Crystallography & Symmetry
patterns derived from their groups
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The thread: From the diffraction back

Nobody has seen a space group. They are inferred from where a crystal scatters and, just as informatively, from where it does not.
the crystal latticewhere it scatterslong in one is short in the otheraxis ratio 1.7 How it is known

The reciprocal lattice

Nobody has seen a space group. Crystals are read from where they scatter, and where they scatter is a second lattice in which long has become short and short has become long.

 115 present6 absentthe glide's signaturecomputed from the atom positions, not from the grouppg How it is known

Systematic absences

The most informative part of a diffraction pattern is the part that is not there. A glide plane cancels alternate reflections along a row, exactly, and those missing spots are how a symmetry nobody can see is identified.

 181 reflections10-fold symmetryforbidden to any latticeinteger combinations of ten star vectorsaperiodic Order without repetition

Order is not periodicity

For most of a century the two words were used interchangeably, because every known ordered structure repeated. A diffraction pattern measured in 1982 forced them apart, and the definition of a crystal was rewritten.

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