Atomic scale analyses of [Image: see text]-module defects in an NiZr alloy

Some specific structures of intermetallic alloys, like approximants of quasicrystals, have their unit cells and most of their atoms located on a periodic fraction of the nodes of a unique [Image: see text]-module [a set of the irrational projections of the nodes of a (N > 3-dimensional) lattice]. Those hidden internal symmetries generate possible new kinds of defects like coherent twins, translation defects and so-called module dislocations that have already been discussed elsewhere [Quiquandon et al. (2016 ▸). Acta Cryst. A72, 55–61; Sirindil et al. (2017 ▸). Acta Cryst. A73, 427–437]. Presented here are electron microscopy observations of the orthorhombic phase NiZr – and its low-temperature monoclinic variant – which reveal the existence of such defects based on the underlying [Image: see text]-module generated by the five vertices of the regular pentagon. New high-resolution electron microscopy (HREM) and scanning transmission electron microscopy high-angle annular dark-field (STEM-HAADF) observations demonstrate the agreement between the geometrical description of the structure in five dimensions and the experimental observations of fivefold twins and translation defects.