König A, Mermin ND. Screw rotations and glide mirrors: crystallography in Fourier space.
Proc Natl Acad Sci U S A 1999;
96:3502-6. [PMID:
10097065 PMCID:
PMC22322 DOI:
10.1073/pnas.96.7.3502]
[Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The traditional crystallographic symmetry elements of screw axes and glide planes are subdivided into those that are removable and those that are essential. A simple real-space criterion, depending only on Bravais class, determines which types can be present in any space group. This terminological refinement is useful in expressing the complementary relation between the real-space and Fourier-space formulations of crystal symmetry, particularly in the case of the two nonsymmorphic space groups that have no systematic extinctions (I212121 and I213). A simple analysis in Fourier space demonstrates the nonsymmorphicity of these two space groups, which finds its physical expression not in a characteristic absence of Bragg peaks, but in a characteristic presence of electronic level degeneracies.
Collapse