The Method of Selection Lawsand Its Applications to Crystallography

Abstract

Abstract-In physics, we often make use of the spatial properties of a system in order to choose a particular geometry to describe it. However, some geometric systems are so simple that we can hardly consider the possibility of their adoption in describing complex physical systems. It is known that, in areas such as crystallography, there are recurring problems involving discrete geometries, given the nature of the study subject. In this work, we show an alternative way of obtaining the atomic coordinates for a crystal using three steps: Finding a base geometric model, applying laws which help us in picking the adequate locations in this geometry and then applying a transformation which takes the geometric model and give us the final atomic coordinates. To illustrate this idea, we depart from the fundamental concepts of a particular model, the Manhattan Geometry, and will demonstrate how it can be a valuable tool in describing many structure types, from simple cubic to quasicrystalline lattices.