Machine learning interatomic potentials for solid-state precipitation

TL;DR

The paper tackles the challenge of parameterizing machine-learning interatomic potentials (MLIPs) to model solid-state precipitation in multi-component alloys. It develops a physics-informed workflow that combines an ACE-based MLIP with a symmetry-based enumeration of transformation pathways and a weighted Kendall-$\tau$ validation framework (including a semi-grand canonical form) to assess low-temperature thermodynamics and phase stability. Applying this to Mg-Nd, the authors obtain an MLIP that accurately reproduces thermodynamics, defect energetics, and early-stage precipitate energies, revealing competition between order-disorder and structural transformations and suggesting a continuous hcp-to-bcc transition during aging. The framework is generalizable to other alloy systems and provides a rigorous, transferable approach for MLIP development in precipitation problems, with implications for faster, large-scale atomistic simulations and alloy design.

Abstract

Machine learning interatomic potentials (MLIPs) are routinely used to model diverse atomistic phenomena, yet parameterizing them to accurately capture solid-state phase transformations remains difficult. We present error metrics and data-generation schemes designed to streamline the parameterization of MLIPs for modeling precipitation in multi-component alloys. We developed an algorithm that enumerates symmetrically distinct transformation pathways connecting chemical decorations on different parent crystal structures. Additionally, we introduce the weighted Kendall-$τ$ coefficient and its semi-grand canonical generalization as metrics for quantifying MLIP accuracy in predicting low-temperature thermodynamics. We apply these approaches to parameterize an MLIP for a dilute Mg-Nd alloy. The resulting potential reproduces the complex early-stage precipitation behavior observed in experiment. Large-scale atomistic simulations reveal competition between order-disorder and structural transformations. Furthermore, these results suggest a continuous transition between high-symmetry hcp and bcc crystal structures during aging heat treatments.

Figures (19)

• Figure 1: (a) Structural transformation from the ideal hcp decoration, $h$-$\beta_1$, to the bcc structure, $\beta_1$. (b) DFT energy landscape along the transformation path between $h$-$\beta_1$ and $\beta_1$. (c) Two possible sublattice decorations of a pre-existing $\beta'$ ordering; Nd substitution on the red sublattice yields $\beta_1$, while substitution on the blue sublattice creates local $\beta"$ ordering. Crystal structures are projected along the hcp [0001] direction. Orange and white circles represent Nd and Mg atoms, respectively. Atoms positioned between lattice sites reside in the layer above the basal plane.
• Figure 2: Sampling workflow for training dataset generation.
• Figure 3: (a) Structures in the reference database and their relationship to material properties. (b) Active learning workflow for discovering new low-energy orderings.
• Figure 4: (a) Crystal structures and symmetry-distinct transformation pathways of $h$-$\beta_1$ illustrated in the two-dimensional strain order parameter space ($e_2$, $e_6$) thomas_exploration_2017natarajan_2019_understandingdeformation. (b) DFT energy profiles along the three transformation paths.
• Figure 5: Schematic energy spectrum of elemental polymorphs, depicting a scenario where multiple stacking-order phases such as fcc, hcp and dhcp lie close to the global ground state.