Ultra-incompressible Ternary Diborides Re_（0.5）Ir_（0.5）B_2,Re_（0.5）Tc_（0.5）B_2,Os_（0.5）W_（0.5）B_2 and Os_（0.5）Ru_（0.5）B_2：Density Functional Calculation

In this paper, density functional computations have been applied to the structural, elastic and electronic properties of ternary transition metal diborides Re0.5Ir0.5B2, Re0.5Tc0.5B2, Os0.5W0.5B2 and Os0.5Ru0.5B2 in hexagonal (P63/mmc) and orthorhombic (Pmmn) structures with both local density approximation and generalized gradient approximation. LDA gives smaller lattice parameters and larger elastic moduli than GGA. Both results show that the hexagonal ones are more stable than orthorhombic ones except Os0.5Ru0.5B2. Moreover, the hexagonal structure has superior elastic property than orthorhombic one. Generally speaking, the calculated elastic moduli of Re0.5Ir0.5B2 and Os0.5Ru0.5B2 are smaller than those values of Re0.5Tc0.5B2 and Os0.5W0.5B2 within the same structure because of the filling of antibonding states. The relativistic effects result in weaker bonds of Tc-B (Ru-B) than those of Re-B (Os-B). All the diborides are ultra-incompressible. Re0.5Tc0.5B2 has the largest shear modulus and it is a promising superhard diboride like Os0.5W0.5B2. The elastic properties are in high correlation with the bond strength. The shear moduli are more sensitive than the bulk moduli to the bond strength.