Understanding stacking fault energy of NbMoTaW multi-principal element alloys by interpretable machine learning

Stacking fault energy (SFE) is a crucial property influencing the deformation mechanisms of multi-principal element alloys (MPEAs). However, experimentally measuring SFE and exploring composition space of MPEAs is challenging. This study explores the SFE in NbMoTaW by integrating machine learning force fields (ML-FF), molecular dynamics simulations (MD), neural networks, and symbolic regression (SR) methods. A SFE dataset containing 2000 different NbMoTaW compositions were generated by combining ML-FF and MD. Then the neural-network model was developed for SFE prediction with an accuracy of 0.981 and a mean absolute error of 0.020. Using SR, the valence electron concentration (VEC), average shear modulus (G), radii gamma (γ) were identified as the key descriptors to determine SFE with the relationship of SFE=0.307·VEC+0.352·(G+γ). This work demonstrated a significant impact of chemical composition on SFE and established an accurate mathematical expression for SFE prediction, enhancing the understanding and alloy design of MPEAs.