First-principles calculations of the lattice instability and the symmetry-lowering modulation of PtSi

Abstract

We have investigated the vibrational properties of orthorhombic PtSi by performing first-principles calculations. The calculated phonon band structure shows unstable phonon modes around the Γ-point. The ionic displacement vectors associated with the unstable Γ-point phonon mode suggest a structural modulation to a lower-symmetry phase, which was confirmed by comparing the theoretical equations of states of the modulated (P212121) and the unmodulated (Pnma) PtSi. The symmetry-reduced modulated orthorhombic PtSi shows a phonon band gap. We attribute the origin of the phonon band gap to the separation of the low-frequency Pt phonon modes and the high-frequency Si phonon modes due to the large atomic mass difference between Pt and Si.