First-principle band calculation of ruthenium for various phases

The total energies and the magnetic moments of Ru for HCP, BCC, FCC, BCT structures were calculated by using a first-principle full-potential linearized augmented plane-wave (FLAPW) method based on the generalized gradient approximation (GGA). HCP has the lowest energy among the structures calculated, which agrees with the experimental result that HCP is the equilibrium phase of Ru. The total energy of BCT Ru has the local minimum at c/a=√2 (FCC) with a=5.13 au, c=7.25 au and c/a=0.83 with a=6.15 au, c=5.11 au. It is pointed out that these phases are possibly metastable. The BCC structure, which corresponds to BCT with a=c=5.78 au, is unstable because it is at a saddle point of the total energy. BCT Ru of c/a<1 has a magnetic moment at the stable volume