Elastic anisotropy of OsB2 and RuB2 from first-principles study

Intrinsic hardness of crystalline solids

“…1, b, except that the hardness values obtained from the linear fit are somewhat higher. In passing, it is noteworthy that the Vickers hardness for the recently synthesized "ultraincompressible" OsB 2 [35] from the hardness-shear modulus curve using the theoretical G of 206 GPa is 25-31 GPa [36]. This value is comparable to 35 GPa [37] calculated with the parameter -free expression Eq.…”

Debye Temperatures of Transition Metal Diborides TMB2 (TM= Ti, Zr, Os, Nb, Ru) Under Pressure

“…The Debye temperature for RuB2 at various temperatures and pressures is given in Table 1 and presented in Figure 1. The calculated Debye temperature at T = 0 K is 796.2J/mol/K, which is in agreement with the result (780J/mol/K) from Hao et al [14]. From Figure 1, one can find: (a) When the temperature keeps constant, the Debye temperature almost linearly increases with applied pressures (b) When the pressure keeps constant, the Debye temperature decreases with the increasing temperatures; (c) The Debye temperature at the temperature of 1100K is lower than that at 300K, which shows that the vibration frequency of the particles in RuB2 changes with the pressures and the temperatures.…”

Advancements in the Search for Superhard Ultra‐Incompressible Metal Borides

“…Various first-principles theoretical studies have also been performed to elucidate the origin of osmium diboride's high hardness. [52,[54][55][56][57][58] Electronic charge density contour plots and local density approximation density of states (DOS) calculations reveal that OsB 2 is metallic, but covalent bonding exists between BÀB and OsÀB leading to the high hardness, the latter due to strong overlap between the transition metal d states and the boron p states. [55,57] The anisotropy of OsB 2 was further studied by density functional theory calculations to determine the ideal shear strength along specific crystallographic directions by Yang et al [59] Their results reveal that in the (001) plane, the ideal shear strength along the h010i direction is 9.1 GPa, whereas along the h100i direction the ideal shear strength is nearly three times as large with a value of 26.9 GPa.…”