## Introduction

Solid state redox reactions are ubiquitous during ion reactions in batteries1 and catalysts2. Understanding how redox reactions propagate can inform designing internal microstructures such that redox reactions can be fully accessed to deliver the desired functionalities. The propagation of redox reactions governs the electrochemical properties of battery materials and their critical performance metrics in practical cells3,4,5. The recent research progress, especially aided by advanced analytical techniques6, has revealed that incomplete and heterogeneous redox reactions prevail in many electrode materials, such as olivine phosphates7,8,9,10,11,12,13,14, layered oxides15,16,17,18,19,20, spinel oxides21,22, and conversion materials23,24. Advanced high-capacity cathode materials for lithium (Li) ion and sodium (Na) ion batteries are mostly polycrystalline materials that exhibit complex charge distribution (the valence state distribution of the redox-active cations) due to the presence of numerous constituting grains and grain boundaries. The redox reactions in individual grains typically do not proceed concurrently due to their distinct geometric locations in polycrystalline particles. As a result, these unsynchronized local redox events collectively induce heterogeneous and anisotropic charge distribution, building up intergranular and intragranular stress25. Therefore, these polycrystalline materials may exhibit weak mechanical stability, leading to undesired chemomechanical breakdown during battery cycling26,27,28,29.

High-nickel, low-cobalt layered oxides show great promise to reduce or even eliminate the use of high-cost, toxic, and socially controversial cobalt in Li ion batteries. However, these materials undergo many phase transformations above 4.0 V vs Li+/Li30, which create large internal stress along grain boundaries and engender microcrack formation25,31,32,33. To fully unlock the high-energy advantage of these nickel-rich layered oxides, methods must be established to guide the redox reaction and to enhance the chemomechanical stability of these polycrystalline materials. Recent studies have discovered that engineering the grain crystallographic orientation could modulate the ion transport pathway in polycrystalline particles to enable rapid ion reactions4,5,34,35,36,37. Furthermore, these studies have concluded that the improved battery performance was attributed to the enhanced chemomechanical properties. Several studies have attempted to investigate the relationship between the compositional38,39,40, morphological26,41,42, and charge complexities15,43 and the battery performance of polycrystalline battery particles. However, there is a lack of a holistic study to spatially and quantitatively elucidate the interplay between grain crystallographic orientation, charge distribution, and battery performance.

Herein, we report the distinct charge distributions (Ni valence state distribution) in two compositionally similar, yet, crystallographically dissimilar (randomly oriented grains vs radially aligned grains) polycrystalline nickel-rich layered oxides. Under the stringently controlled electrochemical protocol, these two layered oxides not only deliver nearly identical initial capacity and voltage profile but also exhibit similar structural and chemical characteristics. Overall, both materials display a “surface-to-bulk” charge distribution modality. However, the three-dimensional charge mapping, covering over 20 million nanodomains, reveals that the internal charge distribution is guided by the crystallographic orientation of the constituent grains. Our mathematical model elucidates that the radially aligned grains, with continuous and radially distributed Li ion pathways, favor the overall charge homogeneity. These results provide fundamental insights into tuning grain crystallographic orientation to improve performance robustness in practical batteries.

## Results

### Li layered oxides of different crystallographic orientations

Two nickel-rich Li layered oxides (LiNixMnyCo1-x-yO2, NMC) with similar redox-active nickel (Ni) content yet different grain crystallographic orientations, named as rod-NMC (with radially aligned grains) and gravel-NMC (with randomly oriented grains), were adopted as the model systems. The energy-dispersive X-ray spectroscopy (EDS, Supplementary Fig. 1) and inductively coupled plasma-mass spectrometry (ICP-MS, Supplementary Table 1) both confirm that the redox-active Ni content among the three transition metals is similar for the rod-NMC (~82%) and gravel-NMC (~80%). These two NMCs are of distinctive morphologies and Li ion pathways, as attested by the scanning electron microscopy (SEM) and scanning transmission electron microscopy high-angle annular dark-field (STEM-HAADF) imaging and nano-beam diffraction (NBD) results. For the rod-NMC, the spherical secondary particles (Fig. 1a) are formed by radially packed rod-shaped grains (Fig. 1b). The radially packed morphology is further demonstrated in Supplementary Fig. 2, in which multiple methods were used to expose the interior of many rod-NMC secondary particles. The Li channels, as illustrated by the arrows in Fig. 1d and Supplementary Fig. 3, are along the radial direction in the rod-shaped grains, indicating that Li ions can transport readily from the bulk of the secondary particle to the surface in the radial direction4,5,34. In contrast, the spherical secondary particles of the gravel-NMC (Fig. 1e) mainly comprise randomly packed gravel-shaped grains (Fig. 1f, Supplementary Fig. 4). The random packing of the grains implies that the Li ion pathways in gravel-NMC are random and likely tortuous. Next, we performed comprehensive multiscale characterization to ensure that we had a structurally and chemically controlled model system to investigate how the crystallographic orientation guides the charge distribution.

Although the two NMCs have different morphologies and crystallographic orientations, they do have similar crystal structure in the pristine and first charged state (Supplementary Fig. 5), respectively. Synchrotron X-ray diffraction (XRD) reveals that all NMCs have the R$$\bar 3$$m structure and the peak positions are similar for the two NMCs in the pristine and first charged state, respectively (Fig. 1g, Supplementary Fig. 6). The powder XRD Rietveld refinement of the two NMCs confirms that their lattice parameters are similar in the pristine state (Supplementary Fig. 6). In addition, the (003)/(104) peak ratio is 1.337 and 1.355 for the rod-NMC and gravel-NMC, respectively. The difference is minor, suggesting the similar cation mixing in these pristine samples. The peak shifts in the charged state are also almost identical for both NMCs, which is consistent with the XANES results (Fig. 2a, Supplementary Table 2) and shows that the same state of charge has reached for the two samples. To further compare the two NMCs, their charge distributions in the pristine state were investigated via the full field transmission X-ray microscopy (TXM). TXM can detect the local valence state by measuring the absorption spectrum of a specific element with a nominal spatial resolution of ~30 nm. Ni is the primary charge compensating element in nickel-rich layered oxides at 2.5–4.5 V, the redox reaction propagation in the NMCs can thus be investigated through quantifying the evolution of Ni valence states. Two-dimensional (2D) TXM was performed on multiple pristine secondary particles, and the results show that the pristine rod-NMC (Fig. 1h–i) and gravel-NMC (Fig. 1j–k) have similar charge distribution. The Ni valence state histograms for the two NMCs are also similar (Fig. 1i, k). The difference of the average Ni K-edge absorption energy for the rod- and gravel-NMC is only about 0.12 eV, which is much smaller than the energy resolution of TXM (~0.8 eV) and demonstrates that the two NMCs have similar charge distribution in the pristine state18,43.

In addition to the charge distribution in pristine state, the global bulk and surface charge states were investigated using hard and soft X-ray absorption spectroscopy (XAS) techniques, respectively. To be specific, the hard XAS can detect the bulk Ni valence state by detecting the Ni K-edge absorption energy, while soft XAS was used to measure the surface Ni valence state by measuring the Ni L-edge absorption spectroscopic fingerprint6. The hard XAS spectra (Fig. 2a, Supplementary Table 2) show that the Ni has almost identical valence state in the pristine state, and after charging to 4.5 V, Ni gets oxidized to a similar extent for both NMCs. The soft XAS spectra indicate that the surface Ni valence states are also similar for both NMCs. Two signal acquisition modes were used in this work: total electron yield (TEY) mode with a probing depth of 5–10 nm and fluorescence yield (FY) mode with a probing depth around 50 nm44. Two L3 peaks can be obtained in the Ni soft XAS spectrum and the L3high/L3low ratios (Supplementary Table 3) can be used to monitor the surface Ni valence state: a larger L3high/L3low value means a higher valence state, and vice versa45. In the TEY mode (Fig. 2b), the rod- and gravel-NMCs have similar Ni valence state in their pristine state. After the first charge, the L3high/L3low peak ratio increase to a similar level, which indicates the surface Ni get oxidized to a similar extent. Similarly, under the FY mode (Fig. 2c), where signals are mainly from the sub-surface, the L3high/L3low ratios are also comparable in the pristine and the first charged state for both NMCs. In summary, the hard and soft XAS results show that the overall bulk and surface Ni valence states are similar for the two NMCs in their pristine and first charged state, respectively.

The rod-NMC (Fig. 2d) has a 209.3 mAh g−1 discharge capacity at the second discharge, and, after 100 cycles, the cell remains a capacity of 197.4 mAh g−1 (94.3% retention). Besides, the rod-NMC has negligible voltage drop between the upper cut-off voltage and the onset of the discharge curve: the onset discharge voltage is 4.46 V for the second cycle and 4.43 V for the 100th cycle (Fig. 2e). The gravel-NMC (Fig. 2f) has a comparable initial capacity (207.8 mAh g−1 for the second discharge), but the capacity retention is noticeably lower after 100 cycles (186.3 mAh g−1, 89.7% retention). The voltage drop of gravel-NMC is also more significant (Fig. 2g). The voltage at the onset of the second discharge is 4.45 V, which is comparable to that of rod-NMC. However, with much faster polarization induced voltage drop during the cycling process, the onset discharge voltage is only 4.37 V at the 100th discharge for the gravel-NMC. We performed the performance measurements for more than three times and the averaged results, shown in Supplementary Fig. 7, clearly show that the rod-NMC exhibits more robust battery performance.

### Charge distributions in the charged state

As discussed earlier, charge heterogeneity has been reported in many battery materials. Recently, Chueh and coworkers reported that the charge heterogeneity is persistent in LixNi1/3Mn1/3Co1/3O2 (NMC333) even after prolonged relaxation (more than 170 h)46. Moreover, another study suggests that charge heterogeneity in battery materials is likely less rate-dependent. The authors observed significant extent of charge heterogeneity in the slowly charged (C/10) LixNi0.6Mn0.2Co0.2O2 (NMC622)18. Here we conduct the charge distribution mapping for nickel-rich NMC in the charged state after a slow charging process (C/10), and we also observe a large degree of charge heterogeneity (Supplementary Fig. 8). Such a prevailing charging heterogeneity phenomenon motivates us to perform a quantitative study about the effect of grain orientation on the charge heterogeneity. In our current study, although the differences in the Ni content, lattice structure and global Ni valence state are negligible between the rod- and gravel-NMCs, the rod-NMC demonstrates improved capacity retention and suppressed polarization. Therefore, we conjecture that the different grain crystallographic orientations play a major role in affecting the redox reaction pathway and charge distribution in the secondary particles, which, in turn, influence their electrochemical performance. Herein, the underlying mechanism was investigated using three-dimensional (3D) TXM, which can probe the local Ni valence state with a 30 × 30 × 30 nm3 nanodomain resolution47,48. Thin film electrodes (~40 μm) were used in this work and the depth-resolved confocal hard XAS (Supplementary Fig. 9) shows that, at the charged state, the local state-of-charge within the thin film electrodes is independent of the depth. Such electrode scale state-of-charge homogeneity promotes the representativeness of the particle level studies. The overall charge distributions within selected particles of the rod- and gravel-NMCs are shown in Fig. 3a, d. Because of the favorable electrical and ionic conductivity near the particle surface, the surface is more oxidized than the bulk in both NMCs, resembling the “surface-to-bulk” model at the secondary particle level (Fig. 3a, d, and Supplementary Fig. 10). However, the spatial pattern of the varying nickel valence state is different, as shown in Fig. 3b, e, for rod- and gravel-NMC, respectively. The 2D nanodomain valence gradient vectors, which are defined as the local variation of the absorption edge energy in two dimension, are mostly parallel to each other for rod-NMC (Fig. 3c) and are random for gravel-NMC (Fig. 3f). Such Ni valence state distribution and 2D nanodomain valence gradient are attributed to the different redox reaction behaviors that are likely guided by the grain crystallographic orientation. The high valence Ni domains are radially oriented in the rod-NMC, in good alignment with the grain crystallographic arrangement. Moreover, the high valence Ni domains appear to be interconnected in 3D, and their size is comparable to that of the single crystalline grains (Fig. 1b, Supplementary Fig. 2).

Based on the experimentally observed charge distribution, here we propose a hypothesis regarding the reaction pathways in the rod-NMC. The delithiation reaction nucleates from single grain surface and propagates to the bulk of each single grain. The redox reaction, on the other hand, can be illustrated using the valence gradient (Fig. 3c)49, which is mostly populated in the tangential orientation for the rod-NMC. After the initiation of delithiation at the single crystal surface, the increased d(003) distance facilitates Li ion transport, which further promotes the delithiation at the surface of single crystal surface along the (003) plane. Combining the TEM (Fig. 1c–d, Supplementary Fig. 3) and 3D TXM results (Fig. 3a–c), we propose that the grain crystallographic orientations can guide the reaction pathway in the polycrystalline NMC particles and, therefore, determine the charge distribution. The alignment of Li ion pathways in the rod-NMC allows for rapid Li ion transport from the surface to the bulk of NMC secondary particles, which potentially contributes to the better performance at a higher charging/discharging rate (Supplementary Fig. 7)4,5,34,35,36,37. For the gravel-NMC, the delithiation also initiates from the surface, as attested by the distribution and dimension of the high valence Ni domains (Fig. 3d–f, Fig. 1f, Supplementary Fig. 4). However, those high valence Ni domains in gravel-MNC do not exhibit clear radial distribution, due to the fact that the gravel-shaped grains are randomly packed and, thus, the Li ion diffusion pathway is tortuous.

### Quantitative analysis of charge distributions

The 3D TXM mapping provides qualitative understanding about the redox reaction and charge distribution mechanisms. Here a mathematic model is developed to quantitatively investigate the effect of the grain crystallographic orientation on charge distribution and charge heterogeneity (overall procedures are shown in Supplementary Fig. 11). In our TXM result, each secondary NMC particle is spatially resolved by over 20 million unique voxels of ~30 × 30 × 30 nm3. While offering a great amount of structural and chemical details, such datasets provide an opportunity for a statistical analysis of the relationship between neighboring voxels. A valence gradient based model was developed to investigate the charge distribution in this work. As shown in Fig. 4a: each voxel (A in Fig. 4a) has six nearest neighboring voxels (A1, A2, A3, A4, A5, and A6 in Fig. 4a) and each voxel has its own Ni valence state, which is determined by the local Ni K-edge absorption energy. In each direction (x, y, and z), there is a partial valence gradient vector (ux, uy, uz), which is defined as:

$${\mathbf{u}}_{\mathbf{x}} = \frac{{{\mathrm{\Delta }}{\mathbf{E}}_{\boldsymbol{x}}}}{{{\mathrm{\Delta }}d_x}}$$
(1)
$${\mathbf{u}}_{\mathbf{y}} = \frac{{{\mathrm{\Delta }}{\mathbf{E}}_{\boldsymbol{y}}}}{{{\mathrm{\Delta }}d_y}}$$
(2)
$${\mathbf{u}}_{\mathbf{z}} = \frac{{{\mathrm{\Delta }}{\mathbf{E}}_{\boldsymbol{z}}}}{{{\mathrm{\Delta }}d_z}}$$
(3)

ΔEx, ΔEy, and ΔEz are the local variation of the absorption edge energy in x, y, and z directions, respectively. The total valence gradient vector (u) is the vector sum of the three partial valence gradient vectors:

$${\mathbf{u}} = {\mathbf{u}}_x + {\mathbf{u}}_y + {\mathbf{u}}_z$$
(4)

For each voxel, connecting it back to the gravity center of the polycrystalline particle (point O in Fig. 4a) gives us another vector v. The angle (θ) between u and v can be calculated as:

$$\theta = {\mathrm{arc}}\;{\mathrm{cos}}\left( {\frac{{{\mathbf{u}} \cdot {\mathbf{v}}}}{{\left| {\mathbf{u}} \right|\left| {\mathbf{v}} \right|}}} \right)$$
(5)

The recovered θ value in this model is related to the local gradient of the Ni valence states, while the size of u is proportional to the charge difference (heterogeneity) between the neighboring voxels. To buildup the model, we first focus on the vector angles (θ) and the amplitude of the vectors (u) is disregarded for now. Moreover, merging the voxels (i.e., artificially reducing the spatial resolution) can help us to amplify the contribution from regions in the vicinity of grain boundaries (Supplementary Fig. 12). In this model, 2 or 3 voxels were combined in the x, y, and z directions, which corresponds to averaging the Ni K-edge energy of 8 (2 × 2 × 2) or 27 (3 × 3 × 3) voxels, respectively. The probability distribution of the θ value for the two NMCs are shown in Fig. 4b, c, respectively. The θ value distribution all have a volcano shape, but with different sharpness. The volcano shape θ distribution is intrinsic to our model (Supplementary Fig. 13). Under the assumption of fully random charge distribution, the distribution of vectors is proportional to sin θ, which is plotted as our baseline reference in Fig. 4b–d. Comparing with the reference, the rod-NMC (Fig. 4b) has more valence gradient vectors with θ near 90°, and the peak sharpness increases dramatically as the voxel size increases. This sharp volcano shape is a fingerprint for the radial distribution of the Ni valence state. In contrast, the gravel-NMC (Fig. 4c) angle distribution is similar to the reference and the change is minor when the effective voxel size is tuned, suggesting that the gravel-NMC has relatively random charge distribution. In both cases (Fig. 4b, c), the peak center is not exactly at 90°, which can be explained by the fact that the secondary particles are not perfect spheres (Fig. 3a, d, Supplementary Figs. 1 and 3).

In the next step, the vector amplitude was taken into consideration for the 3-voxels binning data. Every vector u was divided into multiple unit vectors in the same direction based on the corresponding amplitude, such that the vectors with larger amplitude contribute more to the probability distribution of the vector angle θ. The θ distributions for the rod- and gravel-NMC, before and after considering the vector amplitude, are shown in Fig. 4d, from which we observe a discernible increment at around 90° for the rod-NMC and negligible change for the gravel-NMC. Figure 4d indicates that the rod-NMC has a larger vector size at around 90°, whereas the gavel-NMC has almost the same vector size at each angle. Figure 4b, d indicate that the rod-NMC has more radially distributed Ni valence state, which is guided by the radially distributed crystallographic orientations of the grains. Figure 4c, d illustrate that the gravel-NMC has relatively random charge distribution as a result of the randomly oriented primary grains. Furthermore, we investigated the vector size distribution as a function of θ. We divided the vectors (with θ equals 0–90°) into nine equally spaced θ groups and plotted the vector size distributions of the respective groups in Fig. 4e for the rod-NMC and in Fig. 4f for the gravel-NMC. The rod-NMC has a slightly smaller vector size comparing with the gravel-NMC, which means the charge heterogeneity is smaller in the rod-NMC. The relative probability of the vectors with larger angles are also much larger for the rod-NMC, while gravel-NMC has very similar vector size distribution at large angles. This size distribution further supports that the crystallographic orientation can affect the charge distribution in polycrystalline layered oxides. We calculated the averaged vector size as a function of θ and the result is shown in Fig. 4g. It is evident that the rod-NMC has less charge heterogeneity. The rod-NMC has less stress and a lower degree of charge heterogeneity based on the finite element modeling (FEM, Supplementary Fig. 14, Supplementary Note 1) and 3D TXM, which might help mitigate the polarization and retain capacity.

## Discussion

Polycrystalline nickel-rich layered oxides have recently risen to the top of competitive materials to enable the next-generation, high-energy Li batteries toward 500 Wh kg−1. The chemomechanical instability of these materials has remained a key challenge that prohibits their implementation in practical batteries. The chemomechanical breakdown can significantly increase the specific surface area and accelerate the electrode-electrolyte side reactions26. These side reactions unambiguously contribute to the surface oxygen loss, electrolyte decomposition, cell impedance buildup, and capacity fading29. Therefore, enhancing the chemomechanical properties of polycrystalline cathodes represents a critical research frontier in developing high energy, stable, and safe Li batteries. Grain engineering in polycrystalline materials provides a large playground to modulate the materials properties beyond controlling the chemical composition, and electronic and crystal structures. In particular, the anisotropic ion conducting pathways in layered oxides make the grain crystallographic orientation a critical factor in determining the modality of the redox reactions in these materials. To date, there have been several studies highlighting the importance of controlling the grain crystallographic orientation to improve the cycling stability of Li and Na layered cathode materials4,5,34,35,36,37. However, the underlying mechanism how the charge distribution changes as a function of the grain orientation has not been studied. Such a study would have offered valuable insights into designing microstructure-controlled battery particles for improving battery cycle life. As reported in recent studies, the charge heterogeneity prevails in polycrystalline electrode particles even after an extend period of relaxation18,46. The studies have concluded that the grain boundaries may play a role in directing the Li ion conducting pathways. The present study provides an unprecedented mechanistic understanding of how the charge distribution is guided by the grain crystallographic orientation in polycrystalline battery materials through a suite of advanced synchrotron spectroscopic, diffraction, and imaging techniques. We systematically investigated the charge distribution in two Li layered oxides that had the similar chemical composition, global crystal structure, and surface and bulk electronic structures but different crystallographic orientations. These cathodes exhibited comparable initial discharge capacity but noticeable differences in cell polarization and cycle life. Overall, the radially aligned grains enabled relatively more stable battery performance, which is consistent with recent studies5,6. The electronic characterization, through soft and hard XAS, revealed that these two materials showed nearly identical global state-of-charge. However, the spatially resolved TXM and the associated mathematical quantification demonstrated that the radially align grains created a charge distribution that resembled the grain orientation and more importantly led to relatively smaller charge heterogeneity. Moreover, our finite element modeling (FEM) simulation demonstrates that the delithiation process generates less stress between the grains in the rod-NMC, possibly due to the cooperative alignment of the grains (Supplementary Fig. 14, Supplementary Note 1). This work provides a strong mechanistic incentive to improve the stability of polycrystalline battery materials through proper engineering of grain morphology and orientation.

## Methods

### Materials

The precursor for the rod-NMC was obtained from Shuangdeng Group Co, Ltd. The XRD and SEM images of the precursor are provided in Supplementary Fig. 15. Subsequently, the precursor was calcined at Virginia Tech using the following protocol: the precursor was dried in a vacuum oven at 120 °C for 12 h before the calcination. The dried precursor was mixed with LiOH (5% extra was added to compensate for Li loss) thoroughly and calcined under pure oxygen flow at 2.0 L min−1. The sample was heated at 5 °C min−1 to 160 °C and held there for 1 h. The sample was then heated at 5 °C min−1 to 460 °C and held there for 2 h. Then the sample was heated at 5 °C min−1 to 750 °C and remained there for 6 h. Finally, the furnace was cooled at 5 °C min−1 to 25 °C still under constant oxygen flow to obtain the final powder. The gravel-NMC was provided by the U.S. Department of Energy’s (DOE) CAMP (Cell Analysis, Modeling and Prototyping) Facility, Argonne National Laboratory.

### Electrochemical performance

Composite electrode were prepared using 90% active material, 5% polyvinylidene fluoride, and 5% acetylene carbon black in N-methyl-2-pyrrolidone and then cast onto carbon-coated aluminum foil current collectors. The electrodes were dried under vacuum at 120 °C. The electrodes have a loading of ~4.5 mg cm−2. CR2032-type coin cells were assembled in an argon-filled glove box using the electrode as the cathode and Li metal as the anode. The cathode and anode were separated with a glass fiber separator which was soaked with an electrolyte of 1 M LiPF6 dissolved in a 3:7 weight ratio of ethylene carbonate/ethyl methyl carbonate with 2 wt% vinylene carbonate. All the electrochemical testing was performed using a Neware battery testing system. 1C was defined as fully charging the cathode in 1 h, with a specific capacity of 200 mAh g−1.