Dissertation

Topological Defects in Single and Multi-Layer Graphene

Annevelink, Emil

2021

Overview

Since its monolayer exfoliation in 2004, graphene has been the focus of intense study revealing a multitude of exciting properties that allow for studying fundamental physics and new engineering devices. In particular, monolayer graphene has unique mechanical properties such as high in-plane strength but very low flexural rigidity. This causes in-plane strains to be accommodated through out-of-plane deformation enabling engineering complex 3D deformation of graphene-based on patterned in-plane strain. In addition, monolayer graphene only weakly bonds with itself enabling non-lattice stacking between two graphene layers or graphene and an arbitrary crystalline surface. Non-lattice stacking has created a whole new sub-field called moir ́e engineering, which takes advantage of the larger scale periodicity caused by two periodic interfaces. An exciting possibility of moir ́e engineering is to enable new physics such as the unconventional superconductivity found in twisted bilayer graphene. Common between these are dislocations. Dislocations can be used to a pattern in plane strain and describe the mismatch between two lattices. Dislocations are topological defects that add an extra half-plane of atoms causing a large strain at the core of the dislocation. Dislocations have been studied for both their role in out-of-plane deformation in mono-layer graphene and periodicity in moir ́e superlattices. However, the effect of out-of-plane deformation and weak interlayer bonding on the mechanics of dislocations has not been fully studied. We focus on how dislocation mechanics appear in grain boundary migration and moir ́e patterns. For grain boundary migration, while the structure and energy of dislocations in single layer graphene have been studied, grain boundary dislocations, which nucleate when grain boundaries form kinks and disconnections, are important to understand structure evolution during annealing. However, it is uncertain how these dislocations are impacted by the out-of-plane deformation observed at edge dislocations in graphene. Or, while it has long been suggested that moir ́e patterns are arrays of inter-layer dislocations, there has not been a rigorous connection to dislocation topology nor a formal presentation of a linear elastic theory of dislocation between two 2D materials. In this thesis, we address these two dislocations by defining their topology and developing continuum dislocation models to isolate the mechanics of dislocations in graphene systems from atomistic calculations. This thesis focuses on understanding the mechanics of displacement shift complete (DSC) dislocations and interlayer dislocations. DSC dislocations are dislocations that govern the migration of grain boundaries in graphene. The mechanics of DSC dislocations are studied with both atomistic and continuum models to understand the thermodynamic and kinetic barriers of grain boundary migration. The DSC dislocation model is used to show how the grain boundary structure can be controlled through external shears of graphene. The study of DSC dislocations includes how DSC dislocations and grain boundaries can be used to control 3D deformation in graphene. The control of 3D deformation using topological defects is expanded at the end of the thesis by exploring the computational techniques that would enable the precise control of topological defects in graphene. Interlayer dislocations are dislocations between graphene and another crystalline material. The mechanics of interlayer dislocations are studied using twist and stretch moiré superlattices of bilayer graphene. The topology of interlayer dislocations is presented for 1D and 2D networks of dislocations. Continuum mechanics models utilize the dislocation topology to find the structure and energetics of dislocations; these are validated with atomistic simulations. The continuum dislocation model is applied to understand the structural relaxation of dislocations in twist moiré superlattices that give rise to a structural transition at small rotation angles. Furthermore, the line and junction energies of arbitrary sense interlayer dislocations is presented. The energetics show that screw interlayer dislocations and their junctions are more favorable than edge interlayer dislocations. The mechanics of interlayer dislocations and in-plane dislocations–including DSC dislocations–are combined to develop a moiré engineering technique. The moiré engineering technique is based on how the long-range strain field of in-plane dislocations alters the interlayer dislocation network revealed in the moiré pattern. The moiré engineering technique is developed with mechanistic atomic scale models that are brought to the nanoscale with bond convolution simulations to show the moiré patterns of topological defects in the graphene lattice. The moiré engineering technique is applied to in-operando scanning tunneling microscopy to reveal the atomic structure of grain boundaries thus enabling real-time analysis and decision making regarding growth conditions. In conclusion, this thesis focuses on the understanding of dislocation mechanics in graphene. Two dislocations, the DSC dislocation formed during grain boundary migration of monolayer graphene and the interlayer dislocation present between graphene and another crystalline material, are studied. The mechanics are studied by developing continuum models that find the structure and energy of each dislocation by comparing them to atomistic simulations. Finally, the dislocations mechanics are utilized to develop a moiré engineering technique that enables probing the dislocation structure of graphene grain boundaries.

• Publisher: ProQuest Dissertations & Theses
• Subject: Applied physics / Materials science / Mechanical engineering / Thermodynamics
• ISBN: 9798380105637