Crystal Structures

Introduction

These pages have been developed to help you understand and visualize the 3D nature of crystal structures. A guide to the site is listed below, and the buttons at the bottom of each page will provide sequential access. This is a very brief introduction, further resources can be found at: The International Union of Crystallography.

The Unit Cell

Solids can be divided into two categories based on the arrangement of atoms in the solid structure. An amorphous solid has no regular arrangement of atoms in the solid. In contrast, in crystalline solids the atoms are arranged in regular repeating patterns.

The unit cell is the smallest unit (parallelogram) from which the entire crystal structure can be built by stacking unit cells in three dimensions. There are seven basic shapes, or crystal systems possible for unit cells, each characterized by unique combinations of lengths of edges and angles between edges. These are: cubic, tetragonal, orthorhombic, monoclinic, rhombohedral (trigonal), triclinic and hexagonal.

Most of the crystal systems can have more than one crystal lattice. The crystal lattice defines the location of atoms within the unit cell (x_i, y_i, z_i, for each (i) atom). The different locations are generated by the symmetry of the crystal structure. Atom positions can be generated by: rotations about an axis, reflection across a mirror plane or a combination of the two (an improper axis).

Finally, the unit cell can be classified as primitive or conventional. A primitive unit cell has atoms only at the corners of the unit cell. This will be the simplest representation of the crystal structure, but it may not reflect the symmetry seen in the crystal structure. The conventional unit cell will have atoms at additional sites in the unit cell (i.e. faces, body center etc.) so that the unit cell has the same symmetry as the entire crystal structure. This generates four lattice types: primitive, body centered, and face centered at all or only one face.