RUI: The Subperiodic Subgroups of the Crystallographic SpaceGroups

  • Litvin, Daniel Bernard (PI)

Project: Research project

Project Details

Description

This RUI grant will be used to determine the group theoretical and crystallographic relationships among the subperiodic subgroups of the crystallographic space groups and between the subperiodic subgroups and the crystallographic space groups to provide a systematic, unified theory of these groups. A standard representative group which emphasizes these relationships will be chosen from each class of subperiodic groups. A process called scanning will be developed and used to determine the orientation and origin of the subperiodic symmetry group of all planes and lines in crystals. Atom arrangements invariant under subperiodic groups will be tabulated in the format of the International Tables for Crystallography. Lattices of normal subgroups of the subperiodic groups, which provide a basis for the derivation of the images of the irreducible representations of the subperiodic groups, will be determined and the irreducible representations of the subperiodic groups derived. The subperiodic groups will also be related to the irreducible representations of the three- dimensional crystallographic space groups. The results of this research will be published by the International Union of Crystallography. Parts of the research are being conducted in collaboration with Dr. V. Kopsky of the Institute of Physics of the Czechoslovak Academy of Sciences. %%% Group theory is important in representing mathematically the symmetry inherent in perfect crystals. Much can be learned about the physical properties of crystals by understanding their intrinsic underlying symmetries. The various types of symmetry allowed for three-dimensional crystals is tabulated mathematically in tables which are of importance to crystallographers and other scientists interested in the properties of crystals. In the present research the comparable properties of the subperiodic subgroups of the crystallographic space groups will be studied and tabulated. These subgroups are of interest to scientists interested in one-and two-dimensional properties of crystals such as surfaces or planes and chains. The results of this research will be published as tables by the International Union of Crystallography for use by all researchers.

StatusFinished
Effective start/end date4/15/919/30/93

Funding

  • National Science Foundation: $60,000.00

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