Voronoi-Delaunay analysis of normal modes in a simple model glass

Abstract

We combine a conventional harmonic analysis of vibrations in a one-atomic model glass of soft spheres with a Voronoi-Delaunay geometrical analysis of the structure. ``Structure potentials'' (tetragonality, sphericity or perfectness) are introduced to describe the shape of the local atomic configurations (Delaunay simplices) as function of the atomic coordinates. Apart from the highest and lowest frequencies the amplitude weighted ``structure potential'' varies only little with frequency. The movement of atoms in soft modes causes transitions between different ``perfect'' realizations of local structure. As for the potential energy a dynamic matrix can be defined for the ``structure potential''. Its expectation value with respect to the vibrational modes increases nearly linearly with frequency and shows a clear indication of the boson peak. The structure eigenvectors of this dynamical matrix are strongly correlated to the vibrational ones. Four subgroups of modes can be distinguished.

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• Spatial structure of quasi-localized vibrations in nearly jammed amorphous solids
• Vibrations and Relaxations in a Soft Sphere Glass: Boson Peak and Structure Factors
• Statistical Topology of Three-Dimensional Poisson-Voronoi Cells and Cell Boundary Networks
• Three-dimensional Random Voronoi Tessellations: From Cubic Crystal Lattices to Poisson Point Processes
• Collectivity of motion in undercooled liquids and amorphous solids
• Resonant Coupling and the Non-Phononic Flat Band in Amorphous Solids