Metal deficient AlB$_{2}$-type (Ti$_{0.2}$Zr$_{0.2}$Hf$_{0.2}$Nb$_{0.2}$Ta$_{0.2}$)$_{1-\delta}$B$_{2}$ high-entropy diborides with high hardness

We report the synthesis and characterization of metal deficient (Ti$_{0.2}$Zr$_{0.2}$Hf$_{0.2}$Nb$_{0.2}$Ta$_{0.2}$)$_{1-\delta}$B$_{2}$ high-entropy diborides (HEBs). A single homogeneous AlB$_{2}$-type phase is successfully obtained over the $\delta$ range of 0.03 $\leq$ $\delta$ $\leq$ 0.18. With increasing $\delta$, the unit-cell volume exhibits a nonmonotonic variation with a maximum at $\delta$ = 0.07. These metal-deficient HEBs possess high Vickers hardness of 16.6-18.9 GPa at a load of 9.8 N and their phase stability is attributed to the increased mixing entropy. Our results not only present the first series of metal-deficient AlB$_{2}$-type HEBs, but also suggest the existence of similar multicomponent diborides.