Continuum elastic sphere vibrations as a model for low-lying optical modes in icosahedral quasicrystals

TL;DR

This paper models low-lying optical vibrational modes in icosahedral quasicrystals using continuum elastic spheres, successfully explaining experimental observations and highlighting the importance of clusters in their vibrational behavior.

Contribution

It introduces a continuum elastic sphere model to interpret optical modes in icosahedral quasicrystals, linking cluster vibrations to observed neutron scattering data.

Findings

Most optical modes are explained by the sphere model.

Mechanical connection clarifies mode assignments in Al-Pd-Mn.

Supports the significance of clusters in quasicrystal vibrations.

Abstract

The nearly dispersionless, so-called "optical" vibrational modes observed by inelastic neutron scattering from icosahedral Al-Pd-Mn and Zn-Mg-Y quasicrystals are found to correspond well to modes of a continuum elastic sphere that has the same diameter as the corresponding icosahedral basic units of the quasicrystal. When the sphere is considered as free, most of the experimentally found modes can be accounted for, in both systems. Taking into account the mechanical connection between the clusters and the remainder of the quasicrystal allows a complete assignment of all optical modes in the case of Al-Pd-Mn. This approach provides support to the relevance of clusters in the vibrational properties of quasicrystals.