See International Tables for Crystallography. Volumne A Space-Group Symmetry, Chapter 8 "Introduction to Space-Group Symmetry". Kluwer, 1992.
See also IUCr Online Dictionary of Crystallography
Ångström unit (Å): unit of length. 1 Ångström unit = 10 -8 cm
Crystal lattice: Three-dimensional imaginary array of points (hkl). Each point represents a unit cell.
Crystal system: Unit cell type
Plane group: Symmetry group of a two-dimensional crystal pattern. There are 17 plane groups.
Point group: Symmetry operations involving linear mapping a lattice onto a fixed point. There are 32 three-dimensional crystallographic point groups.
Space group: Symmetry operations applied to points arranged on a crystal lattice. There are 230 unique crystallographic space groups. Space groups are numbered 1-230. Each space group is identified with an international space group symbol which is generated from its point group symbols.
Unit cell: Basic building block of a crystal, repeated indefinitely in three dimensions. Characterized by three vectors ( a , b , c ) and the angles between the vectors ( alph a - angle between b and c ; beta - angle between a and c ; and gamma - angle between a and b ).
A crystal is a solid with a regular repeating internal three-dimensional arrangement of atoms. This periodic arrangement can be exploited to determine molecular identity and structure when the crystal is exposed to x-rays.
X-rays are used because their wavelengths correspond to inter-atomic distances. The arrangement of atoms within the crystal acts as an x-ray diffraction grating. When a crystal is subjected to x-rays, diffraction intensity data is collected resulting in a diffraction pattern. A typical small molecule crystal (>350 atoms) may have 1800 exposures to generate the diffraction pattern.
Pattern location and intensity are used to determine size and composition of the molecule respectively. The phase relations of the diffracted beams are resolved mathematically before a model structure is deduced (referred to as the "Phase Problem").
Using computer software, structure parameters are systematically adjusted to give the best fit between observed intensities and calculations from the model structure. The final determination yields atom identities and positions in the unit cell and bond lengths and angles derived from the atom positions.
Probably the most famous X-ray diffraction image is the photograph of the B form of DNA taken by Rosalind Franklin in May 1952 (Lynne Osman Elkin, "Rosalind Franklin and the Double Helix", Physics Today, 56(3) 2003 http://dx.doi.org/10.1063/1.1570771) With the help of Oxford crystallographer Dorothy Hodgkin, Franklin described the helical backbone and correct crystallographic space group for DNA . Her work was instrumental in Watson's and Crick's correct modeling of DNA, for which they received the Nobel Prize.
The author gratefully acknowledges Dr. Ilia Guzei, Director of the Molecular Structure Laboratory, University of Wisconsin-Madison, for his continued interest in x-ray crystallography information.