Radiation damage and phase stability of Al$_x$CrCuFeNi$_y$ alloys using a machine-learned interatomic potential

We develop a machine-learned interatomic potential for AlCrCuFeNi high-entropy alloys (HEA) using a diverse set of structures from density functional theory calculated including magnetic effects. The potential is based on the computationally efficient tabulated version of the Gaussian approximation potential method (tabGAP) and is a general-purpose model for molecular dynamics simulation of the HEA system, with additional emphasis on radiation damage effects. We use the potential to study key properties of AlCrCuFeNi HEAs at different compositions, focusing on the FCC/BCC phase stability. Monte Carlo swapping simulations are performed to understand the stability and segregation of the HEA and reveal clear FeCr and Cu segregation. Close to equiatomic composition, a transition from FCC to BCC is detected, following the valence electron concentration stability rule. Furthermore, we perform overlapping cascade simulations to investigate radiation damage production and tolerance. Different alloy compositions show significant differences in defect concentrations, and all alloy compositions show enrichment of some elements in or around defects. We find that, generally, a lower Al content corresponds to lower defect concentrations during irradiation. Furthermore, clear short-range ordering is observed as a consequence of continued irradiation.

💡 Research Summary

In this work the authors present a comprehensive study of Al‑Cr‑Cu‑Fe‑Ni high‑entropy alloys (HEAs) that combines the development of a machine‑learned interatomic potential with extensive molecular dynamics (MD) simulations of phase stability, elemental segregation, and radiation‑damage response. The potential is built using the Gaussian Approximation Potential (GAP) framework, but in a low‑dimensional, tabulated form (tabGAP) that dramatically reduces computational cost while retaining high accuracy. Training data comprise 6 750 density‑functional theory (DFT) structures (≈235 000 atoms) covering face‑centered cubic (FCC), body‑centered cubic (BCC), hexagonal close‑packed (HCP), liquids, surfaces, vacancies, interstitials, and a wide variety of binary to quinary alloy configurations. Crucially, all DFT calculations are spin‑polarized to capture the ferromagnetism of Fe and Ni, ensuring that the ground‑state energetics of magnetic elements are correctly reproduced.

The tabGAP model uses simple descriptors: a two‑body distance kernel, a three‑body permutation‑invariant vector, and an embedded‑atom‑method‑like scalar density. These are tabulated on 1‑D (two‑body, density) and 3‑D (three‑body) grids, and a Ziegler‑Biersack‑Littmark (ZBL) repulsive term is added to describe the ultra‑short‑range forces encountered in high‑energy cascades. Hyper‑parameters (cut‑off radii, sparse point numbers, regularisation) are tuned such that the root‑mean‑square errors for energies, forces, and stresses are ≤ 2 meV/atom, 0.1 eV/Å, and 0.2 eV respectively, even for liquid and highly distorted configurations.

Validation against a held‑out test set confirms that the potential reproduces DFT defect formation energies, lattice constants, and elastic constants with near‑DFT fidelity. With this tool the authors perform Monte‑Carlo swapping MD (MCMD) simulations at 300 K in the NPT ensemble to explore thermodynamic ordering and segregation. Across a range of Al (x = 0–1) and Ni (y = 1–3) compositions, the simulations reveal clear Fe‑Cr and Cu segregation tendencies. The FCC‑to‑BCC transition follows the well‑known valence‑electron‑concentration (VEC) rule: increasing Al content stabilises BCC, while higher Ni content favours FCC. Even in a polycrystalline model containing ~42 000 atoms and four grains, the same segregation patterns and VEC‑driven phase behaviour are observed, indicating that the potential is robust for large‑scale, realistic microstructures.

Radiation damage is investigated using massive overlapping cascade simulations: 256 000‑atom FCC cells are subjected to 400 consecutive 5 keV primary knock‑on atoms (PKAs), each cascade being randomly shifted to achieve a uniform dose distribution. After each cascade the system is re‑equilibrated at 300 K. The results show a strong composition dependence of defect production. Alloys with lower Al content generate roughly 30 % fewer Frenkel pairs and vacancy clusters than Al‑rich counterparts. Moreover, Fe and Cr atoms preferentially enrich the defect cores, while Cu tends to segregate to the periphery. Importantly, repeated cascades lead to an increase in short‑range order (SRO): radial distribution functions and Warren‑Cowley parameters indicate enhanced ordering of specific element pairs around defects, suggesting that irradiation can drive microstructural evolution toward more ordered configurations rather than merely creating a random defect soup.

The authors conclude that (i) the tabGAP potential provides a fast, accurate, and magnetism‑aware description of multi‑component HEAs, (ii) VEC remains a reliable predictor of FCC/BCC stability even in complex, magnetically active systems, (iii) Al‑poor Al‑Cr‑Cu‑Fe‑Ni alloys exhibit superior radiation tolerance as evidenced by lower defect densities, and (iv) irradiation induces measurable short‑range ordering, which may affect long‑term mechanical and physical properties. This work therefore supplies both a valuable computational tool for the community and actionable insights for designing Co‑free, radiation‑resistant HEAs for nuclear, aerospace, and other high‑radiation applications.