Machine Learning to Predict Spectral Anisotropy in Valence-to-Core X-ray Emission Spectroscopy

TL;DR

The study introduces a quantitative framework to predict spectral anisotropy in Valence-to-Core X-ray Emission Spectroscopy by defining a continuous metric, SAMS, derived from polarization-resolved spectra. A random forest regressor is trained on a large Materials Project dataset, using geometry and chemical descriptors (notably QAMS, DAMS, and IAMS) extracted from crystal structures and a Corvus/FEFF pipeline to generate targets. The model achieves strong predictive power on held-out data ($R^2 \approx 0.81$, MAE \approx 0.028$) and offers interpretable insights via permutation feature importance, showing the anisotropy descriptors dominate predictions. Per-element analysis reveals robust performance for many 3d metals but notable underperformance for Sc, highlighting intrinsic chemical differences and the need for balanced, diverse training data. The approach paves the way for rapid, AI-assisted screening of materials with tailored local anisotropy and can be extended to other spectroscopies like XAS using transfer learning.

Abstract

Polarization analysis in x-ray spectroscopy provides an orientation dependent sensitivity to local bonding environments. For a cluster of atoms, polarization sensitivity is most often discussed through the lens of point group symmetries. However, this is a discrete, qualitative method of classifying clusters, and it does little to indicate the degree of spectral anisotropy. Here we adopt a random forest model for quantitative prediction of spectral anisotropy. Its input relies on simplified local geometric and chemical information that can be obtained from any crystal structure file. The model is trained on over 10,000 experimentally realized transition metal structures from the Materials Project, with the target being VtC-XES calculated using the real space Green's function code FEFF. We find that the model can strongly predict the degree of spectral anisotropy, with the primary factors being derived from the spatial moments of ligands in a cluster.

Figures (11)

• Figure 1: (a, c) Stretched NiO cluster, with the Ni (silver) to O (red) bond along the z-axis stretched 5% and 50% respectively. (b, d) The Ni VtC-XES polarized along the xy bonds in green and z bond in orange for the clusters in (a) and (c) respectively.
• Figure 2: (a) Crystal structure of LiCrCO$_3$F$_2$, where Cr is bonded to five O atoms and one F atom in a distorted O$_h$ cluster. (b) Polarized VtC Cr XES along the $x$ (blue), $y$ (green), and $z$ (red) axes, with differences between each pair shown below. (c) Spectral Anisotropy Matrix (SAM), where diagonal values are zero and off-diagonal values are the Euclidean norm of the differences ($|x-y|$, $|x-z|$, $|y-z|$).
• Figure 3: QAMS versus SAMS parameters for distorted crystal structures, NiO (a, b) and Cr$_2$O$_3$ (c, d). NiO exhibits a linear relationship between the two parameters in response to stretching, but Cr$_2$O$_3$ has a nonlinear response the in the region of small distortions around the base experimental structure.
• Figure 4: Correlation matrix of the features. Each cell shows the Pearson correlation coefficient between pairs of features, with values ranging from $-1$ (perfect anticorrelation, blue) to $+1$ (perfect correlation, red).
• Figure 5: Overview diagram of the Corvus workflow used to construct the dataset. Materials were obtained from the Materials Project and restricted to compounds containing at least one 3$d$ transition-metal ion that are flagged as experimentally observed.