We use first-principles density functional theory based analysis to understand formation of ripples in graphene and related 2-D materials. For an infinite graphene, we show that ripples are linked with a low energy branch of phonons that exhibits quadratic dispersion at long wave-lengths. Many modes in this branch become unstable as a function of compressive strain and rippling occurs in a way similar to a structural phase transition. We use a simple model to develop understanding of this phenomenon.
At the nanoscale, we find that Stone-Wales (SW) defects play an interesting role. Such defects lead to stresses in a graphene nano-ribbon (GNR) that are relieved through its deformation or reconstruction at the edges. Due to a markedly anisotropic interaction among the SW defects, the resulting localized deformation depends sensitively on the orientation of an SW defect with respective to the edge of the GNR.
Network for Computational Nanotechnology (NCN)
Center for the Prediction of Reliability, Integrity and Survivability of Microdevices (PRISM)
College of Engineering
The Birck Nanotechnology Center
Researchers should cite this work as follows:
Umesh V. Waghmare (2010), "Ripples and Warping of Graphene: A Theoretical Study," https://nanohub.org/resources/9010.
Birck Nanotechnology Building, Room 2001