temperature T(K) and the partial oxygen pressure p(O₂) as

where μ(O₂; T, p) is the chemical potential of molecular oxygen, μ(O₂; DFT) is the total energy of O₂ molecule calculated by DFT, ΔH°(O₂ , T; JANAF) is the standard enthalpy of formation of the O₂ molecule taken from the Joint Army – Navy–Air Force (JANAF) thermochemical tables,^* ΔS°(O₂, T; JANAF) is the standard entropy of the O₂ molecule taken from the JANAF thermochemical tables, R is the universal gas constant.

The Δμ(O) exhibits an approximately linear inverse dependence on temperature and a logarithmic dependence on partial oxygen pressure (see Fig. 6). Thus, Δμ(O) effectively reflects the synthesis conditions. Meanwhile, Δμ(Li) is definedrelative to the lithium chemical potential metal [Δμ(Li) = μ(Li) – μ(Li metal)] and is often used as a proxy for lithium concentration; however, the quantitative relationship between these two quantities remains unclear.[41]

The chemical potentials of lithium and oxygen affectonly the surface energy of polar surfaces, for LiNiO₂ (LNO) and LiCoO₂ (LCO) in Fig. 7. Several studies have reported that Co and Mn have only a minor effect on the surface energy of NMC with a nickel content of x ≥0.8. Therefore, the data obtained for LNO can be used to analyze the general surface energy trends in Ni-rich oxide crystals.[35]

Fig. 7

Surface energies of LiNiO₂ (a) and LiCoO₂ (b) as functions of the oxygen chemical potential.⁴⁰

The energy of the considered nonpolar surfaces (100), (110), and (104) does not depend on external conditions due to their stoichiometric composition and zero charge (see Fig. 7). It was found that the (104) surface has the lowest energy and the (100) surface has the highest energy, which correlates with the number of cleaved M – O bonds.[35][42] The second energy minimum corresponds to the (003) polar surface, which forms upon cleavage of the LiMO₂ crystal along the lithium layers. In view of the fact that the surface layer represents a lithium monolayer, the energy of the (003) surface is a function of the Li chemical potential. Depending on the conditions, several stable configurations are observed where the fraction of occupied lithium sites in the monolayer ranges from 1/8 to 1 (Fig. 8a,c,e).[29][43-45] For LCO, the stoichiometric composition with a Li occupancy of 1/2 in the surface monolayer ensures the minimum (003) surface energy within the oxygen chemical potential range of −2.6 < Δμ(O) < −1.8 eV (Fig. 8e), whereas for LNO, non-stoichiometric compositions are stabilized over a broad range of oxygen chemical potentials (Fig. 8с). Furthermore, decreasing the lithium chemical potential stabilizes surface configurations with lower Li contents (Fig. 8g).

Fig. 8

(a) Top view of the (003) surfaces with 1, 1/2, and 0 lithium in the monolayer (ML); (b) top view of the (012) surfaces with 1, 1/2, and 0 oxygen in the monolayer. Energy of the polar surfaces in LNO/LCO as a function of oxygen chemical potential: (c, d) (003) with different lithium contents in the monolayer; (e, f) (012) with different oxygen contents in the monolayer. (g) Energy of the (003) surface with different lithium contents in the monolayer as a function of the lithium chemical potential. The Figure was created by the authors using published data: (c, d),³⁹ (e, f),⁴⁵ (g).³⁷

The (012) polar surface exhibits the next lowest energy and, similar to the (104) facet, plays a crucial role in electrochemical processes. This is because lithium diffusion channels terminate at the (104) and (012) surfaces; thus, the contribution of these surfaces to the resulting particle shape in the layered oxides substantially influences the (de)intercalation kinetics. This surface can exhibit a variety of structural configurations depending on the oxygen coverage in the surface monolayer. The stoichiometry is achieved for a composition with 1/2 oxygen monolayer on the surface (Fig. 8b); however, this configuration has a relatively high energy (Fig. 8d, f ). In LCO, the (012) surface energy can be lowered under both the oxidating conditions (increasing monolayer oxygen content) and reducing conditions (decreasing monolayer oxygen content) (Fig. 8f ). In contrast, for LNO, it can be decreased due to the formation of Li_Ni – Ni_Li antisite defects (Fig. 8d ).

The calculated surface energies can be used to determine the thermodynamic equilibrium crystal shapes at specified oxygen and lithium chemical potentials. Previous studies have indicated that the Li chemical potential has a lower effect on particle morphology than the oxygen chemical potential.[35][43] However, the chosen chemical potentials must lie within the thermodynamic stability region of LiMO₂ in the Δμ(Li) – Δμ(O) phase diagram (see Fig. 6). Consequently, varying the oxygen chemical potential is often coupled with a corresponding change in the lithium chemical potential.[39][40]

The effect of Δμ(O) on the equilibrium crystal shape of the LiMO₂ particles is illustrated in Fig. 9. For LNO, the (104) and (003) facets are present over the whole range of Δμ(O), with the (104) facet dominating the morphology. The particle shape is virtually invariant in the 0 > Δμ(O) > −0.93 eV range, which corresponds to the low-temperature synthesis conditions (below 500°C). As Δμ(O) further decreases, the (101) and subsequently (012) regions are formed, due to decreasing contribution of the (104) surface. Consequently, the equilibrium particle shape transforms from a trigonal antiprism formed by the (104) and (003) facets to a truncated cuboctahedron formed by the (104), (003), (012), and (101) planes. Conversely, the particle shape in LCO is determined by the (104), (012), and (003) facets. Decreasing Δμ(O) reduces the contribution of the (003) surface from 55% to 15% and contribution of the (012) surface from 20% to complete disappearance at Δμ(O) = −1 eV. Simultaneously, the percentage of the (104) surface increases from 20% to 85%. As a result, the particle shape changes from a hexagonal prism formed by the (104), (012), and (003) surfaces to an antiprism formed by the (104) and (003) surfaces.

Fig. 9

Variation of the equilibrium shape and contributions of surfaces to the resulting particle shape of LNO, LCO, and NMC811 depending on the oxygen chemical potential.^{35, 37, 40}

For NMC compounds, such as NMC811, the particle morphology is characterized by the presence of (104), (003), and (012) surfaces over the whole considered range of oxygen chemical potentials.[35][43] In an oxygen-rich atmosphere or at low temperatures (0 > Δμ(O) > −1.3 eV), an antiprismatic particle shape is formed predominantly by (104) facets, which is optimal for the extraction of lithium from the layered oxide structure. A decrease in the oxygen potential (corresponding to increasing temperature or conducting the synthesis in an oxygen-deficient atmosphere) results in an increase in the contribution of the (012) facets, as the area of (104) facets decreases until they completely disappear at Δμ(O) = −2 eV (~ 1200°C). Simultaneously, the proportion of (003) facets, which are inaccessible to lithium diffusion, increases twofold, which may potentially deteriorate the power characteristics of the cathode material.

Although theoretical and experimental studies have demonstrated that the Wulff construction based on surface energies reliably predicts the shapes of layered LiMO₂ oxide particles, such as NMC333,[29][43] NMC532,[29] NMC622,[29] and NMC811,[29] it is important to note that the real structure of the particle surface may substantially differ from the model structure. For instance, combined theoretical and experimental studies [41][46][47] have shown that doping NMC811 with boron decreases the (003) surface energy relative to the (104) surface energy, thereby stabilizing a plate-like morphology. This energy decrease is attributable to the adsorption of lithium borate, which serves as a source of boron during synthesis; this, in turn, leads to an increase in the lithium chemical potential.[41][46][47] The surface segregation of doping elements can also cause considerable changes in the surface energy, thereby affecting the particle morphology.[48][49] However, it should be noted that that all the trends discussed above apply strictly to thermodynamically equilibrium conditions. The effect of kinetic factors during crystallization on the particle shape is discussed in the next Section.

* NIST-JANAF Thermochemical Tables: official website URL: https://janaf.nist.gov (accessed on June 22, 2026).

Unlike thermodynamic considerations, crystal nucleation and growth kinetics are influenced by numerous factors acting at different stages of crystallization.. The influence is determined by the balance between the nucleation and particle growth rates, diffusion mechanisms, and synthesisconditions.[50] Therefore, study of the influence of kinetic factors on the particle shape presents a more complex challenge from both experimental and theoretical standpoints.[51-53] Irrespective of the composition, the crystallization of particles follows the patterns predicted by the classical nucleation and growth theory.[54] However, the specific features of SC-NMC synthesis limit the applicability of classical approaches for assessing the influence of kinetic factors on crystal size and morphology. Indeed, as shown below in Section 2.3, the synthesis of SC-NMC may include a step of crystallization from solution resulting in the formation of submicron particles of mixed hydroxide Ni_xMn_yCo_z(OH)₂ or carbonate Ni_xMn_yCo_zCO₃ precursors assembled into spherical agglomerates. However, the final size and shape of SC-NMC crystals are determined by the conditions of the high-temperature reaction between the precursor and a source of lithium, in which the morphology of the precursor primary particles and agglomerates is not preserved during lithiation. Currently, there are no comprehensive studies on the influence of kinetic factors on the morphology of SC-NMC crystals. Most likely, Ostwald ripening is likely to be the dominant crystal-growth mechanism, especially if high-temperature lithiation is carried out in the presence of a liquid phase (low-melting-point flux). During crystal growth, redissolution or surface diffusion processes are likely to occur, which is a key factor in the formation of crystal facets. During particle growth, material is deposited relatively uniformly over the crystal surface and can subsequently redistribute via surface diffusion. However, when the rate of surface diffusion is much lower than the particle growth rate, the redistribution cannot keep pace with particle growth, and spherical particles are formed (Fig. 10а).[55]

Fig. 10

(a) Schematic picture illustrating the effect of thermodynamics and kinetics on the resulting particle shape; (b – g) effect of the competition between thermodynamic and kinetic factors on the final shape and size of MnCO3 particles; (b – d) SEM images of MnCO₃ particles obtained at initial Mn²⁺ concentrations of 1.5, 4, and 12.0 mmol L^–1, respectively; (e – g) particle shape and size predicted by the computational model: rhombohedral particles formed at the initial Mn²⁺ concentration of ∼ 1.5 mmol L^–1 (e), cubic particles formed at the initial Mn²⁺ concentration of ∼ 4.5 mmol L^–1 ( f), spherical particles formed at the initial Mn²⁺ concentration of ∼ 12.0 mmol L^–1 (g).⁵⁵ Copyright American Chemical Society.

A comprehensive theoretical and experimental study of the effect of synthesis conditions on the morphology taking into account the kinetic aspects of particle shape evolution was carried out for the model MnCO₃ system.[55] Using phase-field simulations, the authors demonstrated that with increasing concentration of metal cations in solution, the high rate of crystal growth promotes a transition from the equilibrium octahedral morphology, first, to a cubic shape and then to a spherical shape, which is accompanied by a decrease in the particle size (Fig. 10). Although the study involved a system containing the salt of only one metal, the authors noted that this approach can be extended to the synthesis of mixed transition metal salts, composition-gradient materials, and other cathode materials.

Thus, the kinetics of crystal growth is determined by a sequence of stages, each being characterized by a particular rate and depending on numerous factors. The first stage involves diffusive transport of the crystallizing species from the bulk medium to the surface of the growing crystal. The driving force for this transport is the chemical-potential difference between the medium and the crystal (μ_medium – μ_crystal). The diffusion transfer is followed by the adsorption of particles on the crystal surface. The final stage of the process is integration of the adsorbed particles into the bulk crystal. The rate-limiting step in the crystallization kinetics is always the slowest of the above processes. Particular examples of the effect of kinetic factors on the NMC morphology are discussed below, in the context of description of various synthesis methods.

All types of NMC cathode materials, including SC-NMC, must meet a number of technological and performance requirements (Table 2): (1) a homogeneous distribution of transition metals (Ni, Mn, Co) throughout the particle bulk; (2) high tap density; (3) specified particle size distribution; (4) low specific surface area; (5) low moisture content; and (6) moderately alkaline pH of the aqueous extract.[7] As with PC-NMC the chemical composition and spatial distribution of Ni, Mn, and Co are crucial for achieving the target capacity and cycle life in SC-NMC. The tap density, which directly influences the energy density of LIBs, is determined by the particle shape and particle size distribution. This parameter can be optimized through the preparation of particles with appropriate morphology and a narrow size distribution and by using polydisperse systems.

Table 2

\[ \]

Key parameters of SC-NMC cathode materials

(2)

It is known that spherical-like particles[56] provide the highest tap densities owing to their most efficient packing. In the case of spherical particles, the densest packing is achieved in ordered structures such as hexagonal close packing or face-centred cubic lattice in which the space filling factor reaches approximately 74%. However, in real powder systems that were freely poured without external compaction or vibration, monodisperse spherical particles typically form disordered structures with a filling factor of about 64%.[57] Particles with distinct facets, acute corners, and edges tend to form stable arch-like structures that prevent close packing (filling factor of approximately 58 – 60%); therefore, their tap density is lower than that of spherical particles. A low specific surface area is preferred for a cathode material, because this decreases the volume of the electrolyte required for complete wetting of the electrode and also reduces the intensity of the side surface reactions. The pH value of the aqueous extract serves as an indirect indicator of the concentration of surface LiOH and Li₂CO₃ compounds formed upon contact of the material with atmospheric moisture and CO₂ . The solution pH should be moderately alkaline, which makes it possible to avoid the degradation of the polymer binder during the preparation of the electrode slurry (see Table 2).

In order to achieve optimal electrochemical performance, the synthesis of an SC-NMC cathode material should give a material that meets all of the above requirements. Methods for the preparation of SC-NMC can be conventionally divided into two main groups: the precursor-free method and the method involving presynthesized Ni_xMn_yCo_z(OH)₂ precursor. In the latter case, transition metals are typically in the +2 oxidation state (Table 3). However, the oxidation states of cobalt and manganese may differ from the indicated value and depend on the precursor synthesis conditions. In particular, Mn^3+/4+ and Co^2+/3+ hydroxides can be prepared by varying the atmosphere used for the synthesis and concentration of the transition metal in the reaction medium or by using oxidants (for example, H₂O₂).[58]

Table 3

\[ \]

Advantages and disadvantages of various approaches to the synthesis of single-crystalline materials

(3)

According to the first approach, a transition metal source (e.g., oxide, hydroxide, nitrate, or acetate) is mixed with a source of lithium (e.g., LiOH, LiNO₃, Li₂CO₃), followed by heat treatment.[59-63] Although this approach results in the formation of octahedrally shaped single-phase layered samples (space group R3m), control of the morphology and particle size is virtually impossible in this method.[59][62][63] For the formation of single-crystal particles, not only high temperature (>950°C) should be used, but also long annealing time is required, because diffusion of transition metal ions in oxides is hindered due to the strong M – O bond. If low-melting-point fluxes are used, the long-term heat treatment may be accompanied by Ostwald ripening involving the growth of some particles at the expense of dissolution of other particles. Nevertheless, the particle size usually does not exceed 2 μm.[59]

The synthesis of SC-NMC typically involves a two-stage procedure comprising the preparation of an intermediate (precursor) and the subsequent high-temperature treatment of the precursor as a mixture with a source of lithium. Several methods have been developed for the precursors synthesis, including hydro-[64] and solvothermal methods,[65] sol – gel process,[66] spray drying,[67] spray pyrolysis,[68] and so on. However, co-precipitation is the most common and preferable method for the industrial production of NMC cathode material precursors.[69] In the precursor-based method, the problem of chemical homogeneity is solved by precipitating the precursor with a homogeneous distribution of transition metal cations from soluble salts in the presence of a complexing agent.[70][71] Subsequently, the obtained mixed transition metal precursor is subjected to high-temperature lithiation, as in the synthesis of polycrystalline NMC. This synthetic stage is crucial and particularly this stage determines the morphology of the final product. There are two main protocols used for the lithiation of SC-NMC: one is based on high-temperature (950 – 1050°С) treatment of the precursor mixed with a lithium salt in one or several stages with intermediate grinding of the formed agglomerates,[72-79] while the other protocol uses inert salts or eutectic salt mixtures (flux), apart from the source of lithium, in order to obtain crystals of a cathode material by high-temperature treatment (850 – 950°С) in a melt of these salts (molten salt method).[77][80] Despite the simplicity of the synthesis, the main drawback of the former lithiation method is the use of a higher temperature for solid-state synthesis, which results in higher Ni²⁺ concentration in the Li sites of the layered structure of Ni-rich NMC and in the formation of disordered phases with a spinel- and/or rock salt-type structure on the particle surface. All the above features have an adverse effect on the electrochemical performance of cathode materials.[81-83] Furthermore, high synthesis temperatures increase the probability of sintering and formation of large agglomerates; therefore, a final milling stage is required to produce cathode material as single-crystal particles. Meanwhile, milling may cause particle cracking or surface cleavage.[84] Moreover, the synthesis conditions do not allow for effective control of the morphology or particle size distribution of the material, since milling process results in the formation of crystals of arbitrary (polygonal) shapes.[74][75][85]

In the molten salt method, a mixture of low-melting salts (e.g., an eutectic mixture) is used as a flux.[58][86-92] The process of SC-NMC synthesis by heat treatment in a flux melt can be divided into three consecutive stages, each characterized by different mechanisms and phase transformations. The first stage involves heating of a reaction mixture consisting of a hydroxide precursor, hydrated lithium hydroxide, and a flux, with all components being in the solid state. This stage is performed at temperatures of up to ~ 200°C where water is removed from lithium hydroxide monohydrate LiOH · H₂O, while mixed hydroxide forms a monoclinic MOOH phase (space group C2/m)[93] and lithium-deficient spinel phases upon the reaction with dehydrated lithium hydroxide.[94] In the second stage (200°C ≤ T≤ 500°C), M oxide hydroxides undergo thermal decomposition, while simultaneously reacting with a lithium source to form spinel-like intermediates and lithium-containing compounds of the rock salt structural type (space group Fm3^–m).[93] In this case, the process takes place in the solid phase due to the low temperature.[95] The salts used as flux components remain in the solid state because the temperature is not sufficiently high for them to melt. This stage can be described as a pre-lithiation process.[93] The third stage, which occurs at temperatures above 500°C, involves Li/M ordering and the formation of a layered structure. Finally, the intermediate phases are transformed into a layered oxide (space group R3^–m) as the temperature rises during the synthesis. The flux components melt, leading to the formation of a liquid phase, accompanied by a dissolution – recrystallization process. The continuous recrystallization process can furnish virtually pore-free particles. Nevertheless, decomposition of precursor particles and the growth of large SC-NMC crystals can produce internal nanovoids.[96][97] The molten salts fill the spaces between the particles, thus effectively increasing the contact area between them.[80] In addition, the diffusion coefficients of transition metal and lithium cations in the melt are much higher than those in the solid phase.[21] When the flux melting point and the temperature of long-term holding (900 – 1000°C) have been reached, the precursor agglomerates rapidly disintegrate, and the stage of growth of single crystallites begins.[80] As the synthesis temperature increases, the molten flux becomes less viscous, which facilitates mass transfer and, consequently, leads to particle growth.[89] An increase in the holding time promotes further disintegration of the initial agglomerates and the continuous growth of single non-agglomerated particles accompanied by the development of their crystal facets (Fig. 11),[80] with the particle growth occurring by the Ostwald ripening mechanism.[98]

Fig. 11

SEM images showing the stages of disintegration of precursor agglomerates and the growth of single non-aggregated particles during the molten salt crystallization process as a function of temperature and holding time.⁸⁰ Copyright Elsevier.

Differential scanning calorimetry (DSC) was used to identify the key stages of the molten-salt crystallization process occurring in a multicomponent reaction mixture on heating (Fig. 12). Heating of a mixture containing Ni_0.8Mn_0.1Co_0.1(OH)₂ , LiOH · H₂O, and Li₂SO₄ (flux) produced a three-stage weight loss profile. The first stage (~ 105°С) corresponds to the elimination of crystallization water from lithium hydroxide. The second stage (~ 280°С) is associated with decomposition of the mixed transition metal hydroxide to the corresponding oxides with the release of H₂O.[99-102] The third stage (~ 460°C) is characterized by a gradual weight loss and ends with an endothermic peak associated with melting of residual LiOH. Particularly at this stage, the reaction between the lithium-containing component and the transition metal oxides is initiated, leading to the gradual formation of layered structures.[101-103] At the final stage, cation ordering takes place without any significant change in the weight to give a thermodynamically stable phase corresponding to space group R3̅m.

Fig. 12

Thermogravimetric (dashed line) and calorimetric (DSC, solid line) profiles of the reaction mixture consisting of Ni_0.8Mn_0.1Co_0.1(OH)₂, LiOH · H₂O, and Li₂SO₄.

A key role in the synthesis is played by the concentration of the added salts. A salt deficiency leads to the formation of particles with residual agglomeration and a high proportion of solid – solid interfaces due to insufficient wetting of the particle surface (Fig. 13a,b).[104]

Fig. 13

SEM images of SC-NMC111 samples obtained with varying amounts of flux in the synthesis of single crystals: 0 mol.% (a, b), 20 mol.% (c, d), 60 mol.% (e, f), and 80 mol.% (g, h). The high-temperature treatment conditions were the same for all samples.¹⁰⁴ Copyright Royal Society of Chemistry.

Conversely, increasing the salt content decreases the number of direct contacts between solid particles, potentially facilitating crystal growth. However, an excess of salt may lead to an increase in the distance between particles, thus retarding the growth (Fig. 13e – h), which is attributable to an insufficient amount of the supplied material due to the need to cover large distances between particles. A moderate excess of inert salts can promote fast growth of NMC crystals (Fig. 13с,d ).[104][105]

Polycrystalline NMC with a relatively high tap density (2.0 – 2.5 g cm^–3) are typically synthesized using dense spherical precursor agglomerates with an average size of 10 – 12 μm.[106-108] However, a precursor with a high tap density is unsuitable for the synthesis of SC-NMC, as this leads to residual agglomeration.[95] Therefore, to prepare non-agglomerated, single-crystal particles, it is advisable to use precursor agglomerates no larger than 5 μm with a relatively loose morphology,[95] or non-agglomerated precursor particles.

A major benefit of the molten salt synthesis is the possibility of controlling the SC-NMC morphology by varying the composition of the flux. The variation of the composition of the low-melting-point mixture makes it possible to modify the final crystal shape, which is mainly achieved by altering the lithium chemical potential. Nevertheless, kinetic effects on surface formation cannot be completely disregarded, particularly the influence of melt viscosity, which correlates with the melting temperature of the selected flux. For example, the use of KCl instead of lithium salts decreases the lithium chemical potential and makes it possible to prepare crystals with a cuboctahedral morphology,[92] owing to the reduced contribution of the (003) facet and the enhanced contribution of the (101) facet as well as to elimination of the differences between the surface energies of the (111^–) and (003), (012) crystallographic facets.[9] The crystal faceting is defined by the (003) and (101) planes, which are polar (see Table 1) and lithium-terminated, indicating the sensitivity to μ(Li). However, the use of NaCl results in an octahedral morphology due to a higher melting point of the sodium salt compared to the potassium salt and higher viscosity of the melt, which limits mass transfer.[92] It is known that in the presence of Na₂SO₄ as a flux, the SC-NMC particles acquire an octahedral shape, while the addition of Li₂SO₄ leads to the formation of truncated octahedra,[89] which is due to lower melting point of Li₂SO₄ in the presence of LiOH compared to Na₂SO₄ and to simpler mass transfer.[109][110] Presumably, the interaction of the (003), (101), and (111) facets of the NMC crystals with Na⁺ ions inhibits the crystal growth in the directions perpendicular to these facets.[89] A CsCl – LiCl mixture (1 : 4) as a flux makes a contribution to the final morphology, giving rise to truncated octahedral particles, because of the use of a small amount of Cs⁺ salt and more intense growth of the (104) surface. When LiCl is completely removed from the reaction mixture, and only CsCl is used as the molten salt, the growing particles have a polygonal (random) morphology, since μ(Li) decreases, thus increasing the contribution of the (003) surface.[29]

A key objective is to increase the tap density of the cathode powder; this can be achieved by preparing spherical single-crystal particles. For the targeted design of a crystal morphology, relying on the understanding of the kinetic processes occurring during crystal growth by the molten salt method, it is necessary to minimize the contribution of thermodynamic processes that considerably influence the growth of particular facets and to enhance the contribution of the kinetic component. Thus, from a kinetic standpoint, it is necessary to create conditions under which the surface energies of the facets will be equal, in a first approximation. In other words, it is necessary to reduce the surface energy anisotropy of the major crystallographic facets, (104), (003), and (012),[9] which determine the final morphology of SC-NMC. A sharp temperature rise, which enhances the contribution of thermodynamic factors to the final morphology, and tuning of thermodynamic parameters by varying the flux composition would lead to the growth and spread of vicinal surfaces throughout the whole particle surface area and would provide, most likely, spherical and spherical-like particles. Decreasing μ(Li) is favourable for the propagation of the (003) surface, while decreasing p(O₂) stabilizes the (104) facet.[29][43]

Thus, a change in the flux composition plays a substantial role regarding both kinetic and thermodynamic parameters. Mass transfer processes may be accelerated upon the introduction of low-melting-point components, which, according to the phase diagrams of the chosen salts and lithium hydroxide, would occur in the liquid phase at the synthesis temperature. Considering thermodynamic factors, at lower chemical potentials of oxygen, e.g., in a weakly oxidative atmosphere or at higher reaction temperature, the (104) facet predominates in the surface over the (012) facet.[29] On the other hand, the (101) and (003) facets are more sensitive to the lithium chemical potential, and their proportion in the surface increases with decreasing μ(Li). The effect of Na⁺, K⁺, and Cs⁺ salts on Li chemical potential and stabilization of the (104), (101), and (100) facets would depend on the chosen flux composition (Table 4)[111][112]; this would produce particles in the form of truncated octahedra, antiprisms, cuboctahedra, hexagonal prisms, and spheres.

Table 4

\[ \]

Effect of flux composition on the SC-NMC morphology

(4)

In the case of NMC with a high Ni content, the variation in oxygen partial pressure is markedly limited by the need to suppress the partial occupation of Li sites by Ni²⁺ cations, which requires an increase in p(O₂) to stabilize Ni³⁺.[113-116] Hence, μ(Li) is still the key parameter to dictate the morphology of Ni-rich SC-NMC crystals. Furthermore, a decrease in the lithium chemical potential promotes the growth of vicinal planes and the formation of spherical-like particles.[9]

Despite the benefits, the molten salt synthesis method has a number of drawbacks. A major problem is that after the synthesis, the cathode material surface bears the flux residues, which are electrochemically inactive and must be removed by washing. However, washing can also make the particle surface more vulnerable to environmental degradation, particularly in the presence of water and CO₂ , which can have an adverse effect on the electrochemical properties of the material. This issue is addressed by using resintering, which helps to restore the particle surface and improve the particle stability.

In conclusion, it is noteworthy that precursor-free methods for the synthesis of SC-NMC still represent a poorly investigated area. On the contrary, approaches based on the use of pre-synthesized precursors are well-elaborated and commercially utilized processes that yield SC-NMC with a homogeneous distribution of transition metals among particles, high tap density, and a controlled particle size distribution. Meanwhile, solid-state methods have a number of limitations (see Table 3), despite their simplicity and extensive use. The limitations include high (950 – 1050°C) temperatures of the synthesis, long annealing times, the need for intermediate milling and/or lithiation steps, as well as limited control over particle morphology, which mainly includes only controlled particle size. The molten salt synthesis also provides control over the shape of SC-NMC particles via variation of the chemical potentials of lithium and oxygen. However, since this synthesis method includes several heat treatment steps and washing to remove flux components and residual lithium compounds, it remains a more labour-intensive, time-consuming, and energy-intensive process than conventional solid-state synthesis.[30][83][117]

To date, the electrochemical properties of SC-NMC have been investigated most extensively for particles with octahedral, truncated octahedral, or polygonal (irregular) morphologies. Among these, polygonal particles predominate owing to the widespread use of the solid-state synthesis followed by mechanical crushing or milling of the cathode material particles. However, establishing quantitative relationships between the electrochemical performance of SC-NMC and particle morphology (e.g., Savina and Abakumov[118]) remains challenging because of the limited amount of available statistical data. This is primarily due to the fact that most studies have focused on comparisons between SC-NMC and PC-NMC rather than on systematic investigations of morphology-dependent properties within SC-NMC materials. Generally, SC-NMC materials exhibit specific discharge capacities comparable to those of PC-NMC at low cycling rates, whereas the cycle life and rate capability of single-crystal particles are superior to those of their polycrystalline counterparts (Values describing the degradation of specific discharge capacity per cycle are discussed in Sections 2.3, 4.1.3, and 4.1.4). To understand the origin of these differences in the electrochemical behaviour between SC-NMC and PC-NMC, it is necessary to consider the diffusion and kinetic characteristics of the charge/discharge processes in NMC-based cathode materials.

Layered oxides are characterized by two-dimensional lithium diffusion within (003) type planes, while diffusion along the [001] direction is possible only in the presence of vacancies or Li_M defects in the M layers (Fig. 14).[119][120]

Fig. 14

Lithium diffusion in layered oxides

The key mechanisms of lithium diffusion in layered oxides are vacancy[119] and divacancy[121][122] mechanisms (Fig. 15а). The former involves movement of Li⁺ between the octahedral LiO₆ sites along the shortest path through oxygen dumbbells.[119][123] The latter includes movement along a curved path running through intermediate tetrahedral voids (Fig. 15а).[119][123] Although the energy barrier for the divacancy mechanism is half that of the vacancy one, this mechanism becomes accessible only in the presence of lithium divacancies. In the early stages of charging of layered oxides, the divacancy concentration is generally insufficient to make a significant contribution to the diffusion. Therefore, in these stages, the vacancy mechanism remains the dominant lithium transport mechanism. The divacancy mechanism starts to play a noticeable role when the concentration of lithium vacancies exceeds ~ 0.2 (Fig. 15а).[121][124] Indeed, delithiation is accompanied by an increase in the lithium diffusion coefficient, due to increasing concentration of lithium vacancies; this results in a higher contribution of divacancy diffusion mechanism, which has a lower activation energy.[81][125]

Fig. 15

(a) Lithium-ion diffusion coefficient in the course of NMC delithiation. The background colours (green and pink) illustrate the predominant area of vacancy (oxygen dumbbell hopping, ODH) and divacancy (tetrahedral site hopping, TSH) mechanisms of lithium transport, respectively; (b) general view of non-equivalent paths (1 – 6) of lithium migration by the vacancy mechanism within the (003) plane, depending on the local environment and the corresponding activation energies; (c) calculated and experimental values of lithium diffusion coefficients in NMC with different Ni, Mn, and Co ratios; (d) lithium diffusion coefficients as a function of voltage at 20°C for LNO samples synthesised with a Li/Ni ratio ranging from 0.90 to 1.02. The Figures were created by the authors of the review using published data: (a – c),^{119, 121} d¹²⁹.

In view of the fact that the migration barriers for lithium ions strongly depend on the М cations surrounding the diffusion pathway, the lithium diffusion depends on the composition of SC-NMC (Fig. 15b).[119][121] According to DFT calculations, the presence of nickel in the second coordination sphere of the migrating lithium cation results in a reduction of the migration barriers for both the vacancy and divacancy mechanisms (Fig. 15b). The oxidation state of nickel also plays a role: the migration barriers for the divacancy mechanism with neighbouring Ni²⁺ and Ni³⁺ cations are 0.36 and 0.43 eV, respectively. The presence of cobalt or manganese increases in the lithium diffusion barriers for both mechanisms.[113][121] Although faster lithium diffusion is expected for compositions with higher nickel contents, in some experimental and computational studies, the highest lithium diffusion coefficient was found for NMC622 (Fig. 15c, Table 5). This is due to the largest interlayer spacing in this material among the NMC compositions considered, which increases the size of the diffusion channels and decreasing barriers for lithium migration.[121][126]

Table 5

\[ \]

Lithium diffusion coefficients found by various methods for NMCs of various compositions for different degrees of sample delithiation

(5)

It should be noted that experimentally determined lithium diffusion coefficients strongly depend on the measurement technique employed. For example, the values obtained using galvanostatic intermittent titration technique (GITT) and those determined by the potentiostatic intermittent titration technique (PITT) differ by approximately two orders of magnitude (see Table 5)[127][128]. Furthermore, lithium diffusion is affected by a variety of factors, including external conditions, particle size, and defect concentration. For example, in the case of LNO, it was shown[129] that increasing the concentration of Ni_Li defects by 4% leads to an approximately one-order of magnitude decrease in the lithium diffusion coefficient (Fig. 15d ).

Polycrystalline NMC materials contain primary crystallites measuring 100 – 500 nm, which form micron-sized agglomerates; this facilitates the migration of lithium from the centre of primary particles to the surface, as the small size of crystallites shortens the diffusion path. As a result, the vacancy diffusion mechanism, which predominates in the early stages, is rapidly replaced by a divacancy mechanism, which minimizes kinetic hindrances within the agglomerate bulk (Fig. 16)[130]. Thus, the lithium transport in PC-NMC is more efficient and the effect of diffusion barriers decreases.

Fig. 16

Operando transmission X-ray microscopy and X-ray absorption near-edge structure images of single-crystal and polycrystalline NMC particles demonstrating variation of Ni oxidation state during charging. (a – i) Representative maps of nickel oxidation states taken every 40 min during charging up to 4.4 V at 0.15 C rate.¹³⁰ Copyright Wiley.

Numerical modelling of lithium transport in polycrystalline materials, using LCO as a model system, demonstrates that the primary microstructural features governing Li diffusion are the size and misorientation of the primary crystallites.[131] In the case of small-size crystallites (~ 0.2 – 0.4 μm), a crucial factor is the contribution of grain boundaries, whereas in the case of larger crystals (~ 1.6 μm), relative misorientation is the primary factor. Despite the shortening of the lithium diffusion path within the small crystallites in PC-NMC, the presence of grain boundaries has an adverse effect on lithium diffusion.^{9, 112, 120} The boundaries between primary crystals that are randomly oriented relative to one another act as barriers to lithium migration, thus hindering the diffusion path. In addition, grain boundaries accumulate local mechanical stresses during electrochemical cycling; this results in the formation of microcracks and destruction of agglomerates.[132] Electrolyte penetration into the cracks increases the active surface area of the material; this may temporarily accelerate lithium diffusion owing to exposure of new regions for (de)intercalation. However, this phenomenon is detrimental for cycle life of the cathode material, as grain boundary degradation compromises the mechanical integrity of the agglomerates, while an increase in the surface area in contact with the electrolyte accelerates surface degradation.

The larger particle size of SC-NMC compared with the primary crystallites of PC-NMC results in slower lithium diffusion (Fig. 16, single crystal); this is especially evident for high degree of charge.[133][134] Within a single crystal, diffusion predominantly occurs via the vacancy mechanism, which is characterized by a relatively low transport rate due to the limited number of lithium vacancies. In contrast, on the particle surface where the concentration of lithium vacancies is markedly higher, the divacancy mechanism providing faster lithium migration predominates. As the degree of delithiation increases, the difference between the concentrations of lithium vacancies on the surface and in the bulk of SC-NMC becomes more pronounced, and the limited diffusion in the bulk is the key retarding factor.[135] These diffusion limitations in SC-NMC lead to a lithium concentration gradient, which is the main cause for mechanical stresses and the formation of intragranular cracks.[136-138] Furthermore, the absence of grain boundaries in SC-NMC eliminates problems associated with intergranular diffusion.[120][139] Several studies have reported that SC-NMC show higher power characteristics compared to PC-NMC at various current densities.[80][112][132][140-144] There are data indicating that faceting of SC-NMC crystals also affects their power characteristics. For example, polygonal crystals of SC-NMC811 with predominating (014) surfaces have a higher discharge capacity at high cycling rates (6 С) and a higher diffusion rate of lithium compared with octahedral SC-NMC811 crystals in which the predominating surfaces are (012).[112][137] However, the underlying reasons for this behaviour have not yet been elucidated.

The close-packed crystal structure of layered LiMO₂ oxides (see Fig. 4) tends to form various types of defects, which have a substantial effect on the structure stability and electrochemical properties. In the subsequent Sections, we successively consider the main types of defects, their origin, features of formation, and the effect on the SC-NMC structure evolution and degradation during electrochemical cycling.

Point defects include lithium, oxygen, and transition metal vacancies, antisite defects, small polarons, as well as defect complexes representing various combinations of the above types.[49][145-148] Most studies have focused on oxygen vacancies and antisite defects (M_Li , Li_M), the special case of which are antisite defect pairs (M_Li – Li_M) (Fig. 17). These defects have been described in detail in a number of studies,[40][145][148-150] including studies addressing nickel-rich NMC.[116][151]

Fig. 17

Point defects of a layered structure in relation to LNO (ideal case): (a) oxygen vacancy, (b) antisite defect pair, (c) NiLi defect, (d) LiNi defect.

In this study, we present a comparative analysis of point defect formation in SC-NMC and PC-NMC samples of identical stoichiometry, and examine the effect of morphology on the defect structure of the material.

Although the types of point defects present in PC- and SC-NMC are similar, their spatial distribution and thermodynamic stability differ significantly.[152][153] In polycrystalline materials, defects predominantly form along grain boundaries and interfaces, where the local partial oxygen pressure and the chemical potentials of the constituent elements vary during synthesis.[154][155] Conversely, in single-crystal materials, defects are distributed more uniformly throughout the bulk due to the absence of grain boundaries and more intensive homogenization that occurs during the molten salt synthesis, owing to the presence of the liquid phase. As a result, the probability of aggregation of point defects is lower in SC-NMC than in PC-NMC, which reduces the risk of microcracking but may also limit the rate of lithium diffusion.[152] Thus, differences in the morphology determine the type of defect formation and the subsequent structural evolution of the material. Evidently, higher synthesis temperatures used for single-crystal SC-NMC particles (~900°C) compared with PC-NMC (≤750°C) also influence the thermodynamics of defect formation.

Due to the absence of direct literature data dealing with comparative analysis of defect formation in PC-NMC and SC-NMC structures, the subsequent analysis is based on a comparison of scattered experimental and theoretical data, while the drawn conclusions should be regarded as our working hypothesis.

Oxygen vacancies are often regarded as a highly important type of point defects in layered oxides, which can considerably influence their thermodynamic stability, electronic structure, and capacity degradation during electrochemical cycling.[83][156][157] However, the extent to which these defects are actually present in layered oxides remains a matter of debate.

Experimental data show contradictory results. The Rietveld structure refinement based on X-ray powder diffraction data sometimes reveals oxygen non-stoichiometry associated with the presence of oxygen vacancies;[158-160] however, this method may underestimate the actual oxygen content and thus create the illusion of oxygen vacancies.[161] More sensitive techniques for determining oxygen site occupancy, such as neutron diffraction and NMR spectroscopy[162][163] have revealed that the bulk of layered oxides is free of oxygen vacancies under both high states of charge (e.g., in charged LCO[161][164] and NaCoO₂)[165][166] and high-temperature synthesis conditions, as demonstrated for LNO.[167]

In terms of charge balance, the formation of an oxygen vacancy leads to the release of two electrons, which reduce the transition metal cations in the structure (Fig. 17а).[49][168][169] In the Kröger – Vink notation, this reaction in relation to LNO can be written as

(6)

The electrons released upon the oxygen loss reduce the Ni³⁺ ions to Ni²⁺ ions.

According to DFT calculations, the formation energy of oxygen vacancies on the surface of layered oxides decreases in the charged state and becomes negative at high states of charge, whereas the vacancy formation energy in the bulk remains positive, thus making the vacancies thermodynamically unfavourable (Fig. 18).[49] [169] This is in line with experimental data, indicating that oxygen vacancies predominantly arise on the particle surface,[158][170] from where they can diffuse to the bulk and induce the formation of stacking faults, micropores, and regions with a rock-salt structure (space group Fm3^– m).[158][170-172] However, despite the possibility of vacancy migration to the interior, the concentration of vacancies in the particle bulk should not become high, since the formation and stability of such vacancies are limited by the thermodynamic factors indicated above.

Fig. 18

Effect of the partial oxygen pressure (a) and temperature (b) on the formation energy of an oxygen vacancy in the bulk of LiхNiO2 (х = 0, 1) and on the (104) surface of Li_xNiO₂ (х = 0, 1).¹⁶⁹

The particle morphology has a considerable effect on the thermodynamics of oxygen vacancies: oxygen loss is predominantly initiated along grain boundaries and in surface regions; therefore, oxygen loss is more pronounced in polycrystalline NMC than in SC-NMC due to the different numbers of active sites.[150][154][169][173-176] This is confirmed by experimental data, which show that the amount of gas, including oxygen, released from the electrochemical cell during charge/discharge process is much lower for SC-NMC than for PC-NMC, even at elevated cycling potentials.[154]

Conversely, calculations indicate that the oxygen vacancy formation energy decreases with increasing temperature both at the surface and in the bulk.[169][173](Fig. 18b). However, a neutron diffraction study did not reveal oxygen vacancies in LNO synthesized at temperatures below 750°C.[167] This discrepancy can be explained as follows: despite the fact that the formation of vacancies becomes thermodynamically more favourable at high temperatures, their formation in the crystal bulk is highly limited by high energy barriers for migration (1.2 – 1.8 eV in the bulk vs. 0.2 – 0.3 eV on the surface[177]) and by the additional barrier for the formation of dimers with O – O covalent bond (≈ 2.5 eV[173]). Thus, even at high temperatures, oxygen stoichiometry is apparently maintained within the crystal bulk due to the high energy required for the formation and migration of oxygen vacancies.

Crucially, oxygen non-stoichiometry observed in the synthesis or electrochemical cycling[82][178][179] does not necessarily indicate the formation of oxygen vacancies. The structural changes such as transitions from a layered structure to a spinel-like structure, then to a disordered layered structure, and finally to a rock-salt-type structure[133][180][181] may be accompanied by increasing occupancy of the octahedral sites with the М cations, which decreases the О/M ratio, while full occupancy of oxygen sites is maintained.

To compensate for oxygen loss and achieve the target stoichiometry of NMC during high-temperature synthesis, two complementary strategies are commonly employed: (i) using a lithium excess in the precursor mixture, and (ii) annealing in an oxygen-rich atmosphere. However, the latter approach is mainly relevant for nickel-rich NMC.[9][113][114] [182][183] The oxygen loss from the surface regions of the particles can be mitigated by deposition of protective coatings[184][185] or by doping with elements prone to surface segregation.[49][186]

An antisite defect pair is often regarded as a model defect, since the energy required for its formation serves as an indicator of the proneness of layered oxides to disorder.[40] This type of defect arises when lithium and transition metal ions exchange positions, leading to the formation of a pair of antisite defects Li_M and M_Li (Fig. 17b). Thus, the local chemical composition of the material remains unchanged, but charge redistribution may take place. Indeed, Ni³⁺ in the lithium site is reduced to Ni²⁺; in order to maintain the charge balance, one of the adjacent Ni³⁺ ions should be oxidized to Ni⁴⁺.⁴⁰ In the Kröger – Vink notation, this reaction can be written as

(7)

In terms of thermodynamics, the energy of formation of a pair of antisite defects is determined by the difference between the total energies of the defective and ideal structures. Among the transition metals in the series LiNiO₂ – LiCoO₂ – LiMnO₂ , the lowest antisite pair formation energy is inherent in nickel: E(Ni³⁺_Li – Li_Ni) = 0.62 eV, which is markedly lower than that for Co³⁺ (1.80 eV) or Mn³⁺ (1.96 eV).[40][187] However, some of nickel in NMC occurs in the Ni²⁺ state.⁷ In this case, the formation of the Ni²⁺_Li – Li_Ni antisite pair is not accompanied by the formation of an additional Ni⁴⁺ polaron and requires even less energy. Indeed, a systematic study of the effect of the composition of layered oxides on the formation of antisite pairs demonstrated that upon the addition of manganese to LNO, the Ni²⁺_Li – Li_Ni antisite formation energy decreases almost to zero (Fig. 19а).[178] This is attributable to the tendency of Ni²⁺ to occupy lithium positions, especially in nickel-rich NMC in which cation mixing easily occurs due to similar ionic radii of Ni²⁺ (0.69 Å) and Li⁺ (0.76 Å).[116] However, the dimensional factor alone fails to explain the observed dependence of the degree of Ni/Li disorder on the composition. In particular, an increase in the fraction of Ni³⁺ in nickel-rich NMC is accompanied by enhancement of the cation mixing despite the fact that the Ni²⁺ concentration simultaneously decreases.[188][189] This indicates that, along with geometric factors, electronic and magnetic effects play an important role.

Fig. 19

(a) Effect of the composition of layered oxide on the formation energy of antisite (AS) pair. (b) ¹⁹⁰ Schematic view of superexchange interactions in the NiLi – O – M complexes.

According to published data,[190][191] a key factor for stabilization of antisite pairs is superexchange interaction between transition metal ions occurring through the oxygen anions (Fig. 19b). The insertion of Ni²⁺ into lithium sites leads to the formation of energetically favourable Ni²⁺ – O₂⁻ – Ni²⁺ antiferromagnetic interactions, which markedly reduce the energy required for the formation of antisite defect pairs. In nickel-rich NMC, Ni³⁺ is indirectly involved in the defect formation, since after occupying the lithium position, it is reduced to Ni²⁺ and is included in the superexchange interactions. Thus, the high degree of Ni/Li disorder in nickel-rich NMC is not so much caused by the absolute concentration of Ni²⁺, but by the possibility of local formation of Ni²⁺ and subsequent defect stabilization through magnetic interactions. The roles of Mn and Co in this process differ significantly. Manganese (Mn⁴⁺) promotes the formation of Ni²⁺ in the transition metal layer and, therefore, enhances the superexchange interactions through the formation of strong Ni²⁺ – O²⁻ – Ni²⁺ bonds, thus decreasing the energy of antisite pair formation. Conversely, the low-spin Co³⁺ ion is non-magnetic and is not involved in the superexchange; hence, it weakens the magnetic interactions between nickel ions and thus suppresses the tendency for Ni_Li – Li_Ni antisite pair formation. However, the exchange event is followed by local charge compensation: the neighbouring Co³⁺ is oxidized to Co⁴⁺. This Co⁴⁺ ion can form new superexchange bonds, Ni²⁺ – O²⁻ – Co⁴⁺, thus additionally stabilizing the Ni_Li – Li_Ni defect, and may promote further Ni/Li exchange.