Mathematical Models of the Alpha-Beta Phase Transition of Quartz

Files

etd.pdf (558.65 KB)
Downloads: 170

TR Number

Date

1999-07-27

Journal Title

Journal ISSN

Volume Title

Publisher

Virginia Tech

Abstract

We examine discrete models with hexagonal symmetry to compare the sequence of transitions with the alpha-inc-beta phase transition of quartz. We examine a model by Parlinski which employs interactions of nearest and next-nearest neighbor atoms. We numerically determine the configurations which lead to minimum energy for a range of parameters. We then use Golubitsky's results on systems with hexagonal symmetry to derive the bifurcation diagram for Parlinski's model. Finally, we study a large class of modifications to Parlinski's model and show that all such modifications have the same bifurcation picture as the original model.

Description

Keywords

phase transition, quartz, incommensurate, bifurcation

Citation