Tracking the Lithiation State of Li$_x$Si from Machine-Learned XPS Binding Energies

TL;DR

A computational framework that combines machine-learning prediction of core-level binding energies to large-scale atomistic simulations -- Grand Canonical Monte Carlo complemented with molecular dynamics (MD), driven by a ML potential -- for a systematic sampling of lithiation states and local atomic environments is introduced.

Abstract

X-ray Photoelectron Spectroscopy (XPS) is a powerful technique to probe chemical states and interfacial processes in battery materials, but a quantitative interpretation is often hindered by the complex, heterogeneous microstructures that form during operation and dominate electrochemical cycling. Silicon based anodes represent a paradigmatic example in Li batteries, as (de)lithiation proceeds through the formation of strongly disordered Li$_x$Si phases and crystal-amorphous transformations that are hard to characterize. Here, we introduce a computational framework that combines machine-learning (ML) prediction of core-level binding energies to large-scale atomistic simulations -- Grand Canonical Monte Carlo (GCMC) complemented with molecular dynamics (MD), driven by a ML potential -- for a systematic sampling of lithiation states and local atomic environments. This approach yields stoichiometry maps that match the characteristic experimental trends observed in operando and ex situ XPS measurements, including the distinctive Si $2p$ spectroscopic signatures associated with the crystal-to-amorphous disordering driving early delithiation.

Figures (7)

• Figure 1: Schematic of the machine-learning workflow for BE prediction, including data generation, training, and validation steps.
• Figure 2: (Left) Performance of the Gaussian KRR models corresponding to the Li $1s$ (a) and Si $2p$ (c) for the Li$_x$Si train and validation sets. The determination coefficient $R^2$ for the relation between ML predictions and ab initio DFT (target) is reported in the legend. The histogram for the difference between BEs obtained with ML and ab initio DFT is shown as an inset. (Right) Model benchmarking against DFT XPS obtained for an out-of-sample Li$_x$Si structure from Ref.chen2021, the red histograms account for the DFT BEs of Li $1s$ (b) and Si $2p$ (d). The colored areas (curves in darkcyan) represent the XPS spectra obtained by adding Voigt profiles centered on the DFT (ML predicted) BEs.
• Figure 3: Uncertainty estimates for the BE (a,c) and BE$_\text{max}$ (b,d) predictions on the validation set. (a) and (b) panels correspond to the Si $2p$ level, while (c) and (d) show results for the Li $1s$ level. Each plot reports the average calibrated uncertainty $\langle s^{(calib.)}\rangle$, and the insets display histograms of the corresponding uncertainty distributions.
• Figure 4: Radial distribution functions (RDFs) at 300 K of the structures generated using a melt-quench-anneal procedure (a) and a grand canonical Monte Carlo simulation starting from c-Li_3.75Si (b).
• Figure 5: (a) Stoichiometry map showing the peak position of Li $1s$ for Li$_x$Si structures generated using MQA (red) and GCMC simulations starting from c-Li_3.75Si (green) and c-Li_4.4Si (purple), compared to experimental data corresponding to the delithiation of Si electrodes (black crosses and blue triangles). The stars represent the values for the initial structure in the GCMC simulations and the shaded regions correspond to the predicted uncertainties. (b) Delithiation voltage curves from GCMC simulations starting from c-Li_3.75Si (green), c-Li_4.4Si (purple), a-Li_4.4Si (purple dashed) and c-Li_3.25Si (cyan).