RUI: Cystallography of Magnetic and Non-Magnetic Subperiodic Groups

这是本科院校研究项目下的一项理论更新资助。首席研究员将完成非磁性亚周期群（即层、棒和frieze群）的群理论和晶体学性质的理论和推导，以及亚周期群与空间群之间的关系。特别是，所谓的扫描表将提供空间组和层组之间的关系。这项工作将由国际晶体学联合会在他们的国际晶体学表系列中发表，并为国际晶体学和物理界制定这些团体的标准。将确定用于区分铁晶体畴的张量物理性质。扫描表将为确定畴孪晶的层群对称性和性质的研究提供依据。这些基团的研究将扩展到包括磁性亚周期基团的基团理论和晶体学性质的理论和推导。然后将考虑基于磁对称性的域的张量物理性质区分。这将为研究磁畴孪晶的磁层群对称性和性质提供基础。这项研究是由美国国家科学基金会本科院校研究项目资助的，涉及发展理论和推导与某些类型对称群相关的性质。作为这项工作的结果，这些结果将通过即将出版的表格随时可用，并将帮助研究人员在群论，晶体学，凝聚态物理和材料科学。

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.