Elastic properties of graphene flakes: boundary effects and lattice vibrations

TL;DR

This study investigates how boundary effects and lattice vibrations influence the elastic properties of graphene flakes, revealing size-dependent variations in elastic constants and the significance of vibrational zero point motion.

Contribution

It provides a detailed density functional theory analysis of boundary effects and vibrational corrections on graphene's elastic properties, highlighting size-dependent variations.

Findings

Edge effects cause up to 30% change in elastic constants in small flakes.

Vibrational zero point motion decreases bending rigidity by approximately 26%.

Vibrational frequencies and elastic properties depend on flake size.

Abstract

We present a calculation of the free energy, the surface free energy and the elastic constants ("Lam'e parameters" i.e, Poisson ratio, Young's modulus) of graphene flakes on the level of the density functional theory employing different standard functionals. We observe that the Lam'e parameters in small flakes can differ from the bulk values by 30% for hydrogenated zig-zag edges. The change results from the edge of the flake that compresses the interior. When including the vibrational zero point motion, we detect a decrease in the bending rigidity by ~26%. This correction is depending on the flake size, N, because the vibrational frequencies flow with growing N due to the release of the edge induced compression. We calculate Grueneisen parameters and find good agreement with previous authors.