Cobalt-free composite-structured cathodes with lithium-stoichiometry control for sustainable lithium-ion batteries

Lithium-ion batteries play a crucial role in decarbonizing transportation and power grids, but their reliance on high-cost, earth-scarce cobalt in the commonly employed high-energy layered Li(NiMnCo)O2 cathodes raises supply-chain and sustainability concerns. Despite numerous attempts to address this challenge, eliminating Co from Li(NiMnCo)O2 remains elusive, as doing so detrimentally affects its layering and cycling stability. Here, we report on the rational stoichiometry control in synthesizing Li-deficient composite-structured LiNi0.95Mn0.05O2, comprising intergrown layered and rocksalt phases, which outperforms traditional layered counterparts. Through multiscale-correlated experimental characterization and computational modeling on the calcination process, we unveil the role of Li-deficiency in suppressing the rocksalt-to-layered phase transformation and crystal growth, leading to small-sized composites with the desired low anisotropic lattice expansion/contraction during charging and discharging. As a consequence, Li-deficient LiNi0.95Mn0.05O2 delivers 90% first-cycle Coulombic efficiency, 90% capacity retention, and close-to-zero voltage fade for 100 deep cycles, showing its potential as a Co-free cathode for sustainable Li-ion batteries.

Supplementary Note 5.The obtained NM9505 shows a second particle size ranging from 5 to 20 µm which seems to be not affected by the Li stoichiometry.However, the primary particle size is largely dependent on Li stoichiometry.The primary particles of NM9505 obtained with a deficient Li source show needle-like morphology, which is inherited from the Ni0.95Mn0.05(OH)2precursors.
Due to the RS formation, the growth of the primary particles is largely hindered.The average primary particle size increases from 75 nm to 240 nm, with increased Li contents.Without enough Li source, more Ni 2+ exists in NM9505 in the form of the RS phase.The Ni edge then keeps constant after the Li content overpasses 1.0Li, which suggests that Ni has reached its maximum oxidation state of near 3 + and no more Li can be incorporated into the structure.The XANES results are consistent with the XRD refinement results in that the RS phase disappears when enough Li is provided.The valence state of Mn is not significantly affected by the Li contents, as shown in Fig. S12c and d.    f) "Liquid phase sintering", which is modeled through an enhanced magnitude of the surface and the grain-boundary diffusivities.
Different physical phenomena become dominant at different temperatures.For example, removal of water from the transition metal hydroxides is dominant at temperatures lower than 300C, whereas oxidation and reaction with the lithium salt becomes dominant only at temperatures higher than 450C (because the lithium salt, LiOH, melts at around that temperature).Also note that conversion from the rocksalt to the layered phase occurs mostly beyond 600C.All the parameters that govern the reaction kinetics are determined from the experimentally observed evolution of different phases.Similarly, the "liquid phase sintering" is only invoked if excess lithium salt is introduced during the calcination process.During calcination at lower temperatures (<600 ℃), the variations in the particle size (decrease due to the removal of water and increase because of oxidation and lithiation processes) can be considered as a thermodynamic phenomenon.
[1] Whereas the diffusion induced increase in particle size occurs at high temperatures, which is also known as the sintering process, and can be categorized as a kinetic phenomenon.[2,3] There can be several factors influencing the diffusion of mass within the particles of CAMs: [3,4] i.
Calcining temperature, where increasing temperature results in enhanced diffusivity and faster transport of Li and TM species.By considering all these factors, the effects of calcining conditions (such as temperature and Li/TM ratio) on the size and size distribution of the primary particles in the final CAMs are simulated through computational modeling.The NM9505 hydroxide precursor particle microstructure, consisting of spherical particles, is computationally generated in two dimensions (2D) with an average particle diameter of around 35 nm, which is shown in Fig. 4(a) (Main text).The size of these circular particles is assumed to be equivalent to the smaller dimension of the experimentally observed NM9505-hydroxides because diffusion-induced variations mostly occur along the shorter dimension.The computationally generated particle microstructures after calcination were subjected to a very similar temperature profile to the experimental one with 12 h temperature holding at 600 ℃ and another 12 h at 720 ℃.
Particle morphology after holding at 600 ℃ exhibits an average primary particle size similar to that of the initial microstructure despite the dehydration, oxidation, lithiation, and sintering processes.It is almost independent of the amount of lithium (Li/TM ratio) added during the calcination process, with the same magnitude as the precursors (Fig. S17a).This lack of increase in particle size at 600 ℃ can be attributed to the very slow diffusion kinetics at low temperatures.[5][6][7] In addition, the lithiation-induced volume expansion is compensated by the dehydration-induced volume shrinkage.
[1] With lithium stoichiometry greater than unity (Li/TM >1), the slight increase in particle size with increasing lithium content can be attributed to the initiation of the "liquid phase sintering" process, which will be further discussed in detail below.
Substantial growth of the primary particles, with strong dependence on the Li/TM ratio, is observed after the 12 h holding at 720 ℃, (Fig. S17c).It is evident that the rate of increase in particle size is low for Li/TM ratio less than unity (Li/TM<1), while a significantly larger rate of increase is observed at more than stoichiometric amount of Li (Li/TM>1).The qualitative correlation between theory and experiment indicates that the various physicochemical phenomena that occur during the calcination of CAMs at elevated temperatures are well captured by the developed computational framework.Based on experimental and simulation results, primary particle size is largely dependent on the Li/TM ratios in final CAMs, with other synthesis conditions remaining the same.We proposed that primary particle growth is mainly mediated by mass transfer, which is predominantly determined by two mechanisms, namely lithiation-induced crystallization and liquid phase sintering.
For less than a stoichiometric amount of lithium (Li/TM<1), both RS and layered phase exists, showing different lattice structures.Li and TM ions are mixed with each other in the RS phase, and it is hypothesized that the RS phase demonstrates lower magnitudes of diffusion coefficient for the mass transport process.In contrast, the layered phase demonstrates higher diffusivities due to their ease of sliding with respect to each other, where the Li and TM ions exist in distinct layers.
This hypothesis stems from the observation that lithium diffusion is much faster in the layered phase as compared to the disordered RS one.[8,9] Accordingly, in the developed computational model, larger magnitudes of surface, grain-boundary, and bulk diffusivity of the primary particles are assumed for the layered phase as compared to the RS.The effective increase in cathode primary particle size with increasing lithium content, while still maintaining less than a stoichiometric amount of lithium (Li/TM <1), is defined as "lithiation-induced crystallization".Therefore, in the region of Li deficiency, a higher Li/TM ratio leads to a slightly larger primary particle size.
For calcination with excess lithium salt (Li/TM >1), all the primary particles experience complete layering irrespective of the amount of lithium (Fig. S17 (b)), and they demonstrate a very similar extent of "lithiation-induced crystallization".However, experimentally observed primary particles keep increasing in size with lithium content even for more than stoichiometric amounts of Li.It is worth noting that even if more than a stoichiometric amount of lithium is added before the calcination process, only the stoichiometric amount of lithium reacts with the primary particles.
The excess lithium salt, LiOH in the present case, sits around the particles in a molten state because modeling the non-conserved phase parameters) are solved in the phase-field framework.Following previously published techniques, a phase parameter () has been used to differentiate between the solid phase ( = 1) and the voids ( = 0).[12] This particular phase parameter () is a conserved one, and its evolution with time has been modeled using the Cahn-Hilliard equation: [12,13] Here,  indicates time, ∇ ⃑ is the gradient operator,  is the local diffusion coefficient, which depends on location,  indicates the total free energy, and  ⃑ is the velocity vector associated with the bulk motion of the grains.Detailed expression of  and  will be provided later.The exact values of  ⃑ are estimated from the lithiation induced volume expansion of the solid phase, which are calculated by solving the mechanical equilibrium equation explained later.Since the phase parameter  only differentiates between the solid and void phases, it cannot predict the evolution of different grains that participate in the sintering process.To capture the various grains, another set of phase parameter have been introduced, which is defined as  .[14,15] Here, α = 1,2,3, … , , where  indicates the total number of grains within the computational domain.For grain k,  = 1, and all other  = 0, where, α = 1,2, … , (k − 1), (k + 1), … , , and α′ ≠ k.
Since  's are non-conserved parameters, the Allen-Cahn equation has been used to capture their evolution with time: [12,13] where,  is the order parameter scalar mobility, and the rest of the variables have been defined earlier.
The total free energy depends on the bulk chemical free energy (,  ) and the gradient free energy components, which is defined as: [12,13]  = ∫ (,  ) +  ∇ ⃑  + ∑  ∇ ⃑ Here,  indicates infinitesimal volume element of the system, and  and  are gradient energy coefficients.The bulk chemical free energy depends on both the conserved and non-conserved phase parameters,  and  , and can be defined as: [12,13] Here,  and  are constants, and their magnitude depends on the grain-boundary energy ( ) and surface energy ( ) of the corresponding material.It is possible to write the magnitude of  ,  ,  and  in terms of  ,  and interfacial width () as shown below: [13,16]  = (5) The order parameter scalar mobility () can be written in terms of the grain boundary mobility ( ), and the interfacial width () as, [13]  = Magnitudes of the grain-boundary energy ( ), surface energy ( ), grain boundary mobility ( ), and interfacial width () have been provided in Table : I.
The diffusion coefficient () depends on both the phase parameters,  and  , at any particular location, and is defined as: [12]  =  () where,  is the diffusion coefficient in the bulk,  is the surface diffusivity,  indicates the diffusion coefficient within the grain-boundary domain, and  denotes the enhancement in the surface and grain-boundary diffusivities due to the "liquid phase sintering" mechanism in the presence of molten lithium salt.The term () is a polynomial in terms of , which takes a value of 1.0 when  = 1, and becomes 0.0 when  = 0.The exact form of () used in the present analysis has been adopted from literature: [12] () =  (10 − 15 + 6 ) Using Eq. ( 9) and (10) different diffusion coefficients in the bulk, surface region, and grain boundaries have been implemented without explicitly tracking the individual domains.
Since calcination and sintering of LLZO is conducted at elevated temperatures, it is very important to appropriately capture the temperature dependent variation of diffusion coefficients ( ,  ,  ,  ) and grain boundary mobility ( ).An Arrhenius type relation have been adopted to predict the change in transport properties with increasing temperature, which is written as: [13,17]  =  exp − Here,  indicates the pre-exponential factor,  is the activation energy,  and  denotes the universal gas constant and the temperature in Kelvin scale, respectively.Also, different values of  have been adopted for bulk, surface, grain-boundary, and liquid phase sintering induced diffusion coefficients  , ≠  , ≠  , ≠  , .[12] However, the activation energies for all the diffusivities and grain boundary mobility has been assumed to be the same, which changes with the chemical composition of the material.[13] Following existing literatures, the surface diffusion coefficient has been assumed to be 10 times larger than the grain-boundary diffusion  , ~10 , , grain boundary diffusivity is around 40 times larger than the bulk diffusivity  , ~40 , , and the pre-exponential factor for the liquid phase sintering induced diffusivity is assumed to be two orders of magnitude larger than the surface diffusivity  , ~10 , .[12,17] Because of the extremely small size of the computational domain (< 500 nm) as compared to the size of the pellet or the capillary (~ 1 cm), all spatial locations have been assumed to demonstrate the same temperature.[13] The activation energy ( ) and the pre-exponential factor of diffusivity ( ) is assumed to be functions of oxygen  and lithium ( ) concentration, and the extent of layering (̃ ) that occur within the cathode active particles (note that the extent of layering is defined in the form of fractions).The assumed mathematical relations are provided below: Here,  , ,  , ,  , and  , are the activation energies for sintering associated with the basic rocksalt material, oxygenated material, the lithiated particles in disordered rocksalt phase, and the particles that exist in layered phase, respectively, whereas the  's are the corresponding preexponential factors of diffusion.Also,  , and  , are the maximum concentrations of oxygen and lithium within the NiMn9505 particles.All the parameters used for this analysis is listed in Table S1 provided below.
Removal of water (the dehydration process): At the beginning of the calcination process, with increasing temperature water molecules from the transition metal hydroxides are expelled into the environment, which causes a shrinkage in the lattice volume.Note that during this entire dehydration process, the transition metals do not oxidize or reduce, and exist consistently in an oxidation state of 2+.The reaction of water removal occurs at the particle surface, and continuous diffusion of water molecules from the interior of the particles to the surface helps to continue the dehydration reaction.In order to simulate the diffusion of water from the particle interior to the surface, the following species reaction and transport relations are solved computationally: Here, ̃ =   , ⁄ is the normalized water concentration within the cathode precursors,  is the coefficient of diffusivity for single phase diffusion of water molecules within the cathode precursors,  ⃑ is the velocity vector associated with the volume change of the precursor particles, and  indicates the surface reaction of water.The diffusivity of water is assumed to be a function of temperature () according to the Arrhenius relation: Here,  , , is the pre-exponential factor of diffusivity, and  , indicates the activation energy associated with the diffusion of water within cathode.The reactivity of water at the particle surface is given as, where,  () is an interpolation function, integral of which is already defined earlier in Eq. ( 11), that helps to identify the interfacial region, and  , denotes the rate of removal of water molecules from the surface of the cathode precursor particles, which is defined by the Arrhenius relation as, Here,  , , indicates the reference reaction rate coefficient and  , is the activation energy for removal of water at the surface of the cathode particles.Since removal of water is being simulated here, if the concentration of water at the particle surface becomes zero, the rate of reaction is also expected to become zero, which justifies the presence of the normalized water concentration term ̃ in the overall reaction rate (as shown in Eq. ( 17)).All the parameter associated with this water removal process is provided within the list of parameters included later.
Oxygen diffusion process: In order to simulate the diffusion of oxygen within the NMC particles, a multiphase diffusion equation is solved as shown below: Here, ̃ =   , ⁄ is the normalized oxygen concentration within the cathode precursors,  is the diffusion coefficient of oxygen atoms within the cathodes,  ⃑ is the velocity vector indicating bulk motion of the solid phase due to mechanical volume change,  is the chemical potential of oxygen,  indicates the reaction for oxygen at the surface of the cathode particles, and  is the total free energy of oxygen within the cathode.Detailed expression of the total free energy  is provided below: Here,  ̃ is the chemical free energy of oxygen within the cathode particles, for which the detailed expression is provided in Eq. ( 18),  is the gradient energy coefficient and  ,  , ,  , and  , are some constants, detailed values of which will be provided within the list of parameters.The three different phases of oxygen concentration corresponds to the rocksalt (NiMn9505)O phase obtained right after the complete dehydration step, partially oxidized (NiMn9505)3O4 phase considered to be a mixture of (NiMn9505)O and (NiMn9505)2O3, and the completely oxidized (NiMn9505)O2 phase.For these three different phases the concentrations of the second oxygen are 0.0, 0.33 and 1.0, respectively, which is adopted as the values for the  , ,  , and  , parameters.Even though the appearance of these exact phases is debatable, the developed computational technique provides a detailed framework that can be extended for more detailed and accurate analysis of the oxygen diffusion process within the cathode particles during the synthesis process.The magnitude of  and  (in Eqs. ( 21) and ( 22)) depends on the surface energy of oxygen  and length of the interfacial region  through the following equations: The reaction of oxygen at the surface is given as, where,  () is an interpolation function, integral of which is already defined earlier in Eq. ( 11), and  , indicates the rate of reaction, which is defined by the Arrhenius relation as, Here,  , , is the reference reaction rate coefficient and  , is the activation energy for reaction with oxygen at the surface of the cathode particles.Similar to the rate of reaction, an Arrhenius relation is used to capture the temperature dependence of oxygen diffusivity within the cathode particles, Here,  , , is the pre-exponential factor and  , indicates the activation energy associated with the diffusion of oxygen within the cathode particles.Detailed list of parameters is provided later where the values of each of the constants are mentioned.

Lithium diffusion process:
A solid solution type diffusion of lithium is assumed within the cathode particles.The following equation obtained from the Fick's second law is used for capturing the transport of lithium within the cathodes: concentration in the lithium reaction term (see Eq. ( 30)) is consistent with the atomistic calculations, which clearly shows that presence of oxygen at the particle surface is necessary for initiating the lithiation process.Also, the lithium concentration is assumed to be capped by the oxygen level, because lithiation without oxygen is not possible as demonstrated by the atomistic calculations.All the parameter associated with this reaction of Li will be provided within the list of parameters included later.
Conversion from lithiated disordered rocksalt phase to the layered phase: Evolution of the layered phase within the lithiated disordered rocksalt structure occurs through two possible pathways: a) Direct conversion from the disordered rocksalt to the layered phase, which can possibly be captured through a bulk chemical reaction term.
b) Growth of the layered phase which is mediated by the diffusion process.
Both direct conversion and diffusion induced layering is only possible if the lithium concentration is larger than that needed for the formation of the layered domains ̃ > ̃ , , .A solid solution type diffusion of the layered phase is assumed within the cathode particles.The following equation obtained from the Fick's second law is used for capturing the evolution and transport of the layered phase within the cathodes: Here, ̃ indicates the fractional layering at a particular location within the cathode precursors,  is the coefficient of diffusivity experienced by the layered phase,  ⃑ is the velocity vector associated with the volume expansion and contraction experienced by the cathode precursor particles, and  indicates the bulk reaction induced source term that governs the formation of the layered phase Volume expansion and mechanical stress generation: As the NiMn9505(OH)2 precursors convert into the lithiated-NiMn9505-oxides (LiNiMn9505O2), molar volume of the material changes during the entire conversion process.As a result, the precursor particles experience variation of species concentration induced volume contraction and/or expansion.This contraction/expansion leads to stress generation within the cathode particles, and under most of the cases this developed stress exceeds the yield limit and leads to viscoplastic deformation.In order to estimate the magnitude of mechanical stress and the increase in particle size due to volume expansion, the following equilibrium equations are solved: where, ∇ ⃑ is the gradient operator, and  indicates the mechanical stress tensor.Magnitude of stress is directly proportional to the elastic strain tensor   and the constant of proportionality   , which is characterized as the stiffness matrix: Under the assumption of small deformation, the total strain (  ) is divided into the elastic strain, species concentration induced chemical strain   , and viscoplastic strain (  ), in an additive fashion: Change in the concentration of different species leads to expansion and/or contraction of the lattice volume of the transition metal based cathode precursors, which eventually results in a volumetric strain experienced by the cathode active particles.The species concentration induced volume change is assumed to give rise to a hydrostatic strain and depends on the partial molar volume of the transition metal hydroxides Ω ( ) , transition metal oxides (Ω ), oxidized transition metal oxides Ω , and finally the lithiated transition metal oxides Ω within the cathode particles.The incremental chemical strain is defined as: where,  indicates the Kronecker delta function, and Δ̃ , Δ̃ , and Δ̃ denotes the increments in water, oxygen, and lithium concentration.Here, lithiation is allowed to occur only after oxidation of the cathode particles.Adoption of such a complicated expression for the volumetric strain is necessary because the variation of the concentration of multiple different species is simulated here, and each of them have their own influence on the lattice volume.Note that the exact magnitude of the molar volumes depends strongly on the distribution of transition metals within the cathode precursors, such as, NMC111, NMC811 or NiMn9505, should demonstrate different magnitudes of molar volumes for the hydroxides, oxides, and the lithiated phases.The viscoplastic strain rate depends on the shear stress acting on the material, which is given as: Here, ̇ is a multiplying factor (detailed expression provided later),  is the deviatoric stress tensor, and  is the effective von Mises stress.The deviatoric stress is defined as: Here,  indicates the hydrostatic stress, which is defined as: The effective von Mises stress ( ) is defined as: This von Mises stress term indicates a combined form of the shear components of the stress tensor.
The total viscoplastic strain as a function of time is written as: where,  , and  , is the total viscoplastic strain at the next and the present time step, ̇  is the viscoplastic strain rate as shown in Eq. ( 31), and Δ is the incremental time.The detailed expression of the multiplying factor ̇ is given as: Here,  is the yield stress and  is the viscoplastic modulus.Usually,  is a function of temperature, however in the present context no temperature dependence is taken into consideration.The evolution of yield stress  with time is governed by the magnitude of viscoplastic strain (  ): where,  , is the initial yield stress,  is the strain hardening modulus, and  indicates the equivalent viscoplastic strain, which is given as,

Fig. S9 .Supplementary Note 6 .
Fig. S9.Zoom-in of the XRD patterns of NM9505 with different Li contents.The higher Li

Fig. S17 .Supplementary Note 9 .
Fig. S17.Particle size evolution through modeling methods.(a) Computationally predicted Computationally predicted extent of lithiation after the 600C hold (red circles along the right axis in FigureS17(a)) indicates that almost all the lithium salt reacts with the transition metal oxides and intercalates into the cathode particles within 600C, as long as it does not violate the stoichiometry of the final cathode   , ⁄ ≤ 1 .Note that even though complete lithiation of the cathode particles occur after the 600C hold, the lithiated cathodes remain in a disordered rocksalt phase, and does not immediately convert into a layered structure.The solid magenta line in Figure S17 (b) clearly indicates that partial evolution of the layered phase after the 600C hold is predicted by the computational model.Evolution of the layered phase is assumed to occur through nucleation and growth of the layered domains within a disordered rocksalt matrix when the lithium stoichiometry exceeds a certain threshold of 0.85   , ⁄ ≥ 0.85 .The growth process of these layered regions is assumed to be a rate-limiting step, which becomes dominant only during the high temperature hold at 720C.The black solid line in Figure S14 (b) indicates the extent of layered phase evolution predicted by the computational model after the 720C hold, which shows complete layering of the cathode particles with close to, or greater than, stoichiometric amount of lithium (Li TM ⁄ ) ≳ 1 .The experimentally observed extent of layered phase formation after the 720C hold is shown by the black circles, which indicates a qualitative correlation with computational predictions.Even with a close to the stoichiometric amount of lithium (Li TM ⁄ )~0.95 , only 80% layering of the cathode particles is observed experimentally.However, the computational model predicts almost 100% evolution of the layered phase.This mismatch between the theory and experiment, as observed in FigureS14, can possibly be attributed to two different features: a) The computational mode assumes faster reaction rate kinetics for the transformation from rocksalt to the layered phase; b) Mixing of lithium and transition metal ions are not taken into consideration in the computational model, which is extensively observed in cathodes during calcination.Also note that, in Fig.S17(b), even if excess lithium salt is added during the calcination process (Li TM ⁄ ) > 1 , the extent of lithiation cannot exceed unity because lithium-rich cathodes are not being considered in the present context.
ii.Lattice structure of the CAMs, where Li and TM species within the well-defined layered structure should demonstrate faster diffusion compared to that within the disordered rocksalt, or spinel phases where TM and Li ions are intermixed with each other.iii.Presence of sintering aids, where the existence of an extra liquid domain adjacent to the particles facilitates the rearrangement of Li and TM species, thereby enhancing their diffusion through the liquid region.

Table S1 .
inductively coupled plasma of the NM9505 with different Li contents.Li is compared to the sum of the Transition metals.

Table S2 .
Refinement parameters of NM9505 with different Li contents.