Lindemann Parameters for solid Membranes focused on Carbon Nanotubes

TL;DR

This paper investigates how temperature-induced out-of-plane fluctuations affect the Lindemann melting criterion in graphene and carbon nanotubes, revealing that such fluctuations are dominant but have limited impact on melting temperatures.

Contribution

It introduces a self-consistent Born approximation to modify the Lindemann criterion considering out-of-plane fluctuations in 2D materials.

Findings

Out-of-plane fluctuations dominate over in-plane ones.

Large out-of-plane fluctuations minimally affect melting temperature.

Restrictions on Lindemann parameters are identified due to fluctuations.

Abstract

Temperature fluctuations in the normal direction of planar crystals such as graphene are quite violent and may be expected to influence strongly their melting properties. In particular, they will modify the Lindemann melting criterium. We calculate this modification in a self-consistent Born approximation. The result is applied to graphene and its wrapped version represented by single-walled carbon nanotubes (SWNTs). It is found that the out-of-plane fluctuations dominate over the in-plane fluctuations. This makes strong restrictions to possible Lindemann parameters. Astonishing we find that these large out-of-plane fluctuations have only a small influence upon the melting temperature.