Status and outlook for lithium-ion battery cathode material synthesis and the application of mechanistic modeling

As the name suggests, in solid-state synthesis the raw material is used in a solid powder form. Solid-state synthesis is relatively simple, efficient, and scalable synthesis technique. In this process, the precursors are firstly mixed and ground thoroughly, then heated to decompose the precursors and expel the gases [21]. The Li₂CO₃ and Co₃O₄ powder mixture is calcined, reground, and sintered again to form the final LCO (LiCoO₂) particles (figure 3(a)) [41, 42]. Well-shaped crystals of NMC111 (Li[Ni_0.33Co_0.33Mn_0.33]O₂) with sharp edges were obtained through solid-state synthesis of transition metal (TM) acetate salts (figure 3(b)) [43]. Mostly chains of PPs are formed through this synthesis technique.

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Solid-state route is widely applied for synthesizing phosphate based LFP [19, 20] and LCP [21]. Similar solid state route has been employed to synthesize orhtosilicate LFS (LiFeSO₄) [44, 45] and LiFeSO₄/C composite [46, 47]. In LiFeSO₄/C composite a carbon source (sucrose/carbon/coal pitch/carbon nanotube) is added during the grounding and calcination step. Different compositions of Li₂Fe_1−x Co_{x /2}Mn_{x /2}SiO₄ were prepared through rapid solid state synthesis [48]. Solid state synthesis is also employed to generate other promising CAMs such as layered: LNO [15], NCA [14], single crystal NMC622 [49]; spinel: LMO [16], LNM [17, 18, 50]; and tavorite: Li₂CoPO₄F [51], NaLiFePO₄F [52].

In molten salt synthesis, the raw material powders are melted near their eutectic temperatures. Han et al [53] melted the LiCl, Li₂CO₃, and CoCl₂ powders in a muffle furnace to synthesize LCO. Whereas, Polyhedron shaped PPs of NMC111 were obtained through a the molten salt technique (figure 3(c)) [54]. The NMC111 hydroxide precursor was obtained through the co-precipitation synthesis (section 2.3). The solid precursor was then mixed with molten lithium salt and calcined to obtain the final product. Similarly, molten salts of Li₂CO₃, Na₂CO₃, and K₂CO₃ were mixed to obtain (Li_0.435Na_0.315K_0.25)₂CO₃. This carbonate mixture was ball-milled with iron source (FeC₂O₄ · 2H₂O), Li₂SiO₃. After drying and heat treatment Li₂FeSO₄ was obtained [55]. Molten salt synthesis has also been used for generating layered: single crystal NMC particles [27, 56]; spinel: LNM [17, 18, 50]; and olivine: LFP/C composites [57].

The sol–gel process is advantageous over solid state synthesis due to low temperature, good homogeneity, and high purity [21, 50]. In sol-gel a gelling agent is added to the reactor and the solution is heated to obtain the precursor gel. Tang et al dissolved lithium, cobalt acetates into water and added citric acid to the solution. The solution was heated to obtain a transparent gel. The gel was dried, grounded, and the powders calcined to obtain the final LCO nanoparticles product (figure 4(a)) [58]. Shaju and Bruce obtained macro porous NMC particles synthesized through a one-step sol-gel route [59]. Heating during the precursor precipitation generates viscous gel which is then dried, ground, mixed with Li₂CO₃, and calcined to obtain the final product. Type of gelling agent (citric acid, glycine, starch, gelatin) was found to affect the LCO particles synthesized through the sol-gel route (figure 4(b)) [60]. Chains of NMC111 PPs were obtained by using table sugar as the chelating agent during the sol-gel synthesis (figure 4(c)) [61].

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Sol-gel based synthesis of LFP [19, 20] and LCP [21] has been collated. It is emphasized that different parameters of the sol-gel synthesis such as precursors, sintering temperature and time had significant effect on the electrochemical performance. Other CAMs including layered: LNO [15], NCA [14]; spinel: LMO [16, 62], LNM [17, 18, 50]; orthosilicate: LFS, LiFeSO₄/C [63, 64]; and tavorite: Li₂CoPO₄F/C [65] have also been generated through the sol-gel route.

The co-precipitation synthesis is commonly used in industrial production of CAM particles [66, 67]. Different materials such as NMC, NCA have been synthesized through the co-precipitation technique. Figure 5 shows a schematic representation of this synthesis procedure.

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There are multiple variants of the co-precipitation technique. But following steps are common to all. The synthesis starts with aqueous solution of TM salts, suitable precipitating agent, and chelating agent. These raw materials are added and mixed in a continuous stirred tank reactor. The proportions of the raw materials are carefully controlled. Appropriate pH level and temperature is maintained in the reactor. Desirable stirring speed, stirring duration, and reactor atmosphere (N₂ or O₂ or air) is selected. The precipitated precursor is filtered, washed, and dried. Next step involves lithiation and decomposition of the precursor into final product. The lithiation step is a solid state reaction process. The precursor powders are ground in a mortar or milled in a ball-mill and mixed with a lithiating agent. This mixture is heat treated (calcination or annealing or sintering) to obtain the final CAM product.

Noh et al demonstrated that the PP shape depends on the specific NMC composition Li[Ni_x Co_y Mn_z ]O₂ [68]. Decreasing PP size was obtained with increasing Ni content, while surface rough and non-spherical secondary particles were synthesized through co-precipitation. Process parameters like concentrations, pH, temperature, and stirring speed were observed to affect the secondary particle morphology.

Yang et al [69], employed the co-precipitation technique to generate NMC111 hydroxide precursors. Emphasis was placed on the growth analysis of the precursor agglomerates. As the precursor shape largely determines the shape and structure of final CAM particles, such insight in formation and growth of precursors can be used to optimize the synthesis process through use of mechanistic models discussed in section 4. Co-precipitation was employed to generate phase-pure well-ordered Li[Li_0.2Ni_0.2Mn_0.6]O₂ CAM particles with average size of 20 µm and narrow size distribution [70]. Initially irregular precursor particles transformed into smooth porous spheres during vigorous stirring in the reactor. As seen in figures 6(a) and (b), distinct secondary particle morphologies of Ni-rich NMC with radially and randomly-aligned PPs were obtained after calcination of precursors obtained from two different suppliers (Shuangdeng Group Co, Ltd and Argonne National Laboratory) [71]. Little explanation was provided for this phenomenon.

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Few studies deviate from this traditional co-precipitation technique and report distinctly different particle structures. Sun et al modified the addition sequence of the TM metal salts in the stirred tank. Instead of adding stoichiometric amounts of TMs simultaneously, the Ni-rich solution was added first then subsequently Ni-poor solution was added to generate the core–shell particle structure (figure 6(c)) [72]. Such core–shell synthesis examples of layered, spinel, olivine CAMs have been collated along with respective electrochemical performance data [34]. Other variants of this technique include core-concentration gradient shell structure (figure 6(d)) [73] and the full concentration gradient structure [74]. It is important to note that these significantly different structures were resulted by modifying the addition sequence of the TM salts in the reactor. Noh et al applied similar technique and demonstrated significant difference in particle morphology arising from spatially uniform or variable concentration of TMs [75]. The secondary particles consisted of radially aligned nano-rod PPs for the variable concentration of TM salts.

As shown in figure 6(e), hierarchical porous secondary particles have been generated consisting well-aligned faceted PPs for three different chemistries: LiNi_1/3Co_1/3Mn_1/3O₂, LiNi_0.6Co_0.2Mn_0.2O₂, Li_1.2Ni_0.2Mn_0.6O₂ [76]. These morphologies were possible due to use of a high shear reactor in place of the traditional stirred tank. The generated flow field causes exfoliation of the particles creating faceted nano-plates. Such faceted PP structure helps rapid migration of Li-ions resulting in improved electrochemical performance. A later study combined the high shear reactor with sequential addition of TM solutions to generate core–shell NMC523 particles with a void layer between the core and the shell [77]. Zhu et al synthesized four different secondary particle morphologies of Ni_0.6Co_0.2Mn_0.2(OH)₂ by using four different impeller types (propeller turbine, pitched blade turbine, flat blade turbine, Rushton turbine) [78]. Morphologies varied from spherical dense secondary particles to particles made up of flat and flaky PPs. The difference in the morphologies was explained based on different flow fields generated by varying impeller geometries.

Distinct approach using microemulsion based co-precipitation was employed to synthesize single crystals of spinel LNM [79]. Oil-in-water emulsion was used as in-situ co-precipitation site. Aqueous solution of Nickel and Manganese acetates was poured in kerosene oil under stirring to generate microemulsions. Emulsions were stabilized with non-ionic surfactants. This emulsion was dropped into the aqueous solution of the NH₄HCO₃. Due to emulsification single crystals of Ni_0.5Mn_0.5(CO₃)₂ precursor are generated. After grounding with lithiating agent, pelletizing, and sintering single crystals of LiNi_0.5Mn_1.5O₄ are obtained.

Co-precipitation has also been used to generate other CAMs including layered: LiNi_0.5Mn_0.5O₂ [80], LNO [15], NCA [14]; spinel: LMO [16], LNM [17, 18, 50, 81]; and olivine: LFP [19, 20]. Single crystal morphologies (figure 6(f)) of high-Ni CAMs can be generated through milling and high temperature sintering of precursors obtained through the co-precipitation route [82, 83].

From these studies it can be concluded that variety of factors in the synthesis technique affect the final particle morphology during co-precipitation. These include the choice of TM salts, precipitating agents, chelating agents that affect the precursor morphology. The proportions of the starting materials have a significant effect on the final product structure and properties. Figure 6 collates different secondary particle morphologies generated through co-precipitation. More exhaustive comparison of precursor particle structures synthesized through co-precipitation can be found elsewhere [84].

In the self and sacrificial template synthesis method, the co-precipitation technique is followed to obtain a precursor containing a different composition of TMs compared to the composition in final product. The porous precursor is used as a template and desired composition of TMs is achieved during the grounding step.

Uniquely structured particles of NMC111 comprising of nano-sized PPs were generated through a facile template sacrifice as shown in figure 7(a) [85]. MnO₂ microspheres were generated after sintering of the MnCO₃ precursor. Ni and Co nitrate solutions were sequentially added to the solution containing MnO₂ microspheres under stirring to obtain the final NMC111 particles. Wu et al obtained cube shaped hierarchical NMC111 particles through self-template synthesis (figure 7(b)) [86]. First, the cube shaped MnO₂ particles were obtained via precipitation of carbonate precursor and further annealing. These cubes were dissolved in Ni, Co nitrates with LiOH in ethanol. After evaporation the mixture was ground and calcinated to obtain final product particles. Chen et al used silver nitrate as a catalyst in the precipitation process to obtain spherical fluffy MnO₂ particles [87]. Subsequently other TMs were added to obtain the final particles containing fluffy MnO₂ at the core surrounded by short nano-wires. In another study, CaCO₃ was used as sacrificial template to obtain porous spherical size NMC111 particles [88]. The CaMn₃(CO₃)₄ precursor was calcined to obtain MnO₂-CaCO₃. The CaCO₃ was removed to obtain nano-porous MnO₂ spheres. Similar process as above was followed to obtain the final NMC111 particles (figure 7(c)). Template synthesis is also used for single crystal nanowires of spinel LMO [89] and olivine LFP/C composite [90].

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Combustion and thermal synthesis techniques involve high temperature heating of TM salt mixtures. Riley et al synthesized irregular chains of PPs through combustion synthesis [91]. The TM nitrates were melted together then the mixture was allowed to cool down and solidify. After grounding, the powder was mixed with sucrose and water to make a thick red syrup. This mixture was then combusted to obtain the final product. Sucrose-aided combustion method was used to obtain tavorite Li₂CoPO₄F [92]. LiCoPO₄ was first generated from aqueous solutions of LiNO₃, Co(NO₃)₂ · 6H₂O, and NH₄H₂PO₄. Milling, pelletizing, and annealing of LiCoPO₄ and LiF was followed to obtain final Li₂CoPO₄F. Combustion synthesis has also been used for synthesizing spinel LMO [16], LNM [17, 93].

The solvo/hydro thermal synthesis involves heating of the TM salts solution in autoclave. The precursors are dissolved and mixed in solvents, then sealed in an autoclave to react at temperature above the boiling point of the solvent [21]. Ryu et al dissolved the TM acetates and urea in water [94]. Ethylene glycol was also added to the mixture. After continuous stirring, the mixture was annealed in autoclave. Remaining steps to obtain the final product are similar to the co-precipitation route. This solvo/hydrothermal method generates distinctly shaped secondary particles. For example, 3D dumbbells assembled from nano-cubes (figure 8(a)) [94] and peanut-like secondary particles (figure 8(b)) [95].

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TM acetates were heated in autoclave to obtain a precursor. Due to different densification of the inner core and outer shell of the particle, two types of pore sizes were observed. This particle was termed to have hierarchical porous yolk-shell like architecture (figure 8(c)) [96]. The void between the yolk and the shell is speculated to be due to the heterogeneous contraction caused by non-equilibrium heating.

Hydro/solvo-thermal synthesis is also used for other CAMs including layered: NCA [14]; spinel: LMO [16], LNM [97]; olivine: LFP [19, 20, 98, 99], LFP/C nano-plates [100], LCP [21, 101]; and tavorite: Li₂CoPO₄F [102] production.

Microwave heating is advantageous in achieving fast uniform heating of the sample. Microwave heating has been used for the mixture annealing step to generate LiFe_1-x Mn_x PO₄ particles [103]. Depending on the Mn content, high aspect ratio PPs were assembled into flower like secondary particles. Similar microwave synthesis has been employed to generate layered: NMC811 [104], Li_1.2Mn_0.56Ni_0.16Co_0.08O₂ [26, 105]; spinel: LNM [106]; olivine: LFP [19, 20], LCP [21]; and orthosilicate: LFS [107].

SD and FSP technique offer an alternative to the reactor-based synthesis. The lithium and TM salts in aqueous form are pumped into a spray nozzle and the sprayed droplets are dried to obtain the precursor. The precursor is then annealed to obtain the final product. Different examples of spray-dried active material particles and corresponding electrochemical performance have been collated [108].

Crumbling agglomerates and chains of NMC111 PPs were obtained through spray drying (figure 9(a)) [43]. Wang et al demonstrated that preheating of metal salt mixture before spray drying and final heating generates good spherical secondary particles of Mn-rich NMC (Li[Li_0.2Mn_0.54Ni_0.13Co_0.13]O₂) with enhanced electrochemical performance compared to spray dried particles generated without preheating of metal salt mixture (figures 9(b) and (c)) [109].

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The TMs were found to segregate during a spray-pyrolysis synthesis [110]. Spherical NMC442 secondary particles (5–20 µm) had Ni-poor and Mn-rich surfaces. This local migration of elements was observed to be mostly dependent on the thermal annealing process. Fröhlich et al obtained secondary agglomerates consisting nanometer scale round PPs of NMC111 through the flame spray pyrolysis synthesis (figure 9(d)) [40]. TM chlorides were sprayed in a roasting chamber to obtain the intermediate product of large hollow spheres with faceted PPs. After ball-milling during the lithiation step, roughly round secondary particles were obtained.

Zhang et al compared the morphology of the NCA (LiNi_0.8Co_0.15Al_0.05O₂) secondary particles synthesized through the SD and FSP technique [111]. The SD generated large hollow spheres with rough surface (figure 9(e)) while the FSP produced small size particles with relatively smooth surface (figure 9(f)). Along with layered CAMs, spray pyrolysis has also been used for synthesizing spinel: LMO [16], LNM [17, 18], and olivine: LFP [112, 113], LCP [23], LMP [22, 114] CAMs.

Doping of NMC particles with small amounts of dopants has been shown to affect the secondary particle morphology. As shown in figure 10(a), Nguyen et al demonstrated a secondary particle comprising of radially-aligned PP obtained from 0.3% molar doping of Sn in high-Ni NCM [115]. It is observed that different dopants alter the secondary particle structure differently. For doping, the traditional co-precipitation is followed until the lithiation step. A doping agent is added to the precursor along with the lithiating agent during grounding in mortar or milling in ball-mill. After calcination, the particle morphology is significantly altered due to the doping agent. The resulting secondary particle structures were found to be beneficial in resisting micro-cracks and thus improving the degradation performance [116].

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Nano-particle coatings are effective in improving structural stability and cycling performance of micron-sized CAM particles. Different coating materials like Al₂O₃ [91, 117, 118], LiAlO₂ [119], CeO₂ [120], ZnO [121], ZrO₂ [121] have been coated on the surface of CAM particles through the sol-gel [119], dry mechanofusion (figure 10(b)) [122], and ALD [123, 124] techniques. ALD has advantages over other coating methods in terms of regulating film thickness in the Angstrom range, allowing a uniform coating and good conformality [124]. Studies investigating effect of ALD coatings on the electrochemical performance have been collated [123, 124].

Dreizler et al and Wagner et al performed further post-processing of commercially synthesized NMC111 particles by milling to generate nano-particles, then spray drying and sintering to obtain final porous nano-structured particles (figure 10(c)) [125, 126]. Single crystal morphologies have been generated by further milling, high temperature annealing of polycrystalline CAM particles [56, 127].

Crystallization and precipitation is an integral part of the co-precipitation synthesis route. Experimental investigations related to effect of process parameters on CAM particle properties synthesized through co-precipitation have been collated [13, 84].

Few studies in the battery literature apply mechanistic models to investigate the process-product relationship during co-precipitation synthesis [131, 149]. These studies focus on the precipitation process inside a reactor and employ a combination of mechanistic models. A multi-scale mechanistic model simulating the nucleation, growth, and aggregation of particles during co-precipitation of NMC111 hydroxide precursors has been developed [149]. The classical nucleation theory determines the initial number density of the nuclei. Further growth of these PPs is modeled through a continuum growth model based on population balance equations accounting for diffusion of reactants through the solution and precipitation on the particle surface. For aggregation of PPs into secondary particles, lattice based MC method is employed. This multi-scale model predicts that increasing solution pH and decreasing ammonia concentration leads to smaller secondary particle size. The model is then used to perform parametric study and identify optimal parameter values to obtain uniformly sized secondary particles. Although co-precipitation of NMC111 particles was simulated, the computational framework is promising and can be employed to other co-precipitation systems. The model could be used to tune the secondary particle size by controlling the solution pH and ammonia concentration. Few limitations exist in this multi-scale model. The PPs are assumed spherical; thus the internal porosity of the secondary particle cannot be captured. Leading to a bad tap density prediction. Effect of stirrer speed on the particle morphology is not captured. The model focuses on predicting the size of precipitated precursors. The particle morphology can change during the lithiation/calcination step. Model could be developed further to include the effect of calcination on particle size and shape.

A predictive mechanistic model combining the DFT and phase field method is developed for investigating the effect of process parameters on shape of the MnCO₃ precipitates [131]. It is predicted that with increasing metal concentration, particle transitions from rhombohedral to cubic to spherical (figure 12) and the particle size decreases. These observations agree with experiments. The model can capture the particle growth dynamics. This computational framework can be used for prediction of particle shape and size evolution for pseudo single crystal particles in a batch reactor. It is assumed that particle aggregation can be neglected in a batch reactor. Model is developed for single TM salt, further development can include multiple TMs. Currently, this model cannot capture the influence of stirring speed and ammonia concentration on particle size and shape. Further improvement may include incorporation of particle aggregation, internal porosity of secondary particle, and effect of calcination on particle size and shape.

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Multiple mechanistic model based studies simulating crystallization and precipitation process exist outside the battery literature. PBM has been developed to analyze the effect of different process parameters on size and aspect ratio of crystals in the pharmaceutical industry [150]. It is observed that during a three stage crystallization-milling-dissolution process, process parameters like the rotor speed, number of cycles, amount of mass dissolved affect the particle size and aspect ratio. Heuristic optimization is done using the PBM to produce more equant crystals or to control crystal morphology. Qualitative agreement is obtained between the model and experimental results [151].

CFD-PBM coupled mechanistic models have been developed to predict the effect of process parameters on product crystal properties in pharmaceutical [152], minerals [153], and nuclear industry [154, 155]. Review by Bałdyga elaborates application of CFD-PBM models to 'design' product particles [152]. Coupling the CFD predictions of the hydrodynamic properties (velocity gradients, mixing patterns) with PBM enables prediction of the particle properties and their evolution with time. Such models can predict effect of feed concentration, stirrer speed, impeller type on precipitated particle properties and prove useful in investigating scale-up issues. In the mineral industry, CFD-PBM models have been employed for the precipitation of CaC₂O₄ and CaCO₃ [153]. The influence of stirrer speed, feed point position, feed rate, feed tube diameter, energy dissipation, impeller type on particle properties was investigated. The particle properties include mean particle size, surface area, filterability. This computational strategy makes a priori prediction of change in particle properties due to change in operating conditions possible. The model can be further used for scale-up investigations including how the mean size, size distribution, nucleation rate changes with scale up (specific power input, tank volume). The CFD-PBM models have been used to predict size evolution of uranium oxalate crystals during precipitation reaction in the nuclear industry [154, 155]. Simulation of the flow field allowed accurate description of mixing and effect of hydrodynamics on the precipitate properties. It was concluded that the reagent injection position affects the mean crystal size.

The KLMC simulation technique has been implemented to determine the morphology of the co-precipitated agglomerates of multi-component alloy system [9]. The morphology of Fe-Cu-Mn-Ni-Si alloy was classified in core–shell or appendage category through the simulations. There are two distinctive precipitating phases in this system: the fast precipitating Cu-rich phase acts as heterogeneous site for the slow precipitating phase of MnNiSi. The interplay between interfacial and ordering energies along with active diffusion paths determine the core–shell vs appendage morphology. Thus predicting the morphology of the precipitate (figure 13). Guidelines for designing the co-precipitate microstructure for multi-component system were obtained from the simulations. The specific conclusions derived in this study may not be transferable to multi-component CAM like NMC, NCA. But similar simulation methodology could be developed for desired elements (Ni, Mn, Co). Such model could predict morphology of multi-component CAM particles.

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The mechanistic models and corresponding development methodologies discussed above are transferable to the co-precipitation synthesis of CAM. Although these models have some limitations, potential further development specific to the procedure under consideration can be achieved. Such models can identify optimum process parameters to produce CAM particles exhibiting desired properties.

SD and FSP has been used extensively in pharmaceutical, food, dairy, minerals industry to generate particles with varying morphology. Variety of particle designs can be generated through the SD and FSP processes by manipulation of process parameters [156, 157]. These processes can be used to generate 'designer particles' exhibiting desired properties. Although SD and FSP have been used for the synthesis of CAM particles [111], respective mechanistic modeling studies are not available in the battery literature.

Mechanistic modeling of the spray drying process involves two steps. The first step is the development of a model to describe drying of a single droplet. This SDD model is then plugged into a CFD model in the second step to simulate the complete spray drying process. Extensive research has been done in the pharmaceutical and dairy industry to develop SDD models predicting drying kinetics of a single droplet [158, 159]. These models can predict particle properties like size, morphology (hollow/dense), and final moisture content. Multiple application examples of such SDD models in the pharmaceutical and dairy industry have been collated [159].

The CFD models simulate the gas flow, heat and mass transfer, evaporation, and solidification of the sprayed droplets. Most of these CFD studies model the continuous gas phase as a Eulerian medium while the droplets are modeled as discrete Lagrangian entities. CFD has been employed to simulate droplet–droplet interactions [160], droplet deposition on dryer wall [161], coalescence and agglomeration behavior [162]. Scale-up of spray drying process is often challenging and CFD can prove useful as a scale-up tool. Different approaches available for design and scale-up of spray drying have been collated [163]. CFD model based methodology can also be used for process development [164]. They prove useful in constructively designing particles with required size, density, and surface properties.

Mechanistic models based on the DEM have been developed for the spray-drying process of silica nanoparticles [165]. DEM was used to understand the effect of internal structures of spray dried granules on the mechanical properties (figure 14(a)). Structural parameters like the macro void, shell thickness, and micro porosity were varied to generate different granule internal structures. Effect of these internal structures on granule mechanical properties are investigated through fracture strength and strain simulations. DEM based mechanistic model have been used to investigated the segregation phenomenon during spray drying of multicomponent aggregates (figure 14(b)) [166].

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Along with spray drying, the FSP technique is widely used in the ceramic industry to generate metal oxide nanoparticles such as ZrO₂, SiO₂, TiO₂. Extensive research has gone into developing CFD-PBM coupled mechanistic models to simulating the FSP process. The ZrO₂ nanoparticle synthesis was modeled using a Euler–Lagrange framework [167]. The particle dynamics was simulated through a population balance model to obtain evolution of particle volume, area, and number concentration. The simulations can predict the velocity and temperature profiles, droplet evaporation, and particle formation. Figure 15 shows particle and agglomerate diameters predicted through a CFD-PBM model, the predictions are in qualitative agreement with experimental results. The CFD-PBM coupling was used to facilitate tuning of different process parameters to obtain a desired particle size and morphology [168]. Torabmostaedi and Zhang published a series of papers related to mechanistic modeling of the FSP process [169–173]. These simulations enable prediction of particle diameters and variation with respect to multiple process and geometrical parameters. These models require minimal experimental data, hence they are useful for initial process design, reactor optimization, and scale-up.

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Studies reviewed in this section demonstrate that similar mechanistic models based on CFD, PBM, DEM can be developed for CAM particles synthesized through spray drying and FSP [111]. Such models can prove effective in synthesizing particles with desired properties, in understanding the effect of process parameters on particle properties, as well as in scale-up procedures.

Grounding or milling of materials is performed during the lithiation [40], doping [115, 116], or post-processing [125, 126] step of the CAM synthesis. Although ball-milling is most commonly used during CAM synthesis, variety of mill designs are used across different industries. The review by Brunaugh and Smyth comprehensively show the effect of operating parameters and mill design on the particle properties for pharmaceutical milling process [174]. Process parameters like the solids feed rate, milling duration, revolution rate affect the size distribution, shape, surface area of milled particles. Various analytical and computational mechanistic models have been developed to predict the effect of process parameters on milled particle properties in mining, pharmaceutical, and minerals industry.

Dynamic analytical model has been developed for predicting the power draw and energy usage of the tumbling mills used in minerals processing industry [175]. PBM have been developed for milling of pharmaceutical crystals [150]. PBM can simulate the time and space evolution of the particle size distribution during milling as a function of material and mill characteristics. PBM based models for milling are collated [174]. PBM models are usually developed for specific devices and operating conditions hence have limited applicability.

The DEM based mechanistic model is especially suitable for simulating the milling process. Motion of particles in planetary ball-mill has been simulated [176]. Although the actual breakage of the particles was ignored, the energy transfer from the milling tool to the powder can be predicted. This energy transfer can be plugged into correlations to further determine the milling rate. DEM is an effective tool to analyze the impact of mill geometry (figure 16(a)) [177], mill speed (figure 16(b)) [178], filling ratio of milling balls, milling ball properties, and milling time. It can be used to understand the effect of scale-up on the process dynamics. Similar applications of DEM can be found in case of the semi autogenous mill [179] and tumbling mills [180]. DEM has been used to perform a DoE study to understand the complex effect of multiple operating parameters on the ball-milling of iron ore particles and to further improve the mill design [178].

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DEM is suitable for modeling particle interaction, but wet milling demands more complex models. Interaction between the slurry, grinding media, and mill structure needs to be simulated. For wet milling, DEM needs to be coupled with CFD to simulate the liquid phase [177, 181]. Such complex coupled models can be used to understand how various properties and operational parameters affect the properties of milled particles during wet milling.

As grounding or milling plays an important role during the lithiation and doping step of CAM synthesis techniques, similar predictive mechanistic models can be potentially developed to predict process-product relationship and further optimize the milling parameters to consistently obtain desired particle properties.

Calcination and sintering is an integral part of all synthesis techniques. Calcination is signified by removal of CO₂ or H₂O from the precursors to form oxides. Whereas, sintering occurs after the lithiation and doping step. Sintering involves grain growth and densification of the secondary particles. It has been shown that calcination conditions (temperature, ramp rate, holding time) affect the structural and electrochemical properties of cathode materials [182, 183]. The optimum calcination temperature depends on the specific composition and reduces with increasing nickel content [182].

Although mechanistic models for simulating calcination and sintering of TM precursors are unavailable, phase-field method based model has been developed to model sintering of LLZO solid electrolyte used in solid-state batteries [183]. Interface between phases (pores and grains) is tracked as the diffusion of species occurs during sintering. Model demonstrates effect of sintering temperature on particle structure as shown in figure 17.

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Outside the battery literature, mechanistic models have been developed for calcination and sintering processes majorly in cement and ceramics industry. Studies focusing on single particle calcination take into account different reactions occurring at different temperatures [184]. Source terms due to these reactions are then incorporated into the conservation equations (mass, momentum, energy, species). Resulting solutions provide profiles of gas velocity, pressure, temperature, and composition throughout the particle.

Calcination of limestone is often performed in the cement industry in large scale calciners or kilns or furnaces. Number of CFD based modeling studies are available for such calciners [185–188]. Euler–Lagrange coupled simulations are developed to simultaneously track the gas and the solid phase. Governing equations involve the conservation equations (mass, momentum, species, energy) along with reaction rate equations. The model can predict temperature and species distribution throughout the calciner during the process.

Extensive research has been gone into developing mechanistic models for sintering of particles. Initial stage sintering models focus on predicting surface area reduction rate [189, 190]. Sintering process is divided into elemental reactions such as absorption of water, diffusion to the neck region, vacancy creation, desorption of water. Reaction rates are derived analytically for each of the elemental steps. Comparison of respective rates to the experimental rate of surface reduction indicates the rate limiting elemental step of the sintering process. Such models are useful in understanding the influence of sintering temperature and atmosphere on the rate of surface area reduction. Rate of neck growth can be incorporated in population balances to investigate particle size evolution during the sintering process [191].

Atomistic model based on DFT and MD is developed to simulate sintering between two neighboring tungsten particles (figure 18) [130]. DFT is useful in predicting the lattice constants, while MD simulations predict movement of atoms during the sintering process.

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DEM finds applications in procedures where stresses are applied to compact the powder and induce sintering [192]. MC method has been implemented to simulate evolution of pore and grain phases during the sintering process [193]. Sintering simulations at the atomistic, microscopic, and macroscopic scales have been collated [194].

Similar mechanistic models based on the DFT-MD, phase field method, MC, DEM can be implemented for calcination and sintering step of CAM synthesis technique. Such models can provide better understanding into the effect of temperature, ramp rate, holding time on final CAM particle morphology.

ALD technique is advantageous for uniform deposition of conformal coating with controllable thickness on CAM particles [195]. Mechanistic models based on analytical correlations [196, 197], DFT [198–200], MD [201], MC [197, 202], CFD [203] have been applied to investigate the ALD process. Whereas, DEM has been employed to model mechanofusion based dry particle coating [204–206].

Gordon et al developed analytical correlation for achieving uniform coating in a narrow cylindrical hole [196]. The exposure time required to complete the coating increases with increasing aspect ratio of the cylindrical hole. This model was further modified for coating on agglomerates of nanoparticles [197]. Fluidized bed reactor based ALD coating of Al₂O₃ on SiO₂ nanoparticles has been modeled though CFD and analytical correlations [203]. This mechanistic model predicted the bed pressure drop, temperature distribution, and the saturated growth time. Resulting precursor utilization as a function of fluidizing velocity could be used to optimize the coating process. Stochastic MC method has proved useful in predicting coating coverage on 3D structures [202] and agglomerated nanoparticles [197]. Coating of Al₂O₃ on SiO₂ nanoparticles was investigated. As shown in figure 19(a), this approach can predict coating coverage inside nanoparticle agglomerates. With increasing number of particles in the agglomerate, the saturation time increased while the coating coverage decreased (figure 19(b)).

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Mechanistic modeling studies focused on ALD coating have been collated [195, 207]. Similar mechanistic models can be developed for predicting coating quality of CAM particles during the post-processing step.