cond-mat.mtrl-sciMar 8, 2026

AI-Driven Phase Identification from X-ray Hyperspectral Imaging of cycled Na-ion Cathode Materials

Authors: Fayçal Adrar, Nicolas Folastre, Chloé Pablos, Stefan Stanescu, Sufal Swaraj, Raghvender Raghvender, François Cadiou, Laurence Croguennec, +2 more

Organizations: Laboratoire de Réactivité et de Chimie des Solides (LRCS), CNRS UMR 7314, Université de Picardie Jules Verne, Hub de l’Energie, 15 Rue Baudelocque, Amiens, France · Réseau sur le Stockage Electrochimique de l’Energie (RS2E), CNRS FR 3459, Hub de l’Energie, 15 Rue Baudelocque, Amiens, France · ALISTORE-European Research Institute, CNRS FR 3104, Hub de l’Energie, Rue Baudelocque, Amiens, France · Univ. Bordeaux, CNRS, Bordeaux INP, ICMCB, UMR 5026, F-33600 Pessac, France · Synchrotron SOLEIL, L’Orme des Merisiers, 91190 Saint-Aubin, France · CNRS, INSA Lyon, Université Claude Bernard Lyon 1, MATEIS, UMR 5510, 69621 Villeurbanne, France

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Abstract

Na-ion batteries have emerged as viable candidates for large-scale energy storage applica- tions due to resource abundance and cost advantages. The constraints imposed on their performance and durability, for instance, by complex phase transformations in positive electrode materials during electrochemical cycling, can be addressed and are thus not detrimental to their development. However, diffusion-limited Na-ion transport can drive spatially heterogeneous phase nucleation and propagation, leading to multiphase coexis- tence and locally non-uniform electrochemical activity, generating complex reaction path- ways that challenge both mechanistic understanding and predictive material optimization. These challenges can be addressed by investigating single-crystalline regions of materials, i.e. down to the scale of individual particles, although such analyses are often constrained by energetically and/or spatially sparse hyperspectral datasets. Here, we developed an AI-driven method to process hyperspectral data under sparse sampling conditions and generate multiphase maps with nanometer-scale resolution over a micrometer-scale field of view. We applied this processing on scanning transmission X-ray microscopy (STXM) data to determine the distribution and coexistence of phases in individual particles of NaxV2(PO4)2F3 cathode materials, at different states of charge. The methodology relies on a workflow which combines a Gaussian mixture variational autoencoder (GMVAE) algorithm with the Pearson corre- lation coefficient to identify the sodium content and map their spatial distribution. Our approach reveals nanoscale phase heterogeneity and evolution within individual particles, and improves the reliability of phase detection by identifying ambiguity zones, false assign- ments, and transition phases localized at grain boundaries.

Figures & tables

Figure 1: Scanning transmission X-ray microscopy (STXM) experimental setup. (a) Schematic of the STXM setup (not to scale). (b) Illustration of a stack of images acquired with low spatial resolution (low-sampling version of the image shown in panel d). (c) Optical density (OD) spectrum of a NVPF particle acquired with high energy resolution; the dashed line indicates the energies selected for high spatial resolution acquisitions. (d) High spatial resolution image of a NVPF particle (same as in (b)). (e) Illustration of the optical density (OD) spectrum from a low spectral resolution acquisition, where the bars represent the energy levels and their heights correspond to the optical density values.
Figure 2: Reference XANES spectra of NVPF for different levels of Na + extraction. Optical density (OD) of V-L 2,3 and O-K edge X-ray absorption spectra acquired in STXM measurements on individual NVPF particles at different states of charge.
Figure 3: STXM phase mapping workflow. (a) Pearson correlation phase mapping: the Pearson correlation is computed between each spectrum vector ss and each reference vector rnr_{n} ( nn =1,2,3,4,5). The resulting correlation map, ρn\rho_{n} ( nn =1,2,3,4,5), represents the correlation between ss and rnr_{n} across all pixels. The initial phase map is obtained by comparing the correlation values pixel by pixel and assigning each pixel to the reference with the highest correlation. (b) Ambiguity map: pixels where arg⁡max⁡(ρn(i,j)−ρm(i,j))≤0.005\arg\max(\rho_{n}(i,j)-\rho_{m}(i,j))\leq 0.005 , with n≠mn\neq m , are shown in grey and labeled as ambiguous pixels vav_{a} . The ambiguity is resolved by projecting vav_{a} into the latent space of the trained Gaussian mixture variational autoencoder (GMVAE) containing the overall phase distributions, measuring the Mahalanobis distances, and assigning the pixel to the phase corresponding to the nearest phase distribution.
Figure 4: Phase mapping of a Na 2 V 2 (PO 4 ) 2 F sample. (a) Phase map obtained using PCC (b) Map of ambiguous regions, where the correlation coefficient between two phases is close ( ≤0.005\leq 0.005 ), shown in grey. (c) Final phase map with ambiguities resolved using a GMVAE by projecting ambiguous spectra into the latent space and assigning them to the closest phase distribution. The scale bars correspond to 0.2 μ0.2\,\mu m (d) Phase distributions in the GMVAE latent space corresponding to the global latent representation without the projection of ambiguous pixels. (e) Projection of ambiguous pixels (in gray). (f) Latent space after resolution of ambiguous pixels.
Figure 5: Phase maps of four NVPF samples at different states of charge. Phase maps of Na 3 VPF, Na 2 VPF, Na 1 VPF, and Na 1-y VPF, respectively, after ambiguity resolution. Each image corresponds to a sample halted at the state of charge indicated on the electrochemical curve of NVPF.
Figure 6: Phase maps for six particles at the Na 2.0 VPF state of charge. The scale bar corresponds to 0.2 μm\mu\text{m} .
Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Figure S1: On the right, the NVPF electrochemical curves corresponding to each state of charge investigated in this study. On the left, the associated X-ray diffraction (XRD) patterns collected at the same states of charge, highlighting the structural evolution during (de)sodiation.
Figure S2: Le Bail refinements of (a) Na 3 V 2 (PO 4 ) 2 F 3 in the orthorhombic Amam space group, (b) Na 2 V 2 (PO 4 ) 2 F 3 in the tetragonal I4/mmm space group, (c) Na 1 V 2 (PO 4 ) 2 F 3 in the orthorhombic Cmc2 1 space group. (d) Na 2.4{}_{2}.4 V 2 (PO 4 ) 2 F 3 a mixture of phases belonging to the orthorhombic Amam space group and the tetragonal I4/mmm space group, and (e) Na 1−y{}_{1}-y V 2 (PO 4 ) 2 F 3 in the orthorhombic Cmc2 1 space group
Figure S3: a) Reliability maps. b) Combined reliability map with the phase map. c–g) Correlation maps obtained for Na 2.0 VPF. The scale bars correspond to 0.2 μm0.2\,\mu m
Figure S4: Trigonal diagram showing the correlation between the reference vectors using Pearson correlation coefficient.
Figure S5: Gaussian Mixture Variational AutoEncoder (GMVAE) architecture.
Figure S6: Latent space distribution of ten NVPF particles at different states of charge. a) Latent space labeled according to the phase distribution, obtained from Pearson correlation comparison with the reference spectra. b) The projection of the Na 1 VPF particle in figure 4.
Figure S7: (a–d) Reliability maps corresponding to each sample represented in Figure 5, where pixel brightness encodes the confidence in the phase assignment.
Figure S8: Correlation maps of the individual sodium phases associated with the particles presented in Figure 5, from Na 1-y VPF on the left to Na 3 VPF on the right (as indicated above). The expected composition is shown to the left of the corresponding particle.
Figure S9: The reconstructed X-ray absorption spectra obtained using the decoder only architecture from the projected points in the latent space, spanning the Na 3 VPF phase to the Na 1-y VPF phase.
Figure S10: Latent space dimension analysis: (a) K-means clustering of spectra, with each color representing a different cluster. (b) Latent space representation labeled by Pearson correlation, including ambiguous points. (c) Mean intensity of the original spectra along a trajectory following the −z2-z_{2} direction in the latent space. Original and reconstructed spectra for each identified phase: (d) Na 3.0 VPF region, (e) Na 2.0 VPF region, (f) Na 1.0 VPF region, (g) Na 1-y VPF region.
Figure S11: Evolution of the mean squared error and Kullback–Leibler losses for the VAE across the training and validation as a function of the epoch, shown on a logarithmic scale.
 Cm[i]=∑n=1N(rm[n]−rˉm)(X[i,n]−Xˉi)∑n=1N(rm[n]−rˉm)2∑n=1N(X[i,n]−Xˉi)2C_{m}[i]=\frac{\sum_{n=1}^{N}(r_{m}[n]-\bar{r}_{m})(X[i,n]-\bar{X}_{i})}{\sqrt{\sum_{n=1}^{N}(r_{m}[n]-\bar{r}_{m})^{2}}\sqrt{\sum_{n=1}^{N}(X[i,n]-\bar{X}_{i})^{2}}} 
Appendix
Algorithm 1 Phase Mapping using Pearson Correlation with Ambiguity Tracking
 LB=1B∑i∈XB∥xi−x^i∥22⏟reconstruction+βDKL(qϕ(zi∣xi) ∥ ∑k=1KπkN(zi∣μk,Σk))⏟GM prior KL\mathcal{L}_{B}=\frac{1}{B}\sum_{i\in X_{B}}\underbrace{\|x_{i}-\hat{x}_{i}\|_{2}^{2}}_{\text{reconstruction}}+\beta\underbrace{D_{\mathrm{KL}}\Big(q_{\phi}(z_{i}|x_{i})\,\|\,\sum_{k=1}^{K}\pi_{k}\mathcal{N}(z_{i}|\mu_{k},\Sigma_{k})\Big)}_{\text{GM prior KL}} 
Appendix
Algorithm 2 Training GMVAE on XANES vectors using ADAM

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