Graphene: a partially ordered non-periodic solid.

Dongshan Wei,Feng Wang

doi:10.1063/1.4897255

Abstract

Molecular dynamics simulations were performed to study the structural features of graphene over a wide range of temperatures from 50 to 4000 K using the PPBE-G potential [D. Wei, Y. Song, and F. Wang, J. Chem. Phys. 134, 184704 (2011)]. This potential was developed by force matching the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional and has been validated previously to provide accurate potential energy surface for graphene at temperatures as high as 3000 K. Simulations with the PPBE‑G potential are the best available approximation to a direct Car-Parrinello Molecular Dynamics study of graphene. One advantage of the PBE-G potential is to allow large simulation boxes to be modeled efficiently so that properties showing strong finite size effects can be studied. Our simulation box contains more than 600,000 C atoms and is one of the largest graphene boxes ever modeled. With the PPBE-G potential, the thermal-expansion coefficient is negative up to 4000 K. With a large box and an accurate potential, the critical exponent for the scaling properties associated with the normal-normal and height-height correlation functions was confirmed to be 0.85. This exponent remains constant up to 4000 K suggesting graphene to be in the deeply cooled regime even close to the experimental melting temperature. The reduced peak heights in the radial distribution function of graphene show an inverse power law dependence to distance, which indicates that a macroscopic graphene sheet will lose long-range crystalline order as predicted by the Mermin-Wagner instability. Although graphene loses long-range translational order, it retains long range orientational order as indicated by its orientational correlation function; graphene is thus partially ordered but not periodic.

Highlights

Graphene is a two-dimensional (2D) material that has the structure of a graphite monolayer.1 Perfectly flat graphene will have a zero band gap
The thermal-expansion coefficient (TEC) of graphene is negative in the entire temperature range, consistent with a recent study by Pozzo et al with Projector Augmented Wave (PAW)-PBE in a much smaller 512 C simulation box at up to 2000 K.42
We performed molecular dynamics (MD) simulations on large graphene sheets with the realistic and efficient PPBE-G potential recently developed by force matching PAW-PBE at finite temperatures

Summary

INTRODUCTION

Graphene is a two-dimensional (2D) material that has the structure of a graphite monolayer. Perfectly flat graphene will have a zero band gap. The experimental observation of large graphene sheets surprised the scientific community initially This was due to the argument that no 2D material can exist over a large length scale. The PeierlsLandau argument states that there could be no long range crystalline order in 1D and 2D materials This is generally referred to as the Mermin-Wagner instability.. The bonding connectivity between neighboring molecules cannot change This is true for graphene under a wide range of temperatures. The Mermin-Wagner instability only rules out long range translational order but allows the existence of 2D materials Another interesting property that can be derived for nonself-avoiding (phantom) flat membrane is the existence of a universal scaling factor as a function of size for the power spectra of normal-normal correlation function and the heightheight correlation function.

COMPUTATIONAL DETAILS

RESULTS AND DISCUSSIONS

SUMMARY