Electronic structures and properties of Ti, Zr and Hf metals

The electronic structures of pure Ti, Zr and Hf metals with hcp structure were determined by one-atom (OA) theory. According to the electronic structures of these metals, their potential curves, cohesive energies, lattice constants, elasticities and the temperature dependence of linear thermal expansion coefficients were calculated. The electronic structures and characteristic properties of these metals with bee and fee structures and liquids were also studied. The results show that the electronic structures of Ti, Zr and Hf metals are respectively [Ar] (3d(n))(0.4810) (3d(c))(2.0857) (4s(c))(1.0000) (4s(f))(0.4333) [Kr] (4d(n))(0.3968) (4d(c))(2.1428) (5s(c))(1.2620) (5s(f))(0.1984), [Xe] (5d(n))(0.3680) (5d(c))(2.0414) (6s(c))(1.4066) (6s(f))(0.1840). It is explained why the pure Ti, Zr and Hf metals with hcp and bcc structures can exist naturally, while those with fcc structure can not.