Diffraction symbol

Symbole de diffraction (Fr). Beugungssymbol (Ge). Simbolo di diffrazione (It). 回折記号 (Ja). Símbolo de difracción (Sp).

Diffraction symbols were introduced to represent, in as compact a form as possible, all the information that has been obtained by X-ray diffraction concerning the symmetry of a crystalline species. Two symbolisms have been proposed

• Donnay & Harker introduced the concept of aspect as a statement of a set of criteria that govern the systematic absences in one or several space groups, in any given crystal system. The aspect symbol is composed by the capital letter representing the type of unit cell, the screw axes or glide planes that can be inferred by the systematic absences and asterisks (*) in the positions of symmetry elements that cannot be determined by these.
• Buerger introduced a diffraction symbol composed by the symbol of the Laue class followed by the aspect symbol where hyphens (-) are used instead of asterisks

For example, the symmorphic space groups of type Pmmm, P222, Pmm2, P2mm, Pm2m are all represented by the aspect symbol P*** or the diffraction symbol mmmP---.

The diffraction symbol is richer in information than the aspect symbol. For example, Space groups of type I4₁ and I4₁22 have the same aspect symbol I4₁** but two different diffraction symbols 4/mI4₁-- and 4/mmmI4₁--.

In the International Tables for Crystallography, the aspect symbol was adopted in the 1952 edition with dots replacing asterisks or hyphens. In later editions, hyphens were adopted. The term aspect symbol was changed to extinction symbol. In the sixth edition of Volume A, the extinction symbol is no longer present, but the criteria to obtain it are all given.

References

• Donnay, J. D. H. & Harker, D. (1940). Naturaliste canadien, 67, 33, 160.
• Donnay, J. D. H. & Kennard, O (1964). Acta Cryst, 17, 1337-1340 [erratum: Acta Cryst, A25 (1969), 394]
• Buerger, M.J. (1942). X-ray Crystallography. New York : Wiley.