First-principles calculation of the structural stability of $6d$ transition metals

The phase stability of the $6d$ transition metals (elements 103–111) is investigated using first-principles electronic-structure calculations. Comparison with the lighter transition metals reveals that the structural sequence trend is broken at the end of the $6d$ series. To account for this anomalous behavior, the effect of relativity on the lattice stability is scrutinized, taking different approximations into consideration. It is found that the mass-velocity and Darwin terms give important contributions to the electronic structure, leading to changes in the interstitial charge density and, thus, in the structural energy difference.

Figure 1

Equilibrium bulk properties of $4d$ and $6d$ transition metals calculated for the ground-state crystal structures. (Main figure) Wigner-Seitz radii of $4d$ and $6d$ transition metals. (Inset) Bulk moduli for the $4d$ and $6d$ transition metals. For the $4d$ metals, the experimental data[17] are also shown (stars).

Figure 2

(Main figure) Total energies of the bcc (closed symbols) and hcp (open symbols) structures relative to that of the fcc structure for the $6d$ metals. (Inset) Energy differences for the $4d$ metals. For both series, the SR approximation was used.

Figure 3

(Color online) (Upper panel) DOS for silver in the bcc structure. (Lower panel) DOS for roentgenium in the bcc structure. NR (solid line) and SR (dashed line) approximations were used. $s$ DOS (red, dark gray), $p$ DOS (green, light gray), and $d$ DOS (black) are shown.

Figure 4

(Color online) DOS for darmstadtium in the bcc structure. NR (solid line) and SR (dashed line) approximations were used. $s$ DOS (red, dark gray), $p$ DOS (green, light gray), and $d$ DOS (black) are shown.