Lattice dynamics study of vibrational modes in gold Σ5[001] twist boundary

The dynamical matrix was constructed for the equilibrium structure precalculated by means of a molecular statics computer simulation for the case of a bi-crystal with a Σ5[001] twist boundary in gold. The eigenstates analysis indicates a pure boundary mode in a small volume of the Brillouin zone, while a resonance with the bulk states occurs in the complementary volume in momentum space. This degenerated state develops at a frequency equal approximately to 2 × 10¹³ s^-1. The eigenvectors are analyzed and it is shown that the local modes consist of a collective in-plane displacement of the four atoms around the O-lattice point. These modes represent an external libration mode and a coupled breathing mode. The total r.m.s. displacement in the boundary is close to the bulk one. The physical significance of the local mode together with possible implications and its effect on the scattered X-ray intensity are discussed.