Investigation of the Particle Formation Mechanism during Coprecipitation of Ni-Rich Hydroxide Precursor for Li-Ion Cathode Active Material

The following aqueous transition metal solutions were obtained from BASF SE (≥99.0% purity): Nickel(II) sulfate solution (2.6 mol l⁻¹ NiSO_4(aq.)), cobalt(II) sulfate solution (2.6 mol l⁻¹ CoSO_4(aq.)), and manganese(II) sulfate solution (2.6 mol l⁻¹ MnSO_4(aq.)). From these, a mixed metal sulfate solution (MSO_4(aq.)) was prepared by combining the respective transition metal salt solutions in a molar ratio of M = Ni/Co/Mn = 8/1/1 to achieve an overall metal concentration of ${{\rm{c}}}_{{\rm{MSO}}4}$ = 2.6 mol l⁻¹. Furthermore, sodium hydroxide solution (25 wt% NaOH_(aq.) (≡7.9 mol l⁻¹), ≥99.0% purity) and ammonia solution (25 wt% NH_3(aq.) (≡13.2 mol l⁻¹), ≥99.0% purity) were obtained from Bern Kraft GmbH (Germany). All solutions were used as they arrived from the chemical suppliers without any further purification.

The Ni_0.8Co_0.1Mn_0.1(OH)₂ particle formation was investigated during semi-batch coprecipitation reactions in a 480 ml stirred tank reactor under nitrogen atmosphere (with a N₂ purge flow of 2.0 l h⁻¹), equipped with a temperature control unit and a pH-probe (HA 405-DXK-S8, Mettler Toledo) for monitoring the internal pH-value of the solution (for a sketch of the reactor setup see our previous work). ⁷ The glass vessel with a double jacket for circulating a heating fluid had an inner diameter of 8 cm, a height of 15 cm, and an outer diameter of 15 cm; it was equipped with baffles, a three-stage 45° pitch-blade stirrer with a diameter of 5 cm, and three dosing tubes for the respective reactant solutions, namely for the mixed metal solution (MSO_4(aq.)), the sodium hydroxide solution (NaOH_(aq.)), and the ammonia solution (NH_3(aq.)). The three dosing tubes (1 mm inner and 2 mm outer diameter) were introduced through the sealed top of the reactor, separated from each other by 4 cm each (with a total distance of 8 cm between the MSO_4(aq.) and the NaOH_(aq.) inlets); the tube outlets were positioned in the reactor 3 cm above the maximum liquid level, which corresponds to 12 cm from the bottom of the reactor.

Before starting the coprecipitation reaction, the vessel was charged with 200 ml deionized and degassed H₂O as well as with 4.0 ml of 25 wt%NH_3(aq.) solution to achieve an overall NH_3(aq.) concentration in the reactor of 0.25 mol l⁻¹. The temperature was set to 55 °C via circulation of tempered silicon oil through the double jacket and the stirring speed was set to the desired value. The internal reaction pH-value measured at the solution temperature of 55 °C was referenced to an external pH-value measured at 23 °C (pH_{23 °C}; via an InLab^® SemI MIcro, Mettler Toledo) by taking solution samples from the reactor and measuring the pH-value at 23 °C. The internal pH electrode was calibrated at 55 °C, while the external electrode was calibrated at 23 °C; in both cases, buffer solutions with pH_{23 °C} = 7.0 and pH_{23 °C} = 12.0 were employed (Certipure, Merck KGaA).

The semi-batch coprecipitation was initiated by simultaneously feeding the MSO_4(aq.) solution at a volumetric flow rate of 18.0 ml h⁻¹ and the NH_3(aq.) solution at a volumetric flow rate 1.8 ml h⁻¹ into the reactor. The NaOH_(aq.) solution flow was controlled by a flow control-unit (Dulcometer, Prominent) linked to the internal pH-probe to maintain a constant pH-value throughout the reaction; the actual flow was close to the predicted volumetric flow rate of 12.0 ml h⁻¹. The stirring speed was varied between 550, 950, and 1350 rpm, while other remaining process parameters remained unchanged. In desired time intervals, the reaction progress was controlled by withdrawing 4–5 ml of reaction suspension from the reactor, cooling it to 23 °C, measuring the pH-value at 23 °C and determining the particle size distribution by laser diffraction (see below). For investigation of particle morphology by scanning electron microscopy (see below), the particle slurry was filtered, washed with H₂O in a 10:1 precipitate:H₂O weight ratio, and dried in air at 120 °C for 12 h in an oven (universal Oven U, Memmert). After 8.75 h reaction run time, the total solution volume was 480 ml, and the reactant flows were stopped. The obtained product suspension was collected and identically processed.

The reactor suspension sample was homogenously dispersed, and a small amount of the particle slurry was transferred into the particle size analyzer (Mastersizer 2000, Malvern Panalytical GmbH) until a light obscuration between 4.0%–14.0% was achieved. The respective volume-based particle size distribution (PSD) was determined by laser diffraction based on Mie's scattering theory. A refractive index of 1.33 for H₂O as dispersant was selected, while a refractive index of 2.19, identical to the refractive index of NiO, was assumed for the Ni_0.8Co_0.1Mn_0.1(OH)₂ particles. The intensity of the scattered laser beam was collected as a function of the scattering angle for particle sizes in the range of 0.05–70.0 μm by applying a combination of red and blue light. Based on three measurements per sample, the average volume-based percentile particle sizes d₁₀, d₅₀, and d₉₀ were determined. The span (σ) of the PSD was calculated according to the following equation.

$$\begin{eqnarray}&&\sigma \,=\,\displaystyle \frac{{{\rm{d}}}_{90}-{{\rm{d}}}_{10}}{{{\rm{d}}}_{50}}\end{eqnarray} \tag{ 9 }$$

The morphology of the obtained pCAM particles was characterized by attaching the Ni_0.8Co_0.1Mn_0.1(OH)₂ powder on a SEM pin holder (Agar Scientific, Ltd.), which is covered with conducting carbon (Plano GmBH). Subsequently, the sample was coated with a 6 nm platinum layer (SCD 500 Sputter Coater, Bal-Tec AG). Top-view SEM imaging was performed with a thermal field emission cathode and an Everhat-Thornley secondary electron detector at an operating voltage of 5 kV (Ultra 55, Carl Zeiss Ag).

Samples for cross-section measurements were prepared by mixing 2 g of epoxy resin and 0.5 g of epoxy hardener (Buehler, ITW Test & Measurement GmbH) and then adding a few drops of the mixture to the respective Ni_0.8Co_0.1Mn_0.1(OH)₂ precursor sample in a gelatine capsule (Plano GmbH). The resulting slurry was cast onto an Al-foil using a manual coater with a gap size of 0.5 mm and dried in an oven at 40 °C overnight. Small sections thereof were transferred to an ion milling system (ArBlade 5000, Hitachi, Ltd.) equipped with an Ar-ion beam at an operating voltage of 6 kV. Images were taken as described above for the top-view measurements.

Quantitative information about particle circularity as a two-dimensional descriptor for the particle sphericity of Ni_0.8Co_0.1Mn_0.1(OH)₂ particles, which is a three-dimensional property, was determined from SEM top-view images at 1 k magnification by employing a segmentation model. The underlying algorithm implemented for automated image segmentation is based on a convolutional neural network utilizing the U-Net architecture, ⁴¹ which is analogous to the model applied by other authors for the segmentation of primary particles in polycrystalline lithium nickel oxide. ^20,42 The as-measured lengths/areas from two-dimensional projected particles from the original SEM image were captured in the dimension of pixels and converted back to actual lengths/areas after segmentation by using a calibration factor from the image metadata. Additionally, several filters for the segmentation were employed to increase the accuracy of the process. Particles touching the boundary of the image were not evaluated, since particles in this region might not be fully captured. Further, only particles were considered, which exhibited an area of above 200 pixels and a solidity (=ratio between the particle's area and the area of the convex hull that encloses the particle) of ≥0.8. ⁴³ These conditions ascertained that only particles that did not deviate excessively from a spherical shape were recognized. The circularity (C) of the segmented particles that fulfilled the aforementioned criteria was then calculated according to the isoperimetric quotient, which is defined as: ⁴⁴

$$\begin{eqnarray}&&{\rm{C}}\,=\displaystyle \frac{{{\rm{A}}}_{{\rm{particle}}}}{{\,{\rm{A}}}_{{\rm{eq}}.{\rm{circle}}}}=\displaystyle \frac{4\pi {{\rm{A}}}_{{\rm{particle}}}}{{{\rm{P}}}_{{\rm{particle}}}^{2}}\end{eqnarray} \tag{ 10 }$$

Here, A_particle is the area and P_particle is the perimeter of the segmented particle based on a 2D projection of the particle and A_{eq. circle} is the area of a perfect circle that would have the equivalent perimeter as that measured for the segmented particle (= P_particle); note that C equals one for a perfect circle.

Overall, for each sample, the circularity of approximately 60–100 particles was determined to obtain the circularity distribution for each sample. For each circularity distribution the median number-based percentile circularities C₁₀, C₅₀, and C₉₀ were determined. The validity of the segmentation model was verified by comparing algorithm-based circularity distributions of selected samples to distributions attained by manual segmentation via ImageJ. ⁴⁵ Further, similar to the span σ that is used to represent the width of the particle size distribution determined by light scattering (see Eq. 9), the width of the here obtained circularity distributions (C_span) was calculated according to the following equation.

$$\begin{eqnarray}&&{{\rm{C}}}_{{\rm{span}}}=\displaystyle \frac{{{\rm{C}}}_{90}-{{\rm{C}}}_{10}}{{{\rm{C}}}_{50}}\end{eqnarray} \tag{ 11 }$$

The size of secondary particle cores was manually determined from cross-section SEM images of Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles at various magnifications by applying ImageJ. ⁴⁵ For this analysis, only those secondary particles were considered as representative which had been sliced perfectly through the equator of the secondary particle during the SEM sample preparation to ensure fault-free quantification of the core size. This is assured by only selecting particles, which have a similar particle size as was determined by light scattering and for which the core was readily exposed. This prevents falsification of the analysis by in e.g., secondary particles that were sliced through the upper or lower quarter and therefore would result in a non-representative secondary particle core size.

The corresponding equivalent diameter (d_eq.) of a circle with identical area as the determined area of the core (A_core) was calculated according to the following.

$$\begin{eqnarray}&&{{\rm{d}}}_{{\rm{eq}}.}\,=\,2\cdot \sqrt{\displaystyle \frac{{{\rm{A}}}_{{\rm{core}}}}{\pi }}\end{eqnarray} \tag{ 12 }$$

The internal secondary particle porosity of Ni_0.8Co_0.1Mn_0.1(OH)₂ particles were determined by measuring nitrogen physisorption isotherms at 77 K (ASAP2420, Micromeritics). Prior to the measurements, pCAM powders were degassed at 120 °C for three hours. It was demonstrated in a previous work that the internal secondary particle porosity of pCAM particles can be determined via N₂ capillary condensation in these pores at a high relative pressure p/p₀ value of 0.995. ⁷ The SEM imaging analysis of the pCAM particles showed that internal pores were smaller than ∼300–400 nm, which is below the pore diameter below which according to the Kelvin equation liquid N₂ can be formed in these pores at a relative pressure p/p₀ value of 0.995.

The intra-particle porosity ε_intra of Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles can be calculated according to: ⁴⁶

$$\begin{eqnarray}&&{\varepsilon }_{{\rm{intra}}}=\displaystyle \frac{{{\rm{V}}}_{{\rm{N2}},{\rm{liquid}}}}{{{\rm{V}}}_{{\rm{N2}},{\rm{liquid}}}+\displaystyle \frac{1}{{\rho }_{{\rm{cryst}}.}}}\end{eqnarray} \tag{ 13 }$$

where V_N2,liquid is the specific liquid N₂ volume condensed in the pCAM secondary particle pores and ρ_cryst. is the crystallographic density of Ni_0.8Co_0.1Mn_0.1(OH)₂. Here, a molar averaged crystallographic density of 3.96 g cm⁻³ is assumed, based on the crystallographic density of Ni(OH)₂ (=4.10 g cm⁻³), Co(OH)₂ (=3.60 g cm⁻³), and Mn(OH)₂ (=3.26 g cm⁻³) and the transition metal ratio of Ni/Co/Mn = 8/1/1.

The particle growth during semi-batch operation was monitored by sampling the reaction suspension at desired time intervals and determining the corresponding particle size distribution (PSD) by light scattering. The development of the obtained volume median particle sizes (d₅₀) throughout the semi-batch run time (t_run) for coprecipitations conducted with different stirring speeds (n) are depicted in Fig. 2a. Furthermore, Table I lists the d₅₀ values of the Ni_0.8Co_0.1Mn_0.1(OH)₂ particles formed after 5 min, 1.0 h, and 8.75 h as well as the span (σ) values that represent the width of the corresponding PSD for each semi-batch experiment. The d₅₀ values of the initial particles generated after a t_run of 5 min depend inversely on the applied stirring speed, while the spans of the corresponding PSDs are similar in each run and indicate a broad PSD. During the first hour of the coprecipitation reaction, the particle size increases only slightly (by ∼20%–30% between 5 min and 1.0 h, see Table I), accompanied by a minor decrease in PSD span (∼10%–15%). After this early phase, the particle growth over each run appears to follow a power function (see Fig. 2a), as observed by other authors during hydroxide pCAM coprecipitation, ^47,48 which is characteristic for the growth of spherical particles independently of the material class. ^49,50 The final d₅₀ values achieved at the end of each experiment, i.e., after t_run = 8.75 h is roughly inversely proportional to the stirring speed (see Table I). In contrast, independent of the applied stirring speed, the PSD of the particles continuously narrows over the course of the coprecipitation reaction, and the PSD span after 8.75 h of run time is approximately halved compared to the PSD of the initial particles formed after 5 min. A similar behavior, namely an extremely broad span of particles formed throughout the first 45 min of the semi-batch coprecipitation of Ni_0.35Mn_0.65(OH)₂ that is followed by a continuous decrease in span throughout the proceeding particle growth phase was observed by Liu et al., without, however, conducting any further investigations in this phenomenon. ⁴⁷

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To gain further insights into the growth mechanism, the particle growth curves depicted in Fig. 2a were scaled by plotting the determined d₅₀ as a function of the third root of the batch run time (${\sqrt[3]{{\rm{t}}}}_{{\rm{run}}}$) (see Eq. 6). The thus attained particle growth profiles for each of the applied stirring speeds (n) are shown in Fig. 2b. As already indicated above, independent of the stirring speed, the course of particle growth can be divided into two distinct stages: For ${\sqrt[3]{{\rm{t}}}}_{{\rm{run}}}$ < 1.0 h (≙ t_run < 1.0 h), the particle size remains fairly constant and only marginally increases, delineating stage I. After this initial phase, for $\sqrt[3]{{{\rm{t}}}_{{\rm{run}}}}$ ≥ 1.0 h (≙ t_run ≥ 1.0 h), the d₅₀ values for each stirring speed increase perfectly linearly with $\sqrt[3]{{{\rm{t}}}_{{\rm{run}}}},$ illustrated by correlation factors (R) of the linear regression lines of close to one, delineating stage II. The slope of these linear regression lines are a function of the mean particle growth rates (G, defined by Eq. 8) during the respective coprecipitation, which are listed in Table I, and which are roughly inversely proportional to the applied n in the respective semi-batch run.

This analysis suggests that new particles are still being generated during stage I, because the overall volume of coprecipitated solid V_M(OH)2 is increasing with run time (see Eq. 3) while the particle size barely increases (see Fig. 2b). In contrast, in stage II, the increase of the d₅₀ values with $\sqrt[3]{{{\rm{t}}}_{{\rm{run}}}}$ suggests that the continuously coprecipitated solid mass is solely deposited on already existing particles, without any further increase in particle number (N_par., see Eq. 6). This growth behavior in stage II is characteristic for seeded batch crystallization processes, whereby nucleation and formation of new particles is suppressed by charging the reactor with seed particles before initiating the reaction. ^38–40 Hence, after stage I, the semi-batch coprecipitation conducted in this work behaves analogous to a seeded crystallization reaction. Interestingly, despite different applied stirring speeds, the transition from stage I to stage II in the here conducted semi-batch experiments occurs at similar t_run values. This suggests that the cessation of nucleation (i.e., the end of stage I) and the concomitant onset of particle growth (i.e., the beginning of stage II) seems to be mainly dependent on the solid mass fraction in the reactor. It is rationalized that this can be justified by the feedback effect of the existing solid mass in the reactor on the nucleation kinetics, namely by decreasing the existing supersaturation as driving force for nucleation in the system because lattice ions (for the formation of M(OH)₂, the lattice ions are M²⁺ and OH⁻) are contributing to crystal growth on already available solid mass instead to the supersaturation. ^51,52 This is consistent with the observation of a critical seed loading reported for seeded batch crystallization syntheses of various compounds, above of which the formation of new particles is effectively suppressed. ^53,54

Table I also shows that the span values (σ) of the PSDs for the three runs conducted at different stirring speeds decrease with run time. It is rationalized, that the narrowing of the PSD with progressing particle growth implies that the particle size increase of particles within each run is independent of their size, and therefore, nearly the surface mass specific uptake nearly identical for every particle. Consequently, smaller particles "catch up" in mass and volume to larger ones with proceeding t_run, since an equal increase in diameter for particles of varying size denotes a larger gain in volume for smaller particles compared to larger ones. This overall results in a particle size independent growth rate within each run. Please note that the growth rate between each run is different (see G in Table I), which will be explained below.

By Eq. 5 determined values for N_par. of the coprecipitated Ni_0.8Co_0.1Mn_0.1(OH)₂ particles inside the reactor after 5 min, 1.0 h, and 8.75 h for each semi-batch experiment are given in Table II. The particle number during each run was increased within stage I by factor of ∼5–6 (i.e., between t_run of 5 min and 1.0 h, see Fig. 2b), which implies that new particles are formed by nucleation. During the subsequent growth phase, i.e., in stage II, the initial particle number at t_run = 1.0 h in each run decreases by 14%–29% until the end of the experiment at t_run = 8.75 h. A decrease in particle number throughout the course of the coprecipitation reaction can be rationalized by the following scenarios: (a) agglomeration of secondary particles throughout the process; (b) a significant secondary particle porosity, which would lower the assumed crystallographic density (ρ_cryst.) applied for the calculation of the particle volume according to Eq. 3, and thus would result in an underestimation of particle number; and/or, (c) a decrease in solid volume inside the reactor, hence particle number, caused by the sampling of the reaction suspension over the course of the semi-batch operation. An agglomeration of secondary particles (scenario (a)) seems unlikely, since the d₅₀ values during stage II increase with $\sqrt[3]{{{\rm{t}}}_{{\rm{run}}}}$ (Fig. 2b), following the relationship given by Eq. 6 that is based on assuming a constant N_par. value. Furthermore, agglomeration processes are generally a function of agitation, ^55,56 so that the largest decrease in particle number would be expected for the semi-batch coprecipitation conducted at n = 550 rpm, while run 3 conducted at n = 1350 rpm should exhibit the lowest change; this is contrary to the observations based on Table II, where the N_par. value calculated by Eq. 5 decreases most strongly for n = 1350 rpm (∼29% compared to ∼14% for n = 550 rpm).

Table II. Particle number (N_par.) in the reactor at selected stages of particle growth during the semi-batch coprecipitation of Ni_0.8Co_0.1Mn_0.1(OH)₂ conducted at various stirring speeds (n), calculated according to Eq. 5. The subsequent columns give the theoretically resulting particle size at trun = 8.75 h for an assumed constant number of particles during stage II (${d}_{50,8.75\,h}^{theo},$ based on Eq. 13), and the particle number (${N}_{par.,8.75\,h}^{\ast }$) determined on the basis of the intra-particle porosity (ε_intra)-corrected density in Eq. 3. ε_intra was determined by nitrogen physisorption.

Run #	n [rpm]	Npar., 5 min [-]	Npar., 1.0 h [-]	Npar., 8.75 h [-]	${{\rm{d}}}_{50,8.75\,{\rm{h}}}^{{\rm{theo}}}$ [μm]	${{\rm{N}}}_{{\rm{par}}.,8.75\,{\rm{h}}}^{\ast }$ [-]	εintra [-]
1	550	1.4 × 109	8.3 × 109	7.1 × 109	12.9	8.2 × 109	17.1%
2	950	7.9 × 109	4.1 × 1010	3.1 × 1010	7.6	3.8 × 1010	18.1%
3	1350	2.5 × 1010	1.7 × 1011	1.2 × 1011	4.7	1.5 × 1011	17.4%

To examine hypothesis (b), the theoretically resulting particle size at the end of the experiments, i.e., at t_run = 8.75 h (${{\rm{d}}}_{50,8.75\,{\rm{h}}}^{{\rm{theo}}}$), was calculated by assuming that the number of particles would indeed remain constant during stage II, namely between t_run of 1.0 h and 8.75 h, which is obtained by rearranging Eq. 7:

$$\begin{eqnarray}&&{{\rm{d}}}_{50,8.75\,{\rm{h}}}^{{\rm{theo}}}={\left(\displaystyle \frac{{{\rm{V}}}_{{\rm{M}}\left({\rm{OH}}\right)2,8.75\,{\rm{h}}}}{{{\rm{V}}}_{{\rm{M}}\left({\rm{OH}}\right)2,1.00\,{\rm{h}}}}\right)}^{1/3}{{\rm{d}}}_{50,1.0\,{\rm{h}}}\end{eqnarray} \tag{ 13 }$$

Here, V_{M(OH)2 1.0 h} and V_{M(OH)2 8.75 h} is the total volume of Ni_0.8Co_0.1Mn_0.1(OH)₂ particles formed after t_run of 1.0 h and 8.75 h, respectively, which was calculated via Eq. 3, while d_{50 1.0 h} is the volume median particle size of the Ni_0.8Co_0.1Mn_0.1(OH)₂ particles collected after a t_run of 1.0 h, determined by light scattering. A comparison of the thus obtained ${{\rm{d}}}_{50,8.75\,{\rm{h}}}^{{\rm{theo}}}$ values listed in Table II for each semi-batch run to the values obtained by light scattering in Table I reveals that the former are underestimated by ∼0.6-0.8 μm. By inspecting Eq. 3, this could be caused by a particle density that is significantly lower than the crystallographic density of Ni_0.8Co_0.1Mn_0.1(OH)₂ (${\rho }_{{\rm{cryst}}.}$) used for the calculation of ${{\rm{V}}}_{{\rm{M}}\left({\rm{OH}}\right)2},$ which would be the case if the secondary particles have a significant porosity. Therefore, the intra-particle porosity (ε_intra) of the Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles collected after a run time of 8.75 h was determined by nitrogen physisorption. In our previous work it was demonstrated that the internal secondary particle porosity can be determined via N₂ capillary condensation in these pores at a high relative p/p₀ value of 0.995. ⁷ The resulting ε_intra values of ∼17%–18% are listed in Table II, indicating a significant secondary particle porosity. It is assumed that the uniformity of the ε_intra values stems from a nearly constant volume ratio of the porous secondary particle core to the overall secondary particle irrespective of the stirring speed (see below), which implies that ε_intra in the core and outer regions of the secondary particles are very similar independent of the stirring speed. Using these experimentally determined ε_intra values, the volume of the coprecipitated particles (${{\rm{V}}}_{{\rm{M}}\left({\rm{OH}}\right)2}$) was recalculated by multiplying the ${\rho }_{{\rm{cryst}}.}$ term in Eq. 3 by (1-ε_intra) in order to account for the lower secondary particle density on account of their porosity. With the thus corrected ${{\rm{V}}}_{{\rm{M}}\left({\rm{OH}}\right)2}$ values, the corresponding particle numbers for the different runs (${{\rm{N}}}_{{\rm{par}}.,8.75\,{\rm{h}}}^{\ast }$) were calculated from Eq. 5 and are given in Table II. By considering ε_intra, the apparent decrease in particle number over the course of stage I (i.e., between t_run of 1.0 and 8.75 h) amounts to only ∼1%–12%. Thus, within the error of this analysis (e.g., using d₅₀ values rather than a size distribution), the number of coprecipitated particles over the course of stage II remains essentially constant.

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Even though the continuous withdrawal of solid volume by sampling reaction suspension from the reactor might account for part of the remaining decrease in N_par. during stage II (hypothesis (c)), the accumulated amount of sample volume withdrawn by the end of each run amounts to one-fifth of the total suspension volume, whereby the total amount of material lost due to sampling is significantly less. A significant sampling-induced loss of N_par.. would manifest as a deviation from Eq. 6 by an increase in growth rate, resulting in a continuous increase of the slope of the linear regressions depicted in Fig. 2b. Therefore, an impact on the particle growth kinetics and formation mechanism by sampling can be considered negligible.

In light of the above analysis, it is rationalized that the Ni_0.8Co_0.1Mn_0.1(OH)₂ particle formation can be divided in two distinctive stages: Initially, particles with a nearly constant diameter are generated by nucleation until enough solid mass is available in the reactor, so that the process during this period can be denoted as seeding stage (stage I in Fig. 2b). Analogous to seeded batch crystallizations, these particles serve as seed particles in the subsequent growth stage (stage II in Fig. 2b, in which solely particle growth is occurring, without a significant formation of new particles. The applied stirring speed during the semi-batch coprecipitation reaction seems to affect the size and number of particles formed in the seeding phase, which then determines the growth rate (G) during the growth phase, thus, the obtainable particle size after any given run time.

For deeper insights into the particle formation mechanism, the morphology of particles at selected stages of particle growth during the semi-batch coprecipitation of Ni_0.8Co_0.1Mn_0.1(OH)₂ was characterized by top-view SEM imaging. Figure 3 displays SEM images and corresponding PSDs of Ni_0.8Co_0.1Mn_0.1(OH)₂ particles attained at various points in time for the run conducted at n = 950 rpm, whereby the selected run times are marked by the differently colored data points in Fig. 2. It is worthy to note that the PSDs depicted in Fig. 3a are mono modal, which is also true for the PSDs attained by light scattering for the semi-batch run at n = 950 rpm for run times that are not depicted in Fig. 3a, as well as in the other semi-batch experiments. The particles obtained during the initial phase of the coprecipitation run, i.e., after t_run = 5 min exhibit a rather broad PSD (orange line in Fig. 3a) and are composed of undefined and loose aggregates (see Fig. 3b). After a t_run of 1.0 h, consolidation of the inhomogeneous particle clusters into agglomerates has occurred (Fig. 3c), which are comprised of numerous tiny nano spheres and in turn consist of twinned and plate-like shaped primary particles (Fig. 3d) that are characteristic for beta-nickel hydroxide (Ni(OH)₂) ^57–61 and M(OH)₂. ^7,10,62 Please note that here the term aggregate was chosen as definition for loose particle assemblages that can be easily ruptured, while the term agglomerate was selected for particle consolidations that are cemented by solid bridges. ⁶³ During that first hour of run time, the PSD span decreased slightly (by ∼14%, see Table I), but the PSD still remains comparably broad (see purple line in Fig. 3a). Particles collected at a t_run of 2.0 h are aspherical and resemble the initial agglomerate structure with multiple radial extensions (Fig. 3e). At higher magnification (Fig. 3f), the radial orientation of the intergrown sub-micron sized plate-like shaped primary particles within such extensions becomes evident, whereby the vertical side ("edge") of the primary particles is exposed. This vertical side, which corresponds to the 001-plane ^7,60 is pointing away from the center of the corresponding radial extension. With progressing t_run, the number of radial extensions for a given aspherical secondary particle is decreased, while the radial extension size is enlarged (Fig. 3g); this further continues with run time, so that the rather heterogeneous structure exhibited by the initially coprecipitated particles (Fig. 3b) cannot be anymore identified after a t_run of 6.25 h (Fig. 3i). Interestingly, the primary particles are always radially orientated around the secondary particle perimeter, with the vertical side of the primary particles facing away from the secondary particle center (Figs. 3h, 3j). Simultaneously, a continuous decrease in PSD span from 1.16 at t_run = 2.0 h to 1.06 at t_run = 3.75 h and to 0.83 at t_run = 6.25 h is observed. Close to the end of the semi-batch experiment, i.e., at t_run = 8.25 h, the various radial extensions within the secondary particle structure cannot be recognized any more, eventually resulting in spherical secondary particles without any indications of the initial agglomerate structure (Fig. 3k). These particles exhibit a ∼2-fold lower PSD span compared to the initially formed particles (0.76 vs 1.4, see Table I), which is reflected by the PSDs shown in Fig. 3 (black vs orange line). These hierarchically structured secondary particles are comprised of numerous sub-micron sized primary particles, as typically reported for NCM hydroxide precursor particles, ^6,8–10,62 while the edge of the primary particles is consistently orientated towards the perimeter of the secondary particle (Fig. 3l).

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In agreement with the two distinct stages observable in the particle growth profiles depicted in Fig. 2b, the development of the corresponding secondary particle morphology can likewise be divided into two stages:

• (i)  
  The initial particles formed during the seeding stage (t_run < 1.0 h) exhibit a loose and undefined aggregate-like structure, which is originating from a rapid nucleation of nanospheres. These nanoparticles immediately coagulate to particle clusters and are cemented to agglomerates by the ensuing crystal growth via solid bridge formation. That the particle formation during the seeding stage (between a t_run of 5 min and 1.0 h) is governed by an agglomeration mechanism is supported by the inverse correlation of the secondary particle d₅₀ values with the stirring speed during the respective semi-batch coprecipitation (Fig. 2, Table I). This result reflects the fact that the turbulence inside the agitated reaction vessel is governing the particle-particle attachment by agglomeration, which can be manipulated by the stirring speed. ^55,56
• (ii)  
  During the subsequent growth stage (t_run < 1.0 h), the data suggest that the consolidated agglomerates generated during the seeding phase increase in size by lateral crystal growth of individual primary particles ("polycrystallization"), because the vertical side of the primary particles is consistently orientated towards the outer perimeter of the secondary particle during the growth phase (Figs. 3d, 3f, 3h, 3j, and 3l). This seems to result in an overall enhancement of the Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particle sphericity throughout the semi-batch reaction.

To quantitatively verify the increase in secondary particle sphericity over the course of the conducted experiments, SEM top-view images of Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles at selected stages of the semi-batch coprecipitations conducted at various stirring speeds were segmented. The SEM images were taken at 1 k magnification and an automated segmentation algorithm was employed, that is analogous to the model employed by other authors. ^20,42 By two-dimensional approximation of the segmented secondary particles, the area and perimeter of secondary particles was determined. This allows the calculation of the secondary particle circularity (C) as a two-dimensional descriptor for the secondary particle sphericity, which is a three-dimensional property, according to isoperimetric quotient given in Eq. 10. On average, the C values of 60-100 secondary particles per sample were determined and number-based C value distributions were formulated. Figure 4 exemplary displays a SEM image of Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles collected at t_run of 6.25 h during the semi-batch coprecipitation performed at n = 950 rpm (run 2) before (Fig. 4a) and after automated segmentation (Fig. 4b). The secondary particles in the SEM image that were not considered by the algorithm are encircled in green, while particles for which the C value was determined are additionally colored in blue.

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The validity of the algorithm-based segmentation was exemplarily verified by manual segmentation, and the resulting number-based C value distributions extracted from the SEM image displayed in Fig. 4a are compared in Fig. 4c. The obtained distributions are in good agreement, and only minor deviations can be observed for secondary particles exhibiting nearly perfect circularity (C > 0.95) and for rather non-circular particles (C < 0.80). The discrepancy for C > 0.95 might be ascribed to circular secondary particles, which were not considered by the algorithm due to local brightness inhomogeneities across the secondary particle structure that results in a blending with the background brightness. The discrepancy for C < 0.80 might be due to improper segmentation of overlapping secondary particles by the model, which results in an underestimation of the C value for the particle that is being overlapped, whereby such overlapped particles were not considered during manual segmentation. However, these slight discrepancies result in an only minor deviation of ∼2% when comparing the number median circularity (C₅₀) determined from the C value distributions obtained by both methods (data not shown). In an analogous manner, the validity of the segmentation was further exemplarily verified for Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles obtained at a t_run of 3.75 h and 8.25 h during the semi-batch coprecipitation conducted at n = 950 rpm. The resulting number-based C value distributions are given in Fig. A.1. Again, the discrepancy between the automated and the manual segmentation based C₅₀ values is rather minor, with only ∼4% for particles collected at a t_run of 3.75 h and ∼1% for particles collected at a t_run of 8.25 h. It is worthy to note that C values for secondary particles formed at run times shorter than 2.0 h were not determined, due to an excessive deviation of the secondary particles from a circular shape (Figs. 3b–3d). Furthermore, due to the two-dimensional approximation of three-dimensional particles, which is the basis of Eq. 10, some three-dimensional aspherical features of the particle that are not located on or near the perimeter of the particle, are underestimated or even not considered. This, e.g., is the case when radial extensions are orientated towards the camera's line-of-sight in top-view SEM images. Therefore, it is assumed, that values for C obtained via the here presented method as a two-dimensional descriptor for particle sphericity, which is a three-dimensional property, are slightly overestimating the actual sphericity of secondary particles. Regardless, however, it is demonstrated that reasonable results can be obtained by the algorithm-based determination of the secondary particle circularity as descriptor for the secondary particle sphericity from SEM images by the here applied approach. This allows a quantitative assessment of the subjectively observable increase in secondary particle sphericity in Fig. 3.

Figure 5 a depicts the automated SEM image segmentation-based evolution of the C₅₀ values of secondary particles collected after similar run times (within t_run $\pm$ 0.25 h) during semi-batch coprecipitation of Ni_0.8Co_0.1Mn_0.1(OH)₂ conducted at three different stirring speeds. For all three runs, the relative increase in C₅₀ with increasing d₅₀ during the growth stage (stage II in Fig. 2b) between t_run = 2.0 h and t_run = 8.25 h is similar, namely ∼20%-30%. Furthermore, the width of the circularity distributions (C_span, defined by Eq. 11), that is represented by the error bars in Fig. 5a, decreases by factor of ∼4–5 with increasing t_run for all three semi-batch experiments. However, in contrast to the inverse relationship between d₅₀ and the stirring speed (Fig. 2), the C₅₀ values of the particles at a t_run of 2.0 h (left-most data points within each run in Fig. 5a) increase with the stirring speed. It is also interesting to note that even though the slowest stirring speed (n = 550 rpm) yields the largest secondary particles, those particles exhibit the lowest C₅₀ (see Fig. 5a). Close to the beginning of stage II, particles with a d₅₀ of 8.1 μm and a C₅₀ of 0.63 are obtained for n = 550 rpm, growing into particles with a d₅₀ of 13.5 μm and a C₅₀ of 0.83 at t_run = 8.25 h. In comparison, for n = 1350 rpm, much smaller particles with higher circularity are obtained: at t_run = 2.0 h, the secondary particles have a d₅₀ of only 2.9 μm and a C₅₀ of already 0.81, which at t_run = 8.0 h increases to a still rather small d₅₀ of 5.0 μm and a C₅₀ of 0.95. The Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles produced with n = 950 rpm display comparable particle circularities compared to the experiment with n = 1350 rpm, but with larger particle sizes for any given run time (see Fig. 5a). Further, due to the increase of C₅₀ over t_run (thus with increasing d₅₀) for all three conducted runs, C_span must intrinsically decrease with increasing t_run as non-circular particles become more circular over time while already circular particles remain circular. This results in the observed narrowing of C_span with increasing t_run for all three runs.

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The quantitative differences in secondary particle circularity are further visualized by SEM top-view images of the final Ni_0.8Co_0.1Mn_0.1(OH)₂ particles obtained by semi-batch coprecipitation after t_run = 8.75 h at stirring speeds of 1350 rpm (Fig. 5b), 950 rpm (Fig. 5c), and 550 rpm (Fig. 5d). Identical to the secondary particles throughout the growth phase at n = 950 rpm (Figs. 3e–3l), the secondary particles obtained at 1350 rpm and 550 rpm consist of numerous sub-micron primary particles, which is characteristic for NCM hydroxide precursors. ^6–10,62 Furthermore, the vertical side of the primary particles is consistently orientated towards the outer perimeter of the secondary particles, which verifies that independent of the applied stirring speed, the secondary particle size increases by the growth of the individual primary particles. In accordance with the C value analysis conducted above, the Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles prepared at n = 1350 rpm and n = 950 rpm exhibit an equal sphericity with no radial particle extensions or recognizable traces of the initial agglomerate structure, whereby the secondary particles obtained at 1350 rpm are smaller compared to those obtained at 950 rpm. The secondary particles obtained at 550 rpm are the largest, but still exhibit an aspherical shape, which consists out of multiple radial extensions originating from the initially formed agglomerates, consistent with their still relatively low C₅₀ value of ∼0.8 (see Fig. 5a).

In summary, one can conclude that the stirring speed during the semi-batch coprecipitation of Ni_0.8Co_0.1Mn_0.1(OH)₂ determines the initial agglomerate size and number formed during the seeding stage, which not only governs the growth rate and thus the resulting particle size in the subsequent growth phase, but also the ability of the secondary particles to achieve a high degree of sphericity for a given particle size and run time. Overall, with increasing stirring rate, smaller Ni_0.8Co_0.1Mn_0.1(OH)₂ particles with higher sphericity can be obtained (see Fig. 5), while the PSD span is unaffected by the stirring rate (see Table I).

Complementary evidence for a two-stage particle formation mechanism was found by evaluation of cross-section SEM images of Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles obtained by semi-batch coprecipitation after t_run = 8.75 h. Exemplary SEM cross-section images of Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles attained at n = 1350 rpm, 950 rpm, or 550 rpm are displayed in Figs. 6a, 6c, and 6e, respectively. Independent of the stirring speed, the secondary particle structure can be divided into two parts: A particle core consisting of loosely arranged nanometer-sized primary particles, which is followed by a layer of elongated primary particles aligned around the core and orientated towards the outer perimeter of the secondary particle. This coincides well with the above observation that the vertical side of the plate-like shaped primary particles is consistently pointing towards the outer perimeter of the secondary particles. However, it is noteworthy that these core–shell features exhibiting radial patterns can only be observed by cross-sectional SEM imaging if the secondary particle has been perfectly sliced through the equator of the secondary particles during the SEM sample preparation.

Analogous to the size of the initial particles formed during the seeding stage (t_run ≤ 1.0 h), the magnitude of the secondary particle core scales inversely with the applied rotation speed in the respective run. This suggests that the core within the secondary particle structure corresponds to the initial agglomerates formed during the seeding stage, which increase in size by polycrystallization. To quantitatively verify this hypothesis, the size of the core in secondary particles was determined by manual segmentation of cross-sectional SEM images. The area of the porous particle cores of ∼50 cross-sectionally sliced Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles obtained after t_run = 8.75 h for each semi-batch run was determined. The equivalent particle diameter (d_eq.) of a circle with the identical area as the measured area of the particle core was calculated by applying Eq. 12. From the resulting d_eq. values, volume-based core size distributions were constructed. These are shown in Figs. 6b, 6d, and 6f (green colored bars), where they are compared to the PSDs of secondary particles at the transition of the seeding into the growth stage, i.e., at t_run = 1.0 h, which were determined by light-scattering (green colored dashed lines). Overall, the size distributions of the secondary particle cores coincide well with the light scattering derived PSDs at the transition point.

This correspondence was further quantitatively verified by determining the volume-based median core size of the Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles (${{\rm{d}}}_{50,8.75\,{\rm{h}}}^{{\rm{core}}}$) from the respective cross-sectional SEM based core size distribution. Table III gives a comparison of these ${{\rm{d}}}_{50,8.75\,{\rm{h}}}^{{\rm{core}}}$ values with the d_{50, 1 h} values of the secondary particles obtained at the seeding-to-growth transition, i.e., at t_run = 1.0 h (obtained by laser scattering and taken from Table I), revealing an excellent agreement between these two parameters for each of the respective runs (with differences of less than 10%). Consequently, it is reasonable to assume that the core within the secondary particles corresponds to the initial agglomerates formed during the seeding stage and that the core size is inversely proportional to the stirring speed. The somewhat irregular morphology of the core might originate from the inclusion of void spaces during the chaotic aggregation of nanospheres throughout the seeding stage. After the aggregate has solidified to an agglomerate, only primary particles that are in intimate contact with the mother liquor are able to grow, as they are accessible for diffusion of lattice ions towards the solid surface. By contrast, primary particles that are located in the inside of the agglomerate are inaccessible by lattice ions, which could potentially fill the pores among primary particles with crystallizing matter. This results in void spaces in the core compared to the shell, even though void spaces persist in the entire secondary particle structure. Similar core–shell like features of secondary particles exhibiting radially aligned primary particles were also identified by SEM imaging of cross-sectionally cut secondary particles of precipitated Ni(OH)₂, ^60,61 Ni_0.75Co_0.15Mn_0.10(OH)₂, ⁶⁴ Ni_0.83Co_0.07Mn_0.10(OH)₂, ⁶⁵ and Ni_1/3Co_1/3Mn_1/3(OH)₂. ¹²

Table III. The volume-based median core size of Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles (${d}_{50,8.75\,h}^{core}$) determined by the analysis of cross-sectional SEM images of Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles attained by semi-batch coprecipitation after t_run = 8.75 h for various stirring speeds (n). This is compared to the volume-based secondary particle diameter obtained after t_run = 1.0 h (d_{50, 1.0 h}, based on laser scattering and taken from Table I). The last two columns provide the Reynolds Number (Re) calculated by Eq. 14 as well as the average volume energy input (E_avg.) calculated by Eq. 15, both being given for the conditions at t_run = 0.0 h.

Run	n [rpm]	${{\rm{d}}}_{50,8.75\,{\rm{h}}}^{{\rm{core}}}$ [μm]	d50, 1.0 h [μm]	Re [-]	Eavg. [W/l]
1	550	6.2	6.2	41041	1.54
2	950	3.4	3.7	70890	7.94
3	1350	2.5	2.3	100739	22.8

In general, the stirring speed is only an indicator for the turbulence in a stirred-tank reactor, since the turbulent flow caused by stirring also depends on the properties of the stirred fluid as well as the physical dimensions and the other features of the reaction vessel (e.g., stirrer blade configuration). For a better characterization of the prevailing turbulence in an agitated reaction vessel, the dimensionless Reynolds number (Re) and the average volume energy input (E_avg.) can be used. Both values allow comparing the turbulent motion of a fluid between distinctive reactor setups. ^66–68 The Reynolds number represents the ratio of inertial forces to viscous forces of a fluid in a stirred-tank reactor and is defined as:

$$\begin{eqnarray}&&{\rm{Re}}\,=\displaystyle \frac{{\rho }_{{\rm{fluid}}}\cdot {\rm{n}}\cdot {{\rm{d}}}^{2}}{\mu }\end{eqnarray} \tag{ 14 }$$

Here, ρ_fluid is the density of the stirred fluid (=985.0 kg m⁻³ for H₂O at 55 °C, representing the condition at t_run = 0.0 h), n is the stirring speed in units of 1/s, d is the stirrer diameter (=0.05 m), and μ is the dynamic viscosity of the stirred fluid (=0.00055 kg ms⁻¹ for H₂O at 55 °C) The parameter E_avg. describes the kinetic energy imparted into the stirred liquid and can be calculated according to:

$$\begin{eqnarray}&&{{\rm{E}}}_{{\rm{avg}}\cdot }=\displaystyle \frac{{\rm{Ne}}\cdot {\rho }_{{\rm{fluid}}}\cdot {{\rm{n}}}^{3}\cdot {{\rm{d}}}^{5}}{{{\rm{V}}}_{{\rm{total}}}}\end{eqnarray} \tag{ 15 }$$

Here, Ne is the dimensionless Newton Number, which for the here used 45° pitch-blade stirrer and for the turbulent regime with Re > 10000 equals to Ne = 1.3, ⁶⁹ and V_total is the volume of the reaction suspension (=200 ml at a t_run = 0.0 h).

The Re and E_avg. values for the three different stirring rates are listed in Table III. By increasing the stirring speed from 550 rpm to 1350 rpm, Re increases by a factor of ∼2.5, while E_avg. is increased by factor of ∼15. Even though an intensification of turbulence by strong stirring increases the particle collision frequency within the fluid, the shear stress induced by hydrodynamic forces on the aggregates is concomitantly amplified. This in turn results in the breakage of aggregates before cementation occurs via solid bridge formation by the further crystallization reaction. Permanent particle attachment is additionally reduced due to the higher particle velocities with increasing turbulence, hence higher particle momentum. This leads to higher impact energy upon particle-particle collision and effectively decreases the agglomeration probability. These phenomena overall result in a decrease in the maximum aggregate and/or agglomerate size with increasing turbulence, thus increasing Re and E_avg.. ^55,56 The same inverse relationship between Re and E_avg. vs. the aggregate and agglomerate size was observed in this study. Here, during the seeding stage, the Ni_0.8Co_0.1Mn_0.1(OH)₂ particle size (i.e., d_{50 5 min} and d_{50, 1.0 h}, see Table I) decreases by a factor of ∼2.6–2.7 when n (=input parameter for Re and E_avg.) is increased from 550 to 1350 rpm, which corresponds to an increase of n by a factor of ∼2.5. Since the particle size decreases by a factor of ∼2.6-2.7, the particle number (N_{par., 5 min} and N_{par.,1.0 h}, see Table II) increases by a factor of ∼18-20, which closely corresponds to 2.6–2.7³, as is required by a mass balance. Since the number of particles formed during the seeding stage determines the solid surface area, the growth rate (G) during the ensuing growth stage and therefore, the particle size at the end of the semi-batch experiment (i.e., d_{50, 8.75 h}), consequently exhibit similar correlations by factor 2.5 and 2.6 (Table I), respectively. Thus, it is rationalized that the degree of turbulence inside the stirred-tank reactor, which can be quantified by Re and E_avg., regulates the aggregation and agglomeration during the seeding stage, which governs the size and number of Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles formed during the seeding stage.

Similar reports on the impact of stirring speed on agglomeration rates, thus agglomerate size, have been reported for the coprecipitation of various material classes in stirred-tank reactors operated in (semi-)batch ^70–72 or continuous mode. ^73,74 Additionally, a decrease of the final secondary particle size accompanied by an increase in secondary particle sphericity has been observed during the continuous coprecipitation of Ni_1/3Co_1/3Mn_1/3(OH)₂, ¹⁰ Ni_0.90Co_0.05Mn_0.05(OH)₂, ⁷⁵ and Ni_0.80Co_0.15Al_0.05(OH)₂ ⁷⁶ in a Couette Taylor reactor when increasing the rotational speed of the inner cylinder. The analogous observations have been made when increasing the stirring speed in a stirred-tank reactor during the coprecipitation of Ni(OH)₂, ⁷⁷ Ni_0.5Co_0.2Mn_0.3(OH)₂, ⁹ Ni_0.6Co_0.2Mn_0.2(OH)₂, ⁷⁸ and Ni_0.225Co_0.125Mn_0.65(OH)₂. ⁷⁹

Considering the two distinctive stages in the development of the Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particle size (Fig. 2b) and respective morphology (Figs. 3 and 6) as well as the increase in secondary particle circularity as descriptor for particle sphericity (Fig. 5) during the growth phase, the two-step particle formation mechanism of Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles depicted in Fig. 7 is proposed. Initially nucleation (I) induces the formation of nanosized spheres comprised of several twinned plate-like primary particles (II) that are subjected to rapid and chaotic aggregation to randomly arranged particle clusters (III). Due to solid bridge formation by ensuing lateral crystal growth of individual primary particles, the generated loose aggregates are consolidated to agglomerates, while primary particle growth in direction away of the agglomerate core results in radial extensions leading to aspherical secondary particles (IV). Continuous secondary particle growth by polycrystallization, which is characterized by the lateral crystal growth of individual primary particles leads to a smearing out of the initial irregular agglomerate structure, so that eventually well-defined spherical secondary particles with a core–shell structure (V) are attained. The size of the initial agglomerates can be manipulated by the turbulence, which governs the growth rate and the capability of secondary particles to become spherical after a given run time. Additionally, the particle size increase within each run is independent of their size and therefore, the surface mass specific uptake is nearly identical for every particle. This results in a narrowing PSD with progressing particle growth throughout the coprecipitation reaction.

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Despite an analogous development of secondary particle morphology from irregular-shaped agglomerates to polycrystalline spherical secondary particles was observed by SEM imaging in several studies, ^{6,47,61,80,81} the overall proposed particle formation mechanism in this work is in contrast with prevailing theories present in the literature for the coprecipitation of M(OH)₂ in a stirred-tank reactor. Numerous studies report that the secondary particle enlargement during coprecipitation of M(OH)₂ results from a continuous agglomeration of primary particles. ^{9,48,75,82–84} In other instances, Ostwald ripening is suggested as the underlying particle growth mechanism, hence dissolution of generated nuclei and/or small primary particles, followed by recrystallization on existing secondary particles, ^6,39,85 which is suggested to also result in a decrease in particle size distribution width with progressing coprecipitation time. ⁸⁶ Others have also been claiming a simultaneous occurrence of agglomeration and Ostwald ripening. ^80,81

Since the particle collision frequency followed by permanent particle attachment during agglomeration is based on a statistic encounter of primary particles due to the isotropic turbulence in stirred vessels, ^55,87,88 a random primary particle orientation would be attained as it is in the case for true aggregates and agglomerates. ^89,90 Hence, a consistent orientation of the vertical side of the primary particles towards the outer perimeter of the spherical secondary particle as observed for M(OH)₂ (co)precipitation, accompanied by a radial alignment of primary particles around the secondary particle core, can hardly be justified by agglomeration. Furthermore, an overall irregular-shaped particle structure would be expected in contrast to spherical secondary particles. An increase in secondary particle sphericity by shear force at higher degrees of turbulence, which makes particles more spherical over time, is also questionable, as this would result in a considerable number of attritional fragments, ^91,92 which were not observed by light scattering or SEM imaging, and which would lead to a deviation from the d₅₀∼$\sqrt[3]{{{\rm{t}}}_{{\rm{run}}}}$ relationship during particle growth, due to the formation of new particles. Additionally, the emergence of a second particle modal originating from a second nucleation event after prolonged reaction time, observed by Kim et al. during semi-batch coprecipitation of Ni_0.855Co_0.155(OH)₂, ⁹³ is difficult to conciliate with an agglomerate mechanism, when considering that there is no driving force for continuously generated primary particles at a certain point throughout the coprecipitation reaction to suddenly form new secondary particle agglomerates instead of agglomeration with already existing secondary particles. A surface charge controlled self-assembly of primary particles in the sense of a controlled agglomeration of primary particles as origin for circular arrangement of primaries is also highly unlikely, because the surface charge results from an electrochemical double layer that is surrounding the particles and that decreases drastically in thickness with increasing ionic strength of the solution. Accordingly, it is reported that above an ionic strength of 0.1 M, the thickness of the electrochemical double layer is below 4.0 nm for a 1:1 electrolyte, and is even further decreased for electrolytes of higher valency. ⁹⁴ For the relatively highly concentrated feed solutions (2.6 M MSO_4(aq.) and 7.9 M NaOH) as well the volumetric flow rates in this work, the salt concentration of 0.1 M in the reaction mixture is already exceeded after only 20 min of the semi-batch coprecipitation reaction due to Na₂SO₄ formation according to Eq. 1. At such high ionic concentrations, surface charge driven phenomena become insignificant, as the critical ion concentration above which coagulation was observed to occur for Na⁺ salt based systems was reported to be already above 0.12 M. ⁹⁵ This is further emphasized by the fact that during the very early stage of crystallization the agglomeration of nanospheres for the formation of the secondary particle core could not proceed in a controlled manner and resulted in chaotic particle clusters as shown in Figs. 3b–3d. ⁹⁶

The size-dependent growth rate induced by Ostwald ripening of a solid depends amongst others on the bulk solubility of the ripening solid. ⁹⁷ The coprecipitation of M(OH)₂ is typically conducted in the pH-regime of 11.0–13.0, in which the solubility of Ni²⁺, Co²⁺, and Mn²⁺ is <200 ppm. ^5,37 Even though the Ni²⁺ solubility is increased by the formation of [Ni(NH₃)_n]²⁺ in alkaline media, the solubility of Co²⁺ and Mn²⁺ is only negligibly affected, due to a low affinity for the complexation reaction. ⁵ Furthermore, since the reactants are continuously fed in the stirred vessel, supersaturation is continuously generated, which creates a steady driving force for M(OH)₂ crystallization rather than its dissolution. Therefore, it is rationalized that the essential driving force required for the dissolution of M(OH)₂ primary particles on the peripheral regions in the secondary particles and even secondary particles itself is extremely low. Hence, that the occurrence of Ostwald ripening as particle growth mechanism during coprecipitation of Ni_0.8Co_0.1Mn_0.1(OH)₂ is rather marginal. The argument that dissolution is unlikely to occur is further supported by the result presented in Fig. 6: Independent of the applied stirring speed for a given run, the PSD at the end of the seeding stage at t_run of 1.0 h coincides well with the size distribution of the secondary particle core for particles collected after t_run of 8.75 h. A reduction in Ni_0.8Co_0.1Mn_0.1(OH)₂ PSD width, i.e., that is σ (see Eq. 9), with progressing coprecipitation time, i.e., that is t_run, induced by Ostwald ripening is also unlikely, as it is expected that the dissolution of small particles and recrystallisation on larger particles would actually result in an increase of span instead of a decrease, since the smaller particles would decrease in size due to dissolution over the batch run time (the size of the smaller particles is represented by the d₁₀ in Eq. 9), while the large particles increase in size, (the size of the larger particles is represented by the d₉₀ in Eq. 9). Since an increase in σ with increasing t_run was not observed in this work, the effect of Ostwald ripening on the particle size distribution width can be excluded.

However, nucleation at the contact point of the injected MSO_4(aq.) with the bulk alkaline reaction suspension inside the stirred tank reactor followed by an immediate dissolution of thereby formed nuclei and subsequent deposition as dissolved ions on primary particles within already existing secondary particles, thus resulting in crystal growth, cannot be excluded. Nonetheless, this does not interfere with the proposed particle formation mechanism that secondary particle growth occurs by growth of individual primary particles.

Interestingly, Andreassen analogously demonstrated for the precipitation of vaterite that the particle growth mechanism is governed by "spherulitic growth," hence growth of distinctive primary particles from a common core. This lead to the formation of a spherical polycrystalline secondary particle structure. ^98,99 Furthermore, spherulitic crystallization as underlying particle growth mechanism was identified for several materials such as Li₂CO₃, ¹⁰⁰ Y₂(OH)₅(NO₃), ¹⁰¹ and l-glutamic acid. ¹⁰² This conclusion was in contrast with the formerly assumed agglomeration mechanism of primary particles or nano-crystals resulting in the formation of secondary particles. ^103,104 Additionally, polycrystallization can also lead to aspherical secondary particles, which deceivingly looks like an agglomerate structure, even though it does not originate from an agglomeration of primary particles, as it was suggested for Al(OH)₃. ¹⁰⁵ Considering this, it is rationalized that the particle enlargement during the coprecipitation of Ni_0.8Co_0.1Mn_0.1(OH)₂ secondary particles is remarkedly similar to spherulitic growth. However, it is worthy to note that independent of the crystal composition, the particle growth mechanism also depends on the applied process conditions (concentration of reactants, volumetric flow rates etc). ¹⁰⁶ Hence, a deviation to the proposed mechanism can be expected if the coprecipitation conditions diverge considerably from the applied process parameter in this work. Nevertheless, the demonstrated relationships in this work allow to optimize the secondary particle sphericity by manipulation of the turbulence in a stirred-tank reactor at otherwise constant process parameters, thereby tailoring M(OH)₂ based pCAM particle size and morphology to satisfy the requirements for powder processing on an industrial scale.