Crystal structures, elastic properties, and hardness of high-pressure synthesized CrB2 and CrB4

Hardness, elastic, and electronic properties of chromium monoboride

“…Figure S2 shows the relative cell parameters as a function of pressure; 19 CrB displays more nearly isotropic compressibility compared to CrB 2 . 11 As expected, the c-axis is slightly less compressible than the a and b axes because the zigzag boron-boron chains are primarily along the c direction. While along the a and b directions, the axial compressibility is mainly determined by the strength of Cr-B and Cr-Cr bonds.…”

“…As shown in Figure 2, the determined asymptotic hardness of CrB is $19.6 (0.7) GPa, which is comparable to that of the well-known WC and OsB 2 . However, CrB shows higher hardness over CrB 2 (16 GPa under the load of 500 g), 11 indicating that the boron content is not necessarily a determining factor for the design of hard and superhard materials. As will be discussed later in the paper, the enhanced mechanical behavior of CrB is mainly attributed to the strong 3D Cr-B and zigzag B-B bonding networks.…”

“…Consequently, a series of diborides and tetraborides of transition metals have been synthesized and investigated by both experiments and theoretical calculations. [6][7][8][9][10][11] Of the transition metal diborides, OsB 2 , 6 RuB 2 , and ReB 2 7 are typical examples that can be synthesized at ambient pressure. OsB 2 possesses high elastic moduli but a low hardness due to the presence of weak metallic bonds.…”

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

“…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.…”

“…On the other hand, d valence electrons are also considered to contribute to the hardness of TM compounds. According to this design criterion, many TM borides have been synthesized, such as ReB2 [5], OsB2 [6], RuB2 [7], YB4 [8], MnB4 [9][10][11], FeB4 [12], CrB4 [13,14] and son on. Also, WB4 with a hexagonal structure (P63/mmc, Z = 4) was synthesized at ambient pressure and was proposed to be a potential superhard material with the claimed hardness of 31.8-46.2 GPa [15].…”