Date of Award

5-2017

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Tim P. Schulze

Committee Members

Steven Wise, Kenneth Stephenson, Yanfei Gao

Abstract

Continuum models in computational material science require the choice of a surface energy function, based on properties of the material of interest. This work shows how to use atomistic bond-counting models and crystal geometry to inform this choice. We will examine some of the difficulties that arise in the comparison between these models due to differing types of truncation. New crystal geometry methods are required when considering materials with non-Bravais lattice structure, resulting in a multi-valued surface energy. These methods will then be presented in the context of the two-dimensional material graphene in a way that correctly predicts its equilibrium shape.

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