Phonons in the beta-tin, Imma, and sh phases of Silicon from ab initio calculations

We present a new interpretation of measured Raman frequencies of a high-pressure structure of Silicon which was assigned previously to the beta-tin phase. Our results show that the beta-tin->Imma->sh phase transitions have been already indicated in this experiment which was performed before the discovery of the Imma phase. We have calculated phonon-dispersion curves for the beta-tin, Imma, and sh phases of silicon using the plane-wave pseudopotential approach to the density-functional theory and the density-functional perturbation theory within the local density approximation. With the new assignment, the calculated phonon frequencies display an excellent agreement with the experimental data, and can be also used to determine precisely the transition pressure for the Imma->beta-tin phase transition. The sh->Imma transition is accompanied by soft modes.Comment: 4 pages, 5 figure