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.
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".
