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
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.