Revisiting the Phillips ionicity of conductors and the quantitative determination of the hardness of carbides and nitrides of transition metals using the LDA ++ U technique

The Phillips ionicity is modified, simulated and calculated for conductors. The results show that the percentage of metallic bonding in multiplex chemical bonds of transition metal (TM) carbides and nitrides is large; this affects the Phillips ionicity. The redefinition of Phillips ionicity has been applied to estimate the hardness of TM carbides and nitrides; the values obtained are in agreement with experimental and theoretical evidence. In addition, materials with the zinc blende structure are harder than those with rock salt structure.