Simulation of axisymmetric stepped surfaces with a facet

A crystal lattice with a small miscut from the plane of symmetry has a surface which consists of a series of atomic height steps separated by terraces. If the surface of this crystal is not in equilibrium with the surrounding medium, then its evolution is strongly mediated by the presence of these steps, which act as sites for attachment and detachment of diffusing adsorbed atoms ('adatoms'). In the absence of material deposition and evaporation, steps move in response to two main physical effects: line tension, which is caused by curvature of the step edge, and step-step interactions which can arise because of thermal step fluctuations, or elastic effects. This thesis focuses on axisymmetric crystals, with the result that the position of a step is uniquely described by a single scalar variable, and the step positions obey a coupled system of "step-flow" Ordinary Differential Equations (step flow ODEs). Chapter 2 of this thesis concentrates on the derivation and numerical solution of these equations, and their properties in the limits of slow adatom terrace diffusion and slow adatom attachment-detachment. Chapter 3 focuses on the analysis carried out by Margetis, Aziz and Stone ('MAS') [78] on a Partial Differential Equation (PDE) description of surface evolution.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Fok, Pak-Wing

Advisor dc:contributor.advisor

• Rodolfo Ruben Rosales and Dionisios Margetis.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/34548

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/34548