Cluster-Model-Embedded First-Principles Study on Structural Stability of Body-Centered-Cubic-Based Ti-Zr-Hf-Nb Refractory High-Entropy Alloys

Refractory high-entropy alloys (RHEAs) with body-centered-cubic (BCC) structure are a new class of alloy materials and have great potential for high temperature applications. The present work investigated the BCC structural stabilities of Ti-Zr-Nb-Hf RHEAs with both first-principles calculations and experimental characterization. The cluster-plus-glue-atom model (cluster model) for the presentation of chemical short-range ordering (CSRO) in solid solutions was applied to construct the model input for the first-principles method, in which the density functional theory was used. Three cluster structural units were considered, [Ti-Hf14]Nb3, [Ti-Zr8Hf6]Nb3, and [Ti-Zr8Hf4Ti2]Nb3. The corresponding alloys were fabricated, and microstructural characterization was performed. The calculated results of the formation energies and free energies of these three alloys indicate that the [Ti-Zr8Hf4Ti2]Nb3 has the highest BCC structural stability due to its lowest formation energy and free energy. It is well consistent with the experimental observation, where the [Ti-Zr8Hf4Ti2]Nb3 alloy exhibits a single BCC structure without any precipitation, while a small amount of α and/or ω phases would precipitate from the BCC matrix in the other alloys. The cluster-model-embedded first-principles method could provide a new approach for accurate calculations.