Icosahedral order in glass: Acoustic properties

Abstract

An icosahedral crystal in the non-Euclidean three-dimensional space ${S}^{3}$ models domains of icosahedral order in metallic glass. Crystal symmetries allow explicit construction and classification of vibrational eigenstates. We evaluate phonon frequencies numerically. Long-wavelength, low-frequency vibrations follow the predictions of continuum elastic theory in ${S}^{3}$, and of a hypothetical perfect icosahedral crystal in ${R}^{3}$. Isotropy of elastic moduli distinguishes icosahedral order from face-centered-cubic order.