Crystallography
Crystallography is the science of crystalline matter (structure, growth, properties and applications). It is part of the Science of Materials (understanding materials in the solid-state).
Crystal
Crystal is a homogeneous solid with a periodic, long-range, three-dimensional internal order. In crystals, atoms or their aggregations are periodically repeated in all three dimensions of space. It is the most stable form in which solids are found.
![](images/piromorfita_fig1.png)
Fig. 1.- Pyromorphite (Horcajo, Ciudad Real) 7x6x6 cm (Museum of Geology, University of Sevilla)
We can consider "ideal crystal" as a mathematical model of nodes and vectors (lattice), which represent in a simplified form the real atoms and "real crystal" including other parameters such as the different types of atoms, the symmetry of the motif, defects, etc.
The crystalline matter is a periodically ordered medium, i.e. it implies the existence of a period or vector of repetition known as "translation".