Solid-solid phase transitions and soft phonon modes in highly condensed Si

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Abstract
The pseudopotential method is used to examine the structural transitions of Si from β-Sn to simple hexagonal (sh) to hexagonal close packed (hcp). The calculated transition pressures, transition volumes, and c/a ratios are in good agreement with the measured values. Furthermore, the phase-transition pressure from hexagonal close packed to face-centered cubic is predicted to be 1.2 Mbar. The phonon frequencies are also calculated with use of the frozen-phonon approximation for the β-Sn, sh, and hcp phases. For both the β-Sn and sh phases, pressure-sensitive soft phonon modes exist. These are the longitudinal optic mode at the Brillouin-zone center for β-Sn and the transverse acoustic mode at the Brillouin-zone boundary for sh in the [001] direction. These soft modes are most likely associated with the phase transformations from β-Sn to sh to hcp. The metallic sh phase has strong covalent interlayer bonding. This is opposite to the case for the graphite structure. The weak bonding in the hexagonal plane of the sh phase causes the soft transverse mode for this phase.