Statistical White-Line Analysis in High-Throughput TXM-XANES for Chemical State Quantification

Abstract

The transmission X-ray microscopy (TXM) based X-ray absorption near-edge structure (XANES) technique provides three-dimensional mapping of element-specific chemical states at nanometer-scale spatial resolution and micrometer-scale fields of view. However, compared to conventional volume-averaged XANES (VA-XANES) measurements, the inherently small voxel size in TXM-XANES leads to a lower signal-to-noise ratio, making full-spectrum analysis computationally demanding and less robust. Here, we present the structural and compositional conditions for a statistical white-line analysis framework under which chemical state information can be directly extracted from the white-line peak position in voxel spectra without the need for voxel-wise background subtraction or normalization, under well-defined structural and compositional conditions. The method is validated on layered oxide cathode materials, where low-order polynomial fitting accurately reproduces white-line features, and the extracted energy distributions correlate strongly with VA-XANES results. This statistical approach enables high-throughput, dose-efficient, and noise-robust chemical state quantification in TXM-XANES, offering broad applicability to functional materials requiring nanoscale oxidation-state mapping.

1. Introduction

X-ray absorption near-edge structure (XANES) refers to the fine structure in the X-ray absorption spectrum of an element. The XANES signal depends on the electronic structure, local atomic configuration, and oxidation state of the absorbing atom. By comparing spectral features to theoretical models or reference compounds, XANES provides both qualitative and quantitative insight into the chemistry of functional materials and thus broad applications in diverse fields, including chemistry, biology, physics, material sciences, etc.

Transmission X-ray microscope (TXM) is a full-field X-ray microscope that measures a sample volume of tens of micrometers at tens of nanometer spatial resolution. By acquiring tomographic datasets at multiple X-ray energies (typically 5–11 keV) and aligning the reconstructed images, position-resolved XANES spectra can be obtained for every voxela method referred to as transmission X-ray microscopy-based XANES (TXM-XANES). − This technique extends conventional XANES capabilities into the spatial domain, enabling three-dimensional full-field, nanometer-resolution mapping of chemical states across micrometer-scale sample volumes. Compared to scanning probe-based imaging techniques, TXM has a faster acquisition rate per unit sample volume, thus enabling rapid measurement of a large number of sample sets within a relatively short time.

TXM-XANES holds broad potential across a wide range of functional materials, enabling nanoscale correlation of morphology, defect structure, and local chemical states in three dimensions. , Battery electrode materials are a prime example where electrochemical performance is determined not only by the average composition but also by microstructural and chemical heterogeneity. In synthesis optimization, TXM-XANES can reveal how precursor chemistry and thermal treatments shape particle architecture and defect populations. During long-term cycling, it can directly visualize the emergence of surface reconstruction, crack propagation, phase segregation, and non-uniform redox activityall of which critically influence capacity retention and safety. , Such correlative imaging of structure–chemistry relationships offers unique opportunities to accelerate the design, discovery, and deployment of advanced energy-storage materials and related technologies.

The linear combination fitting (LCF) method is a common option in the conventional volume-averaged XANES (VA-XANES). LCF has been implemented in a few TXM-XANES analysis packages − and utilized in a few works. − However, TXM-XANES is inherently a transmission-based measurement, and in three-dimensional datasets each spectrum originates from an individual voxel with a volume of only tens of nanometers on a side. Consequently, the signal-to-noise ratio (SNR) is generally lower than that in VA-XANES, where the probed sample volume is much larger. Various denoise pre-processing methods have been developed to improve SNR in TXM-XANES analysis. −

The white-line peak is the strong absorption peak located just above the absorption edge of the absorbing atom. In 3d transition metals K-edge spectra, the position, shape, and intensity of the white-line peak are influenced by a multiple factors, such as unoccupied 4p density of states, the local geometric structure, the oxidation state, and the covalency between the absorbing atom and the ligands. , The quantitative features of the white-line peak in a spectrum, e.g., peak position, peak shape, peak intensity, are used as descriptors or fingerprints for describing the spectrum. , The white-line peak position alone is not usually used to indicate the atom’s oxidation state because the peak is also influenced by other factors. Nonetheless, the white-line peak of an absorbing atom is well-defined if the atom is in the octahedral site in its local structure. The white-line peak position can also show a positive correlation to the oxidation state of the atom due to the core-hole effects. Provided that the correlation relation between the white-line peak position and the actual oxidation states is known, the white-line peak position can represent the oxidation state of the atom unambiguously. ,,

In this work, we develop a statistical white-line analysis framework for TXM-XANES. We establish the theoretical conditions under which white-line peak positions can be aggregated into histograms to quantify both the mean oxidation state and its spatial heterogeneity without voxel-wise background subtraction or normalization. Using layered oxide cathode materials as a model, we demonstrate that low-order polynomial fitting yields accurate white-line energies and that the resulting distributions strongly correlate with VA-XANES benchmarks. By combining nanoscale chemical-state mapping with morphological and defect analysis, this approach provides a unified pathway for probing the coupled structural and chemical evolution of energy materials, thereby supporting the development of next-generation batteries with higher performance, longer lifetime, and improved safety.

2. XANES White-Line Analysis: Theoretical Considerations

Assuming that the incident X-ray beam has uniform flux I ₀, the general transmission of X-ray through a sample, which has its range along z within [0,τ(x,y)] and its projection along z being confined in an area A, can be expressed as

$$C(E)=I_0(E)·\mathrm{\Delta }T(E)·{\iint }_A{e}^{-{\int }_0^{\tau (x,y)}\mu (x,y,z;E)\mathrm{d}z}\mathrm{d}x\mathrm{d}y$$ 1

where I ₀ is incident X-ray beam flux, ΔT is detector counting time, and τ(x,y) is the sample thickness at position (x,y).

In VA-XANES measurements, it is assumed

• C1 : the sample has uniform thickness over the entire area. Thus, τ(x,y) is a constant τ ₀;

• C2 : the sample has stochastically homogeneous over τ ₀ at all (x,y) positions,

It should be mentioned that it does not require that the sample is homogeneous along the z direction. Imagine that the sample is divided into N sections. The integral in the exponential power part in eq can be written as

$$\stackrel{\circledR }{a(x,y;E)}={\int }_0^{{\tau }_0}\mu (x,y,z;E)\mathrm{d}z=\sum _{i=0}^N{\int }_{i·{\tau }_0/N}^{(i+1)·{\tau }_0/N}\mu (x,y,z;E)\mathrm{d}z=\sum _{i=0}^N\stackrel{\circledR }{{\mu }_i(x,y;E)}·\frac{{\tau }_0}{N}=\sum _{i=0}^N\stackrel{\circledR }{a_i(x,y;E)}=\stackrel{\circledR }{\mu (x,y;E)}·{\tau }_0=\stackrel{\circledR }{\mu (E)}·{\tau }_0$$ 2

μ(x,y,z; E) is not necessarily a constant with respect to its position (x, y, z). For instance, preparing solid samples to make pellets is the most common method in XAS sample preparation. The sample and binder powders are mixed and pressed together to make pellets. Obviously, the integrated μ(x, y, z; E) over a thickness smaller than the typical powder particle size will not result in a constant $\stackrel{\circledR }{a_i(x,y;E)}$ everywhere. As a result, the measured attenuation $\stackrel{\circledR }{a(x,y;E)}$ is an average of the contributions from all positions in the sample along the z direction. The grinding and mixing requirements in making pellet sample ensure the samples satisfy condition C2 , which ensures the attenuation coefficient in eq to be position independent.

Substituting eq into eq leads

$$C(E)=I_0(E)·\mathrm{\Delta }T(E)·A·e^{-\stackrel{\circledR }{a(E)}}$$ 3

To obtain $\stackrel{\circledR }{a(E)}$ from C(E), it needs to normalize C(E) with the incident beam I ₀ (E)·ΔT(E)·A

$$c(E)=e^{-\stackrel{\circledR }{a(E)}}$$ 4

$$\stackrel{\circledR }{a(E)}=-\ln c(E)$$ 5

In the standard XANES analysis, it also requires pre-edge background subtraction and post-edge baseline normalization

$$\chi (E)=\frac{\stackrel{\circledR }{a(E)}-\stackrel{\circledR }{a_{\mathrm{b}}(E)}}{\stackrel{\circledR }{a_{\mathrm{p}}(E_{\mathrm{e}})}-\stackrel{\circledR }{a_{\mathrm{b}}(E_{\mathrm{e}})}}$$ 6

where $\stackrel{\circledR }{a_{\mathrm{b}}(E)}$ and $\stackrel{\circledR }{a_{\mathrm{p}}(E)}$ are the fitted pre-edge background and post-edge baseline curves, and E _e is the attenuation at the XANES edge energy. Background subtraction isolates the signal of interest from underlying, unrelated absorption processes, and normalization removes extraneous variations in signal magnitude due to experimental conditions or sample properties like thickness. The normalized spectrum χ(E) can be further analyzed quantitatively to obtain the sample chemical state information.

In XANES measurements based on either position scanning probe or full-field imaging approaches, non-conventional experimental protocols and data analysis methods need to be utilized due to, e.g., X-ray beam radiation effects on samples, a slow data acquisition rate, fast dynamic change in samples, relatively poor data quality, etc. For instance, Lim et al. chose only four energy points: two of them are close to the peak maximum of the Fe²⁺ L-edge spectrum, and other two are close to the peak maximum of the Fe³⁺ L-edge spectrum, in the operando experiments that measured Fe-ion oxidation state evolution during the LiFePO₄ delithiation process. In such a case, the characteristic features at a few energy points in a spectrum can be used to represent a specific chemical state if there is sufficient prior information on the sample system available.

Three-dimension (3D) TXM-XANES based on full-field transmission X-ray microscope can achieve tens of nanometers spatial resolution in a volume of interest of tens of micrometers scale. , A 3D tomographic volume of a sample is obtained at each X-ray energy. The value at each voxel in the 3D volume is the sample’s attenuation by the voxel. Stacking the 3D volumes at different X-ray energies forms a 4D dataset that is composed of a 2D absorption spectrum at each voxel. Thus, 3D TXM-XANES provides position dependent chemical state information on the sample. As a full-field technique, it can measure billions of spectra at nanometer spatial resolution in a short time. It can be used to screen large amounts of samples and provide quantitative or qualitative information for further characterizations and analyses. On the other hand, TXM is a bright-field microscope technique. The 3D TXM-XANES signal is from very small volumes (voxels). The signal from each voxel is superimposed on the signals from many other voxels. Thus, the detection sensitivity is relatively low, and the noise level is relatively high, compared to the VA-XANES. Directly adapting data analysis methods developed for the conventional VA-XANES into TXM-XANES voxel-based data analysis usually suffers from poorer signal quality.

The white-line peak corresponds to the largest attenuation position in an XANES spectrum around which the sample attenuation usually changes significantly, so the white-line peak position could be used as a characteristic feature in a spectrum. It is possible to obtain the chemical state of a sample by the white-line peak position in its spectrum provided the following conditions are satisfied

• C3 : the white-line peak is well-defined;

• C4 : the white-line peak position has monotonic correlation with the sample chemical state;

• C5 : the sample’s chemical composition is stochastically almost homogeneous, and the sample density is almost a constant.

The conditions C3 and C4 ensure the white-line position can be used as an indicator to the sample’s chemical state. The condition C5 is necessary for averaging raw XANES spectra at different sample positions without the need for the background subtraction and spectrum normalization pre-processing steps defined in eq . For a sample satisfying condition C5 , the contribution of the weak and smooth varying unrelated absorption processes is small and similar at all sample positions. Thus, the change of the sample attenuation to the incident X-ray is dominated by the interested element. Integrating spectra at all sample positions will enhance the concerned attenuation process relative to the weak and smooth irrelevant absorption background. Indeed, the integration process is similar to that in eq except that the integration is over voxels in 3D space in the current case than the thickness in eq

$$\stackrel{\circledR }{a(E)}={\int }_{V}a(x,y,z;E)\mathrm{d}x\mathrm{d}y\mathrm{d}z=\sum _{j=0}^M{a}_j(E)$$ 7

Because of condition C4 , the histogram $\mathcal{H}(E)$ of the white-line energy distribution can be treated as the probability distribution of the sample’s chemical state. Thus, the mean chemical state can be calculated with

$$\mathrm{S̅}={\int }_{E_{\mathrm{s}}}^{E_{\mathrm{e}}}\mathcal{H}(E_{wl})·S(E_{wl})\mathrm{d}{E}_{wl}$$ 8

here S(E _wl ) is a chemical state function with respect to the white-line energy. The form of S(E _wl) depends on the specific XANES analysis method used in volumetric XANES analysis to derive the chemical state information. For instance, the chemical state function can be defined as the charge transfer if LCF method is used.

It needs to be noted that S(E _wl ) must be an addition-meaningful character. Although white-line peak position is used as an indicator of chemical state, it is not addition meaningful in general. To see this, rewrite eq as

$$\stackrel{\circledR }{a(E)}=N{\int }_{E_{\mathrm{s}}}^{E_{\mathrm{e}}}\mathcal{H}(E_{\mathrm{w}\mathrm{l}})·a(E,E_{\mathrm{w}\mathrm{l}})\mathrm{d}{E}_{wl}$$ 9

where N is the total number of voxels. The space integral in eq is replaced by a population integral based on $\mathcal{H}(E)$ in eq . The resultant spectrum function $\stackrel{\circledR }{a(E)}$ is not necessarily a single-peaked function even a(E,E _wl) functions are single-peaked functions at all E _wl. For instance, $\stackrel{\circledR }{a(E)}$ may show two peaks if there are two species that have distinct white-line peaks well apart away. However, it can be proved that $\stackrel{\circledR }{a(E)}$ is a single-peak function provided following conditions are satisfied,

• C6 . Parabolic Approximation of a(E,E _wl ) near E ≈ E _wl: a(E,E _wl) is approximately parabolic with respect to E in the vicinity of E ≈ E _wl where $\mathcal{H}(E)$ is significant;

• C7 . Approximately Constant Curvature: ${\frac{{\partial }^{2}a(E,E_{\mathrm{w}\mathrm{l}})}{\partial E^2}|}_{E=E_{\mathrm{w}\mathrm{l}}}<0$ is approximately constant for all E _wl where $\mathcal{H}(E)$ is significant.

Then, the peak position of $\stackrel{\circledR }{a(E)}$ can be approximated as

$$\max (\stackrel{\circledR }{a(E)})={\int }_{E_{\mathrm{s}}}^{E_{\mathrm{e}}}\mathcal{H}(E_{\mathrm{w}\mathrm{l}})·E_{\mathrm{w}\mathrm{l}}\mathrm{d}{E}_{\mathrm{w}\mathrm{l}}$$ 10

Accordingly, the deviation of the white-line peak position distribution can be calculated as

$${\sigma }_{\mathrm{w}\mathrm{l}}^2={\int }_{E_{\mathrm{s}}}^{E_{\mathrm{e}}}\mathcal{H}(E_{\mathrm{w}\mathrm{l}})·{(E_{\mathrm{w}\mathrm{l}}-\mathrm{S̅})}^2\mathrm{d}{E}_{wl}$$ 11

Conditions C6 and C7 simply assume the white-line peaks of different chemical states concentrate in a narrow white-line energy range and have a parabolic form of almost the same shape. Under conditions C6 and C7 , the average white-line peak position can then be used to represent the average chemical state of a sample.

In the case that conditions C6 and C7 are not satisfied, the white-line peak position will not be sufficient to represent the chemical state of a sample. Thus, full XANES measurements and analysis must be considered. In such a case, the sample needs to be stable both physically and chemically during a longer scan time at more energy points for full XANES spectra acquisition.

3. XANES White-Line Analysis: Experimental Examples

The white line of an absorbing atom tends to have a well-defined sharp peak due to the strong continuum resonance focusing effect if the absorbing atom is at a centrosymmetrical site, e.g., octahedral site. ,, The peak energy is roughly following the 1/R ² rule; R is the bonding distance between the absorbing atom and ligand atoms. Higher oxidation states often come with a smaller bonding distance R, due to increased Coulombic attraction. Thus, the white-line peak energy and the higher oxidation of an absorbing atom usually have a positive correlation.

Many transition metal (TM) oxides have octahedral symmetry. These include the popular cathode materials in sodium- or lithium-ion batteries, e.g., lithium nickel manganese cobalt oxide (NMC) and lithium cobalt oxide (LCO). The k-edge XANES spectra of the transition metals have well-defined sharp white-line peaks. The white-line peak position could be used as a fingerprint of the corresponding TM oxidation state. Furthermore, the TM k-edge spectra in these battery cathode materials also satisfy conditions C6 and C7 . Figure presents a set of example spectra of Ni, Co, and Mn k-edges of NMC82 (LiNi_0.82Co_0.11Mn_0.07O₂) material. The white-line peaks of these spectra are fitted with 2nd, 3rd, and 4th order polynomial curves. Table provides the quantitative metrics, root mean square error (RMSE), R ², and adjusted R ², of the fitting results. A fitting result with a smaller RMSE and R ² and adjusted R ² closer to 1 generally matches the input data better. It can be seen that the parabolic fitting curves can satisfactorily represent the white lines in the measured spectra. Thus, the histogram of white-line peak positions over the measured volume in TXM-XANES can provide the mean oxidation state in the measured volume and the deviation distribution from the mean state.

1.

Polynomial fitting to the white-line peaks of Ni, Co, and Mn k-edge spectra in NCM82 charged to 4.4 V. The results show that parabolic (second-order polynomial) curves can closely approximate the white-line peaks.

1. Merit Metrics of the Fitting Results.

	Order 2			Order 3			Order 4
	Ni	Co	Mn	Ni	Co	Mn	Ni	Co	Mn
RMSE	1.82 × 10–2	3.91 × 10–4	9.22 × 10–4	7.23 × 10–4	2.72 × 10–4	6.35 × 10–4	6.45 × 10–4	2.28 × 10–4	6.15 × 10–4
R 2	9.98 × 10–1	9.99 × 10–1	9.87 × 10–1	1.00 × 100	1.00 × 100	9.94 × 10–1	1.00 × 100	1.00 × 100	9.94 × 10–1
Adjusted R 2	9.98 × 10–1	9.98 × 10–1	9.82 × 10–1	1.00 × 100	1.00 × 100	9.90 × 10–1	1.00 × 100	9.99 × 10–1	9.89 × 10–1

Figure presents the results of an experimental case. The sample is a single-crystal lithium-nickel-manganese layered oxide (LiNi_0.9Mn_0.1O₂), which is referenced to SNM in this article. Coin-type half-cells (CR2032) were assembled with SNM as the cathode material, lithium foil (200 μm) as the negative electrode, Celgard 2325 as the separator, and 40 μL of 1.2M LiPF₆ dissolved in a 3:7 (v/v) mixture of ethylene carbonate (EC) and ethyl methyl carbonate (EMC) as the electrolyte. The in situ SNM VA-XANES measurements were taken during the first charging cycle with a cut-off potential of 4.4 V. The ex situ TXM-XANES measurements for SNM were harvested from the cycled cells that were stopped at 3.8, 4.2, and 4.4 V during the first charging cycle. All postcycling handling was performed in an argon-filled glovebox. The harvested electrodes were quickly rinsed with dimethoxyethane (DME) to eliminate the residual electrolyte and subsequently dried under a vacuum for 15 min. Active material was then carefully scraped from the electrode surface and transferred onto Kapton tape. The prepared samples were sealed in vacuum bags and mounted on holders for subsequent TXM-XANES measurements.

2.

White-line peak position analysis on VA-XANES and TXM-XANES of the SNM. (a–c) White-line peak position slice images retrieved from TXM-XANES at 3.8 4.2, and 4.4 V, respectively; (d) spectra from a single voxel and a super voxel by a binning factor 5 × 5 × 5 from a TXM-XANES dataset at 4.2 V; (e) spectra for 3.8 4.2, and 4.4 V, obtained by summing up all voxels in the corresponding TXM-XANES datasets; (f) 2nd order polynomial fits to the spectra in (e); (g) histograms of white-line peak position distributions calculated from TXM-XANES results; (h) VA-XANES spectra at Ni k-edge; (i) comparison between white-line peak positions in VA-XANES spectra and mean white-line peak positions calculated from TXM-XANES.

Figure (a–c) shows representative 2D slice images from 3D white-line peak position maps of SNM that are retrieved from ex situ TXM-XANES measurements at charging voltages 3.8, 4.2, and 4.4 V, respectively. Figure (d) shows a spectrum at a representative voxel and a supervoxel that is obtained by binning 5 × 5 × 5 around the representative voxel in the TXM-XANES dataset at 4.2 V. The spectrum at the single voxel is noisy, and averaging the spectra in a larger region can greatly reduce the noises. Figure (e) displays the spectra for 3.8, 4.2, and 4.4 V, obtained by summing up all voxels in the corresponding TXM-XANES datasets; Figure (f) shows 2nd order polynomial fits to the spectra in (e). The white-line peak energies determined from the fitted curves are 8353.19, 8353.99, and 8354.46 eV at 3.8, 4.2, and 4.4 V, respectively. Figure (g) displays the histograms of white-line peak position distributions in these 3D peak position maps. The centroids and standard deviations calculated with eqs and are (8353.10 eV, 0.14 eV), (8353.94 eV, 0.36 eV), and (8354.31 eV, 0.79 eV) at 3.8, 4.2, and 4.4 V, respectively. The white-line energies determined directly from volume-averaged spectra in Figure (f) are very close to those determined from the histogram in Figure (g). This confirms eq . Both the centroid and standard deviation of the white-line position distribution increase with charging voltage, which indicate increased heterogeneity at higher charging voltages. Figure (h) shows the normalized in situ VA-XANES spectra of SNM in the vicinity of the Ni k-edge. The edge energies for 3.8, 4.2, and 4.4 V are 8349.0, 8351.4, and 8352.0 eV, respectively. The corresponding white-line peak position are 8352.2, 8353.6, and 8354.0 eV, respectively. Although the relative white-line peak position shifts between different charging voltages are not exactly equal to the relative edge energy shifts, these two sets of positions have positive correlation. Figure (i) displays the calculated white-line position centroids at different charging voltages. As a comparison, the white-line peak positions measured from VA-XANES spectra in Figure (h) are also displayed. The offset between two sets of white-line positions is due to lack of absolute energy alignment between the spectra obtained from two different beamlines. As suggested in others’ works, ex situ XANES of cathodes at higher charging states might be lower than that measured at same nominal charging states but under in situ measurement conditions. , The discrepancy is due to factors, e.g., reductions of the highly oxidized transition metals after removal of an external electrical field or exposure to oxygen and moisture during sample preparation in ex situ measurements. Nonetheless, the ex situ and in situ XANES results at lower charged states tend to match more closely to each other. Thus, Figure (i) also displays the white-line centroid positions from ex situ TXM-XANES that are offset to have the white-line centroid at 3.8 V coincide with that measured from the in situ VA-XANES spectrum. Both the offset centroids at 4.2 and 4.4 V are lower than that measured from in situ VA-XANES, which suggests relaxation of the Ni oxidation state in the ex situ TXM-XANES samples.

4. Conclusions

TXM-XANES is complementary to conventional VA-XANES. With VA-XANES results as prior information, TXM-XANES data analysis can be largely simplified to identify fingerprint features rather than full XANES analysis. Specifically, white-line peak position is a good descriptor of measured atom’s oxidation states in terms of its robustness to the signal noise if the white line peaks of the atom’s spectra are well-defined and have a definitive correlation to the oxidation states. Many materials that have centrosymmetrical coordination around the measured atoms, e.g., the layered cathode materials in lithium or sodium ion batteries, satisfy these conditions. More descriptors should be considered for materials that do not satisfy these conditions. For a general case in which there are mixed phases, more advanced methods should be considered. A few exploratory works have been done. , Nevertheless, it will impose certain data quality for reliable analysis then.

#.

J.W., W.Z., and W.H. contributed equally.

The authors declare no competing financial interest.