Accelerated computational design of BCC refractory high entropy alloys using metaheuristics, CALPHAD, and artificial neural networks

Refractory high-entropy alloys are a novel class of materials for diverse fields. Their design has been enhanced by several empirical models, thermodynamic calculation methods, and artificial intelligence techniques, allowing continuous advancements in the search for specific properties. In this study, RHEA was designed to maximize the stabilization temperature range of a high temperature BCC single-phase (high-temperature single-phase, HTSP) while maintaining the mixing entropy ( ∆ S mix ) as high as possible, comparable to that of an equimolar composition. Metaheuristic algorithms (particle swarm optimization, genetic algorithms and artificial bee colony), thermodynamic calculations, and artificial neural networks, with a global fitting >0.99 were employed to determine the optimal chemical composition from over 20000 candidates. Theoretically, the TiNbZrTaMo, TiNbZrTaMoV, TiNbZrTaMoHf, and TiNbZrTaMoVHf alloy families were investigated. From the theoretically obtained results, the Ti 17.5 Nb 17.5 Zr 13.5 Ta 15.5 Mo 17.5 V 18.5 alloy was chosen in order to prove that the predictive expectations can be reproduced experimentally. The alloy composition was synthesized using an arc-melting furnace under an inert atmosphere and characterized via X-ray diffraction (XRD), scanning electron microscopy (SEM), and energy-dispersive X-ray spectroscopy (EDS). Additionally, mechanical properties were evaluated through the Vickers microhardness test. The XRD results showed the formation of a single BCC phase, confirming the theoretical predictions. Elemental segregation was also observed in the microstructure, with a remarkable concentration of Zr and Nb in the interdendritic region. Furthermore, the measured Vickers microhardness value was 480 ± 5.2 HV, being higher than previously studied HEAs, highlighting the effect of incorporating a sixth alloying element. These findings demonstrate the feasibility of using thermodynamic calculations and artificial intelligence for the materials design.