Structural and electronic properties of $\mathrm{Os}{\mathrm{B}}_2$: A hard metallic material

We calculate the structural and electronic properties of $\mathrm{Os}{\mathrm{B}}_2$ using density functional theory with or without taking into account the spin-orbit (SO) interaction. Our results show that the bulk modulus with and without SO interactions are 364 and $365\mathrm{GPa}$, respectively, both are in good agreement with experiment $(365–395\mathrm{GPa})$. The evidence of covalent bonding of Os-B, which plays an important role to form a hard material, is indicated both in charge density, atoms in molecules analysis, and density of states analysis. The good metallicity and hardness of $\mathrm{Os}{\mathrm{B}}_2$ might suggest its potential application as hard conductors.

Figure 1

(Color online) The crystal structure for $\mathrm{Os}{\mathrm{B}}_2$. The lattice vectors are denoted as $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{c}$.

Figure 2

(Color online) (a) The valence charge density contour (in $\mathrm{e}∕{\mathrm{a.u.}}^3$) plot in the plane including Os1, Os2, B2, and B3. (b) and (c) show, respectively, the valence charge density and difference charge density contour (in $\mathrm{e}∕{\mathrm{a.u.}}^3$) plot in the plane including Os1, B1, and B2. The charge density shown here is the result from the $\mathrm{LDA}+\mathrm{SO}$ calculation. The LDA charge density has similar character. Os1, Os2, B1, B2, and B3 refer to the atoms labeled in Fig. 1a.

Figure 3

(a) Band structure of $\mathrm{Os}{\mathrm{B}}_2$ from the LDA calculation. (b) Band structure of $\mathrm{Os}{\mathrm{B}}_2$ from the $\mathrm{LDA}+\mathrm{SO}$ calculation. $\Gamma =(0,0,0)$, $M=(0,0.5,0)$, $N=(0.5,0.5,0)$, $K=(0.5,0,0)$, and $A=(0,0,0.5)$.

Figure 4

(Color online) Partial and total DOS of $\mathrm{Os}{\mathrm{B}}_2$ from the LDA and $\mathrm{LDA}+\mathrm{SO}$ calculations.