We study the behavior of a simple cubic crystal interface through the analysis and simulation of the Ising model in three dimensions; we use an algorithm which permits local temperature variations by emulating thermal diffusion. We derive a description of the interface based on the thermal fluctuation population at equilibrium and then use it to identify the equilibrium and dynamic roughening transitions observed under a variety of circumstances including a planar interface at equilibrium, a metastable bulk inclusion, an evaporating inclusion and a planar interface in the presence of a driving force. We also study strongly driven interfaces which exhibit an instability and pattern formation behaviour known as the Mullins-Sekerka instability. We use a special two-dimensional version of the simulation model to examine the linear growth of unstable modes of a driven interface; we compare our simulation data to theoretical predictions for the cases of an unstable flat interface and circular disk interface. Returning to the fully three-dimensional code, we present simulation data of late-time dendrites growth, including an analysis of the information available in the thermal fields. We also show that, at low temperatures, the tips of dendrites are facetted and demonstrate a response to the driving force which is consistent with the dynamic roughening transition.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.39776 |
| Date | January 1992 |
| Creators | Jürgenson, Loki Michael |
| Contributors | Harris, Richard (advisor) |
| 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 | Doctor of Philosophy (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001326481, proquestno: NN87591, Theses scanned by UMI/ProQuest. |
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