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h k
|F| phi

5. Symmetry (2)

In this section we will look at another example of the effect of crystallographic symmetry on the structure factors, with a 3-fold rotation axis.

The map and structure factors now show a 3-atom structure with a 3-fold rotation axis perpendicular to the plane of the map. The symmetry equivalent positions are:

Using the second symmetry operator, repeat the calculation on the previous page to find any relationships between reflections. Also look for relationships between a reflection and its Friedel opposite. Compare your results with what you observe in the map.

When a reflection is related to itself with a phase shift, it must be systematically absent. When a reflection is related to itself but with no phase shift, there are no restrictions on its value. When a reflection is related to its Friedel opposite, then it is called a centric reflection, and can only take on one of two phases, separated by 180 degrees.

The previous example included some centric reflections, some systematic absences, and all reflections were related to symmetry partners. In the example on this page, none of the relationships relate a reflection to its Friedel opposite or introduce a phase shift, and so all the reflections are general, however each is related directly to three other reflections, and to three Friedel opposites.