Generalized Crystallography of Rod Systems

点击翻译按钮获取中文摘要

Cylindrical rods with long enough are arranged in some order. The motivation is to construct a generalized crystallography, which unifies periodic and nonperiodic arrangements. It serves as compilation of basic knowledge of arranging and packing, which are fundamental phenomena in physical world.A systematic investigation is done focusing on the possible periodic arrangements of rods with rather high density and/or high symmetry. The directions of rods are restricted to a n kinds, where n=3,4,6, which are, for example, referred to as 3-axs arrangement and so on. The 3-axscase is rather simple. In the 4-axs case, high symmetry and high density are another problem. The 6-axs case is intensively investigated and the possible structures are exhaustively studied within a certain condition. Though the investigation is not perfect and is still going on.The concepts of support and self-support are introduced. The present subject has relationship with many fields ; for example, composite materials, crystallography of rather complex structure like garnet.