Theoretical insights on structural, mechanical and thermodynamic properties of MCoB (M=Nb, Mo, and W) ternary borides under high pressure

In this work, the effects of the high pressure on the structural, mechanical and thermodynamic properties of MCoB (M = Nb, Mo, and W) ternary borides were calculated through the first-principles. The formation enthalpy and phonon dispersion results indicate that these ternary borides are thermodynamically and dynamically stable. In addition, the high pressure can enhance the thermodynamic stability of these ternary borides. The elastic constants and elastic modulus of these ternary borides increased with the pressure increase, and the elastic anisotropy sequence is NbCoB > MoCoB > WCoB. The states density proved that no phase transition occurs at pressures between of 0 and 50 GPa, and that the stability of these ternary borides also increased with the pressure increase. Furthermore, the influence of high pressure (0-50 GPa) and temperature (0-1500 K) on the thermo-dynamic properties of these ternary borides are systematically studied based on the Quasi-harmonic Debye model. The findings show that the isothermal bulk modulus and the Debye temperature of these ternary borides increase by increasing the pressure and decreasing the temperature, while the volume showed a reverse change trend. The constant volume heat capacity and the constant pressure heat capacity of these ternary borides slowly decrease with the pressure increase, while the thermal expansion coefficient of these ternary borides is more sensitive to the pressure than to the temperature.