Ab initio study of high-pressure behavior of a low compressibility metal and a hard material: Osmium and diamond

We performed Density-Functional electronic structure calculations in order to investigate the high pressure behavior of Os beyond what is tractable experimentally with a diamond-anvil cell. In addition to the room-temperature and pressure structure hcp, two hypothetical structures of Os have been considered: fcc and $\omega$ (hexagonal phase with three atoms by unit cell). Phase transitions are suggested by these calculations. For calculating the bulk modulus, the reciprocal of the compressibility, of Os and that of diamond, the computed total energies vs volume curves were fit to three different equations of state. Several volume ranges have been considered during the fitting procedure. First, it is shown that the claim of Cynn and co-workers [Phys. Rev. Lett. 88, 135701 (2002)] is confirmed at weak compression. Osmium is less compressible than diamond which is known as the hardest and the least compressible material. However, with increasing pressure osmium becomes more compressible than diamond. At strong compression, osmium transforms to the $\omega$ phase. It is also shown that the reconstructive phase transition $\mathrm{hcp}\to \mathrm{fcc}$ could be induced by cooling in this low compressibility material.

Figure 1

Total energy convergence (fhi98md package, Ref. 13). Computed total energy of osmium as function of basis set size (right) and electronic self-consistency iterations (left).

Figure 2

(Left) Total energy of diamond as a function of volume (open circles). For comparison, results obtained by two other groups are reported [crosses (Ref. 19) and dots (Ref. 20)]. Solid line is the best fit which can be achieved with Vinet or Poirier-Tarantola EOS. (Right) Total energy of osmium as a function of volume with a small basis set (hcp-1) and a more larger basis set (hcp-2).

Figure 3

Total energy vs volume for the hcp structure and two hypothetical structures of Os: fcc and $\omega$ $(D_{6h}^1=P6∕mmm)$. $V_o$ is the equilibrium volume of the hcp structure (see Fig. 2). Arrows show crossing points. Pressures at which occur phase transitions are given by the common tangents.