Symmetry and features of structure in materials described in the space higher than three dimensions.

这个项目从1990年10月底开始，进行了17个月。这一时期的研究结果如下：1。2.成员个人工作和合作工作的结果；在上述期间与本专业相关研究者的讨论会议中，前者进行了三类研究：(1)不相称相的结构研究，准晶和非晶材料的研究，(2)高维结构特征及其性质的解释，(3)高维空间对称性的研究。在(1)类中，分析了Ca_2CoSi_2O_7、Bi-oxide系列高Tc超导体和钛酸锆的结构。作为基础性的贡献，新开发了测定复合晶体结构的计算机程序，并建立了用会聚束电子衍射法测定四维空间群的方法。用高分辨率电子显微镜分析了Al-Ni-Co和Al-Cu-Co体系的准晶结构，用x射线衍射法分析了Al-Co-Ni和Al-Cu-Li体系的准晶结构。用x射线衍射和EXAFS方法研究了Ca (Mg， M) (Si, Al)_2O_6 （M: Mn, Fe, Co, Ni）玻璃中过渡金属的配位。建立了用小角x射线衍射测定溶液波动的方法，并成功地应用于酒精溶液和水的混合物。在第(2)类中，提出了“图形测地线”的新概念。这一方法被用于表征与准晶体结构密切相关的三角彭罗斯瓷砖的内在规律性。在(3)中，对复合晶体的超空间群、空间群的非特征轨道、晶体的点群的统计量以及椭圆的填充特性进行了研究。在后者中，1991年1月举行了第一次讨论会，1992年2月举行了第二次讨论会。该项目的成员与该项目的相关调查人员出席了会议，并介绍了他们的研究结果。讨论富有成果。少

This project has been carried out since the end of Oct. in 1990, and proceeded for 17 months. The results obtained in this period are as follows :1. the results by individual works of the members and by their cooperative works, and 2. the discussion meetings held in the above period with the investigators related to the proicclIn the former, three categories of studies have been carried out : (1) structural studies on incommensurate phases, studies on quasicrystals and on amorphous materials, (2) interpretation of feature of the structures and their properties in higher dimensions, and (3) studies on symmetries in the space higher than three dimensions. In category (1) , the structures of Ca_2CoSi_2O_7, of high Tc superconductors in Bi-oxide series and of zirconium titanates have been analyzed. As fundamental contributions, a computer program for structure determination of composite crystals was newly developed and a method to determine four-dimensional space group by convergent-beam e … More lectron diffraction was also established. Structures of quasicrystals in Al-Ni-Co and Al-Cu-Co systems were clarified by high-resolution electron microscopy and those in Al-Co-Ni and Al-Cu-Li systems were elucidated by X-ray diffraction method. The coordinations of transition metals in Ca (Mg, M) (Si, Al)_2O_6 (M : Mn, Fe, Co, Ni) glasses were studied by X-ray diffraction and EXAFS methods. A method to determine fluctuation of solutions by small angle X-ray diffraction was also established and was successfully applied to mixtures of alcoholic solutions and water. In category (2), a new concept "a graphical geodesic" was proposed. This was applied to characterize intrinsic regularity of the triangulated Penrose tilings which are closely related to the structures of qusicrystals. In (3), Studies on super space groups of composite crystals, on non-characteristic orbits of space groups, on statistics of point groups of crystals and on characters of packing of ellipses have been carried out.In the latter, the first discussion meeting was held in January, 1991, and the second one in February, 1992. The member of this project together with the investigators related to the project attended the meeting and the results of their studies were presented. The discussions were fruitful. Less