Abstract
The crystal structures of all R1+εFe4B4 compounds are composed of two intepe-netrating tetragonal substructures. and form the Vernier structures. The symmetries of R1+εFe4B4 are characterized by two approaches, those of the space group under the commensurate model Rp(Fe4B4)q and the superspace group. The results indicate that the space gtoup symmetry can be applied to R1+εFe4B4 by constructing a long period superstructure Rp(Fe4B4)q, whose symmetries have been shown to be dependent on the parity of p and q. Space groups P42/n, Pccn, and Ccca(in a revised supercell) can cover the symmetry of Rp(Fe4B4)q for the different parity combinations of p and q, which is in agreement with the experimental results. The supersymmetry of all these compounds can be represented by an orthogonal superspace group PssiCmma. The related systematic extinctions are discussed, and the selection rules of Vernier structures, those can not be explained by three-dimensional space group, are obtained.
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