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Centric and acentric reflections: Difference between revisions
→Reciprocal space
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== Reciprocal space == | == Reciprocal space == | ||
In reciprocal space the situation is quite similar. A reflection is centric if there is a reciprocal space symmetry operator which maps it onto itself. Reciprocal space symmetry operators can be obtained from the real space symmetry operators by following two rules: | In reciprocal space the situation is quite similar. A reflection is centric if there is a reciprocal space symmetry operator which maps it onto itself (or rather its Friedel mate). Reciprocal space symmetry operators can be obtained from the real space symmetry operators by following two rules: | ||
a) take the rotation matrix and transpose it | a) take the rotation matrix and transpose it | ||
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Whereas rule b) makes things slightly easier in reciprocal space, we must be aware that in reciprocal space we have additional symmetry, namely Friedel symmetry. This means for each reciprocal symmetry operator we also have to consider the Friedel-related operator (all elements of the matrix multiplied by -1). | Whereas rule b) makes things slightly easier in reciprocal space, we must be aware that in reciprocal space we have additional symmetry, namely Friedel symmetry. This means for each reciprocal symmetry operator we also have to consider the Friedel-related operator (all elements of the matrix multiplied by -1). | ||
To find centric reflections, we just solve the Eigenvalue problem A v = v, now considering each reciprocal space symmetry operator in turn. | To find centric reflections, we just solve the Eigenvalue problem A v = -v, now considering each reciprocal space symmetry operator in turn. | ||
Centric reflections in space group P2 and P2<sub>1</sub> are thus those with 0,k,0. There exist space groups without centric reflections, like R3. | Centric reflections in space group P2 and P2<sub>1</sub> are thus those with 0,k,0. There exist space groups without centric reflections, like R3. | ||