Structural phase transitions in Si under hydrostatic and uniaxial compression

Phase transitions induced by hydrostatic and uniaxial compression of Si are examined using a density functional–based metadynamics method. A metastable Cmcm structure is predicted to form under hydrostatic compression at 300 K in the pressure range near 20 GPa. Enthalpy calculations indicate that this new phase of Si is energetically competitive with the other Si structures found in this pressure range. This phase is shown to be dynamically stable, with a structure closely related to that of the β-Sn and Imma structures previously identified in experiments. Uniaxial compression at 15 GPa and 300 K obtained simple hexagonal Imma and β-Sn structures. The low energy barrier for the formation of the Cmcm structure from the diamond ambient pressure form suggests that this structure may be seen in experiment with the proper experimental conditions.

Figure 1

The calculated enthalpies per Si atom for selected structures in the pressure range 0–100 GPa. A single curve is used for the Imma and $sH$ structures that have similar enthalpies. Above 15.9 GPa, full optimization on the Imma structure yields the $sH$ structure.

Figure 2

(a) Evolution of the six collective variables (CV) indicating a phase transition in the first 60 metasteps, from the metadynamics simulation at 20 GPa and 300 K. (b) The simulation cell before and after the phase transition, viewed on the (001) and (110) planes. The neighboring crystallographic planes are separated by using different colors (darkness), to highlight the stacking sequence.

Figure 3

The Cmcm and β-Sn structures viewed from three directions. The structures are depicted in the unit cells convenient for structural comparison.

Figure 4

The enthalpies from uniaxial metadynamics trajectories of Si starting from the diamond form at 300 K and 15 GPa. The solid points are the enthalpies of the supercell after quenching to 0 K. Also shown are the quenched diamond, $sH$, and β-Sn structures taken from metasteps 1, 90, and 166.

Figure 5

The calculated (a) phonon dispersion relations and (b) electronic band structure for the predicted Cmcm structure of Si at 24 GPa.

Figure 6

Calculated valence charge densities for the predicted Cmcm structure at 24 GPa.