Vacancy order–disorder transition and band convergence in HfRu1.5Sb: A first-principles study

Abstract

The discovery of vacancy-driven short-range order in the half-Heusler-like HfRu_1.5Sb is reported, along with its quantified impact on the electronic structure. By integrating density-functional total energies with cluster expansion and large-cell Monte-Carlo annealing simulation, it was found that the order-disorder phase transition occurred at 1100K, which is consistent with the experimental 1170K. And two nearly degenerate ground-state configurations (GS1 and GS2) are identified at room temperature, distinguished by the spatial arrangement of Ru vacancies on the 4d sub-lattice. Although short-range order parameters reveal similar ordering tendencies in both GS1 and GS2, it is specifically in GS2 that Ru vacancies form tetrahedral configurations encapsulating Hf atoms, thereby weakening adjacent Hf–Ru bonding interaction. These tetrahedral motifs introduce additional valence band valleys, whose weight scales with the degree of disordering, enhancing the band convergence effects. This study systematically reveals the formation mechanism of the order-disorder transition of vacancies in HfRu_1+xSb and its effect on the electronic structure, providing theoretical guidance for optimizing thermoelectric performance and designing advanced half-Heusler-like materials.