N-Body Fourier-Sampled Kernel for Machine Learning Potential

Irradiation induces the formation of vacancy and interstitial defects in crystalline materials, which can aggregate into larger clusters. The structure and mobility of self-interstitial clusters remain a largely unresolved issue. For the past 60 years, the scientific community has regarded the formation of interstitial clusters in metallic materials as an accumulation of mono-interstitials that, through diffusion, can aggregate into 2D dislocation loops with a well-defined Burgers vector, progressively growing to observable nanoscale sizes. Recently, we have shown that interstitial clusters in face centered cubic (FCC) metals can aggregate into 3D objects with a well-defined underlying crystallographic structure that ultimately dissociates into dislocation loops [1]. This results complete the puzzle of compact phase accumulation under irradiation, previously emphasized in body centered cubic metals (BCC) [2] and seems to be a general phenomenon.<br/>Further understanding the aging of these newly discovered nano-phases requires precise, large-scale molecular dynamics simulations. Studying the recombination mechanism of atomic scale defects into dislocations, as well as dislocation maturation, necessitates the development of new interatomic potentials. Machine learning potentials offer a compelling solution for atomistic simulations due to their unique ability to balance precision with computational efficiency. Therefore, we have embarked on the development of an innovative machine learning potential within the framework of kernel regression. The strength of our method is derived from: (i) introducing a novel descriptor that captures the many-body aspects of the metallic interatomic force fields, up to 5-body terms. To maintain invariance within the description of this local atomic environment, we employ and reformulate the permutation-invariant polynomials [3]. And (ii) solving the kernel regression in the descriptor space through the kernel-sampled Fourier transform method, avoiding the need for large matrix inversion. This force field was implemented in the Machine Learning Dynamics framework [4]. The intriguing aspect here is that while each of these approaches has previously existed independently, their integration marks a potential watershed moment, ushering in a new horizon of opportunities for atomistic simulations.<br/>To investigate the mechanism governing the formation of compact clusters within FCC and BCC crystals, we conducted a series of simulations based on the newly developed interatomic potential. The kinetics of these processes were delineated through extensive molecular dynamics simulations at finite temperatures in Fe, Ni, and Al. Furthermore, we assessed the relative stability of these clusters through free energy calculations [5]. Lastly, we are actively engaged in the pursuit of intermediate states within the recombination mechanism of these nanophases. To achieve this, we will systematically explore the complex energetic landscape of these clusters at 0 K.<br/>[1] A. M. Goryaeva, C. Domain, A. Chartier, A. Dézaphie, T. D. Swinburne, K. Ma, M. Loyer-Prost, J. Creuze, M.-C. Marinica, Nat Commun 14, 3003 (2023).<br/>[2] M.-C. Marinica, F. Willaime, and J.-P. Crocombette, Phys. Rev. Lett. 108, 025501 (2012)<br/>[3] C. van der Oord, G. Dusson, G. Csányi, and C. Ortner, Mach. Learn.: Sci. Technol. 1 015004 (2020)<br/>[4] M.-C. Marinica, A. M. Goryaeva, T. D. Swinburne <i>et al</i>, MiLaDy - Machine Learning Dynamics, CEA Saclay, 2015-2023: <u>https://ai-atoms.github.io/milady/</u> ;<br/>[5] A. Zhong, C. Lapointe, A. M. Goryaeva, J. Baima, M. Athènes, and M.-C. Marinica,, Phys. Rev. Mater. <b>7</b>, 023802 (2023)