Indexing of a Powder Pattern

The correct unit cell may be identified by associating indices to n inter-planar distances, where n depends on the lattice symmetry. In accordance with Table 7.3, the minimum values of n are n=l for the cubic system, n = 2 for tetragonal and hexagonal crystals, = 3, 4, 6 for orthorhombic, monoclinic and triclinic systems, respectively. 

Once the reciprocal cell parameters have been calculated, the direct cell is easily derived. The goodness of indexing results depends on the quality of [Qhki], and therefore on the accuracy of the peak positions. The importance of data accuracy has been emphasized by de Wolff  

The indexing problem is essentially a puzzle (. . . ). It would be quite an easy puzzle if errors of measurement did not exist. 

Powder indexing is not like structure analysis, which works well on good data and will usually get by on poor data given a little more time and attention. Powder indexing works beautifully on good data, but with poor data it will usually not work at all. 

Special attention and care are required when numerical relationships between cell axes exist (geometrical ambiguities, see Section 7.2.3). In addition, the presence of impurities makes the indexing process more difficult. Errors in Q ki modify the problem to one of finding [Ay] satisfying the following relation  

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Smith and Snyder compared T n and M20 performances, analyzing a set of compounds belonging to triclinic, orthorhombic and cubic systems. They emphasized the superiority of T n with respect to M20 because the latter is (a) defined for exactly 20 lines, (b) strongly dependent on the crystal class and the space group. But Werner ° noted that the increasing value of M20 with symmetry is not a disadvantage, since a cubic indexing of a powder pattern is more probable than a triclinic one. 

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