RUI: The Subperiodic Subgroups of the Crystallographic SpaceGroups

该RUI补助金将用于确定集团理论和 的亚周期子群之间的晶体学关系 晶体空间群和亚周期 子群和晶体空间群，以提供 系统的，统一的理论。 标准 强调这些关系的代表性团体将是 从每一类亚周期群中选出。 这个过程被称为 扫描将被开发并用于确定方向 和所有平面的亚周期对称群的起源， 水晶中的线条 亚周期条件下原子排列不变 将按照国际表格的格式对各组进行制表 晶体学 的正规子群格 亚周期群，这提供了一个基础的推导 次周期的不可约表示的象 群，将被确定和不可约的表示， 亚周期群的产生。 各次定期小组还将 与这三个不可约表示有关- 三维晶体空间群 的结果 研究将由国际联合会出版。 晶体学。 部分研究正在进行， 与物理研究所的V. Kopsky博士合作， 捷克斯洛伐克科学院 %%% 群论在数学上表示 完美晶体所固有的对称性。 我们可以了解到 了解晶体的物理性质， 内在的潜在对称性对称的各种类型 三维晶体所能达到的极限 在对晶体学家和其他人来说很重要的表格中， 对晶体的性质感兴趣的科学家 在 目前的研究亚周期的可比性质 将研究晶体空间群的子群， 列表。 科学家们对这些亚群很感兴趣 对晶体的一维和二维性质感兴趣， 如表面或平面和链。 这项研究成果 将由国际农业联合会以表格形式公布。 供所有研究人员使用的晶体学。

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.