Crystal Lattice Structures: Reference Date: 1 Jan 1998
Last Modified: 21 Oct 2004

About Space Group Files

Files containing the rotational and translation properties of the point groups of each lattice are presented in two forms, in Cartesian coordinates and in lattice coordinates. These are presented in a form which can be read by programs used or developed in the Center for Computational Materials Science. The first section of each file contains the rotational and inversion matrices for each operation. In the Cartesian coordinate file, each rotation consists of three lines, while in the lattice coordinate file, each line contains two rotations. Translational operations are listed in the below the rotations. These are in lattice coordinates in both of the files.

The primitive lattice vectors and basis sets used to generate these files are the ones given on the corresponding lattice page. In most cases, if the space group contains the inversion, the origin of the lattice is taken to be at an inversion site.

These pages use the true primitive lattice. Many sources, including Pearson's Handbook and Wyckoff, often use a larger unit cell. For example, these sources list the alpha U structure as orthorhombic, with four atoms in the unit cell, while the true unit cell is body-centered orthorhombic, with two atoms in the unit cell. Since electronic structure calculations scale with a power of the number of atoms in the system, the smaller unit cell is preferred.

For further information about space groups, see

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Space Group Index

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Structures indexed by: This is a mirror of an old page created at the
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The maintained successor is hosted at
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M. Mehl et al., Comput. Mater. Sci. 136 (Supp.), S1-S828 (2017).