Bond deformation paths and electronic instabilities of ultraincompressible transition metal diborides: Case study of ${\mathrm{OsB}}_2$ and ${\mathrm{IrB}}_2$

The energetically most stable orthorhombic structure of ${\mathrm{OsB}}_2$ and ${\mathrm{IrB}}_2$ is dynamically stable for ${\mathrm{OsB}}_2$ but unstable for ${\mathrm{IrB}}_2$. Both diborides have substantially lower shear strength in their easy slip systems than their metal counterparts. This is attributed to an easy sliding facilitated by out-of-plane weakening of metallic Os-Os bonds in ${\mathrm{OsB}}_2$ and by an in-plane bond splitting instability in ${\mathrm{IrB}}_2$. A much higher shear resistance of Os-B and B-B bonds than Os-Os ones is found, suggesting that the strengthened Os-B and B-B bonds are responsible for hardness enhancement in ${\mathrm{OsB}}_2$. In contrast, an in-plane electronic instability in ${\mathrm{IrB}}_2$ limits its strength. The electronic structure of deformed diborides suggests that the electronic instabilities of $5d$ orbitals are their origin of different bond deformation paths. Neither ${\mathrm{IrB}}_2$ nor ${\mathrm{OsB}}_2$ can be intrinsically superhard.

Figure 1

(a) Formation energy of ${\mathrm{OsB}}_2$ and ${\mathrm{IrB}}_2$ calculated by DFT to determine the possible ground-state phases of 33 commonly observed Tm-B, Tm-C, Tm-N, Tm-Al, Tm-Si ICSD structure types and the newly reported diborides by the crystal structure evolutionary search method. Calculated phonon dispersion curves for (b) ${\mathrm{OsB}}_2$ and (c) ${\mathrm{IrB}}_2$ in oP6[59] structure.

Figure 2

Bond structures at equilibrium for (a) ${\mathrm{IrB}}_2$ and (b) ${\mathrm{OsB}}_2$. The isosurface maps of the valence charge density difference (VCDD) correspond to ±0.01 electrons/${\mathrm{bohr}}^3$. Partial electronic density of states of (c) ${\mathrm{IrB}}_2$ and (d) ${\mathrm{OsB}}_2$. The numbers close to Ir and Os atoms are the Bader charges.

Figure 3

(a) Stress-strain and (b) energy-strain relationships for ${\mathrm{IrB}}_2$ and ${\mathrm{OsB}}_2$ along the weakest deformation path [100](001). The isosurfaces of deformed valence charge density difference (VCDD) at shear strain of (c) γ = 0.2899 (before) and (d) γ = 0.4660 (after) instability for ${\mathrm{IrB}}_2$, and (e) γ = 0.2899 (before) and (f) γ = 0.4660 (after) instability for ${\mathrm{OsB}}_2$ in the (001)[100] slip system. The isosurfaces of VCDD correspond to +/−0.01 electrons/${\mathrm{bohr}}^3$.

Figure 4

Orbital-decomposed electronic density of states of ${\mathrm{IrB}}_2$ (a) at equilibrium (b) at strain of 0.2899, (c) at strain of 0.4660, and of ${\mathrm{OsB}}_2$ (d) at equilibrium (e) at strain of 0.2899, (f) at strain of 0.4660.