Microstructural and compositional design principles for Mo-V-Nb-Ti-Zr multi-principal element alloys: a high-throughput first-principles study

Due to the vast compositional space of multi-principal element alloys (MPEAs), the rational design of MPEAs for optimized microstructures is difficult. Therefore, a high-throughput first-principles study of Mo-V-Nb-Ti-Zr, a refractory MPEA, was conducted to gain insights into the underlying microstructures. Using Monte-Carlo simulations powered by cluster expansion, we uncover the principles governing the MPEA's microstructures across a large compositional space that includes non-equiatomic compositions and encompasses the constituent binaries, ternaries, and quaternaries. In the spirit of Hume-Rothery rules for complete solid solubility, we present a quantitative expression for predicting solid solution formation from the composition. Within a consistent framework, our results reproduce the microstructural observations (solid solution vs. segregation) from numerous experiments and provide microstructural predictions for unexplored regions in the compositional space. Our work illuminates the MPEA's microstructures in terms of the separation and clustering tendencies of the elements, presenting a set of simple but powerful design principles for future experiments to rationally design MPEAs with the desired microstructures for superior mechanical properties.