Abstract
Many crystalline materials of interest to the Canadian Nuclear Program have the potential to undergo phase transitions in their range of application. During such phase transitions, a representation of the space group of the higher symmetry polymorph softens to induce the transition. This report is the first in a series of reports concerned with the group-theoretic properties of phase transitions in crystalline materials. The object of the research is to identify all spectroscopically-active soft modes for the 230 three-dimensional space groups. Identification of these soft modes will enable a detailed examination of phase transitions in materials of interest to the Canadian Nuclear Program and aid in the optimization of material properties. In this report, the group-theoretic properties of crystal structures and phase transitions are reviewed. It is demonstrated that the problem of extending a group reduces to that of determining its automorphisms. The automorphism groups of the crystallographic and icosahedral point groups are derived using a consistent presentation.
Walker, J R;
[1]
Boyle, L L
[2]
- Atomic Energy of Canada Ltd., Chalk River, ON (Canada). Chalk River Nuclear Labs.
- University Chemical Laboratory, The University, Canterbury, England (United Kingdom)
Citation Formats
Walker, J R, and Boyle, L L.
Phase transitions in crystalline solids 1. Automorphisms and extensions of crystallographic and icosaheadral point groups.
Canada: N. p.,
1993.
Web.
Walker, J R, & Boyle, L L.
Phase transitions in crystalline solids 1. Automorphisms and extensions of crystallographic and icosaheadral point groups.
Canada.
Walker, J R, and Boyle, L L.
1993.
"Phase transitions in crystalline solids 1. Automorphisms and extensions of crystallographic and icosaheadral point groups."
Canada.
@misc{etde_10138344,
title = {Phase transitions in crystalline solids 1. Automorphisms and extensions of crystallographic and icosaheadral point groups}
author = {Walker, J R, and Boyle, L L}
abstractNote = {Many crystalline materials of interest to the Canadian Nuclear Program have the potential to undergo phase transitions in their range of application. During such phase transitions, a representation of the space group of the higher symmetry polymorph softens to induce the transition. This report is the first in a series of reports concerned with the group-theoretic properties of phase transitions in crystalline materials. The object of the research is to identify all spectroscopically-active soft modes for the 230 three-dimensional space groups. Identification of these soft modes will enable a detailed examination of phase transitions in materials of interest to the Canadian Nuclear Program and aid in the optimization of material properties. In this report, the group-theoretic properties of crystal structures and phase transitions are reviewed. It is demonstrated that the problem of extending a group reduces to that of determining its automorphisms. The automorphism groups of the crystallographic and icosahedral point groups are derived using a consistent presentation.}
place = {Canada}
year = {1993}
month = {Sep}
}
title = {Phase transitions in crystalline solids 1. Automorphisms and extensions of crystallographic and icosaheadral point groups}
author = {Walker, J R, and Boyle, L L}
abstractNote = {Many crystalline materials of interest to the Canadian Nuclear Program have the potential to undergo phase transitions in their range of application. During such phase transitions, a representation of the space group of the higher symmetry polymorph softens to induce the transition. This report is the first in a series of reports concerned with the group-theoretic properties of phase transitions in crystalline materials. The object of the research is to identify all spectroscopically-active soft modes for the 230 three-dimensional space groups. Identification of these soft modes will enable a detailed examination of phase transitions in materials of interest to the Canadian Nuclear Program and aid in the optimization of material properties. In this report, the group-theoretic properties of crystal structures and phase transitions are reviewed. It is demonstrated that the problem of extending a group reduces to that of determining its automorphisms. The automorphism groups of the crystallographic and icosahedral point groups are derived using a consistent presentation.}
place = {Canada}
year = {1993}
month = {Sep}
}