What Defines a Crystal?

Abstract

The effective defining feature of the crystalline state is translational symmetry, which can be exploited to develop an efficient and practical description of a molecular crystal structure. A crystal structure contains a common building block that is translated in three dimensions over a length scale much greater than the dimensions of the building block. This leads to the simplifying concepts of lattices and unit cells, which provide a general framework to describe crystal structures. The positions of the atoms within a crystal are expressed as coordinates relative to the edges of the unit cell and the periodic nature of the structure means that a description of the unit cell is in effect a description of the entire crystal structure. The definitions of the lattice, unit cell and fractional coordinates are independent of the metric properties of the crystal, but the metric properties provide the link between the fractional coordinates and the actual distances and angles between atoms.