Unrevealing hardening and strengthening mechanisms in high-entropy ceramics from lattice distortion

Revealing the hardening and strengthening mechanisms is crucial for facilitating the design of superhard and high-strength high-entropy ceramics (HECs). Here, we take high-entropy diborides (HEB$_2$) as the prototype to thoroughly investigate the hardening and strengthening mechanisms of HECs. Specifically, the equiatomic 4- to 9-cation single-phase HEB$_2$ ceramics (4-9HEB$_2$) are fabricated by an ultra-fast high-temperature sintering method. The as-fabricated 4-9HEB$_2$ samples possess similar grain sizes, comparable relative densities (up to ~98%), uniform compositions, and clean grain boundaries without any impurities. The experimental results show that the hardness and flexural strength of the as-fabricated 4-9HEB$_2$ samples have an increasing tendency with the increase of metal components. The first-principles calculations find that lattice distortion is essential to the hardness and strength of HEB$_2$. With the increase of metal components, an aggravation of lattice distortion accompanied by B-B bond strengthening is determined, resulting in the enhancement of the hardness and flexural strength. Moreover, the correlation between other potential indicators and the hardness/flexural strength of HEB$_2$ has been disproved, including valence electron concentration, electronegativity mismatch, and metallic states. Our results unravel the hardening and strengthening mechanisms of HECs by intensifying lattice distortion, which may provide guidance for developing superhard and high-strength HECs.