Negative Thermal expansion of pure and doped Graphene

TL;DR

This study investigates the negative thermal expansion behavior of pure and doped graphene using ab initio calculations, revealing the dominant role of transverse acoustic phonon modes in this phenomenon.

Contribution

It provides a detailed ab initio analysis of how B/N doping affects the negative thermal expansion in graphene and highlights the importance of ZA phonon modes in 2D materials.

Findings

LTEC of pure graphene is approximately -3.26×10⁻⁶ K⁻¹ at room temperature.

B/N doping makes the LTEC more negative across the temperature range studied.

ZA phonon modes are primarily responsible for negative thermal expansion in graphene.

Abstract

Graphene and its derivatives distinguish themselves for their large negative thermal expansion even at temperatures as high as 1000K. The linear thermal expansion coefficients (LTEC) of two-dimensional honeycomb structured pure graphene and B/N doped graphene are analyzed using ab initio density functional perturbation theory (DFPT) employed in VASP software under quasiharmonic approximation. One of the essential ingredients required is the phonon frequencies for a set of points in the Brillouin zone and their volume dependence. These were obtained from the dynamical matrix which was calculated using VASP code in interface with phonopy code. In particular, the transverse acoustic modes (ZA) behave drastically differently as compared to planer modes and so also their volume dependence. Using this approach firstly thermal expansion for pure graphene is calculated. The results agree with earlier calculations using similar approach. Thereafter we have studied the effect of boron and nitrogen doping on LTEC. The LTEC of graphene is found to be negative in the entire range of temperature under study (0-1000K) and its value at room temperature (RT) is around -3.26X10-6K-1. The value of LTEC at RT becomes more negative with B/N doping in graphene. In order to get an insight into the cause of negative thermal expansion, we have computed the contribution of individual phonon modes of vibration. We notice that it is principally the ZA modes which are responsible for negative thermal expansion. It has been concluded that transverse mode in 2D hexagonal lattices have an important role to play in many of the thermodynamical properties of 2D structures. We have extended the study to calculate the LTEC of h-BN sheet also.