Optimising descriptors to correlate stability of C- or N-doped high-entropy alloys: a combined DFT and machine-learning regression study

Abstract

Interstitial doping is a common approach to improve the mechanical or functional properties of high-entropy alloys (HEAs); their stability is usually predicted by a specific single descriptor. Herein, we consider six types of microstructure-based descriptor, seven types of electronic-structure-based local-environment descriptor and their combinations to predict the stability of the C- or N-doped VNbMoTaWTiAl_0.5 (BCC) HEA, mainly using density functional theory (DFT) calculations. A machine-learning interatomic potential and Monte Carlo simulations were employed to verify the short-range order in the HEA. The microstructure-based descriptors include the composition of the first-, second-, and third-nearest neighbour shells (1NN, 2NN and 3NN), OctaDist distortion parameters (ζ, Δ, Σ, Θ), the Voronoi volume (V_Voronoi) of the dopant, and the volume change of the unit cell after doping (ΔV_cell); the electronic-structure-based local-environment descriptors include the local potential (LP), the electrostatic potential (EP), the charge density (CHG), the electron localization function (ELF) at the vacant doping site, the d-band center (ε_d), the mean electronegativity (EN) of the 1NN shell around the dopant, and the Bader charge of the C or N dopants. For a single descriptor, the best correlation between the descriptor and the doping energy (indication of HEA stability) is found for 1NN with coefficient of determination (Q²) values of ∼51 or ∼61% obtained using the LOOCV (leave-one-out cross-validation) approach for C or N doping, respectively. After adding volume descriptor(s) into the linear regression model with the 1NN descriptor, Q² increases to 72 and 76% for C and N doping, respectively. After further adding the electronic-structure-based EP descriptor, Q² further increases to 75 and 80% for C and N doping, respectively, despite the poor correlation using a single volume descriptor. This study quantitatively combined and compared the independent contributions of different types of local-environment descriptors to the stability of the C- or N-doped HEA, demonstrating the importance of considering both key microstructure-based and electronic-structure-based local-environment descriptors using the regression models to achieve more accurate correlation of dopant stability in HEA; these combined approaches could be further applied to other materials systems, research fields and applications.