First-principles structural design of superhard material of ZrB4

Abstract

Using the first-principles calypso algorithm for crystal structure prediction, we have predicted two orthorhombic Cmcm and Amm2 structures of ZrB4, which are energetically much superior to the previously proposed WB4-, CrB4-, and MoB4-type structures and stable against decompression into a mixture of Zr and B at ambient pressure. The two orthorhombic structures consist of a hexagonal B ring and ZrB12 units connected by edges and one hexagonal B ring in Cmcm and Amm2 structure, respectively. The calculated large shear modulus (e.g., 229 GPa) and high hardness (42.8 GPa for Cmcm and 42.6 GPa for Amm2) reveal that they are potentially superhard materials. The high hardness is attributed to a stacking of B-Zr-B "sandwiches" layers linked by strong covalent B-B bonding.

First-principles study of the electronic and optical properties of a new metallic MoAlB

“…Zhang et al 14. predicted the structure of ZrB 4 and investigated the mechanical, and electronic properties of ZrB 4 by using the PAW method.…”

Crystal Structure and Physical Properties of HfB4 via First-Principles Calculations

“…[66], FeB4 [13,67,68], MnB4 [70], ZrB4 [23], and TaB4 [27] but very close to those of HfB2 [43][44][45][46] and CrB4 [13,69]. This suggests that the Cmcm-HfB4 may be a potential superhard material.…”

“…By using a strain-stress method, we obtain the elastic constants Cij of the Cmcm-HfB4 phase at 0 GPa. The calculated results are listed [13,67,68], Cr [13,69], Mn [70], Zr [23], and Ta [27]). For a sable orthorhombic structure, the independent elastic stiffness tensor consist of nine components C11, C22, C33, C44, C55, C66, C12, C13, and C23, and its mechanical stability criteria is given by [71,72], Cii>0 (i=1, 2, 3, 4, 5, 6),…”

“…The calculated bulk modulus, shear modulus, Young's modulus, and Poisson's ratio of the Cmcm phase together with the reference materials mentioned above are tabulated in Table 2. As shown in Table 2, the calculated bulk modulus of the Cmcm-HfB4 (243 GPa) is larger than those of HfB [39,40], ZrB12 [63][64][65], and YB4 [8,66] but is comparable to those of HfB2 [43][44][45], HfB12 [48], and other TMB4 (TM= Fe [12,13,67,68], Cr [13,14,69], Mn [11,70], Zr [23], and Ta [27]), indicating its strong ability to resist the volume deformation. Moreover, the bulk modulus (B=243 GPa) for the Cmcm-HfB4 is in consistent with that directly obtained from the fitting results (B0=244 GPa) of the third-order Birch-Murnaghan equation of states, which further demonstrates the good accuracy of our elastic calculations.…”

“…However, the later studied results have shown that the hexagonal WB4 phase is instable and it is actually WB3 with a MoB3-type structure [16][17][18][19]. Theoretically, based on the crystal structure search code and first-principles calculations, the structure and physical properties of boron-rich TM (TM=Ti, V, Mn, Zr, Nb, Mo, Tc, Ta, W, Re, Os, and Ir) compounds have been extensively investigated [20][21][22][23][24][25][26][27][28][29][30]. The obtained results showed that these materials possess high bulk and shear moduli.…”