Geometrical Implications

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Geometrical Implications

Clearly the first step in space-group determination involves indexing our powder diffraction data. It is important that all peaks in the powder pattern are accounted for: uncertainies in peak indexing can lead to uncertainties in space-group determination. Indexing and unit-cell refinement provides the geometric parameters a, b, c, α, β, and γ. It is important to realize that the geometric solution provides indicative information only concerning possible crystal systems: for example, if the unit cell has a ≠ b ≠ c, then it is safe to deduce that the crystal system is not cubic, tetragonal, hexagonal, or trigonal: it cannot be assumed that the crystal system is orthorhombic, since it is possible that the powder pattern corresponds to a monoclinic substance with a monoclinic angle equal to 90° within experimental error. In practice, deduction of the crystal system from the lattice geometry information refined from powder diffraction data is usually much safer than in a single-crystal experiment. The reason is simple: powder diffractometers are designed with (and require) a much higher 2θ resolution than the equivalent single-crystal machines.

Before any deductions concerning space-group symmetry can be made, it is necessary to have an understanding of the effects of certain symmetry elements on the diffraction process. In particular, the presence of centred lattices, glide planes, and screw axes in the crystal structure of the material will all affect the number of peaks observable in a diffraction experiment. In particular, these symmetry elements all lead to various types of reflection condition in the diffraction data. The next few pages describe these in more detail.

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