In situ Synchrotron X‐ray Metrology Boosted by Automated Data Analysis for Real‐time Monitoring of Cathode Calcination

Abstract

Synchrotron X‐ray‐based in situ metrology is advantageous for monitoring the synthesis of battery materials, offering high throughput, high spatial and temporal resolution, and chemical sensitivity. However, the rapid generation of massive data poses a challenge to on‐site, on‐the‐fly analysis needed for real‐time process monitoring. Here, a weighted lagged cross‐correlation (WLCC) similarity approach is presented for automated data analysis, which merges with in situ synchrotron X‐ray diffraction metrology to monitor the calcination process of the archetypal nickel‐based cathode, LiNiO₂. The WLCC approach, incorporating variables that account for peak shifts and width changes associated with structural transformations, enables rapid extraction of phase progression within 10 seconds from tens of diffraction patterns. Details are captured, from initial precursors to intermediates and the final layered LiNiO₂, providing information for agile on‐site adjustments during experiments and complementing post hoc diffraction analysis by offering insights into early‐stage phase nucleation and growth. Expanding this data‐powered platform paves the way for real time calcination process monitoring and control, which is pivotal to quality control in battery cathode manufacturing.

An automated approach is developed for fast “on‐the‐fly” analysis of the massive data generated from in situ synchrotron X‐ray metrology during the calcination of cathode active materials (CAMs). Expanding this data‐powered platform paves the way for real time monitoring and predictive control of the calcination process, ensuring the production of CAMs with the desired structure, morphology, and surface properties.

1. Introduction

In situ metrology is commonly employed in industrial manufacturing to monitor deviations or abnormalities using in‐line sensors and detectors, enabling timely adjustments for product quality and consistency.^{[ 1} , ^{2 ]} Similarly, in situ metrology is desirable in battery manufacturing, particularly for the real time process monitoring and control of cathode calcination. However, the high temperature and harsh environments in cathode calcination challenge sensor durability. Moreover, few measurement techniques can track the complex calcination process and the involved phase transformations, crystallization, and structural and morphological changes during the process, as exemplified by the calcination of Ni‐based CAMs from hydroxides in Scheme 1 .^{[ 3 ]} Like other solid‐state reaction processes, calcination involves multiple phases, evolving from heterogeneously mixed precursors to a homogeneous phase.^{[ 4 ]} While the overall phase transformation process from the initial hydroxides to the intermediate rock salt or spinel, to the final layered phase, is well known, the crystallization thermodynamics and kinetics governing the calcination process are poorly understood.^{[ 3} , ⁴ , ^{5 ]} It remains unclear how the calcination conditions cause the vastly varying structural and morphological properties and electrochemical performance of the final products. Understanding the nucleation, crystallization, and growth during the calcination is crucial to determining the process‐structure‐property‐performance intercorrelation and predictive control in industrial production.

Scheme 1.

Synchrotron X‐ray based in situ metrology for real time monitoring and predictive control of battery cathode calcination, using the example of the Ni‐based layered cathode (LiNiO₂; right) synthesized from hydroxide precursor (Ni(OH)₂; left). In situ metrology using synchrotron X‐ray facility (middle) enables real time monitoring of the intermediates and calcining conditions/parameters (such as composition, temperature (T), pressure (P), …). However, the rapid generation of a large amount of data poses a challenge to the data analysis (top), calling for artificial intelligence (AI)‐assisted data analysis to facilitate the calcination process prediction and control (bottom).

Until now, optical/laser‐diffraction‐based techniques have primarily been employed for in situ measurement of particle size and morphology during high‐temperature calcination, but their resolution is limited to micron‐mm scales.^{[ 6 ]} Synchrotron X‐ray‐based in situ techniques are powerful for monitoring materials synthesis, offering a wide range of length scales, high‐throughput, high temporal resolutions, and chemical sensitivity. These techniques provide valuable insights into the phase transitions, crystal structures, and chemical composition of the materials during calcination. X‐ray diffraction (XRD) is especially valuable for characterizing polycrystalline battery materials and arguably the most powerful tool among various scattering and spectroscopy techniques for in situ characterization of calcination and other synthesis reactions. Modern synchrotron facilities, with advanced instrumentation and fast detectors, can quickly acquire high‐quality XRD patterns, identifying intermediates and minor impurity phases during synthesis.^{[ 7 ]} Meanwhile, the large datasets produced during in situ synchrotron experiments create challenges for on‐site on‐the‐fly data processing and analysis. Data analysis is often done manually and off‐site after experiments are completed. Efficient on‐site data analysis is desired for fast decision‐making, agile experimental design, and adjustment, ultimately leading to optimized experiments.^{[ 8 ]}

Various data‐treatment approaches, such as the Pearson correlation functions and machine learning (ML)‐based automated approaches, have recently been developed to accelerate the extraction of information extraction from large datasets.^{[ 9 ]} Significant advancements in ML‐based automated approaches allow for automated and rapid XRD data analysis.^{[ 10 ]} For instance, supervised ML was used to classify crystallographic information and identify phases from XRD patterns.^{[ 11} , ^{12 ]} The auto XRD probabilistic deep learning convolutional neural network (CNN) interprets multiphase diffraction spectra for identifying inorganic materials,^{[ 13 ]} using both experimental and simulated data sets to improve accuracy. An adaptive ML algorithm was developed for phase identification, utilizing a CNN for fast, automatic crystalline materials identification and categorizing phases with high accuracy.^{[ 14 ]} An automated deep neural network addresses µ‐XRD mapping in large synchrotron in situ XRD experiments, emphasizing the use of experimental XRD data for developing robust ML on XRD.^{[ 15 ]} Supervised ML algorithms and physics‐based data augmentation to automate multi‐label phase identification, aiding in the diagnosis and treatment of urinary tract calculi.^{[ 16 ]} ML models also analyze powder XRD patterns from inorganic crystal structures for symmetry identification, property prediction, and low‐dimensional embedding.^{[ 17 ]} However, as with all ML models, these methods depend on the inclusion of relevant reference phases in training data and are not specifically trained to track phase evolution during in situ experiments over a range of temperatures.

In this work, we develop a novel weighted lagged cross correlation (WLCC) similarity approach that integrates automated data analysis with in situ synchrotron X‐ray metrology to monitor real time intermediates during the calcination of LiNiO₂ (LNO), an archetypal Ni‐based cathode from hydroxides (Scheme 1). The WLCC function has been used as a similarity measure in other characterization techniques such as Raman spectroscopy^{[ 18 ]} and 1H NMR Spectra^{[ 19 ]} for materials classification. It has been used in various fields for real time monitoring and quality control such as medical image registration,^{[ 20 ]} dual‐comb spectroscopy,^{[ 21 ]} and analyzing EEG signals.^{[ 22 ]} Our method extends the application of WLCC to in situ XRD metrology, introducing a novel method for rapid detection of pattern evolution associated with material transformation. Our data‐driven, “no‐training‐required” approach completes the analysis of tens of XRD patterns in just 10 s, significantly speeding up data analysis for real time monitoring and predictive control of the calcination process. This efficient model eliminates the need for extensive training and large datasets, focusing, instead, on extracting phase information from known phases predetermined by XRD. Moreover, our rapid analysis provides crucial insights into early‐stage phase nucleation and growth, complementing traditional Rietveld‐refinement‐based methods.

2. Results

2.1. Synchrotron XRD‐Based In Situ Metrology for Cathode Calcination

Figure 1 shows the setup for in situ synchrotron X‐ray metrology and the acquired temperature‐resolved XRD data during the calcination of LiNiO₂ (LNO) from hydroxide precursors (Ni(OH)₂) in the presence of Li source (LiOH). Overall, three major phases, Ni(OH)₂ with a trigonal structure (S.G.: P‐3 m1), lithiated rocksalt Li_xNi_1−xO (RS‐LNO) (S.G.: Fm‐3m), and layer‐structured LiNiO₂ (S.G.: R‐3m) are involved, as shown by the water‐fall plots in Figure 1b. Ni(OH)₂ started to decompose at ≈330 °C, followed by a complicated phase transformation into the Li‐containing rocksalt Li_xNi_1−xO and layered LiNiO₂, with high structural similarity. At temperatures above ≈880 °C, diffraction peaks shifted to lower values, indicating the decomposition of the layered LNO due to the Li/O loss. However, the information regarding the phase progression and crystallization in the sample cannot be extracted immediately from the XRD plots without sophisticated post hoc quantitative analysis. Rietveld refinement is mostly applied for such XRD data analysis, starting with structural modeling, by assigning parameters representing the unit cell dimension, atomic position and occupancy, micro‐strain, and crystalline sizes, phase composition, etc.^{[ 23 ]} Analyzing a vast amount of the in situ XRD data is time‐consuming and computationally intensive. Additionally, the complexity of the data, including overlapping peaks and noisy signals, requires sophisticated algorithms for accurate interpretation.

Figure 1.

Synchrotron XRD based in situ metrology for battery cathode calcination. a) Illustration of the experimental setup for the in situ experiments at the Quick X‐ray Absorption and Scattering (QAS) beamline. See the photo of the setup (Figure S1, Supporting Information). b) Water‐fall plots of the temperature‐resolved in situ XRD data acquired during heating Ni(OH)₂ with LiOH as Li source, from room temperature to 950 °C continuously at 20 °C per min. See the 2D contour plots in Figure S2 (Supporting Information). Ni(OH)₂ (S.G.: P‐3m1), NiO (S.G.: Fm‐3m), and LiNiO₂ (S.G.: R‐3m) are also provided in Figure S3 (Supporting Information).

2.2. Automated Data Analysis

We implement the WLCC‐based similarity measure, Equation 1, which offers a global similarity measure that compares the entire XRD pattern, instead of specific peaks and intensities alignment. The WLCC method incorporates the peak shifts and peak width variations that are critical for evaluating calcination data, thus, works better than point‐wise similarity measures such as cosine similarity.^{[ 24 ]} Consider the intensity of an experimental XRD at the temperature t given as a vector X_t and the intensity of the reference XRD for a given phase as a vector Y_i where i  =  1 to n and n is the number of reference‐XRDs used in phase identification. For comparison, we scale both the intensity profiles between 0 and 1. The X _t and Y _i assume continuous functions f_t (x) and g_i (x), where x is the domain of 2θ. The weighted lagged cross‐correlation of phase i at temperature t is given as:

$$S_{fg}=\frac{\int c_{fg}\left(r\right)w\left(r\right)dr}{{(\int c_{ff}\left(r\right)w\left(r\right)dr\int c_{gg}\left(r\right)w\left(r\right)dr)}^{1/2}}$$ (1)

where c _fg (r) represents the lagged cross‐correlation between two continuous functions f_t (x) and g_i (x). Optimizing the c _fg (r) value involves sliding the function g(x) along the 2θ axis and calculating the integral products at each position to find the shift that maximized the peak alignment. Each experimental XRD is assessed against the reference XRD of the known phase resulting in a phase score. A phase score is calculated by subtracting the minimum similarity scores from each of the S_fg values to extract phase evolution information. The normalization process, confined to a range of 0 to 1, involves dividing the similarity scores for individual phases by the maximum similarity score among all phases. This generates a comparative scale where higher values indicate better matches. This allows for rapid extraction of crucial phase evolution information contained in XRD. The more detailed methodological description is provided in the Experimental Section and shows procedures for generating the phase score from the temperature‐resolved in situ synchrotron XRD data in comparison to the XRD patterns of the reference phases. The mathematical framework is provided in Section 1 of the Supporting Information.

Figure 2 illustrates the WLCC similarity approach for automated analysis of the temperature‐resolved in situ XRD data taken during cathode calcination (Figure 1b). The temperature‐resolved in situ XRD patterns are compared to the known XRD patterns of the phases expected to be present in the mixture for the four phases (with reference spectra in Figure 2a). Contextually, matching a reference XRD to a mixture XRD ideally provides information about the phase evolution. The resulting phase score, defined in Equation 2, is plotted as a function of temperature for the XRD data sets, Figure 2b, which is indicative of the phase evolution, to be discussed in detail in Figure 3 . The phase score profiles for XRD data sets capture the critical temperature points observed during the cathode calcination process.

Figure 2.

a) XRD standard spectra of different structures and phases, Ni(OH)₂ with a trigonal structure (space group (S.G.): P‐3m1); LiOH (Tetragonal, P4/nmm); rock salt‐type NiO (S.G.: Fm‐3m); and layered LiNiO₂ (S.G.: R‐3m). b) The phase score profiles retrieved for the in situ XRD data sets (Figure 1b) capture the crucial information of the phase progression as a function of temperature.

Figure 3.

a) Phase score as a function of temperature showing changes for Ni(OH)₂, NiO, and LiNiO₂ phases present in the mixture using WLCC similarity, which is indicative of phase progression. The vertical dashed lines correspond to critical changes associated with phases. b) Weight % of major phases by the traditional diffraction analysis of in situ XRD data. The similarity between the phase score on XRD data and the Weight % profile indicates our approach can rapidly assess XRD with a high degree of accuracy.

2.3. Phase Progression Extracted by Automated Data Analysis

Figure 3a shows the phase score versus temperature relationship representing the progression of the four phases, Ni(OH)₂, lithiated rocksalt Li_xNi_1−xO, layered LiNiO₂, and LiOH. Here, the phase score can be interpreted as the quantity of phase(s) present in experimentally collected XRD spectra. The presence of a wide‐matching temperature range with a higher phase score indicates a particular phase is present over a broad temperature range and that the phase retains its crystal structure and exhibits a strong resemblance to the reference pattern across a wide range of temperatures. It becomes possible to identify the temperature range where phase transitions or structural changes occur within the material by analyzing the temperature at which the maximum and minimum phase scores occur. We also performed a Non‐negative Matrix Factorization (NMF) method for further comparison. Though the phase score calculated using NMF, Figure S4 (Supporting Information), looks promising, it cannot be applied for a real time application, as a complete data set is required to perform NMF analysis.

The Ni(OH)₂ phase shows a high phase score at low temperatures with the maximum match. This is expected as Ni(OH)₂ is the precursor for the calcination of LiNiO₂. While the relatively lower score of LiOH is due to its low scattering power, as indicated by the weak peaks in the XRD patterns (Figure 1b). As the temperature increases, the Ni(OH)₂ phase decomposes to Li‐containing RS‐LNO and the layered LNO. At ≈300 °C, the RS‐LNO phase has the most similarity, indicating a higher concentration of the phase. At ≈530 °C, the layered LNO phase is the dominant phase present and grows up to ≈880 °C and then decreases above it.

The phase score versus temperature relationship is compared to the phase weight % (weight fraction) profile of the major phases calculated using post hoc analysis through refinement of the in situ XRD, as shown in Figure 3b. A strong match between the phase score and weight % profile is observed, indicating that the phase score versus temperature relationship captures all the critical temperatures (300 °C, 530 °C, and 880 °C). Moreover, our method can probe the subtle changes with increasing temperature and at an early stage of phase nucleation and growth, which are missed by traditional XRD analysis approaches. The presence of layered LiNiO₂ phase below 300 °C can be attributed to the overlapped (003) LiNiO₂ peak and Ni(OH)₂ peak, highlighted in Figure S6 (Supporting Information). Further nuanced approach might be necessary to handle critical overlapping peaks. Leveraging WLCC, the ability to rapidly analyze XRD spectra allows it to extract phase information in real time, leading to real time monitoring and control of critical phases. Developing on the current platform opens opportunities for performing on‐the‐fly data analysis on the in situ XRD (Figure 4 ).

Figure 4.

Workflow of the data‐driven approach to extract phase evolution information from in situ XRD patterns in Figure 1b. The XRD data are compared to standard XRD patterns of known phases using WLCC similarity. Normalizing the similarity scores gives the phase score, which provides evolution information as a function of temperature. Our approach allows for the extraction of crucial phase evolution information contained in XRD in real time.

3. Discussion

Traditional refinement methods, such as Rietveld, serve as the workhorse for XRD analysis to identify crystal structure phases. Operationally, the Rietveld refinement technique determines the precise atomic structure of a crystalline material from X‐ray diffraction data. It is widely used to extract information about atomic arrangement in a crystal lattice, including positions, thermal vibrations, and other structural parameters.^{[ 25 ]} The technique is precise and provides quantitative information about a crystal structure. Nevertheless, it relies on high‐quality data – preferably exhibiting a low signal‐to‐noise ratio, which is influenced by the initial crystal structure assumption – which could lead to convergence challenges and is time‐consuming and resource‐intensive.

Compared to Rietveld refinement, our approach tackles a distinct challenge: the fast on‐site assessment of phase change within an experimental XRD signal of complex phase mixtures. Specifically, our method identifies phases present in a mixture by implementing a similarity assessment between the XRD pattern of known phases and the experimental XRD pattern. This approach effectively transforms the issue of identifying phases into quantifying the presence of specific phases within the mixture. By doing so, we refine the scope and narrow down the data domain over which similarity analysis is performed.

The WLCC similarity approach is further applied to another in situ XRD dataset taken during calcination of Ni(OH)₂ at a low rate (10 °C min⁻¹), with the main results on the phase score versus temperature relationship provided in Figure S5a (Supporting Information). The results are comparable both to the weight fraction obtained by refinements of the in situ XRD and to the results from MCR analysis of the in situ XAS data taken from the same heating experiments (Figure S5b,c, Supporting Information).^{[ 25 ]} This, again, indicates the high reliability of our approach to extracting crucial information from in situ data (as discussed above). Those early‐phase nucleation and growth of the rocksalt and layered phases being extracted by MCR from the in situ XAS are also captured in the phase score curves by our WLCC similarity approach, but absent the Weight fraction curve from refinement. This demonstrates the WLCC similarity approach is powerful in gaining insights into early‐stage phase nucleation and growth, complementing traditional post hoc diffraction analysis in gaining a comprehensive understanding of the calcination process.

An integral aspect of our approach is the streamlined workflow requiring a minimum of two XRD spectra to significantly accelerate the data analysis. Moreover, in contrast to ML models developed for XRD phase analysis, our method can operate effectively with a small data set, eliminating the need for larger models and reducing memory costs. However, it is important to note that our approach does not incorporate the identification of unknown phases present in the mixture. Therefore, a critical operational prerequisite for optimal performance of our method is a priori knowledge of the known structures and phases present in the mixture. Our method leverages this information to characterize the XRD data for known phases efficiently and rapidly.

Overall, our methodology bridges a crucial gap between the domains of materials characterization and process control. In the case of calcination of LiNiO₂, tracking the real time phase changes allow recognition of the temperature‐of‐interest for further robust post hoc refinement methods. By focusing on real time analysis, our approach merges the in situ synchrotron X‐ray metrology and refinement methods for qualitative and quantitative analysis of XRD data. Integrating our data‐powered lightweight and rapid analysis platform into the in situ/in‐line metrology would enable a dynamic feedback loop and pave the way for the realization of real time process monitoring and predictive control of calcination processes.

4. Conclusion

In summary, we present the development and implementation of the WLCC approach for automated data analysis of in situ synchrotron XRD patterns. A specific example was given to demonstrate its effectiveness in boosting in situ synchrotron X‐ray metrology for the calcination of the cathode LiNiO₂, to tackle the challenges associated with the complexity and nonequilibrium intermediates during the process. The rapid automated analysis of the XRD data, as it is generated during cathode calcination, provides information for agile on‐site adjustments during experiments and provides critical insights into the early phase nucleation and growth during calcination. This methodology development aims to bridge the gap between the in situ synchrotron X‐ray metrology and post hoc refinement methods by providing an on‐the‐fly XRD data analysis tool. It represents an important advancement in addressing the critical challenges in monitoring and controlling the calcination process, opening new possibilities for industrial applications in manufacturing high‐performance battery cathodes.

5. Experimental Section

In Situ Synchrotron X‐ray Experiments

XRD measurements were performed at 07 BM (QAS) beamline at NSLS–II, the Brookhaven National Laboratory. Pellets of Ni(OH)₂ with and without LiOH precursor were calcined in a Linkam TS1500 oven up to 1200 °C at the ramp rate of 20 °C min⁻¹. Sequential XRD and X‐ray absorption spectra (XAS) were measured and performed with the frequency of one XRD spectra (12 s) and two XAS spectra (1 min). The XAS spectra were used elsewhere for correlating with XRD analysis. XRD measurements were carried out at 20 K eV using a PerkinElmer 1621 area detector. XRD measurements on the CeO₂ sample were used to calibrate the actual temperature scale using its standard lattice expansion.

WLCC Similarity Analysis

The WLCC method was used for similarity analysis to compare the experimental XRD with the reference XRD of known phases (Ni(OH)₂, LiOH. Li_xNi_1−xO, and LiNiO₂). In general, similarity metrics quantify the resemblance or likeness between two or more signals representing spectra, images, audio, or more. The WLCC function is defined in Equation 1 for comparative analysis of XRD spectra. The methodology is part of a larger array of methods available in the materialsIN's product, materialsINspect –a solution‐centric product designed to extract information from limited data. Utilizing similarity analysis, a phase score was developed, which is a normalized WLCC similarity, to extract phase evolution information from the temperature‐resolved in situ XRD.

WLCC had been used to analyze spectral signals, including XRD and the Raman spectroscopy.^{[ 18} , ^{26 ]} WLCC is an effective metric for assessing the resemblance between experimental XRD spectra and reference patterns due to its scale invariance, angular independence, and geometric interpretation. However, the method struggles with accurately separating overlapping peaks and handling varying peaks in the spectra. The WLCC similarity performs a global assessment of pattern resemblance, which is invariant to scale and rotation but does not explicitly consider the individual line positions and relative intensities. A more generalized expression involving the use of normalized integral of a weighted cross‐correlation function has been proposed by de Gelder et al.^{[ 25 ]} Under this framework, two spectra in question X _t and Y _t are expressed as two continuous functions f(x) and g(x), and a lag parameter r is introduced that accounts for potential relative shifts in peak positions. We first define the lagged cross‐correlation between the two as:

$$c_{fg}=\int f\left(x\right)g\left(x+r\right)dx$$ (2)

The normalized lagged cross‐correlation is given as:

$${\stackrel{\sim }{c}}_{fg}\left(r\right)=\frac{c_{fg}\left(r\right)}{{(c_{ff}\left(r\right)c_{gg}\left(r\right))}^{1/2}}$$ (3)

The normalization allows for relative evaluation of the similarity, enabling the identification of phases present in the experimental data and assessing the quality of the match with the reference patterns. Next, a weight function w(r) as a function of the lag parameter is used to assign different weights to different positions of the lag, depending on the function definition. The weighted lagged cross‐correlation function is thus defined as:

$$S_{fg}=\frac{\int c_{fg}\left(r\right)w\left(r\right)dr}{{(\int c_{ff}\left(r\right)w\left(r\right)dr\int c_{gg}\left(r\right)w\left(r\right)dr)}^{1/2}}$$ (4)

The expression for S_fg resembles the cosine similarity expression at r  =  0 by assuming w(r)  =  δ(r). For this experiment, we have chosen a Gaussian weight function defined as $w(r)=1/\sqrt{2\pi {\sigma }^2}exp(-\frac{{(r-\mu )}^2}{2{\sigma }^2})$ that ensures a localized weighting of the cross‐correlation using the hyperparameters μ and σ. The μ and σ hyperparameters accommodate for possible a peak shift and peak width variation for the reference XRDs, essentially accounting for thermal variation in experimentally collected XRDs. This expression is used for S_fg to calculate the phase score. Different phases have different peaks that are naturally shifted relative to each other and vary in width requiring different hyperparameters for each Gaussian noise. Like weight fraction, the weighted lagged cross‐correlation function captures the contribution or intensity of a specific phase Y_i relative to a reference or total signal X_t and thereby quantifies the relative contribution of each phase over temperature. Therefore, assuming the experimental XRD intensity is proportional to the weight fraction of a phase in the mixture, a higher phase score corresponds to a higher weight fraction implying a stronger presence of that phase in the mixture.

The data‐driven product, materialsINspect, enables the extraction of phase progression information from the temperature‐resolved in situ synchrotron XRD patterns in real time, providing valuable insights into the phase evolution and crystallization during calcination. The WLCC method significantly improved the analysis capabilities compared to standard cosine similarity, Figure S7 (Supporting Information), by allowing to modulate the peak shifts and width parameters embedded in the Gaussian weight function. Essentially, the WLCC method enhanced the similarity comparison due to its ability to account for structural changes and crystal growth associated with the thermal variation in XRD patterns.

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

Supporting Information

Dongol R., Mukherjee A., Bai J., et al. “In situ Synchrotron X‐ray Metrology Boosted by Automated Data Analysis for Real‐time Monitoring of Cathode Calcination.” Small Methods 10, no. 2 (2026): 2400181. 10.1002/smtd.202400181

Data Availability Statement

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