Design criteria for single-phase non-equiatomic refractory multiprincipal element alloys from the Nb-Ti-Zr system

Refractory high entropy alloys (RMPEAs) hold promise as candidate materials for high-temperature applications challenging widely used nickel-based superalloys. RMPEAs application is currently limited by their low structure and phase stability in the presence of oxygen, which can be improved by single-phase alloy design. This study establishes design criteria for achieving single-phase, non-equiatomic RMPEAs through a systematic exploration of the Nb-Ti-Zr compositional space. Using combinatorial synthesis via magnetron co-sputtering and high-throughput characterization, we map phase stability across a broad compositional range. We identify a stable single-phase BCC region for compositions containing 19.5–55 at.% Nb, 43–59 at.% Ti, and less than 30.5 at.% Zr. Monte Carlo simulations were used to predict the phase formation at high temperatures along with electron microscopy revealing phase segregations at high-Zr compositions, exploring the role of soluble oxygen in phase formation. Our findings provide a foundation for the rational alloy design, explain the effect of each element, and pave a path for further exploration and modification of the identified compositional space.