First-principles study on the high-pressure behavior of the zone-center modes of lonsdaleite silicon

Using a first-principles method, I have studied the static and vibrational properties of the lonsdaleite-silicon. The frequencies of the Raman active modes of the lonsdaleite-Si at ambient pressure agree very well with the ex perimental results. Among these Raman active modes, the E-2g mode can be an indication mode of the lonsdaleite-Si. The high-pressure behavior of the z one-center modes of the lonsdaleite-Si is first studied and a pressure-indu ced mode softening is found. The E-2u mode of the lonsdaleite-Si exhibits r ed shift under compression and its frequency decreases to zero as the appli ed pressure increases to around 14 GPa. The pressure-induced mode softening of the E-2u mode indicates that the lonsdaleite-Si has a phase transition before the applied pressure reaches 14 GPa.