Nine-element machine-learned interatomic potentials for multiphase refractory alloys

Abstract

New refractory alloys are being continuously designed and characterised for applications requiring good high-temperature mechanical properties and stability. Computational design from atomistic simulations is limited by interatomic potentials missing key elements, being too inaccurate, or computationally too slow for large-scale simulations. Here we present development of a refractory alloy database and two computationally efficient and general-purpose machine-learned potentials (tabGAP and NEP). We also design a cross-sampling strategy for effective sampling of training data using predictions from two potentials with completely different underlying architecture. The potentials support arbitrary alloy compositions of elements in groups four to six in the periodic table (Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W). The database is diverse yet multitargeted to enable simulations of refractory metals and alloys across different pure-metal, solid-solution, intermetallic, and glassy phases. We demonstrate the usefulness of the potentials by reproducing known pressure-, temperature-, and solute-induced phase transitions, grain boundary segregation, and simulations of radiation damage in the WTaCrVHf metallic glass.

Figures (8)

• Figure 1: RHEA training database. Illustration of the content of the training database comprised of 22 477 structures and in total 694 078 atoms. The central element grid shows the atom fractions of each element and the outer circular chart shows the atom fractions of one- to nine-element structures along with representative snapshots of the various groups of structures.
• Figure 2: Train and validation errors. Column (a) shows parity plots and RMSEs for energies and force components for the training set, test set A (combination of the Mo-Nb-Ta-V-W test set from Ref. byggmastar_simple_2022 with the W-Mo training data from Ref. nikoulis_machine-learning_2021), and test set B (subset of the training data from Ref. song_generalpurpose_2024 that shares the same elements). Panel (b) shows energy-volume curves comparing the tabGAP and NEP to DFT for all binary B2 alloys, the most stable C15 Laves binary alloys, and all available ternary alloys from the Materials Project database. Panel (c) shows parity plots and RMSEs of the equilibrium formation energies and bulk moduli extracted from the energy-volume data in (b).
• Figure 3: Validation for the nine pure metals. Energy-volume curves for isotropic volume-scaling of stable and hypothetical crystal phases, comparing tabGAP and NEP to DFT. The right column shows various material properties compared to DFT and experimental data.
• Figure 4: Pressure-temperature phase diagrams of Ti, drawn based on free-energy calculations and solid-liquid simulations using the tabGAP and NEP. The dotted lines show the phase boundaries drawn from experiments dewaele_high_2015.
• Figure 5: Phase stability validation during heating and cooling. Potential energy during heating and cooling of six different alloys to beyond the melting point and back to 100 K using the tabGAP and NEP. The various phase transitions occurring are indicated. Column (c) shows validation of both MLIPs as comparison of energies to DFT for structures sampled from the tabGAP trajectories.