Structural, anisotropic elastic and thermal properties of MB (M=Ti, Zr and Hf) monoborides

Insight into structural, mechanical, electronic and thermodynamic properties of intermetallic phases in Zr–Sn system from first-principles calculations

“…Generally, the C 11 , C 22 and C 33 reflect the resistance to linear compression along x, y and z directions, respectively [52]. From Table 4, it can be seen that the values of Table 5.…”

“…Moreover, the bulk modulus also provides a measure of the average bond strength of atoms for the given crystal [52], which means the Zr 5 Sn 3 has the strongest average bond strength of atoms and the ZrSn 2 has the weakest one among Zr-Sn intermetallic compounds. From Table 5 and Table 2, one may remark that the bulk modulus B of the Zr-Sn intermetallic compounds are a little higher than B 0 except Zr 5 Sn 3 with a difference lower than 1 %.…”

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.…”

“…Compared with the bulk modulus, the shear modulus of a material describes its resistance to the shear deformation and is a more accurate predictor of the potential hardness. From Table 2, the calculated shear module for the predicted Cmcm phase is 240 GPa, which is bigger than those of HfB [39,40], HfB12 [48], ZrB12 [63,64], YB4…”

“…Recently, an experimental study showed that the high-pressure cubic HfB12 phase can be successfully stabilized in the Y1-xHfxB12 system under ambient pressure [37]. Furthermore, the crystal structure and related physical properties of HfB, HfB2, and HfB12 have been widely investigated [38][39][40][41][42][43][44][45][46][47][48]. However, there is no experimental report on the synthesis of hafnium tetraborides; besides, the theoretical research works of hafnium tetraborides are also seldom up to now.…”