Influence of alloying elements on the mechanical and thermodynamic properties of ZrB₁₂ceramics from first‐principles calculations

Abstract

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...

Anisotropy in elasticity, sound velocity, thermal conductivity, and thermodynamics properties of dodecaboride Zr0.5Y0.5B12

“…The relatively small value of σ (0.151) suggests the strong covalent bonds in Zr 0.5 Y 0.5 B 12 . The intrinsic Vickers hardness of Zr 0.5 Y 0.5 B 12 is larger than the previously reported results of ZrB 12 (~32.9 GPa [12] and 33.6 GPa [22]), which is attributed the change of localized hybridization between B and Zr atoms due to the Y doping [12]. The difference of Vickers hardness between our calculation and experimental result (45.8 GPa) [3] maybe result from the effects of sample morphology, microstructure and other minor precipitated phases, et al The fracture toughness is 3.067 MPaÁm 0.5 , approaching the value of 3.12 MPaÁm 0.5 of α-Si 3 N 4 [23], and smaller than that of diamond 5-7 MPaÁm 0.5 [19].…”

“…Alloying is an effective method to enhance the Vickers hardness of materials. The effects of alloying elements (Nb, Mo, W, Re, and Os) on the hardness and thermodynamic properties of ZrB 12 were investigated using the first-principles calculation [12]. They deemed that the alloying elements improved the localized hybridization between B and Zr atoms, which increased the Vickers hardness [12].…”

“…The effects of alloying elements (Nb, Mo, W, Re, and Os) on the hardness and thermodynamic properties of ZrB 12 were investigated using the first-principles calculation [12]. They deemed that the alloying elements improved the localized hybridization between B and Zr atoms, which increased the Vickers hardness [12]. Akopov et al have synthesized Zr 1Àx Y x B 12 solid solutions at ambient pressure by arc-melting [3].…”

New insight into the structural, mechanical, electronic, and thermodynamic properties of the monoclinicTMAl3‐type aluminides

“…Therefore, it is concluded that the five novel monoclinic stable TMAl 3 aluminides: ScAl 3 , TiAl 3 , VAl 3 , CrAl 3 , and WAl 3 are first predicted. To study the mechanical properties, it is studied the elastic properties and intrinsic hardness (H v ) [55][56][57][58] of TMAl 3 . Here, the elastic properties of a solid have four key parameters: bulk modulus (B), shear modulus (G), Young's modulus (E), and Poisson ratio (σ) [59,60].…”

New Zirconium Diboride Polymorphs—First-Principles Calculations

“…Both experimental and theoretical results were in good agreement. In Reference [ 15 ], however, the mechanical properties of ZrB were calculated. The Vickers hardness of zirconium boride was 32.9 GPa, which is in good agreement with other theoretical results [ 14 , 16 , 17 ].…”