Abstract
Graphene was first isolated in the lab in 2003 and this work was first published in 2004 by a research team at The University of Manchester. Since that date, graphene research has exploded due to its special properties. Phonons and molecular dynamic simulation provide valuable tools to study the molecular systems under different structure forms. They are helpful to study graphene ribbons and defects. On the other hand, many machine learning techniques were extensively used to analyse the enormous amounts of data resulted from the molecular simulations. As such, this thesis aimed to use one of the machine learning techniques to study phonons of graphene with single vacancy defect and graphene armchair nanoribbons. PCA can be used to transform the atomic velocities into orthogonal eigenvectors such that each eigenvector represents one of the phonon modes of graphene. This is helpful to visualize the atomic motion of a specific phonon mode. To provide orthogonal eigenvectors, PCA needs the data to be of gaussian distribution. The atomic velocities resulted from the molecular simulations follow gaussian distribution at the equilibrium state. Hence, the assumption of gaussian distribution needed by PCA is achieved. However, only some of the phonon modes can be calculated from the atomic velocities in their real space. Most of the phonon modes are calculated after transforming the atomic velocities to a reciprocal space (k space) using spatial Fourier transform. The k space atomic velocities are not following gaussian distribution. This thesis introduced a novel method to use PCA to isolate and visualize the phonon modes extracted from the k space velocities. To prove the feasibility of using PCA to isolate k space phonons, we conducted classical molecular simulations of graphene with different structures. The effect of single vacancy defect on graphene phonons was studied in comparison to the perfect graphene. In addition, the effect of the armchair ribbon width on graphene phonon modes was investigated. The results of the conducted molecular simulations were used with PCA to visualize some of the phonon modes of pristine graphene and armchair nanoribbons of graphene. We used PCA to present the evolution of the atomic motion of specific k space phonon modes of armchair ribbons: the first overtone of TA phonon mode and the highest overtone of TO phonon mode. The presented motions showed that the breathing like mode is a transition state between two opposite atomic motions of TA mode. In the method we introduced using PCA, we used the eigenvectors with the lowest eigenvalues to study the Fourier transformed atomic velocities. This method rotated the k space atomic velocities into the eigenvectors with the lowest eigenvalues which helped to isolate and visualize the k space phonon modes.