Machine-Learned Interatomic Potentials for Structural and Defect Properties of YBa$_2$Cu$_3$O$_{7-δ}$

TL;DR

This study develops and benchmarks four machine-learned interatomic potentials (ACE, MACE, GAP, tabGAP) for YBa$_2$Cu$_3$O$_{7-\delta}$ to enable accurate, large-scale simulations of bulk, defects, and thermodynamics under irradiation. Using a purpose-built DFT database that spans equilibrium and irradiation-like environments, the potentials are validated against DFT benchmarks and experimental data, with MACE achieving the highest accuracy albeit at greater cost. ACE and tabGAP offer favorable accuracy-efficiency trade-offs and enable large-scale MD studies of oxygen stoichiometry and defect evolution, including an orthorhombic–tetragonal phase transition. Collectively, the work provides robust tools for modeling radiation-damage pathways in complex HTS materials, facilitating design choices for fusion-relevant magnets and shielding strategies.

Abstract

High-Temperature Superconductors (HTS) such as YBa2Cu3O7-delta (YBCO) are essential for next-generation Tokamak fusion reactors, where Rare-Earth Barium Copper Oxides (REBCO) form the functional layers in HTS magnets. Because YBCO's superconductivity depends strongly on oxygen stoichiometry and defect structure, atomistic simulations can provide crucial insight into radiation-damage mechanisms and pathways to maintain material performance. In this work, we develop and benchmark four Machine-Learned Interatomic Potentials (MLPs) for YBCO: the Atomic Cluster Expansion (ACE), the Message-Passing Atomic Cluster Expansion (MACE), the Gaussian Approximation Potential (GAP), and the Tabulated Gaussian Approximation Potential (tabGAP), trained on an extensive Density Functional Theory (DFT) database explicitly designed to include irradiation-damaged-like configurations. The resulting models achieve DFT-level accuracy across a wide range of atomic environments, faithfully capturing the interatomic forces relevant to radiation damage processes. Among the tested models, MACE delivers the highest accuracy, although at greater computational cost, while ACE and tabGAP provide an excellent balance between efficiency and fidelity. These machine-learned potentials establish a robust foundation for large-scale molecular dynamics simulations of radiation-induced defect evolution in complex superconducting materials

Figures (16)

• Figure 1: Structure diagram of YBa$_2$Cu$_3$O$_7$. The numbers contained within atoms are the site numbers for symmetrically distinct O/Cu atoms.
• Figure 2: Overview of the structural diversity within the dataset. All structures' images are downloaded from the Materials Project Jain2013 database, apart from the active learned configuration. Each point corresponds to a structure represented by its SOAP descriptor, with pairwise similarities computed via the average kernel implemented in DScribe himanen2020dscribe. The resulting similarity matrix was projected onto two dimensions using t-distributed stochastic neighbor embedding (t-SNE) soni2020visualizingpedregosa2011scikit. Three principal high-density “islands” are observed within the YBCO region (encircled by a dotted line): the left cluster corresponds to low-energy YBCO$_7$ configurations, the lower cluster to low-energy YBCO$_6$ structures, and the upper cluster to defect-containing configurations. Highly strained and distorted structures extend toward the upper-left region. Distinct structural classes are colour-coded for clarity. The accompanying composition chart shows the relative abundance of each structure type, with the number of configurations indicated in brackets.
• Figure 3: Parity plots for YBCO$_7$ (left) energy, YBCO$_6$ (center) energy, and forces (right) predicted by (a) YBCO_MACE and YBCO_ACE and by (b) YBCO_GAP and YBCO_tabGAP. RMSE values over the whole validation set for both energies and forces are included with the models' corresponding colors.
• Figure 4: Comparison of lattice parameters (in Å) for YBCO$_7$ and YBCO$_6$ from YBCO_MACE, YBCO_ACE, YBCO_tabGAP, YBCO_GAP, DFT, and experiment williams1988joint. Experimental values are not included for YBCO$_6$ as they are not available. The lattice parameters are color-coded based on their error relative to the DFT ground truth.
• Figure 5: Comparison of the energy–volume curves and lattice parameters for YBCO$_6$ (top) and YBCO$_7$ (bottom) using DFT, YBCO_MACE, YBCO_ACE, YBCO_GAP, and YBCO_tabGAP models.