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Efficient small-cell sampling for machine-learning potentials of multi-principal element alloys

Yan Liu, Jiantao Wang, Hongkun Deng, Yan Sun, Xing-Qiu Chen, Peitao Liu

TL;DR

This work tackles the challenge of modeling multi-principal element alloys (MPEAs) with machine-learning potentials by introducing an efficient one-shot small-cell sampling (SCS) protocol. By enumerating symmetry-inequivalent unary and binary configurations within 4-, 8-, and 12-atom cells and filtering near-binary convex-h hulls from the Materials Project, the authors generate diverse training datasets augmented with targeted perturbations, avoiding iterative active learning and large-cell DFT. They train two ML potentials (MTP and MACE) and validate the approach across TiZrHfCuNi, TiZrVMo, CoCrFeMnNi, and AlTiZrNbHfTa, demonstrating accurate structural, thermodynamic, and ordering predictions, including phase transformations and SRO evolutions. The results establish a scalable, low-cost pathway toward universal MPEA MLPs and offer insight into how small-cell data can effectively represent complex multicomponent energy landscapes for accelerated materials discovery.

Abstract

Multi-principal element alloys (MPEAs) exhibit exceptional properties but face significant challenges in developing accurate machine-learning potentials (MLPs) due to their vast compositional and configurational complexity. Here, we introduce an efficient small-cell sampling (SCS) method, which allows for generating diverse and representative training datasets for MPEAs using only small-cell structures with just one and two elements, thereby bypassing the computational overhead of iterative active learning cycles and large-cell density functional theory calculations. The efficacy of the method is carefully validated through principal component analysis, extrapolation grades evaluation, and root-mean-square errors and physical properties assessment on the TiZrHfCuNi system. Further demonstrations on TiZrVMo, CoCrFeMnNi, and AlTiZrNbHfTa systems accurately reproduce complex phenomena including phase transitions, chemical orderings, and thermodynamic properties. This work establishes an efficient one-shot protocol for constructing high-quality training datasets across multiple elements, laying a solid foundation for developing universal MLPs for MPEAs.

Efficient small-cell sampling for machine-learning potentials of multi-principal element alloys

TL;DR

This work tackles the challenge of modeling multi-principal element alloys (MPEAs) with machine-learning potentials by introducing an efficient one-shot small-cell sampling (SCS) protocol. By enumerating symmetry-inequivalent unary and binary configurations within 4-, 8-, and 12-atom cells and filtering near-binary convex-h hulls from the Materials Project, the authors generate diverse training datasets augmented with targeted perturbations, avoiding iterative active learning and large-cell DFT. They train two ML potentials (MTP and MACE) and validate the approach across TiZrHfCuNi, TiZrVMo, CoCrFeMnNi, and AlTiZrNbHfTa, demonstrating accurate structural, thermodynamic, and ordering predictions, including phase transformations and SRO evolutions. The results establish a scalable, low-cost pathway toward universal MPEA MLPs and offer insight into how small-cell data can effectively represent complex multicomponent energy landscapes for accelerated materials discovery.

Abstract

Multi-principal element alloys (MPEAs) exhibit exceptional properties but face significant challenges in developing accurate machine-learning potentials (MLPs) due to their vast compositional and configurational complexity. Here, we introduce an efficient small-cell sampling (SCS) method, which allows for generating diverse and representative training datasets for MPEAs using only small-cell structures with just one and two elements, thereby bypassing the computational overhead of iterative active learning cycles and large-cell density functional theory calculations. The efficacy of the method is carefully validated through principal component analysis, extrapolation grades evaluation, and root-mean-square errors and physical properties assessment on the TiZrHfCuNi system. Further demonstrations on TiZrVMo, CoCrFeMnNi, and AlTiZrNbHfTa systems accurately reproduce complex phenomena including phase transitions, chemical orderings, and thermodynamic properties. This work establishes an efficient one-shot protocol for constructing high-quality training datasets across multiple elements, laying a solid foundation for developing universal MLPs for MPEAs.
Paper Structure (11 sections, 7 figures, 2 tables)

This paper contains 11 sections, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Computational details
  3. First-principles calculations
  4. Training of machine-learning potential
  5. Results and discussion
  6. Outline of the SCS protocol
  7. Validation of the SCS protocol
  8. Phase transformation in the TiZrVMo MPEA
  9. SRO parameters in the CoCrFeMnNi MPEA
  10. Thermodynamics and SRO parameters in the AlTiZrNbHfTa MPEA
  11. Conclusion

Figures (7)

  • Figure 1: Workflow illustrating the key steps in the SCS protocol.
  • Figure 2: Principal component analysis of structures with one and two elements (denoted as 1C+2C), three elements (3C), four elements (4C), and five elements (5C).
  • Figure 3: MTP predicted (a) energies, (b) forces, and (c) stress tensors against DFT results for the TiZrHfCuNi MPEA. The MTP was trained using the SCS-generated dataset (i.e., the 4-8-12-mp dataset in Table \ref{['tab:performance']}).
  • Figure 4: Transformation of the equimolar TiZrVMo MPEA from the initial HCP structure to the BCC structure during hybrid MC/MD simulations. (a) Initial configuration at 0 ns. (b)-(c) The structure after 5 ns and its elements distribution.
  • Figure 5: (a) SRO parameters for the first shell in CoCrFeMnNi MPEA, averaged over the last 1000 steps and three independent runs. (b)-(c) Snapshots from hybrid MC/MD simulations at $T=300$ K and $T=720$ K, respectively.
  • ...and 2 more figures