Towards an enhanced understanding of the particle size effect on conversion/alloying lithium-ion anodes

The synthesis of nano-sized Zn_0.9Co_0.1O (Zn_0.9Co_0.1O^nano) was performed according to the procedure described by Mueller et al [30]. In brief, stoichiometric amounts of zinc(II) gluconate hydrate and cobalt(II) gluconate hydrate (both from ABCR) were dissolved in deionized water, resulting in a total metal ion concentration of 0.2 M. This solution was added to an aqueous 1.2 M sucrose solution and stirred for 15 min. Subsequently, the water was evaporated at 160 °C and the solid residue was dried at 300 °C, manually ground and calcined for 3 h at 400 °C under ambient atmosphere (heating rate: 3 °C min⁻¹) in a tube furnace (Nabertherm, RD 30/200/11). The Zn_0.9Co_0.1O samples with an increased particle size were prepared by sintering the Zn_0.9Co_0.1O^nano powder at different temperatures, ranging from 750 °C to 1000 °C (heating rate: 3 °C min⁻¹) in a tube furnace for 3 h under ambient atmosphere (for the samples sintered at >750 °C) or under argon atmosphere (for the sample sintered at 750 °C). In all cases, 1 g of the as-synthesized Zn_0.9Co_0.1O^nano powder was manually ground and pressed into a pellet at 5 t for 1 min to ensure high inter-particle contact. For the subsequent sintering, the pellet was placed in an yttria-stabilized zirconia crucible. For the carbon coating, 1 g of Zn_0.9Co_0.1O was mixed with 0.5 g of sucrose and 2 g of ultra-pure water. The mixture was homogenized by planetary ball milling (Pulverisette 4, Fritsch) for 1.5 h and dried at 80 °C. For the carbonization of the sucrose, the mixture was thermally treated at 500 °C for 4 h under argon atmosphere in a tube furnace. These procedures were exactly the same for the Sn_0.9Fe_0.1O₂ samples, with the initially obtained Sn_0.9Fe_0.1O₂ ^nano being synthesized as reported earlier by Mueller et al [22]. The only difference was that the sintering was conducted under ambient atmosphere for all the different temperatures.

The investigation of the crystal structure was conducted via x-ray diffraction (XRD) using a Bruker D8 Advance diffractometer (Cu–Kα radiation, λ = 0.154 nm) within a 2θ range from 20° to 100°. Scanning electron microscopy (SEM) was conducted by means of a Zeiss Crossbeam 340 field-emission electron microscope. Tranmission electron microscopy (TEM) was carried out using a JEOL JEM-3000. The ex situ samples were galvanostatically cycled in Swagelok-type cells with a lithium counter and reference electrode and a 1 M solution of LiPF₆ in a mixture of ethylene carbonate (EC) and diethyl carbonate (DEC) (EC:DEC 3:7 w/w) as the electrolyte. After cycling, the cells were disassembled in an argon-filled glove box, and the electrodes were rinsed with dimethyl carbonate (DMC). Subsequently, the rinsed electrodes were transferred to the SEM using an airtight transport box. The mass ratio of the carbon coating was determined by thermogravimetric analysis (TGA; Model Q5000, TA Instruments) under oxygen atmosphere in the temperature range from 40 to 850 °C (heating rate: 10 °C min⁻¹). The Brunauer–Emmett–Teller (BET) surface area was determined via nitrogen adsorption using an Autosorb-iQ (Quantachrome).

Electrodes were prepared by mixing the active material and carbon black (Super C65, Imerys) and adding this mixture to a 1.25 wt% solution of sodium carboxymethyl cellulose (CMC, Dow Wolff Cellulosics) in ultra-pure water. The dry composition of all electrodes was 75 wt% of the active material, 20 wt% carbon black, and 5 wt% CMC. The resulting dispersion was mixed by planetary ball-milling for 2 h. The homogenized slurry was cast on dendritic copper foil (Schlenk, thickness ∼20 μm) utilizing a laboratory-scale doctor blade with a wet film thickness of 120 μm. The electrode sheets were dried initially at 80 °C for 5 min and subsequently at room temperature overnight. Disc electrodes were punched (⊘ = 12 mm) and dried at 120 °C for 12 h under vacuum. The average active material mass loading was about 1.5 mg cm⁻².

The electrochemical characterization was performed in three-electrode Swagelok-type cells and in two-electrode coin cells (Hohsen). All cells were assembled in an argon-filled glove box (MBraun; oxygen and water content <0.1 ppm). A sheet of glass fiber fleece (Whatman, GFD), soaked with a 1 M solution of LiPF₆ in a mixture of EC and DEC (EC:DEC 3:7 w/w, UBE) served as the separator. Battery-grade lithium metal (Honjo) served as both counter and reference electrodes. Galvanostatic cycling was conducted at 20 °C using a Maccor Battery Tester 4300 with the cells being placed in a climatic chamber (BINDER). A dis-/charge rate of 1 C corresponds to a specific current of 1000 mA g⁻¹.

For the simulation of the volume changes of the CAM anodes with different particle sizes, the commercial finite element package ABAQUS was used. In order to solve the mass diffusion problem, the volume expansion was simulated by heat transfer, which shows analogies to mass diffusion, according to Prussin [49]. The assumed volume increase during lithiation was taken from the literature [14]. In the simulation, the active material was treated as a solid-element with a Young's modulus of 133 000 MPa and the liquid electrolyte as a smoothed particle hydrodynamics (SPH) element with a Young's modulus of 100 MPa. The boundary conditions allowed the sample to move freely in the y-direction and did not allow any expansion in the other directions. To simulate the large expansion upon lithiation, the sample was 'heated' to 2000 K in the simulation. The probed sample volume was 100 × 100 × 100 LE³ and the particles had a radius of 10 LE for the smaller particles and 15 LE for the larger ones. While this difference in size does not completely reflect the difference in particle size of the real sample, it was chosen as a compromise to keep the computational time acceptable.

Operando XRD upon electrochemical cycling was performed by using a self-designed two-electrode cell [50]. The electrode slurry, with the same composition as mentioned above, was homogenized by planetary ball-milling for 2 h and cast on a beryllium (Be) disc (25 mm diameter, 0.25 mm thickness; Materion electrofusion). The beryllium disc served simultaneously as the current collector and 'window' for the x-ray beam. After the coating, the Be disc was dried for 4 h at room temperature and at 60 °C under vacuum overnight. Metallic lithium served as the counter and reference electrode and glass fiber fleeces (diameter 19 mm), drenched with 300 μL of the electrolyte (1 M LiPF₆ in EC:DEC 3:7 w/w, UBE) served as the separator. The 21 range was set to 20°–65°.

First, we synthesized nano-sized Zn_0.9Co_0.1O (Zn_0.9Co_0.1O^nano) according to an earlier reported procedure [30]. This material served as reference (with regard to our previous studies [16, 30]) and 'precursor' for the compounds with a larger particle size, which were obtained via sintering at different temperatures [51]. Sintering is a process that involves applying thermal energy to a compacted powder by subjecting it to elevated temperatures below its melting point. Under these conditions the small particles of the powder aim to minimize their surface energy and the thermally enabled atomic/ionic diffusion yields a densification and growth of the particles [52]. The growth of particles during sintering is also called coarsening. During the sintering the temperature is practically the most important factor and there is an increase in grain size with an increasing temperature owing to the greater diffusion of the atoms/ions [53]. Targeting a range of elevated particle sizes, we chose three different sintering temperatures, i.e. 750 °C, 900 °C, and 1000 °C. The corresponding samples are hereinafter referred to as Zn_0.9Co_0.1O-750, Zn_0.9Co_0.1O-900, and Zn_0.9Co_0.1O-1000, respectively. Figure 1(a) shows the comparison of the XRD patterns recorded for these four samples. All samples have a hexagonal wurtzite structure, matching the reference PDF 01-071-6424 reference data, and do not reveal any additional reflections. This indicates that the Co dopant has been successfully introduced into the ZnO crystal structure and that this structure was well preserved during the sintering step, independent of the temperature applied. Nonetheless, the width of the reflections is continuously decreasing when applying the additional sintering step along with an increasing temperature, which is in line with the expected increase in crystallite size. Accordingly, the BET surface area is decreasing when applying the subsequent sintering and with an increasing sintering temperature, from 32 m² g⁻¹ (Zn_0.9Co_0.1O^nano) to 4.5 m² g⁻¹, 1.7 m² g⁻¹, and 0.8 m² g⁻¹ for Zn_0.9Co_0.1O-750, Zn_0.9Co_0.1O-900, and Zn_0.9Co_0.1O-1000, respectively (figure 1(b)). Performing SEM and TEM further supports these findings by revealing a particle size of about 30 nm for Zn_0.9Co_0.1O^nano (figure 1(c)) and around 100–250 nm for Zn_0.9Co_0.1O-750 (figure 1(d)), 300–750 nm for Zn_0.9Co_0.1O-900 (figure 1(e)), and 1–2 μm for Zn_0.9Co_0.1O-1000 (figure 1(f)).

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To investigate the influence of the particle size on the electrochemical behavior, we prepared electrodes based on the different active materials and cycled these in half-cell configuration with lithium metal counter (and reference) electrodes. The dis-/charge profiles for the first (figure 2(a)) and second (figure 2(b)) cycle generally reveal the same shape as reported in a previous study [30], indicating that the overall reaction mechanism, i.e. the reduction to LiZn, Co⁰, and Li₂O and subsequent reoxidation is the same for all samples studied herein. Please note that the choice of the of the upper cut-off voltage of 3.0 V is motivated by the scientific interest to be able to study the complete de-/lithiation reaction of this material. Practical applications would require a much lower delithiation cut-off [54], which, as a matter of fact, would beneficial for the energy density and energy efficiency also for CAMs, as reported earlier [15]. Nonetheless, for the sake of scientific interest, we applied a significantly higher delithiation cut-off for our investigation. In the case of Zn_0.9Co_0.1O^nano, the first cycle discharge profile (figure 2(a)) shows a higher capacity at potentials above the voltage plateau and, consequently, also a higher overall discharge capacity. This is assigned to the small particle size and relatively highest specific surface area, favoring the decomposition of the electrolyte at the electrode/electrolyte interface and the formation of the SEI at about 0.8 V [55, 56]. Upon the subsequent charge (delithiation), the voltage profiles of all samples are very similar during the dealloying reaction (below 1 V). This indicates that the initial lithiation reaction, including both conversion (i.e. the reduction of the oxide to metallic cobalt and zinc) and alloying (i.e. the formation of LiZn), is complete—independent of the particle size. The capacity of the reconversion reaction, occurring at higher potentials, however, gradually decreases with increasing particle size, leading to a decreasing overall delithiation capacity. It is thus concluded that the particle size is mostly affecting the reconversion reaction, i.e. the reoxidation of the (dealloyed) metals to the oxide(s). For the second cycle (figure 2(b)), this consequently results in a lower lithiation capacity, while the dealloying capacity is essentially the same for all four samples and the trend of a reduced reversibility of the reconversion reaction remains. Given the rather continuous trend in electrochemical behavior as a function of particle size, we focused for the following experiments on the comparison of Zn_0.9Co_0.1O^nano (with the smallest particle size) and Zn_0.9Co_0.1O-1000 (with the largest particle size). Figure 2(c) shows the evolution of the specific capacity of these two samples upon constant current cycling at C/20 (50 Ma g⁻¹). The capacity of around 800 mAh g⁻¹ recorded for Zn_0.9Co_0.1O-1000 is stable for a few cycles, before it starts to decrease gradually. This gradual decrease largely originates from a steadily decreasing contribution of the reconversion reaction at elevated potentials as apparent from the corresponding dis-/charge profiles presented in figure 2(d), but there is also a little decrease for the dealloying reaction. For Zn_0.9Co_0.1O^nano, the capacity is initially much higher with more than 900 mAh g⁻¹ and remains being higher, and even increases gradually after 12 cycles. This increase is caused by an increase in capacity close to the upper cut-off voltage for the delithiation reaction, which has been assigned to the quasi-reversible SEI formation [31, 43, 50]. Besides the additional capacity close to the cut-off potentials, the voltage profiles of Zn_0.9Co_0.1O^nano reveal little changes over the course of 20 cycles.

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Summarizing, there are two main differences in the electrochemical performance for small Zn_0.9Co_0.1O^nano, and large Zn_0.9Co_0.1O-1000 particles. First, the reversible capacity of Zn_0.9Co_0.1O-1000 is lower from the start due to a partially irreversible reconversion reaction. Second, the increased particle size leads to capacity fading, which sets in after a few cycles and then progresses continuously. To understand this behavior, we investigated the influence of the particle size on the electrochemical performance on three different length scales: the electrode (i.e. many particles), the particle, and the crystal structure (i.e. at the atomic level).

At the electrode level, one potential reason for capacity fading when using CAMs as the active material is the continuous volume variation upon cycling [14], which can lead to contact loss with the conductive carbon and the current collector [57]. To investigate this issue for the different particle sizes, we simulated the mechanical stress and the displacement of individual particles upon lithiation (figure 3). According to a previous study, zinc-based CAMs expand by about 120% at the particle level upon lithiation [14]. This volume increase leads to mechanical stress in the electrodes, which might cause a degradation of the microstructure. Generally, the overall deformation in an electrode can be expressed as the sum of the mechanical deformation (including elastic and elastic-plastic deformations), thermal and chemical deformation. The biggest contribution upon cycling is related to the chemical deformation owing to the incorporation of lithium. Given the analogy between chemical and thermal deformation, however, one may assess the eventual behavior of the electrode also by simulating a thermally induced volume expansion of the particles. Additionally, we restricted any expansion of the electrode to the z direction (i.e. the thickness of the electrode, commonly being in the μm range) as the most relevant one and fixed the dimensions in the x and y direction (i.e. the length and width of the electrode, commonly being in the range of several cm at least). For the sake of simplicity, the CAM particles were simulated as rigid balls (a solid element with a Young's modulus of 133 MPa) and the pores between the particles were filled with the electrolyte (with a Young's modulus of 100 MPa, figure 3(a)). We limited the model to these two components, as the amount and nature of the binder and conductive carbon was the same for both electrodes. The sample size had a volume of 100 × 100 × 100 LE³ (units of length) and the small and large particles were represented by spheres with a radius of 10 UL and 15 LE, respectively. The electrochemical lithiation was simulated by 'heating' the sample to 2000 K. During the expansion, a displacement of the particles was observed (figures 3(b) and (c)). Mapping the displacement after the expansion, revealed that the electrode with the smaller particles expands rather homogenously (figure 3(b)), while severe local displacement was observed for the larger particles (figure 3(c)). This displacement might eventually result in contact loss and electronic isolation of the induvial particles, which then do not contribute to the electrochemical reaction anymore. Accordingly, the capacity fading recorded for Zn_0.9Co_0.1O-1000 is anticipated to originate—at least in part—from the substantially greater displacement upon cycling—especially when considering the much greater difference in size between Zn_0.9Co_0.1O^nano and Zn_0.9Co_0.1O-1000 compared to the two modeled electrodes.

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The large expansion of the CAM particles does not only have an impact on the electrode integrity, but also on the integrity of the particles as such, potentially causing fracturing of the particles, which would further add to a capacity loss upon cycling [58]. In fact, for silicon with a much greater volume variation of about 300%, it has been found that the particles crack when exceeding a diameter of around 150 nm [59]. To investigate, if a larger particle size can also lead to cracking in CAMs, we subjected electrodes based on Zn_0.9Co_0.1O^nano and Zn_0.9Co_0.1O-1000–10 de-/lithiation cycles and conducted an ex situ SEM analysis. The results are presented in figure 4. The Zn_0.9Co_0.1O^nano nanoparticles (as expected) do not reveal any fracturing (figure 4(a)). Differently, the much larger Zn_0.9Co_0.1O-1000 particles show some elongated cracks (figure 4(b)). Together with the displacement observed at the electrode level via simulation, this cracking at the particle level is expected to further add to the capacity fading in the case of Zn_0.9Co_0.1O-1000.

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In order to better understand the reason for the particle-size dependent reversibility of the reconversion reaction, we performed a comparative operando XRD analysis of Zn_0.9Co_0.1O^nano (figure 5) and Zn_0.9Co_0.1O-1000 (figure 6). In both cases, the discharge and charge process can be roughly divided into five different regions, i.e., Region A–C for the lithiation (discharge) as well as Region D and E for the delithiation (charge), depending on the structural changes occurring. The detailed reaction mechanism has already been discussed in detail earlier [16, 30–32]. Therefore, the structural changes are only discussed briefly in the following to maintain the focus on the differences observed for the different particle sizes. For Zn_0.9Co_0.1O^nano (figure 5), during the first five scans in Region A, the potential decreases to the onset of the voltage plateau at about 0.55 V. In this region, the intensity of the main reflections of the wurtzite structure remains essentially unchanged, which agrees with the abovementioned electrolyte decomposition and SEI formation taking place in this voltage range. In Region B, the reflections corresponding to the wurtzite structure are significantly decreasing and a very broad reflection between 41.0° and 45.0° appears starting from scan #6, with a maximum intensity at around 42.6°. The intensity further increases during the following scans (see the corresponding close-up in figure 5). This 2θ value is slightly lower than the 2θ value of 43.0° reported for the main reflection of metallic zinc (PDF 00‐004‐0831), which might indicate the formation of a CoZn alloy, as recently found for Zn_0.9Fe_0.1O in the vicinity of the TM dopant, i.e., the formation of a FeZn alloy in that case [31]. In fact, the main reflection reported for a Co_1.76Zn_13.24 alloy (PDF 01-072-9823) appears at 42.8°, very close to the value that we observed—potentially owing to a higher cobalt content. Accordingly, we assigned this newly appearing reflection to a CoZn alloy with an unknown composition (Co_x Zn). Nevertheless, considering the broadness of the reflection, the simultaneous formation of an additional Zn⁰ reflection cannot be excluded—and appears likely, indeed. Besides, the very broad shape of this refection clearly indicates a very small crystallite size, presumably in the range of a few nanometers only. Upon further lithiation, in Region C, the intensity of this reflection with a maximum at 42.6° decreases and a new reflection at 41.0° appears, which is in excellent agreement with the reference data for the LiZn alloy (PDF 03‐065‐3016).

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Upon delithiation (charge), the alloying reaction is reversed, as indicated by the decrease of the LiZn reflection at 41.0° and the appearance of a broad reflection between 40.0° and 45.0° (see a close-up of Region D in figure 5). However, in contrast to the broad refection in Region B (i.e. during the lithiation), the new feature shows an additional shoulder at 43.0° and thereby appears to be composed of two reflections, presumably corresponding to the formation of metallic Zn⁰ and Co_xZn (at 43.0° and 42.6°, respectively). In Region E, the reflection at 42.6°/43° decreases in intensity and completely vanishes at 3.0 V. Simultaneously, a broad reflection between 30° and 38° appears, which indicates the reappearance of a wurtzite-structured oxide phase, but with a substantially reduced crystallinity and/or crystallite size compared to the pristine material.

We may note that a minor fraction of the original wurtzite Zn_0.9Co_0.1O^nano remains throughout the experiment, which we ascribe to an issue with the electronic contact for these remaining particles, as a previous study has revealed the complete reduction [30]. Nevertheless, this does not affect the major findings concerning the comparison with Zn_0.9Co_0.1O-1000 as discussed in the following.

The results for the operando XRD analysis of Zn_0.9Co_0.1O-1000 are presented in figure 6. The general evolution of the crystal structure is the same as observed for Zn_0.9Co_0.1O^nano, as also indicated by essentially the same voltage profile (see also figure 2). Also in this case, in Region A, the potential drops to around 0.55 V, and the main reflections corresponding to the wurtzite structure remain basically unchanged. In Region B, the intensity of these reflections decreases and a very broad reflection with a maximum at around 42.6° forms, which has been earlier assigned to a Co_x Zn alloy with a very small crystallite size (and low crystallinity). Different from Zn_0.9Co_0.1O^nano, however, a very clear additional refection with a maximum at 43.0° appears already during the lithiation, which is significantly narrower than the one at 42.6°, and continues to grow in intensity upon further discharge. As mentioned above, this 2θ value of 43.0° is in excellent agreement with the position of the main reflection reported for metallic zinc (PDF 00‐004‐0831). The narrower shape indicates a substantially larger crystallite size and/or crystallinity compared to the observations for Zn_0.9Co_0.1O^nano. In Region C, this reflection at 43.0° decreases and completely vanishes in scan #33. Simultaneously, new reflections appear at about 37.0°, 41.0°, and 42.7°. The positions and relative intensity of these new reflections are in excellent agreement with the data reported for Li_0.105Zn_0.895 (PDF 01‐071‐9525), i.e. a lithium-poor alloy with zinc. These findings reveal that the metallic zinc starts to alloy electrochemically with lithium, forming a Li_x Zn alloy with an initially low lithium content. From scan #38 onwards, the reflections corresponding to this lithium-poor Li_x Zn alloy phase vanish and a rather narrow reflection at 41.0° appears, i.e., the main reflection corresponding to LiZn (PDF 03‐065‐3016), which continues to increase in intensity until it reaches its maximum in scan #46.

Upon delithiation (charge), the alloying reaction is reversed, as indicated by the decrease in intensity of the LiZn-related reflection at 41.0° and the increase of the Li_x Zn-related reflections at about 37.0°, 41.0°, and 42.0°. Starting from scan #52, the reflections corresponding to the Li_x Zn alloy disappear again and a reflection at 43.0° (corresponding to Zn⁰) was observed and increases in intensity upon scan #52 to scan #57. In Region E, the reflection at 43.0° decreases in intensity and completely vanishes at 3.0 V. Simultaneously and comparable to Zn_0.9Co_0.1O^nano, a broad reflection appears between 30° and 38°, which indicates the reappearance of a wurtzite-structured oxide phase with a rather small crystallite size and/or low crystallinity.

In sum, the comparative operando XRD analysis reveals that the size of the Zn_0.9Co_0.1O particles affects the reaction mechanism with regard to the crystallite size of the metallic zinc alloying phases. In fact, for Zn_0.9Co_0.1O^nano, all new reflections occurring upon lithiation and delithiation remain very broad, reflecting a small crystallite size. Differently, for Zn_0.9Co_0.1O-1000, the Zn⁰ and LiZn phases are characterized by a comparably very narrow shape, indicating a rather large crystallite size. This is highlighted in figures 7(a) and (b) by directly comparing the XRD patterns recorded for Zn_0.9Co_0.1O^nano and Zn_0.9Co_0.1O-1000 at the end of Region C (figure 7(a)) and Region D (figure 7(b)), showing the reflections corresponding to the LiZn and the Zn⁰ (as well as the Co_x Zn) phase, respectively. In both cases, the reflections recorded for Zn_0.9Co_0.1O-1000 are much sharper and more intense compared to the ones observed for Zn_0.9Co_0.1O^nano. For a rough estimation of the crystallite size, we used the Scherrer equation (equation (1)) to evaluate exemplarily the reflections corresponding to the LiZn phase (41.0°) at the end of Region C (figure 7(a)). The calculation revealed a crystallite size of about 60 Å and 150 Å, for Zn_0.9Co_0.1O^nano and Zn_0.9Co_0.1O-1000, respectively.

$$\begin{align}{\text{FWHM}} = \frac{{k*\lambda }}{{D*\cos \left( \theta \right)}}{ }{\text{.}}\end{align} \tag{ 1 }$$

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In this equation, FWHM is the full width at half-maximum of the diffraction reflection, k is a dimensionless shape factor, λ is the x-ray wavelength, D is the crystallite size and θ is the Bragg angle. We may note that these values have to be taken with a certain care, but the trend is evident. An initially smaller particle size favors the formation of very fine metallic zinc and alloying phases, which apparently affects particularly the reversibility of the conversion reaction at elevated potentials. Generally, the nucleation and growth of metallic nanograins in a Li₂O matrix is a complex solid-state reaction which involves charge and mass transport. According to a previous study on metal fluorides [60], the size of the metallic nanograins is decisive for the reversibility of the conversion reaction and larger metallic nanograins are less capable of ensuring an electronically conductive network within the original active material particle. This is in agreement with our findings, as the reconversion is apparently hindered when larger metallic zinc and alloying phases are formed as in the case of Zn_0.9Co_0.1O-1000 (see figure 7(c) for a schematic illustration).

Given the fact that the chemical composition of the two materials is the same, one might wonder why the larger particles show the tendency to form larger zinc (alloy) grains. One possible explanation might be the different current density per unit surface area of the samples—comparable to the different initial reaction pathway reported for Co₃O₄ [61, 62]—as the surface area is substantially different for the two samples (see figure 1(b)). To investigate the impact of the applied specific current on the reversibility of the conversion and alloying reaction, we studied the de-/lithiation at different dis-/charge rates. For this purpose, however, we first applied a carbonaceous coating (hereinafter referred to by adding a 'C' to the sample name) to overcome the capacity fading observed earlier for Zn_0.9Co_0.1O-1000 (see figures 2(c) and (d)). The carbon content was in the range of 8.5–11.0 wt% for all samples (figure S1). The coating and additional carbonization step at 500 °C did not significantly alter the original particle morphology or crystal structure (figure S2), neither did they affect the general trend concerning the electrochemical behavior as a function of the particle size, i.e., the reversibility of the conversion reaction was still decreasing with an increasing particle size (figure S3). Accordingly, we focused again on the comparison of Zn_0.9Co_0.1O^nano-C and Zn_0.9Co_0.1O-1000-C (figure 8). Figure 8(a) presents the constant current cycling at C/5 (200 mA g⁻¹) of half-cells employing working electrodes with Zn_0.9Co_0.1O^nano-C (in black) and Zn_0.9Co_0.1O-1000-C (in green) as the active material. The capacity is very stable for both compounds with about 880 mAh g⁻¹ for Zn_0.9Co_0.1O^nano-C and around 720 mAh g⁻¹ for Zn_0.9Co_0.1O-1000-C. The carbon coating was apparently effective in stabilizing the capacity. The corresponding dis-/charge profiles are depicted in figure 8(b), revealing that the contribution of the alloying reaction at potentials up to about 1 V was essentially the same for both materials and that the lower capacity in the case of Zn_0.9Co_0.1O-1000-C was related to a limited reconversion reaction at elevated potentials—just as found also for the non-coated materials. Subsequently, we subjected the cells to a series of different dis-/charge rates (after an initial formation cycle at C/20), ranging from C/10 to 10 C (i.e. up to 10 000 mA g⁻¹). The plots of the specific capacity vs. the cycle number are shown in figure 8(c). At lower C rates, the capacity is higher for Zn_0.9Co_0.1O^nano-C with, e.g., about 870 mAh g⁻¹ compared to 750 mAh g⁻¹ for Zn_0.9Co_0.1O-1000-C at C/10. This is consistent with the previous findings. However, the difference is decreasing with an increasing C rate. In fact, for very high C rates of 5 C and 10 C, the specific capacity is essentially the same for the two samples, maybe even slightly higher for Zn_0.9Co_0.1O-1000-C. This is counterintuitive at first view, since nano-sized materials commonly show a better rate capability due to the shorter transport pathway for the lithium cations and the higher electrode/electrolyte contact area, resulting in a lower current density per unit surface area. The careful inspection of the corresponding dis-/charge profiles (figure 8(d)) revealed that the contribution of the alloying reaction was fairly the same for both compounds at all C rates up to 2 C (remarkably, also the corresponding overpotential), while the extra capacity for Zn_0.9Co_0.1O^nano-C was obtained at elevated delithiation potentials, i.e., related to the contribution of the conversion reaction. At very high C rates of 5 C and 10 C, however, the overpotential was higher for Zn_0.9Co_0.1O^nano-C, resulting in a slightly lower overall capacity. This suggests that the SEI formed upon cycling, which is more pronounced in the case of Zn_0.9Co_0.1O^nano-C (see figure S3), eventually determines the achievable specific capacity by hindering the charge transport (in)to the active material particles. While this observation highlights the need for a well-designed interface with the electrolyte (as well as the interphase formed), the most intriguing finding was that the kinetics of the alloying reaction are very little, if at all, affected by the Zn_0.9Co_0.1O particle size. In fact, this, in turn, indicates that the Li⁺ transport within the active material particles is not limiting the achievable capacity, since this would expectedly result in a significantly lower capacity for larger particles. Moreover, a rough separation of the contribution of the reconversion and dealloying reaction by considering the change in slope at about 1 V (increasing with an increasing specific current; figure 8(d)) shows that the contribution of the (de-)alloying reaction is decreasing less with an increasing C rate compared to the contribution of the (re-)conversion reaction. Accordingly, the nanosized particles are losing their 'capacity advantage' at very high C rates, which also contributes to the comparably greater decrease in overall capacity at 5 C and 10 C.

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These findings are important with respect to the potential application in lithium-ion cells, for which the upper cut-off potential will have to be limited to 1.5 V or even lower values in order to realize a reasonably high output voltage for the full-cell. In this regard, the independence of the alloying reaction from the particle size and the favorable de-/lithiation kinetics for the alloying contribution at low potentials in combination with the fast Li⁺ transport within the particle are, indeed, beneficial.

In order to confirm the applicability of the results for CAMs in general, we extended the investigation also to Sn_0.9Fe_0.1O₂, which provides a relatively higher contribution of the alloying reaction (ca. 50% compared to about 30% [15]) and contains Fe rather than Co as TM dopant. The XRD patterns, BET analysis, and SEM micrographs for the as-synthesized Sn_0.9Fe_0.1O₂ ^nano as well as the samples sintered at different temperatures (i.e., 750, 900, and 1000 °C) are presented in figure S4. Also, in this case, the additional sintering step results in an increasing crystallite and particle size, ranging from around 10 nm (Sn_0.9Fe_0.1O₂ ^nano) over 40 nm (Sn_0.9Fe_0.1O₂-750) and 80 nm (Sn_0.9Fe_0.1O₂-900) up to 0.5 μm (Sn_0.9Fe_0.1O₂-1000), accompanied by a continuous decrease in specific surface area. Subsequently, we applied a carbon coating prior to the electrochemical characterization in order to obtain stable cycling [26, 63]. The results are presented in figure 9. In fact, just like for Zn_0.9Co_0.1O, an increase in particle size led to lower capacities (figure 9(a)), originating from a reduced (re-)conversion capacity, while the capacity obtained by the alloying contribution was not affected by the different particle size (figure 9(b)). Moreover, the comparison of the rate capability, depicted in figure 9(c) exemplarily for Sn_0.9Fe_0.1O₂ ^nano-C and Sn_0.9Fe_0.1O₂-1000-C, revealed that the difference in reversible capacity was decreasing with an increasing C rate. At very high C rates of 5 C and 10 C, the capacity was eventually the same for the two samples. The plot of the corresponding charge (delithiation) profiles (figure 9(d)) shows that the contribution of the alloying reaction decreased only very little up to 1 C and slightly at 2 C, before dropping to substantially lower values at 5 C and 10 C for both samples, while the contribution of the conversion reaction decreased at a faster pace with an increasing current applied. Moreover, also for Sn_0.9Fe_0.1O₂, the polarization was greater for Sn_0.9Fe_0.1O₂ ^nano-C at very high C rates, indicating that the charge transport through the (in this case more pronounced) SEI became rate-determining.

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