This is a theoretical renewal grant under the Research at Undergraduate Institutions program. The principal investigator will complete the theory and derivation of the group theoretical and crystallographic properties of the non-magnetic subperiodic groups, i.e., the layer, rod and frieze groups, and the relationships between the subperiodic groups and space groups. In particular, so called scanning tables will provide the relationship between space groups and layer groups. This work will be published by the International Union of Crystallography in their series of International Tables For Crystallography, and set the standards for these groups for the international crystallographic and physics communities. The tensorial physical properties which distinguish domains of ferroic crystals will be determined. The scanning tables will provide a basis for a study to determine the layer group symmetry and properties of domain twins. The study of these groups will be extended to include the theory and derivation of the group theoretical and crystallographic properties of magnetic subperiodic groups. The tensorial physical property distinction of domains based on their magnetic symmetry will then be considered. This will provide the basis for a study of the magnetic layer group symmetry and properties of magnetic domain twins. %%% The research funded through the NSF program for Research at Undergraduate Institutions involves developing the theory and deriving the properties associated with certain types of symmetry groups. These results will be readily available through the tables to be published as a result of this work and will assist researchers in group theory, crystallography, condensed matter physics and materials science.
