The main purpose of this thesis is to justify the density functional theory of freezing in the case of a crystal with square symmetry. In the first part, I discuss the widely used technique of molecular dynamics to characterise the dynamics and statistical observables of a system undergoing a phase transition. I then outline the advantages and the main drawbacks of this technique: slow implementation and poor performance for long time scales. It is shown that order parameter or phenomenological theories of freezing paliate those problems. These theories describe the dynamics of one parameter that starts in a highly symmetric state and which symmetry is broken during the phase transition. The dynamics of the order parameter, which in our case is the time averaged density, is governed by the topology of a free energy functional. We derive such a free energy functional for two theories and explain why one of these can be applied to give freezing into arbitrary symmetry groups. The study of freezing into square symmetry and various elastic deformations of two-dimensional crystals form the last part of the thesis.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.84048 |
| Date | January 2005 |
| Creators | Kröger, Jens, 1981- |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 002269583, proquestno: AAIMR22740, Theses scanned by UMI/ProQuest. |
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