Date Published: November 01, 2018
Publisher: International Union of Crystallography
Author(s): Abdullah Sirindil, Raphael Kobold, Frédéric Mompiou, Sylvie Lartigue-Korinek, Loic Perriere, Gilles Patriarche, Marianne Quiquandon, Denis Gratias.
This article describes the observation and determination of -module defects (twins, translation faults and module dislocations) in NiZr by high-resolution electron microscopy (HREM), and scanning transmission electron microscopy bright-field (STEM-BF) and high-angle annular dark-field (STEM-HAADF).
The present article is the experimental continuation of a search to identify possible new defects in structures where the atoms, in addition to being periodically distributed, are located on a long-range-ordered subset of the nodes of a -module.
After Kirkpatrick et al. (1962 ▸), the orthorhombic phase NiZr has the space group Cmcm with lattice parameters |A| = 0.3268, |B| = 0.9973 and |C| = 0.4101 nm. It is defined by two Wyckoff positions 4cm2m (0, y, 1/4) with yNi = 0.0817 and yZr = 0.3609 as shown in Fig. 1 ▸.
In order to check the validity of our previous predictions from the -module description, we prepared samples of NiZr for high-resolution TEM investigations in high-resolution electron microscopy (HREM) and scanning transmission electron microscopy high-angle annular dark-field (STEM-HAADF) modes. Samples used in the present study were obtained by two different methods:
Samples (a) were thinned by mechanical grinding down to 100 µm and eventually thinned to electron transparency using ion milling (Gatan PIPS) until the formation of a hole. Samples (b) were electropolished using a Tenupol with a solution of 10% perchloric acid and 90% methanol at 243 K under 35 V.
All ultra-high-resolution HAADF or BF images presented in this study are various realizations of a single-module crystal in the sense that the entire observation areas are described on a unique -module that is invariant everywhere on the picture: vectors relating any two (equivalent) white dots on the micrographs are integer linear combinations of the five pentagon unit vectors with constant sum.
This article is the experimental counterpart of a former one (Sirindil et al., 2017 ▸) based on the idea of testing whether certain structures can be described in the context of -modules, i.e. in high-dimension spaces, rather than in the standard framework based on three-dimensional lattices. We have shown here that the orthorhombic phase NiZr can be faithfully described in a five-dimensional space with high internal symmetry generating possible defects at the symmetry breaking induced by the projection back in the three-dimensional space. The ultra-high-resolution electron microscopy pictures have shown perfect agreement between observed and predicted defects. This set of experiments supports the use of -modules in crystallography; this is indeed an interesting and fruitful unifying concept, even in direct space, where it is both an elegant formulation and an efficient tool to predict new possible defects including interface dislocations in structures with hidden non-crystallographic symmetries, in a unique mathematical framework.