Using higher-angle lines is therefore unwise.
In practice, only the first 20–30 observed lines are useful for two main reasons: (1) they are less sensitive to small changes in the cell parameters than the higher-angle lines and (2) higher-angle lines (even if they seem to be single peaks) actually often consist of more than one overlapping peak and their positions cannot be accurately evaluated. In theory, if we had available an experimental pattern at infinite resolution with well resolved peaks with no overlapping, the determination of the six cell parameters corresponding to a problem with six degrees of freedom would be easy (Shirley, 2003 ). In particular, the experimental information used for carrying out the indexing process is the d hkl interplanar spacings, which are related to the diffraction angles by the well known Bragg law: Whatever the method used, working in the parameter or index space, powder pattern indexing aims to recover the three-dimensional information from the positions of the diffraction peaks in the observed profile. This is because the information about the three-dimensional reciprocal space is compressed into the one-dimensional experimental powder pattern. (In this chapter, `line' and `peak' are used synonymously.) In the case of powder diffraction, the determination of the cell parameters is not a trivial task, and it is much more difficult than in the single-crystal case. The cell-determination process (which operates in a 6-dimensional continuous parameter space) is also called `indexing' because it consists of assigning the appropriate triple ( hkl) of Miller indices of the lattice plane to each of the N l experimental diffraction lines (in a 3 N l-dimensional integer-valued index space) (Shirley, 2003 ). Knowledge of the crystal structure strongly depends on the determination of the cell: a cell incorrectly defined does not lead to the solution. In other words, the first step in the solution pathway is the identification of the unit-cell parameters.
The crystal structure solution process presupposes that the crystal cell and the space group are known.