Enhanced Vibrational Stability in Glass Droplets

Abstract

We show through simulations of amorphous solids prepared in open boundary conditions that they possess significantly fewer low-frequency vibrational modes compared to their periodic boundary counterparts. Specifically, using measurements of the vibrational density of states, we find that the $D(\omega )\sim {\omega }^4$ law changes to $D(\omega )\sim {\omega }^{\delta }$ with $\delta \approx 5$ in two dimensions and $\delta \approx 4.5$ in three dimensions. Crucially, this enhanced stability is achieved when utilizing slow annealing protocols to generate solid configurations. We perform an anharmonic analysis of the minima corresponding to the lowest-frequency modes in such open-boundary systems and discuss their correlation with the density of states. A study of various system sizes further reveals that small systems display a higher degree of localization in vibrations. Lastly, we confine open-boundary solids in order to introduce macroscopic stresses in the system which are absent in the unconfined system, and find that the $D(\omega )\sim {\omega }^4$ behavior is recovered.

arXiv comment12 pages, 11 figures

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• Testing the Heterogeneous-Elasticity Theory for low-energy excitations in structural glasses
• Further testing the validity of generalized heterogeneous-elasticity theory for low-frequency excitations in structural glasses