Unit cell reduction algorithms

The first two reduction rules are normally employed only during the indexing. They usually do not produce a standard choice of the unit cell since at this stage the space group symmetry, and often even the lattice type, are not involved. For example, in the orthorhombic space group symmetry Pnma (a standard setting) the condition a b c is not necessarily obeyed. 

There are two broadly accepted methods of unit cell reduction. One of them was introduced by Delaunay and then applied to a transformation of a 

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As is obvious from columns 2 and 3 in Table 5.24, different indexing algorithms result in different choices of the unit cell for the same lattice and, therefore, unit cell reduction is especially important to compare the results in triclinic symmetry. The unit cell dimensions, reduced using the WLepage program, are listed in Table 5.24 in columns 6-8. Obviously, all of them are represented by the same unit cell, except the incorrect solution shown in row 2. The triclinic unit cell was confirmed by a single crystal diffraction experiment, as shown in row 6. 

This algorithm realizes a zone search indexing method combined with the Delaunay-Ito technique (see section 5.10.1) for the reduction of the most probable unit cell. The most commonly used versions of computer codes are ITO 13 and IT015. The program arrives at a solution by using the following algorithm ... 

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