Physical properties of the $6d$-series elements from density functional theory: Close similarity to lighter transition metals

We have calculated some of the physical properties of the recently discovered 6$d$ elements by density functional theory. Comparison with those of the 5$d$ metals shows that there is a close analogy for the crystal structures, for parabolic variation of equilibrium atomic volumes and bulk moduli, and an almost linearly increasing behavior of the pressure derivative of the bulk modulus across the 6$d$ series. The Friedel model that is used to explain these trends for homologous series also holds for 6$d$ metals. These elements also seem to be placed correctly in the Periodic Table.

Figure 1

Relative energy (Ry/atom) as a function of volume (Å${}^3$) for Rf in hcp, ω (omg), bcc, and fcc structures.

Figure 2

Comparison of equilibrium atomic volumes (Å${}^3$) across the 6$d$ and 5$d$ transition-metal series.

Figure 3

Comparison of bulk moduli across the 6$d$ and 5$d$ transition-metal series.

Figure 4

Comparison of pressure derivative of bulk modulus ($K_0$′) across the 6$d$ and 5$d$ transition-metal series.

Figure 5

Density of states (DOS) in states/eV of Rf, Hs, and Ds compared to Hf, Os, and Pt. The line at zero energy indicates the Fermi energy.