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

Technical Deep Dive: Tracking Lithiation State of Li$_x$Si Using Machine-Learned XPS Binding Energies

Overview

This work introduces a machine learning (ML) framework that enables accurate, scalable, and uncertainty-aware prediction of X-ray Photoelectron Spectroscopy (XPS) core-level binding energies (BEs) in structurally complex Li$_x$Si systems. The ML models achieve near-DFT accuracy for Li $1s$ and Si $2p$ levels while remaining computationally efficient for large, amorphous configurations. The authors use this approach to construct stoichiometry maps that quantitatively link XPS peak positions to lithium content and structural evolution during (de)lithiation of Si anodes.

Problem & Context

XPS is a powerful technique for probing chemical states and interfacial processes in battery materials, but its quantitative interpretation is challenging due to the complex, heterogeneous microstructures that form during electrochemical cycling. Si-based anodes, in particular, exhibit extreme volume changes and complex phase transformations that generate large mechanical stresses and drive particle fracture, pulverization and loss of electrical contact.

Existing approaches based on DFT are prohibitively expensive for the structurally complex or disordered materials typical of battery applications. To overcome this limitation, the authors leverage ML techniques to approximate DFT-level predictions at far lower computational cost.

Methodology

The authors developed a machine learning workflow that combines:

1. Core-level BE Prediction: A kernel ridge regression (KRR) model trained on DFT-computed Li $1s$ and Si $2p$ BEs to predict BEs for arbitrary Li$_x$Si structures, with uncertainty estimates.
2. Atomic Environment Descriptor: The smooth overlap of atomic positions (SOAP) power spectrum is used to describe the local atomic environments as input to the KRR models.
3. Atomic Structure Generation: Two approaches are used to generate realistic Li$_x$Si structures:
   • Melt-quench-anneal (MQA) protocol to generate near-equilibrium amorphous structures.
   • Grand canonical Monte Carlo (GCMC) simulations coupled with molecular dynamics to capture metastable and partially ordered configurations relevant to early delithiation.

Data & Experimental Setup

The training dataset for the ML models was constructed by selecting 245 diverse Li$_x$Si structures from a larger dataset of ~62,000 configurations, and computing their DFT-level Li $1s$ and Si $2p$ BEs.

The authors validated the ML models against an out-of-sample Li$_x$Si structure, as well as experimental XPS data from two studies on a-Si thin film electrodes.

Results

1. ML Model Performance: The KRR models achieved R^2 values of 0.97 and 0.94 for Li $1s$ and Si $2p$ BEs, respectively, on the validation set. The calibrated uncertainty estimates are consistent with typical XPS experimental resolutions, falling below 0.1 eV on average.
2. Stoichiometry Maps: Applying the ML models to the MQA and GCMC-generated structures, the authors constructed stoichiometry maps that relate XPS peak positions to Li content and structural evolution during delithiation:
   • The Li $1s$ BE shows little dependence on Li concentration, while the Si $2p^3/2$ BE exhibits a clear upward trend upon delithiation.
   • The Si $2p^3/2$ BE maps capture the distinctive spectroscopic signatures associated with the crystal-to-amorphous transition during early delithiation.
3. Voltage Profiles: GCMC simulations of delithiation from different crystalline Li$_x$Si phases reveal two-phase voltage plateaus, with the amorphous phase exhibiting a lower onset voltage compared to the crystalline phases.
4. Structural Analysis: A SOAP similarity analysis shows that delithiation of crystalline phases proceeds through the persistence of crystalline domains, providing a microscopic explanation for irreversible capacity loss in Si anodes.

Interpretation

The ML framework developed in this work enables quantitative interpretation of XPS data from Si-based electrodes under realistic operating conditions, overcoming the limitations of DFT-based approaches. The stoichiometry maps and structural insights reveal clear spectroscopic signatures of the crystal-to-amorphous transition and the persistence of crystalline domains during early delithiation, offering new understanding of the complex phase transformations that drive capacity fade in Si anodes.

Limitations & Uncertainties

• The ML models were trained on a limited dataset of Li$_x$Si structures, and their performance may be affected by the diversity and representativeness of the training data.
• The experimental XPS data used for validation exhibits some discrepancies between different studies, likely due to differences in energy calibration and surface composition.
• The GCMC simulations, while capturing metastable and partially ordered configurations, may not fully represent the complex microstructural evolution during cycling under realistic operating conditions.

What Comes Next

Future work could explore:

• Expanding the training dataset with more diverse Li$_x$Si structures, including those generated under different cycling conditions.
• Incorporating additional experimental data, such as operando XPS measurements, to further validate and refine the ML models.
• Coupling the ML-based XPS analysis with other characterization techniques (e.g., XRD, TEM) to obtain a more complete picture of the structural evolution in Si anodes.
• Applying the ML framework to other battery materials systems beyond Li$_x$Si to demonstrate its broader applicability.