Mathematical Models of the Alpha-Beta Phase Transition of Quartz

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1999

Author dc:creator

• Moss, George W.

Chair dc:contributor.committeechair

• Rogers, Robert C.

Committee members dc:contributor.committeemember

• Renardy, Michael J.
• Boisen, Monte B. Jr.
• Sun, Shu-Ming
• Lin, Tao

• phase transition
• quartz
• incommensurate
• bifurcation

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-081099-142433

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/28607