Elastic Moduli in Nano-Size Samples of Amorphous Solids: System Size Dependence

TL;DR

This paper presents a theoretical explanation for the observed decrease in shear modulus in nano-sized amorphous solids, attributing it to the increased influence of surface modes as sample size diminishes.

Contribution

It introduces a theory linking surface effects to elastic modulus reduction in nano-sized amorphous solids, supported by eigenvalue analysis of the Hessian matrix.

Findings

Surface modes significantly impact shear modulus in nano-sized amorphous solids.

The reduction in shear modulus is more pronounced in amorphous than crystalline samples.

The theory aligns with recent experimental observations.

Abstract

This Letter is motivated by some recent experiments on pan-cake shaped nano-samples of metallic glass that indicate a decline in the measured shear modulus upon decreasing the sample radius. Similar measurements on crystalline samples of the same dimensions showed a much more modest change. In this Letter we offer a theory of this phenomenon; we argue that such results are generically expected for any amorphous solid, with the main effect being related to the increased contribution of surfaces with respect to bulk when the samples get smaller. We employ exact relations between the shear modulus and the eigenvalues of the system's Hessian matrix to explore the role of surface modes in affecting the elastic moduli.