Space Groups & The International Tables for Crystallography

From examination of a space group in "The International Tables for Crystallography" Vol. A, you should be able to ascertain the following information:

• Herman-Mauguin (H-M) Symbol (Long, Short)
• Point Group (H-M, Schoenflies)
• Locate and identify symmetry elements
• Understand Wyckoff site multiplicity and symmetry
• Distinguish general and special positions
• Extinction conditions
• Identify possible subgroups and supergroups

Understanding the Herman-Mauguin Space Group Symbol
Space groups are typically identified by their short Herman-Mauguin symbol (i.e. Pnma, I4/mmm, etc.). The symmetry elements contained in the short symbol are the minimum number needed to generate all of the remaining symmetry elements. This symbolism is a very efficient, condensed form of noting all of the symmetry present in a given space group. We won’t go into all of the details of the space group symbol, but I will expect you to be able to determine the crystal system, Bravais Lattice and point group from the short H-M symbol. You should also be able to determine the presence and orientation of certain symmetry elements from the short H-M symbol and vice versa.
The H-M space group symbol can be derived from the symmetry elements present using the following logic.
The first letter identifies the centering of the lattice; I will hereafter refer to this as the lattice descriptor:

• P � Primitive
• I � Body centered
• F � Face centered
• C � C-centered
• B � B-centered
• A � A-centered

To continue reading click on the link below:

http://cbc-wb01x.chemistry.ohio-state.edu/~woodward/ch754/sym_itc.htm