Chemical short-range ordering and its strengthening effect in refractory high-entropy alloys

In this work, we perform first-principles calculations, coupled with synchrotron small-angle x-ray scattering (SAXS) to investigate electronic origins of the chemical short-range ordering (CSRO) and to reveal the relationship between CSROs and mechanical properties in a typical bcc (body-centered-cubic) TiZrHfNb high-entropy alloys (HEAs). It was found that existence of an appropriate degree of CSROs not only stabilizes the HEA lattice structure, but also enhances the hardness, elastic modulus, and ideal strength. Comprehensive electronic structure analyses uncover that the reduction of $d$ electrons at the Fermi level due to the development of (Ti, Zr)-based CSROs stabilizes the bcc HEA, and the CSRO-induced strengthening is attributed to the local lattice distortion and the $d$-electron transfer from high-energy to low-energy states under applied strains. This finding not only gives insight into understanding the nature of CSRO strengthening in bcc HEAs, but also provides a paradigm for achieving desired mechanical properties via tailoring CSROs in HEAs.