Metal deficient AlB$_{2}$-type (Ti$_{0.2}$Zr$_{0.2}$Hf$_{0.2}$Nb$_{0.2}$Ta$_{0.2}$)$_{1-δ}$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 $_{0.2}$ ) $_{1 - δ}$ B $_{2}$ high-entropy diborides (HEBs). A single homogeneous AlB $_{2}$ -type phase is successfully obtained over the $δ$ range of 0.03 $\leq$ $δ$ $\leq$ 0.18. With increasing $δ$ , the unit-cell volume exhibits a nonmonotonic variation with a maximum at $δ$ = 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.

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

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

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Metal deficient AlB22​-type (Ti0.20.2​Zr0.20.2​Hf0.20.2​Nb0.20.2​Ta0.20.2​)1−δ1−δ​B22​ high-entropy diborides with high hardness

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Metal deficient AlB22​-type (Ti0.20.2​Zr0.20.2​Hf0.20.2​Nb0.20.2​Ta0.20.2​)1−δ1−δ​B22​ high-entropy diborides with high hardness

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

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

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