Optimising Descriptors to Correlate Stability of C- or N-doped High Entropy Alloys: A Combined DFT and Machine-Learning Regression Study

Abstract

The interstitial doping is a common approach to improve the mechanical or functional properties of high entropy alloys (HEA); their stability is usually predicted by some specific single descriptor. Herein, we consider six types microstructure-based and seven types electronic-structure-based local-environment descriptors and their combinations to predict the stability of C- or N-doped VNbMoTaWTiAl_0.5 (BCC) HEA using mainly density functional theory (DFT) calculations. The machine-learning interatomic potential and Monte Carlo simulations were employed to verify the short-range order in HEA. The former descriptors include the composition of first-, second-, third-nearest neighbour shell (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 latter involves the local potential (LP), electrostatic potential (EP), charge density (CHG), electron localization function (ELF) at the vacant doping site, d-band center (ε_d), mean electronegativity (EN) of the 1NN shell around the dopant, and Bader charge of C or N dopants. For a single descriptor, the best correlation between the descriptor and the doping energy (indication of HEA stability) is 1NN with ~ 51 or ~ 61% of coefficient of determination (Q²) from LOOCV (leave-one-out cross-validation) for C or N doping, respectively. After adding volume descriptor(s) into the linear regression model with 1NN descriptor, the Q² raises to 72 and 76 % for C and N doping, respectively. After further adding electronic-structure-based EP descriptor, the Q² further improve 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 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.