Keywords

crystallography, rigid unit modes, group representation theory

Abstract

  1. The cooperative rigid unit modes (CRUM's) of cubic perovskite were investigated at non-special k-points using ISODISTORT and Shared Shifts Mathematica code. CRUM's were generated by the T4 irrep on the T line which confirms previously published results.
  2. The solution space of the MtM CRUM detection method was determined and compared to that of the M method. Analysis by example and by theory showed the solution spaces of both methods are identical. MtM was realized to be effectively M with a lower tolerance. An improved row reduction routine is being developed that uses an adaptable ratio-driven tolerance instead of an absolute tolerance.
  3. The CRUM's responsible for the structural phase transitions of tridymite and quartz were explored using ISODISTORT’s visualization applet. For tridymite, the responsible irreps are Γ5+, Γ5- , and Γ1-. For quartz, the responsible irrep is Γ3. The results were compared and confirmed with previously published results.

Description

This paper was completed during the 2017 Research Experiences for Undergraduates in Physics (REU) program. More information about this program can be found here.

Document Type

Report

Publication Date

2017-08-18

Language

English

College

Physical and Mathematical Sciences

Department

Physics and Astronomy

University Standing at Time of Publication

Sophomore

Course

REU summer research program

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