Although ZrB 12 is a promising advanced material because of the boron cuboctahedron cages, the hardness of ZrB 12 remains controversy. Here, we apply first-principles calculations to study the influence of transition metals (4d-and 5d-) on the hardness and thermodynamic properties of ZrB 12 . The calculated hardness of ZrB 12 is 32.9 GPa, which is in good agreement with the previous theoretical result. Importantly, the calculated hardness of Re-doped ZrB 12 is up to 40.0 GPa, which is a potential superhard material. The essential reason is that the alloying element of Re enhances the localized hybridization of B B and Zr B atoms, and then forms the strong B B covalent bond and Zr B bond. The result is well demonstrated by the chemical bonding and lattice parameter. Here, our work shows that the alloying elements of Nb, Mo, and Re enhance the thermodynamic properties of ZrB 12 . The Debye temperature of Re-doped ZrB 12 is 1225.2 K, which is larger than that of the parent ZrB 12 (1213.5 K). K E Y W O R D S borides, elastic modulus, first-principles calculations, hardness, thermodynamic properties, ZrB 12 1 | INTRODUCTION Hard and superhard materials (≥40 GPa) are very important industrial materials, which are widely used in various industrial applications because of their high hardness, ultracompressibility, high melting point, and excellent thermal stability etc. [1-10] In comparison to diamond and boron nitride (c-BN), the transition metal borides (TMBs) are attractive potential superhard materials because of the network and shorter covalent bonding such as B B covalent bond and TM B bond. [11][12][13][14][15][16][17][18][19] Diborides (TMB 2 ) and transition metal tetraborides (TMB 4 ) have been widely investigated over the last years. [20][21][22][23][24] However, the reported Vickers hardness of TMB 2 or TMB 4 is difficult to meet the requirement of superhard material. [25][26][27][28][29] Naturally, the Vickers hardness of TMBs mainly relies on the shorter and network covalent bonds. In other words, the high concentration of boron plays a crucial role in Vickers hardness of TMBs. Among these TMBs, it is obvious that the transition metal dodecaborides (TMB 12 ) are potential superhard materials in comparison to TMB 2 and TMB 4 .Recently, ZrB 12 has evoked great interest because of the high concentration of boron and the network B B covalent bonds. [30] This dodecaboride is composed of the boron cuboctahedron cage (24 atoms) and 12-coordinate transition metals at the center of cubic structure. This structural feature is possible to enhance the Vickers hardness of TMBs. However, the Vickers hardness of ZrB 12 remains controversy. Korozlu et al. have found that the calculated Vickers hardness of ZrB 12 is 40.1 GPa, which is believed to a potential superhard material. [31] However, the recent works have shown that the Vickers hardness of ZrB 12 is 35.4 GPa by Chen et al. [32] and 29.3 GPa by Li et al., [33] which are different from Korozlu's result. On the other hand, even if the Vickers hardness of ZrB 12 remains...
