Nanoscale Mapping of Transition Metal Ordering in Individual LiNi_0.5Mn_1.5O₄ Particles Using 4D‐STEM

ABSTRACT

The electrochemical performance of the spinel LiNi_0.5Mn_1.5O₄, a high‐voltage positive electrode material for Li‐ion batteries (LIBs), is influenced by the transition metal arrangement in the octahedral network, leading to disordered ($Fd\underset{\_}{3}m$ S.G.) and ordered (P4₃32 S.G.) structures. However, widely used techniques lack the spatial resolution necessary to elucidate the ordering phenomenon at the particle scale. Using the 4D‐STEM technique, we present the first direct observation of ordering distribution in individual LiNi_0.5Mn_1.5O₄ particles with nanometric spatial resolution. We propose a quantification method for the local degree of ordering based on the ratio of ordered to disordered spinel lattices along the particle thickness extracted from electron diffraction spot intensities. In an ordered spinel LiNi_0.5Mn_1.5O₄, the transition metal ordering is consistently observed throughout the primary particle. However, the extent of ordering in the spinel phase depends on its distribution at the particle scale, a factor influenced by the annealing conditions. The 4D‐STEM analysis elucidates the boundary between highly‐ordered and low‐ordered LiNi_0.5Mn_1.5O₄ particles.

Short abstract

Precession‐assisted 4D‐STEM reveals nanoscale transition‐metal ordering in individual LNMO particles. By extracting ordering‐specific diffraction intensities, a local order parameter maps spatial heterogeneity across single particles, providing a direct bridge between diffraction signatures and structural disorder in high‐voltage spinel cathode materials.

1. Introduction

The increasing demand for electric vehicles and portable devices has driven the need to develop low‐cost and higher energy density Li‐ion batteries (LIBs) [1]. Among the eligible candidates for positive electrode materials, the spinel LiNi_0.5Mn_1.5O₄ (LNMO) with a Co‐free, Li‐poor, and Mn‐rich composition allows to reduce the overall cost [2]. It also delivers a high energy density of 650 Wh/kg thanks to its high working potential of 4.7 V versus Li⁺/Li and a theoretical capacity of 147 mAh/g [3, 4].

Research on LNMO has shown that the degree of ordering between nickel and manganese atoms in the spinel framework has a major effect on its electrochemical performance. This degree of ordering is mainly driven by the Ni/Mn stoichiometry and annealing conditions [5, 6, 7, 8]. The disordered LNMO materials are often characterized by a Ni/Mn ratio lower than 1/3, and thus by the presence of a mixed valence for Mn (Mn³⁺, Mn⁴⁺) for charge compensation. In this case, the Ni and Mn transition metals are statistically distributed on the 16d octahedral sites within a unit cell described in the $Fd\underset{\_}{3}m$ space group. Disordered spinels typically demonstrate electrochemical capacities near the theoretical limit. However, a portion of the attainable capacity is impeded by the presence of electrochemically inactive impurities. Concurrently, these impurities are susceptible to degradation and capacity decay through Mn dissolution, attributable to the mixed valence states of Mn³⁺ and Mn⁴⁺ [9]. On the contrary, ordered LNMO is described within the P4₃32 space group with Ni and Mn atoms in distinct octahedral crystallographic sites, 4b and 12d, respectively. Its lower specific capacity, especially at high rates, is attributed to a weaker electrical conductivity due to an extended order between Ni²⁺ and Mn⁴⁺ cations. Its superior structural stability during extended cycling is attributed to the absence of Mn³⁺ redox activity in this perfectly stoichiometric composition with a Ni:Mn ratio of 1:3 [10].

Analytical techniques, such as neutron diffraction, Raman and NMR spectroscopies, reveal how extended is the transition metal ordering in spinel LNMO [4, 7, 11, 12, 13, 14, 15]. To explain the underlying ordering mechanism, an antiphase boundary model has been proposed based on averaged structural information obtained from neutron diffraction data collected for different LNMO compositions [12, 16]. According to this model, the LNMO sample consists solely of coherent ordered domains that are increasing in size with the degree of ordering rather than of mixtures of ordered and disordered domains. To validate or refute this model, complementary localized observations and detailed investigations are essential.

In 2022, a spatially‐resolved d‐spacing and strain mapping analysis was performed by Spence et al. [17] on a partially ordered LNMO sample using hard x‐ray nano‐diffraction with 50 nm of spatial resolution. It revealed a heterogeneous distribution of d‐spacing within the selected particles, which was interpreted as domains with different Mn³⁺ contents (i.e. with different Ni/Mn ratios), and thus heterogeneous degrees of ordering. Nevertheless, the direct correlation between the lattice parameter and the composition remains inadequately defined for this system. Additionally, the presence of impurities can strongly influence the actual composition and thus lattice parameters of the spinel phases [14, 18, 19]. Additionally, it is noteworthy that the literature reports surprisingly Mn³⁺‐rich ordered and Mn³⁺‐poor disordered LNMO samples [8, 13], underlying the complexity of the ordering‐composition relationship.

More recently, Tertov et al. [20] combined neutron diffraction with high‐resolution scanning transmission electron microscopy (HR‐STEM) to show that ordering in LNMO is not uniform, but instead forms a mosaic of nanosized ordered domains separated by disordered regions. They further established a correlation between Mn content and the degree of ordering, with higher Mn fractions favoring disordering. These results provide valuable nanoscale insights into the link between composition and ordering, obtained with a depth resolution of 10 nm. At the same time, questions remain about how ordering heterogeneity extends throughout the full particle thickness and how it can be quantified with high spatial resolution, motivating further investigation.

Transmission electron microscopy (TEM) achieves exceptionally high spatial resolution due to the emergence of spherical aberration correctors [21]. Recently, the four‐dimensional scanning transmission electron microscopy (4D‐STEM) has emerged as a powerful technique, enabling the acquisition of spatially resolved datasets that combine two‐dimensional (2D) electron diffraction patterns in reciprocal space with 2D real‐space scanning coordinates [22, 23]. Recent studies have demonstrated the relevance of 4D‐STEM for battery materials, including orientation mapping, strain mapping, and phase‐domain analysis during electrochemical transformations. For example, Chen et al. combined 4D‐STEM with EELS to resolve oriented phase domains and strain gradients in spinel MnO₂ nanoparticles during ion insertion, highlighting the ability of 4D‐STEM to capture nanoscale structural heterogeneity in electrode materials [24]. The use of a precessed electron beam further improves diffraction pattern quality, facilitating the generation of high‐resolution structural maps. In materials science, 4D‐STEM has been effectively employed to produce orientation and phase maps [25, 26, 27], strain maps [28, 29], and ptychography reconstructed imaging [30, 31]. One widely adopted implementation is the Automated Crystal Orientation Mapping technique (ACOM) [32, 33, 34], developed by Rauch et al. and commercialized by Nanomegas (Astar), which offers spatial resolution down to 1 nm and has been extensively used for metals and alloys [35]. In parallel, open‐source Python‐based toolkits such as py4DSTEM [36] and pyXEM [37] have been developed to support advanced data analysis in 4D‐STEM. More recently, the ePattern tool introduced by Folastre et al. [38] has further improved pattern matching by enabling precise peak detection and robust denoising, thereby increasing the accuracy and reproducibility of orientation and phase determinations. Notably, ePattern also reduces user bias during data processing, ensuring more consistent and reliable interpretation of complex 4D‐STEM datasets [39].

In this study, we introduce the application of the 4D‐STEM technique to determine the extension of the transition metal ordering in spinel LNMO and to compare this result with analyses performed by neutron powder diffraction (NPD). This study enables a statistically robust, spatially resolved characterization of polycrystalline LNMO powders by combining 4D‐STEM techniques with a data science approach. Individual particles are probed across the sample, allowing for the extraction of statistically meaningful information beyond averaged measurements. We also comprehensively discuss the experimental parameters and data analysis workflows used to interpret the 4D‐STEM datasets. Crucially, we demonstrate for the first time that the degree of transition metal ordering in spinel LNMO can be quantitatively mapped at the single‐particle level. Our approach discriminates between perfectly ordered, partially ordered, and disordered regions within individual crystallites.

2. Description of the Global Structure

This study focuses on three LNMO samples obtained through different annealing conditions from the same initial batch that targeted a stoichiometric Ni:Mn 1:3 ratio, each showing particles with platelet‐like morphology (Figure S1) (180 nm in average thickness and 1 µm in average diameter) and having different degrees of transition metals' ordering as determined by average (i.e. at long range distances) analysis. Preparation of the samples are discussed in detail in Supplementary Information. As shown by the x‐ray and neutron diffraction patterns given in Figure S2, all samples appear as single spinel phases with cubic structures and lattice parameters ranging between 8.1759(2) Å for the disordered LNMO (d‐LNMO), 8.1697(6) Å and 8.1679(4) Å for the two ordered LNMO's (o1‐LNMO and o2‐LNMO, respectively). The decrease of the cell parameter within this series is attributed to changes in Ni/Mn composition and thus in Mn³⁺ content: the richer in Mn³⁺ cations, the higher is the cell parameter of the spinel phase. The NPD allows to characterize the extent of ordering in LNMO. The neutron diffraction pattern of disordered d‐LNMO can be indexed in the $Fd\underset{\_}{3}m$ space group, while the other two collected patterns for o1‐LNMO and o2‐LNMO were indexed in the P4₃32 space group. The ordering peaks' width was used to determine the size of the ordered domains within the spinel structure. For o1‐LNMO, the ordered domain size was calculated to be 33 nm, while o2‐LNMO presented larger domains of 45 nm. The composition of the spinel phase was calculated by refining the NPD patterns with Rietveld method and found to be LiNi_0.462Mn_1.538O₄ for d‐LNMO, LiNi_0.476Mn_1.524O₄ for o1‐LNMO, and LiNi_0.492Mn_1.508O₄ for o2‐LNMO as reported in Figure S3 and Table S1. The estimated Mn³⁺ content required for charge compensation is 4.9% in the disordered d‐LNMO sample, and decreases to 1.1% in the highly ordered o2‐LNMO spinel. Interestingly, the o1‐LNMO sample, despite its classification as ordered, exhibits a slightly Mn‐rich composition, with an estimated Mn³⁺ content of 3.2%, which is atypical for a stoichiometrically ordered phase.

Upon examining the electrochemical signatures obtained for the three LNMO materials, as depicted in Figure S4, distinct behaviors are observed between these three samples. In agreement with their structural descriptions using NPD, the Ni²⁺/Ni³⁺ redox couple activity is associated to a solid‐solution mechanism for d‐LNMO, as expected for disordered LNMO, whereas a biphasic reaction plateau is observed for the two o1‐ and o2‐LNMO samples, as expected for ordered LNMO. However, a notable discrepancy arises in the contribution of the Mn redox reaction occurring at lower potentials. The Mn³⁺ content is estimated to be 4% in disordered d‐LNMO. As expected, this content decreases to 1% in the sample ordered o2‐LNMO. However, even though in agreement with the NPD refinement results, o1‐LNMO showcases 4% Mn redox activity and also presents two‐shouldered redox signatures at 3.96 and 4.20 V, as opposed to a single step around 4.10 V for d‐LNMO and o2‐LNMO. This behavior is seen for Mn‐rich ordered spinels before and attributed to a Ni/Mn disordering between 4b and 12d sites [8, 20]. This highlights that even though both o1‐ and o2‐LNMO are ordered according to their description in the P4₃32 space group thanks to NPD, they significantly differ in terms of their compositions and local arrangements of their transition metals leading to the presence of defects.

3. (Dis)Ordering With Spatial Resolution

Figure 1a,b compare the crystal structures of disordered and ordered LNMO, described by the $Fd\underset{\_}{3}m$ and P4₃32 space groups, respectively. For each prepared LNMO sample, we have examined by 4D‐STEM ACOM technique individual particles, selected randomly according to their position on the TEM grid. A single isolated particle is chosen (Figure 1c–e for each sample to illustrate the mapping of dis(ordering) at the particle level.

FIGURE 1.

Electron diffraction identifying ordered and disordered LNMO phases. (a,b) Crystal structures of disordered LNMO described in the $Fd\underset{\_}{3}m$ space group and ordered LNMO described in the P4₃32 space group, respectively. Lithium atoms are represented by green balls, manganese by purple balls, nickel by orange balls, and oxygen by red balls. The, below, from left to right, the disordered (d‐), the ordered (o1‐), and the ordered (o2‐) LNMO samples: (c,d,e) TEM images of selected particles for phase mapping. The colored crosses correspond to the electron diffraction patterns shown in (f,g,h). (f–h) Electron diffraction patterns acquired through 4D‐STEM ACOM on the points localized by colored stars at the center of the particles in (c,d,e). (i,j,k) Integration of line profiles on the dash lined orientation given in the associated diffraction patterns. Asterisks mark the ordering spots.

Using the 4D‐STEM technique, we performed full‐particle scans in diffraction mode with a quasi‐parallel electron beam, employing a convergence semi‐angle of 0.4 mrad and a step size of 10 nm. A precession angle of 0.8° was applied to mitigate dynamical scattering effects and enhance pattern quality. This configuration enabled the acquisition of high‐resolution diffraction datasets within a reasonable experimental duration (∼30 min per map), while also streamlining subsequent data processing. At each pixel (10 × 10 nm²), the recorded diffraction patterns were systematically compared using pattern matching to simulated reference patterns corresponding to the two distinct structural phases of LiNi_0.5Mn_1.5O₄: the fully disordered spinel phase ($Fd\underset{\_}{3}m$ space group) and the perfectly ordered spinel phase (P4₃32 space group). These phases can be distinguished based on their electron diffraction signatures, notably the presence or absence of reflections with mixed‐parity (hkl) indices, which are permitted in the primitive P4₃32 lattice but forbidden in the face‐centered $Fd\underset{\_}{3}m$ lattice, as illustrated in Figure S5.

Figure 1f–h shows the electron diffraction pattern taken at the selected pixel indicated with a cross in Figure 1c–e. Additionally, Figure 1i–k shows the line integration profile associated with the dashed‐lined orientation given in the diffraction pattern. In all of them, the [110] direction is chosen in order to be able to distinguish the diffraction spots associated with the ordering (i.e. 110, 330, 550). The observed diffraction patterns and associated integration line profiles align perfectly with the phase mapping results (Figure S6). In the pattern collected for the disordered d‐LNMO the ordering spots are absent, whereas in the two ordered o1‐LNMO and o2‐LNMO patterns the ordering spots are clearly visible.

4. Ideal Phase Mapping Conditions

When performing phase mapping, careful selection of the particles to be analyzed is crucial to ensure the reliability of the results and to minimize the risk of misinterpretation or overestimation. Our detailed evaluation of the collected phase maps has revealed several critical parameters that must be taken into account to ensure accurate analysis. These parameters can be classified into two main categories: experimental constraints, such as specimen thickness and crystal orientation, and software‐related limitations, including pattern matching accuracy and detection thresholds. Addressing both sets of factors is essential to obtain robust and interpretable spatial phase distribution maps.

The first essential experimental condition to be considered is the particle thickness. This is because the experimental diffraction patterns are compared with the theoretical ones calculated under kinematical considerations, where the incident wave maintains a constant amplitude upon scattering. This consideration can be experimentally valid when the specimen is ultrathin (less than 20 nm). However, if the specimen is electron‐transparent but not sufficiently thin, the incident electrons interact strongly with matter, and the diffracted beam can act as new multiple incident beams, leading to multiple scattering. To minimize these dynamical effects, we targeted a thin platelet morphology (180 nm in average thickness) and applied a beam precession of 0.8° throughout the mappings. However, when the particle thickness remains substantial, several artifacts may arise. In ordered phases, the intensity of characteristic ordering reflections may be significantly attenuated or even suppressed, leading to their non‐detection. Conversely, in disordered regions, diffuse scattering can produce spurious intensity at positions corresponding to ordering reflections, potentially resulting in misidentification and inaccurate phase mapping (Figure S7).

The second critical experimental parameter is the crystal orientation during data acquisition. Accurate identification of ordering reflections is significantly facilitated when the crystal is aligned along a zone axis, as this geometry optimizes the visibility and symmetry of characteristic diffraction spots. However, even a slight misorientation can lead to mistaken phase attribution. This sensitivity is illustrated in Figure S8, and further evidenced by the deviation from the zone axis in the o1‐LNMO particle, as revealed by nonnegative matrix factorization (NMF) clustering [40] (Figure S9). The underlying cause of this limitation stems from the pattern‐matching algorithm employed in the ASTAR software, which determines the crystallographic phase by summing the positions and intensities of diffraction spots within a defined search radius (see Figure S10). Deviations from ideal orientation can distort spot intensities and spatial distributions, thereby compromising the reliability of phase identification.

Even though all the ideal experimental conditions of phase mapping are achieved, it is possible to lose information due to software‐related limits. One of the key factors influencing phase detection is the size of this radius used for matching experimental and theoretical patterns, as just mentioned. Due to the curvature of Ewald's sphere, when we move away from its center, the sphere intersects only a minor portion of the diffracting domains. Consequently, diffraction spots farther away from the central beam (corresponding to large g vector distances in reciprocal space) will have less intensity, especially for extra spots exhibiting much lower intensity. Since the software determines the phase based on a comparison of intensities at specific spot positions, selecting a too large search zone can lead to a shift in the choice of the software. For example, selecting the disordered phase instead of the ordered phase despite the presence of ordering spots (Figure S10).

A second significant software‐related limitation lies in the intensity detection threshold, which may result in phase misclassification or the designation of certain regions as unreliable (Figure S11). This limitation stems from the reliance on theoretical intensity calculations based on single‐crystal models of the P4₃32 and $Fd\underset{\_}{3}m$ space groups under kinematical approximation. In contrast, experimental datasets often reflect the superposition of multiple stacked lattices, where dynamical scattering effects, though mitigated by beam precession, remain non‐negligible and lead to unpredictable variations in diffraction spot intensities. As a result, regions with inherently weak or attenuated signals may be incorrectly assigned by the software, highlighting the need for cautious interpretation of low‐intensity features in 4D‐STEM datasets.

5. Mapping the Degree of Ordering

Under the kinematical approximation, a correlation can be established between the intensity of ordering reflections in patterns and the number of ordered lattice planes contributing to the signal. In an ideal scenario, where dynamical scattering effects are negligible or effectively suppressed by beam precession, and the LNMO platelets exhibit uniform thickness, a fully ordered crystal with P4₃32 symmetry is expected to produce an intensity ratio between ordering‐specific reflections and those common to both ordered and disordered ($Fd\underset{\_}{3}m$) phases that closely aligns with theoretical predictions. However, if the experimentally measured intensity ratio of the ordering reflections is lower than expected, it suggests a partial or incomplete ordering along the beam direction. This deviation reflects a coexistence of ordered (P4₃32) and disordered ($Fd\underset{\_}{3}m$) domains along the crystal thickness, leading to a cumulative diffraction intensity that underrepresents the ideal ordering contribution.

Since the phase mapping outputs showed overall P4₃32 phase indexation for both ordered o1‐LNMO and o2‐LNMO, we focused on extracting information on the extent of the ordering. For both datasets, ordering spots along the [110] direction is chosen, as they are commonly visible throughout the particles (marked with red dots in Figure 2b–f). The selection of suitable spots, crucial for intensity analysis, is detailed in Figure S13.

FIGURE 2.

Ordering intensity maps for LNMO indexed as P4₃32 phase. Process, including the selection of diffraction peaks for structural metal ordering mapping. (a,e) Virtual dark field images obtained from selected diffraction spots. Brighter zones indicate high intensity, while dark zones signify their absence. Two points are chosen on each particle, they correspond to the observed highest and lowest integrated ordering spots' intensities. The ordered o1‐LNMO on the top (a), and the ordered o2‐LNMO on the bottom (e). (b,f) Integration along the [110] direction on selected electron diffraction patterns given in (a,e). The ordering spots are marked with asterisks. The difference in their observed intensity between the integration of line profiles for each particle highlights the distribution of ordering degrees across the particle. (c,g) Selected diffraction spots (in red) for ordering intensity search by virtual dark field. The [110] direction is chosen on both zone axes because of its visibility around the particle. Selection details are given in Figure S12. (d,h) Ordering intensity map represented with a colored scheme based on gray values. Multicolored zones on particles indicate a heterogeneous ordering distribution with a spatial resolution of 10 nm.

The selected spots are then used as a virtual aperture, where a virtual dark field image is obtained by averaging the intensity of the collected diffraction pattern (Figure 2c–g). Obtained virtual dark maps were then color‐coded based on their gray values, as shown in Figure 2d–h. Here, a white pixel corresponds to intensity saturation at 255 in grayscale, indicating a strong presence of ordering spots. On the other hand, a black pixel represents an intensity value of 0, indicating the absence of the searched ordering spots in that region. This provides a visual indication of the degree of ordering across the material, with brighter regions presenting a higher density of ordering spots.

In the case of the o1‐LNMO, a heterogeneously colored intensity map is observed in Figure 2d. The center of the particle exhibits a high concentration of intensity, as shown in the associated electron diffraction pattern in Figure 2c. However, as we move toward the outer parts of the particle, the ordering spot intensity decreases, as in the example given in Figure 2b (bottom). This observation indicates a variation in the degree of ordering within the particle, with higher intensity concentrated in the center and lower intensity toward the edges.

On the other hand, for the o2‐LNMO, an overall high intensity is detected in the obtained intensity map shown in Figure 2h. Similar to the o1‐LNMO, the center of the particle exhibits the highest ordering spots' intensity, as shown in the associated diffraction pattern in Figure 2g. However, in this case, when the outer parts of the particle are analyzed, there is a preservation of the ordering spots' intensity even in the lowest intensity zone (Figure 2h).

6. Automated Quantification of Ordering

Two key limitations inherent to pattern‐matching algorithms can still result in information loss during software‐based phase mapping, even under ideal experimental conditions, and strongly impact the assessment of the degree of ordering in LNMO. First, a large matching radius may overlook weak extra spots due to Ewald sphere curvature, leading to incorrect phase identification (i.e., misattribution as a disordered domain). Second, intensity thresholds based on ideal models fail to account for experimental complexities like overlapping lattices and dynamical effects. These factors cause unexpected intensity variations that the software may misinterpret, especially in regions with weak signals. To overcome these limitations, we developed a data science strategy with the ePattern software [38]. This tool can individually detect Bragg spots both in position and in intensity, enabling a precise separation between principal and extra spots.

To quantify the degree of ordering (order parameter) at the particle level using the 4D‐STEM ACOM dataset, we defined an order parameter, α, as the ratio between the mean intensity of the ordering‐specific diffraction spots and that of the principal diffraction spots, which are common to both ordered and disordered lattices. To ensure comparability across measurements, all values were normalized with respect to a simulated diffraction pattern of a perfectly ordered reference structure, for which the maximum observable parameter was 0.8. This normalization was introduced through a scaling factor β = (1/0.8) = 1.25, leading to following expression:

$$\alpha =\beta \frac{⟨I_e⟩}{⟨I_p⟩}$$ (1)

where α is the order parameter, I_e :  is the ordering spot intensity and I_p : is the principle spot intensity.

For a quantitative extraction of the intensities, the initial step involves processing diffraction pattern data using ePattern [38], which extracts the positions and intensities of diffraction spots from each diffraction pattern, allowing the reconstruction of the diffraction patterns without noise. All diffraction patterns were recentered by aligning their central spot with the chosen reference center. We assess the number of principal and ordering spots, determine their intensities, and compute the order parameter according to Equation (1). The workflow is illustrated in Figure S14. We have developed a python program (ePattern_Ordering) to facilitate spot selection within diffraction patterns using the output of the ePattern (a csv file containing the positions and intensities of each diffraction spot in our dataset). By extracting the coordinates of both principal and ordering spots after alignment of the central spot, we define circular regions of a fixed radius around these coordinates. This allows us to access to the intensity of each spot, then to classify a spot as “ordering” or “principal.” We use a coordinates criterion, as the positions of the ordering and principal spots are based on the pattern calculated from the CIF file (Figure S15). Figure 3a illustrates the experimental setup for 4D‐STEM, along with the process of selecting diffraction spots. This selection enables the computation of the order parameter, leading to the structural mapping of transition metal ordering. Figure 3b shows the intensity distributions of the ordering spots, principal spots, and central spots for the o1‐LNMO particle (orange shades) and the o2‐LNMO particle (green shades).

FIGURE 3.

Detailed analysis of order parameter maps for two LNMO samples. (a) Schematic of the 4D‐STEM acquisition process, including the selection of diffraction peaks for structural order mapping. (b) The intensity distribution for o1‐LNMO is represented in orange shades, while o2‐LNMO is depicted in green shades. Three distinct distributions are observed, one for the extra spots, one for the principal spots, and one for the central spots. (c,d) The corresponding distribution of order parameters for o1‐LNMO and o2‐LNMO particles, respectively. (e,f) Examination of the order parameter distribution (considering only values above 0.0001) provides further insights into the quantification values and the box plot highlights the order parameter outliers.

The ordering spots in o2‐LNMO exhibit higher intensities than those in o1‐LNMO, whereas the principal spots show the opposite trend. This suggests a higher degree of ordering in o2‐LNMO compared to o1‐LNMO in agreement with previously discussed software‐based results. The quantifications of the order parameter are shown in the maps in Figure 3c,d, where different colors represent varying degrees of ordering within the LNMO particles. All order parameter values were normalized with respect to a simulated diffraction pattern of a perfectly ordered reference structure, for which the maximum observable order parameter was 0.80 (Figure S15). Notably, no zones without ordering were detected (blue regions indicate values higher than 0.0001). The in red zones indicate zones of uncertainty where elevated noise levels hinder the reliable detection of low‐intensity ordering spots against the background.

Figure 3e,f display histograms of the order parameter distribution for o1‐LNMO and o2‐LNMO, respectively. In o1‐LNMO, values range from approximately 0.0076 to 0.44, whereas o2‐LNMO exhibits a broader distribution, extending from 0.0059 to ∼0.46. The boxplot for o1‐LNMO shows more outliers starting from approximately 0.26 and extending to higher values, with no outliers detected at lower values. The o2‐LNMO boxplot exhibits outliers primarily at lower values, approximately below 0.05, and fewer outliers at higher values. In terms of data distribution, the box plot indicates that for o1‐LNMO, the first 25% of values range from 0.0076 to approximately 0.09, while the middle 50% of the values lie between 0.09 and 0.15. For o2‐LNMO, the lower 25% of values range from 0.0059 to around 0.17, and the central 50% spans from approximately 0.17 to 0.25. Overall, o2‐LNMO tends to show a higher degree of ordering, as evidenced by the greater prevalence of orange and yellow regions in Figure 3c,d, corresponding to order parameter values between 0.20 and 0.40. Notably, localized regions within o1‐LNMO also exhibit high ordering, with values approaching 0.44, highlighting spatial heterogeneity in the transition metal ordering.

To further assess the reproducibility of the ePattern‐based quantification, the same order‐parameter workflow was applied to two additional LNMO particles prepared under the o1‐LNMO and o2‐LNMO annealing conditions, respectively (see Figure S20 in the Supporting Information). These additional analyses confirm that spatially heterogeneous ordering is reproducibly detected at the single‐particle level, while also highlighting expected particle‐to‐particle variations in the mean order parameter and local ordering distribution.

To enhance the reliability of our quantification method, we investigated the relationship between local thickness (Figure S16) and zone axis misalignment (Figure S17) with the calculated order parameter values. A comparison between the intensity of the central diffraction spot and the order parameter at each pixel revealed no direct correlation between the thickness and order parameter. The deviations from the ideal zone axis were effectively highlighted by comparing the intensities of opposing diffraction spots (e.g. the ordering spots corresponding to (4̅40) and (44̅0)). The ordered o1‐LNMO particle exhibits two regions that are clearly off‐zone axis, while the o2‐LNMO particle remains largely aligned along the zone axis. These off‐zone‐axis regions (Figure S17e and S7j) coincide with the ambiguous and low‐order regions identified in the initial quantification maps (Figure 3c,d). Notably, o1‐LNMO also displays two distinct principal spot intensities in the distribution shown in Figure 3b, which is attributed to the presence of an off‐zone‐axis area (Figure S17c). This of‐zone‐axis area was previously identified as one of the highest‐intensity regions in the virtual aperture selection for ordering spots (Figure 2d). These observations highlight both the accuracy of our quantification method and the importance of validating its reliability.

Differences in lattice parameters serve as a reliable indicator of the composition in spinel LNMO. As discussed in the “Description of the Global Structure” section, the lattice parameter of disordered LNMO is typically larger than that of the ordered phase. Here, we calculated local lattice parameters with a spatial resolution of approximately 10 nm using 4D‐STEM datasets, based on the diffraction spots highlighted in Figure S18. Details of the pattern calibration procedure used to obtain absolute distances are provided in the Supplementary Information. Due to dynamical scattering and calibration uncertainties in camera length and detector geometry, lattice parameters obtained from electron diffraction can deviate in absolute value from those obtained from x‐rays. Therefore, the electron diffraction values were calibrated against the average lattice parameters obtained from x‐ray diffraction: 8.1759(2) Å for d‐LNMO, 8.1697(6) Å for o1‐LNMO, and 8.1679(4) Å for o2‐LNMO.

Figure 4 presents the lattice parameter maps and corresponding distributions, illustrating the spatial variations for d‐LNMO, o1‐LNMO, and o2‐LNMO. In the disordered particle, significant local variations in lattice parameter are evident, which may reflect compositional inhomogeneities such as variations in Mn³⁺ content or local defects. By contrast, the o2‐LNMO sample exhibits an exceptionally homogenous lattice parameter distribution, with a coefficient of variation (CV = σ/µ) of 0.0032 compared to 0.0065 for d‐LNMO. The largest deviations are observed at the particle edges, where high noise and/or low diffraction spot intensities were noted previously. Interestingly, although o1‐LNMO is both globally and locally ordered and has an average lattice parameter close to that of o2‐LNMO, its CV (0.0034) is higher, and its local lattice parameter distribution resembles that of the disordered d‐LNMO particle. Similar to the order parameter analysis, the lattice parameter measurements therefore reveal considerable spatial heterogeneity in o1‐LNMO.

FIGURE 4.

Lattice parameter map calculated from 4D‐STEM data. (a, b, c) Lattice parameter distributions for d‐LNMO (red), o1‐LNMO (orange), and o2‐LNMO (green). Dashed lines indicate the mean values obtained from x‐ray powder diffraction, which were used to calibrate the average lattice parameters extracted from electron diffraction data. Black curves show Gaussian fits with the extracted standard deviation (σ) used as a measure of distribution width. (d, e, f) Lattice parameter distribution maps for d‐LNMO, o1‐LNMO, and o2‐LNMO, respectively. (g, h, i) Deviations of the lattice parameters from their average value for the corresponding particles. (j, k, l) Diffraction patterns acquired from samples d‐LNMO, o1‐LNMO, and o2‐LNMO, respectively. Red squares indicate principal spots selected for lattice parameter calculation.

To further assess the coupling between transition‐metal ordering and lattice distortion, local Pearson correlation maps were calculated between the order parameter (S) and the lattice parameter (a) (see Figure S19). The coefficient r(x,y) was computed in a 7 × 7 pixel sliding window centered on each pixel, corresponding to a local area of approximately 70 × 70 nm². Positive values indicate that (a) and (S) vary in the same direction, negative values indicate an anticorrelated response, and values close to zero indicate no clear local linear relationship. The maps reveal a spatially heterogeneous coupling, especially in o1‐LNMO, where alternating positive and negative correlation domains are observed. This is consistent with its broader lattice‐parameter distribution and heterogeneous order‐parameter map. In contrast, o2‐LNMO shows weaker local correlation contrast over most of the particle, in agreement with its more homogeneous ordering and narrower lattice‐parameter distribution. These results support the interpretation that o1‐LNMO is only partially homogenized at the nanoscale, whereas o2‐LNMO is closer to a uniformly ordered state.

7. Discussion and Conclusion

In this study, we have thoroughly investigated the spatial distribution of transition metal ordering in spinel LiNi_0.5Mn_1.5O₄ (LNMO) using advanced 4D‐STEM combined with a data science‐driven analytical pipeline. Starting from a globally disordered LNMO sample d‐LNMO, two annealing conditions produced structurally ordered samples o1‐LNMO and o2‐LNMO, both indexed in the P4₃32 space group by neutron diffraction. However, our 4D‐STEM analysis reveals that despite their long‐range crystallographic similarity, these two samples exhibit markedly different local ordering behaviors at the nanoscale. By integrating diffraction datasets with robust pattern matching and spot‐intensity analysis, we present the first spatial mapping of ordering heterogeneity with a direct quantification of transition metal ordering within individual LNMO particles.

Spatially resolved phase and order parameter mapping with 10 nm resolution confirmed the presence of transition metal ordering across the particle thickness in both ordered samples. However, significant differences emerged. The o2‐LNMO sample, annealed longer and under continuous oxygen flow, exhibited a consistently higher and more homogeneous order parameter. In contrast, o1‐LNMO, annealed for a shorter time under ambient air, showed lower overall ordering and pronounced spatial heterogeneity. Notably, its local lattice parameter distribution closely resembled that of the disordered d‐LNMO, suggesting incomplete ordering. It is important to note that these trends were consistently observed across multiple particles per sample, confirming the statistical robustness of our findings.

These observations challenge previous structural models that propose uniform coherent ordering in LNMO crystallites. Our data suggest that the global ordering behavior is governed at the nanometric scale, aligning with findings by Tertov et al. [20], who observed a distribution of nanosized ordered domains separated by disordered regions using aberration‐corrected TEM. However, within our nanometric resolution limit, we did not observe isolated disordered domains surrounding larger ordered domains, as reported in their study. This difference likely arises from specimen thickness: their analysis was performed on relatively thin lamellae (∼50 nm), comparable to the size of individual domains, which enabled direct imaging of ordered and disordered regions. By contrast, our 4D‐STEM measurements were conducted on significantly thicker samples (∼180–200 nm), where overlapping contributions from multiple domains are unavoidably averaged through the sample thickness.

If complete ordering extended through the particle thickness, the detected spot intensities would remain uniform. In the case of the ordered samples, however, especially in o1‐LNMO, we detect significant variations in the ordering parameter, which we attribute to the coexistence of ordered and disordered domains along the thickness of the particle.

The contrasting behaviors of o1‐ and o2‐LNMO indicate that oxygen partial pressure is a critical factor: higher oxygen availability during annealing appears to suppress defect formation and stabilize the ideal, ordered phase. Interestingly, no secondary phases or rocksalt‐type defects were detected in either o1‐LNMO or d‐LNMO. Quantitative analysis shows that Mn³⁺ content decreases from 4.9% in disordered d‐LNMO to ∼3.2% in o1‐LNMO and further to ∼1.1% in highly ordered o2‐LNMO. This compositional trend is consistent with the lattice parameter distributions calculated from 4D‐STEM analysis: d‐LNMO shows significant local variation with higher values, o1‐LNMO retains a heterogeneous distribution resembling the disordered state, while o2‐LNMO exhibits a highly homogenous distribution. Together, these results indicate that the transformation from d‐LNMO to o1‐LNMO can be attributed to partial ordering of Ni/Mn on the 4d/12d sites, accompanied by a moderate reduction of Mn³⁺ content, whereas the homogeneity in ordered domains as in the o2‐LNMO sample requires extended annealing under oxygen flow.

A novelty of this work is integrating a data science‐based methodology to overcome limitations in 4D‐STEM phase mapping, such as intensity thresholding and spot matching radius issues. Using the ePattern software, we developed a robust framework to detect individual Bragg spots in position and intensity. This was coupled with a custom Python routine (ePattern_Ordering) to compute a local order parameter (α) based on the intensity ratio of ordering‐specific to principal diffraction spots. To ensure accurate quantification, we addressed key experimental limitations, namely, sample thickness and crystal orientation, both of which can obscure ordering detection through dynamical scattering or off‐zone‐axis effects. These challenges were mitigated in our case by performing precession‐assisted 4D‐STEM on thin, platelet‐shaped LNMO particles and a systematic analysis by considering each technique's limitations.

Altogether, this work offers new insights into the nanoscale structural complexity of LNMO and establishes a reproducible and transferable methodology for mapping local orderings. Our findings provide a new framework to understand the interplay between synthesis conditions, local structure, and electrochemical performance, which is essential for the rational design of battery materials.

8. Methods

8.1. Material Preparation

LNMO materials were synthesized using molten salt synthesis as described in detail in our previous work [41]. The Ni(NO₃)₂·6H₂O and Mn(NO₃)₂·4H₂O precursors were mixed in stoichiometric amounts (1:3) with an excess amount of LiCl salt with a ratio number of moles of LiCl over the number of moles of transition metals of 35. The powder mixture was calcinated at 750°C for 4 h in a tubular furnace under an air atmosphere. At the end of synthesis, the residual salt was eliminated by washing with water and then ethanol. The obtained sample was named the disordered d‐LNMO according to the description of its crystal structure in the $Fd\underset{\_}{3}m$ space group. To order the transition metals, this material d‐LNMO was reannealed at 700°C for 4 h (two times to homogenize the material) under air atmosphere or for 24 h under continuous O₂ flow, they were named ordered o1‐LNMO and ordered o2‐LNMO, respectively. All samples share a common platelet morphology characterized by an average size of 1 µm and a thickness of 180 nm.

8.2. 4D‐STEM and TEM Techniques

Two different microscopes were used in this study. The electron diffraction patterns given on Figure S5 in Supplementary Information were collected on a transmission electron microscope JEOL JEM‐2100 (LaB6) at 200 kV, using the selected area technique (SAED) with a Gatan Orius 200D camera. 4D‐STEM ACOM studies were conducted on a FEI Tecnai F20 TEM at 200 kV equipped with NanoMEGAS Astar system and Gatan Oneview CMOS camera. For the 4D‐STEM study, the spot size was set to 5, gun lens to 3 and a 10 µm condenser aperture (C2) was used (semi‐convergent angle of 0.4 mrad). A step size of 10 nm (the width of one pixel) was set for all scans, defining the resolution of the obtained maps To reduce dynamical effects, the electron beam was processed at an angle of 0.8°. The use of beam precession improves the reliability of the diffraction intensity analysis by reducing dynamical scattering effects. However, it does not render the intensities strictly kinematical. The 0.8° precession angle was selected after testing angles from 0.1° to 1.0°, as it provided the best compromise between reducing dynamical contrast and preserving the weak ordering‐related reflections.

8.3. Order Degree Quantification

The data science workflow for 4D‐STEM ACOM data, as illustrated in the schematic in Figure S14, is structured into two main phases: ePattern_Registration and ePattern_Ordering. This approach enables high‐precision, quantitative analysis of crystallographic ordering at the nanoscale by leveraging automated peak detection, spatial alignment, and custom intensity‐based metrics.

The first phase, ePattern_Registration, begins with the identification and quantification of diffraction spots. In this step, the ePattern software processes each diffraction pattern collected across the 4D‐STEM scan, determining the exact position and intensity of every Bragg spot. This step is essential for generating a clean, standardized dataset that captures both the structural information and spatial variation present in the sample. Following this, a pattern alignment procedure is applied to ensure consistency across the dataset. All patterns are aligned based on the coordinates of the central (direct) beam spot, effectively centering the dataset and correcting for any minor shifts or drift during acquisition. This spatial normalization ensures that all subsequent comparisons between spots are meaningful and accurate.

The second phase, ePattern_Ordering, focuses on the evaluation and mapping of the degree of ordering using a calculated metric called the order parameter. This begins with the definition of the selection zone, where specific Bragg spots are selected for analysis. Using custom‐developed algorithms, the user or software can define circular or rectangular regions that isolate the relevant ordering‐specific spots (e.g., those present in the ordered phase but forbidden in the disordered one) and the principal spots common to both phases. Once the spot coordinates are established, the order parameter (α) is calculated at each scan point using the intensity ratio between these two groups of reflections. Specifically, α is defined as the mean intensity of the extra (ordering‐specific) spots divided by the mean intensity of the principal spots. This parameter serves as a quantitative proxy for the degree of local cation ordering within the sample. Finally, the computed α values are used to reconstruct spatial maps that visualize the ordering distribution across the entire particle with nanometric resolution.

8.4. X‐Ray Diffraction

The powder x‐ray diffraction measurements were performed on a PANalytical Empyrean Diffractometer with Cu Kα radiation (λ_Kα1 = 1.54056 Å and λ_Kα2 = 1.54439 Å) in Bragg–Brentano configuration. The diffraction patterns were collected in a 2ϑ range of 15–120°(2ϑ) with a scan step of 0.008° for a total acquisition of 20 h. Structural parameters were calculated through Le Bail refinements using the FullProf program [42]. The spinel domain sizes were calculated from Scherrer's equation [43] after removing the instrumental contribution.

8.5. Powder Neutron Diffraction

The room temperature powder neutron diffraction was performed on the D2B high resolution diffractometer of the Institut Laue‐Langevin in Grenoble, France in transmission mode and using a wavelength of 1.594 Å. The data were evaluated via full pattern matching using the FullProf Program (Le Bail method). The ordered domain sizes were calculated using a selective broadening model (size‐model = −14) using the Williamson–Hall method, a description of the peak profiles by the Thomson–Cox–Hastings Pseudo‐Voigt function and an instrumental resolution file.

8.6. Electrochemistry

The positive electrode was prepared by mixing 80 wt.% of LNMO powder, 10 wt.% of carbon black conductive additive (Alfa Aesar, 99.9%), and 10 wt.% of Poly(vinylidene fluoride) (PVDF, Sigma‐Aldrich) binder in 1‐methyl‐2‐pyrrolidone as solvent (NMP, Sigma Aldrich, 99.5%). CR2032‐type coin cells were assembled in an Ar‐filled glovebox using Li metal as negative electrode, Whatman separator and 1 M LiPF₆ EC/DMC electrolyte (1:1 w/w ethylene carbonate (E.C.)/dimethyl carbonate (DMC)). The electrochemical performance of LNMO materials was assessed using the galvanostatic charge‐discharge method. All the electrochemical experiments were conducted at 25°C.

Author Contributions

Gozde Oney synthesized the analyzed materials, carried out the x‐ray and electron diffraction experiments, and the electrochemical measurements, and interpreted the data across all techniques. Fayçal Adrar quantified the local order parameter and calculated lattice parameter distributions from 4D‐STEM data, developed dedicated 4D‐STEM analysis codes for these analyses, and interpreted the data. Gozde Oney and Chunyang Zhang performed the 4D‐STEM data acquisitions with Arnaud Demortière and Muriel Véron. Jacob Olchowka performed the nonnegative matrix factorization clustering analysis. Emmanuelle Suard was responsible for the neutron diffraction data acquisition. Gozde Oney wrote the first draft of the manuscript. Jacob Olchowka, Laurence Croguennec, François Weill, and Arnaud Demortière supervised the project and interpreted the results. All authors took part in the scientific discussion and contributed to the writing and revision of the manuscript.

Supporting information

Supporting File: smtd70900‐sup‐0001‐SuppMat.docx.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.