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The phase stability and mechanical properties of tungsten borides W(2)B, WB, WB(2), W(2)B(5) and WB(4) were extensively studied by first-principles calculations within density functional theory. The thermodynamic and mechanical stabilities were examined. Our calculations on the enthalpy-pressure relationship and convex hulls have demonstrated that at zero pressure, the experimentally observed W(2)B-W(2)B (W(2)B-W(2)B represents W(2)B in W(2)B structure type, the same hereinafter) and WB-WB, and assumed WB(2)-ReB(2) phases are stable against decomposition into other components. The estimated hardness of WB(2)-ReB(2) is 39.4 GPa, suggesting that it is a potentially hard compound. At 60 GPa, the most stable phases are WB-WB and WB(2)-WB(2). WB-WB, WB(2)-AlB(2) and WB(4) are the ground state phases at 100 GPa. The phase transition mechanism for WB(2) was discussed. The synthesis of WB(2)-AlB(2) could be conducted at high pressures.

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The phase stability and elastic properties of Re-B system were systematically investigated by use of the density functional theory. The formation enthalpies are negative for Re(3)B, Re(7)B(3), Re(2)B, ReB, Re(2)B(3), and ReB(2), indicating that they are thermodynamically stable. Re(7)B(3), Re(2)B, ReB, Re(2)B(3), and ReB(2) are mechanically stable. Combining the study of enthalpy and pressure relationship with the convex hull, it was found that the ground state phases are Re(3)B, Re(7)B(3), and ReB(2) at zero pressure, in agreement with the experimental observations. At the pressure of 90 GPa, Re(3)B, and ReB(2) are the most stable phases.

The structural, electronic, and mechanical properties of TaN were investigated by use of the density functional theory (DFT). Eight structures were considered, i.e., hexagonal WC, TaN, NiAs, wurtzite, and CoSn structures, cubic NaCl, zinc-blende and CsCl structures. The results indicate that TaN in TaN-type structure is the most stable at ambient conditions among the considered structures. Above 5 GPa, TaN in WC-type structure becomes energetically the most stable phase. They are also stable both thermodynamically and mechanically. TaN in WC-type has the largest shear modulus 243 GPa and large bulk modulus 337 GPa among the considered structures. The volume compressibility is slightly larger than diamond, but smaller than c-BN at pressures from 0 to 100 GPa. The compressibility along the c axis is smaller than the linear compressibility of both diamond and c-BN. The estimated hardness is 34 GPa. Thus, TaN in WC-type structure is a potential candidate to be ultra-incompressible and hard. The unique mechanical properties of TaN in WC-type structure would make it suitable for applications under extreme conditions.

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