Coordination Shape's Classification Theory Of Crystal Space

This dissertation is concerned with classification of crystal space in crystal structure geometry. Classification of crystal space has two problems to consider: one is that different kinds of basic object classify crystal space, and myriad basic object bodies of the same kind can be piled up into the particular crystal shape; the other is that a kind of abstract mathematical form classifies crystal space, and this mathematical form exactly is derived from the former basic object. In this dissertation, we would make a detailed discussion about a new mathematical form of crystal space classification: coordination shape set.Therefore, the basic conception of crystal space classification is firstly explained in this dissertation; and then selection rule of Bravais' cell and Niggli's cell theory are introduced in turn; after that, conception of coordination shape is presented and discussed; at last, the derivation and its result of coordination shape set of 2-dimension crystal lattice and part of 3-dimension crystal lattice are given.The most creative place would be that coordination shape's classification theory of crystal space has been established and its conclusion about 2-dimension and 3-dimension (partly) crystal lattice has been given. And there are still some of other new viewpoints to be proposed in this dissertation: generalizing the relational expression, "crystal structure=basic object+ space lattice" while indicating the strict definition of crystal space classification; presenting the conception of 8-quarter single cell body and considering it as a kind of basic object form of crystal space classification; having found a kind of set whose elements have a fixed sequence and that has the periodicity in itself, etc.