Machine Learned Interatomic Potentials for Ternary Carbides trained on the AFLOW Database

Abstract

Large density functional theory (DFT) databases are a treasure trove of energies, forces and stresses that can be used to train machine learned interatomic potentials for atomistic modeling. Herein, we employ structural relaxations from the AFLOW database to train moment tensor potentials (MTPs) for four carbide systems: HfTaC, HfZrC, MoWC and TaTiC. The resulting MTPs are used to relax ~6300 random symmetric structures, and are subsequently improved via active learning to generate robust potentials (RP) that can relax a wide variety of structures, and accurate potentials (AP) designed for the relaxation of low-energy systems. This protocol is shown to yield convex hulls that are indistinguishable from those predicted by AFLOW for the HfTaC, HfZrC and TaTiC systems, and in the case of the MoWC system to predict thermodynamically stable structures that are not found within AFLOW, highlighting the potential of the employed protocol within crystal structure prediction. Relaxation of over three hundred Mo$_{1-x}$W$_x$C stoichiometry crystals first with the RP then with the AP yields formation enthalpies that are in excellent agreement with those obtained via DFT.