Doctoral Dissertations

Date of Award

12-2019

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Tim Schulze

Committee Members

Ken Stephenson, Steve Wise

Abstract

We study the influence of edge energy anisotropy on the morphology of crystal surfaces in non-equilibrium growth. The motivation comes from the fact that edge energy in a Graphene lattice can be multivalued in some orientations, and as a result one can obtain two edge energy curves, reconstructed and non-reconstructed. To determine which is more important in non-equilibrium growth, we used Kinetic Monte Carlo (KMC) simulations to implement a slanted boundary condition that allows us to vary atomic step orientations and change step edge energy. In simulations with Bravais lattices, the edge energy curve can be used to predict stability of the growing front under a small perturbation. In the Graphene lattice, an example of non-Bravais lattices, the result shows the reconstructed energy curve appears to be more important than the non-reconstructed energy curve.

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