Structure determination of the hexagonal quasicrystal approximant μ′-(Al,Si)4Cr by the strong reflections approach

Structure solution of the Al69.2Cu20Cr10.8 ϕ phase

The stable ϕ phase that forms below ∼923 K around the Al69.2Cu20.0Cr10.8 composition was found to be hexagonal [P63, a = 11.045 (2), c = 12.688 (2) Å] and isostructural to the earlier reported Al6.2Cu2Re X phase [Samuha, Grushko & Meshi (2016). J. Alloys Compd. 670, 18–24]. Using the structural model of the latter, a successful Rietveld refinement of the XRD data for Al69.5Cu20.0Cr10.5 was performed. Both ϕ and X were found to be structurally related to the Al72.6Cu11.0Cr16.4 ζ phase [P63/m, a = 17.714, c = 12.591 Å; Sugiyama, Saito & Hiraga (2002). J. Alloys Compd. 342, 148–152], with a close lattice parameter c and a τ-times-larger lattice parameter a (τ is the golden mean). The structural relationship between ζ and ϕ was established on the basis of the similarity of their layered structures and common features. Additionally, the strong-reflections approach was successfully applied for the modeling of the ϕ phase based on the structural model of the ζ phase. The latter and the experimental structural model (retrieved following Rietveld refinement) were found to be essentially identical.

Explanation of structural differences and similarities between the AT2Al10 phases (where A=actinide, lanthanide or rare earth element and T=transition metal)

In the current work we have studied the crystallographic relationship between the AT2Al10 phases (where A = actinide, lanthanide and rare earth element and T = transition metal). It is known that with this stoichiometry two structure types exist: tetragonal CaCr2Al10 and orthorhombic YbFe2Al10. It was found that both CaCr2Al10 and YbFe2Al10 types are structural derivatives of the ThMn12 type structure (which has more general formula of AT x Al12− x , with x > 2). CaCr2Al10 structure has a group-subgroup relationship with the ThMn12 structure, while the relationship of the YbFe2Al10 to the ThMn12 was proved applying the strong reflection approach, suggested initially for approximants of quasi-crystals. Proposed here relationship between the studied structures explains the small difference in total energies, calculated using Density Functional Theory. Understanding the connection between these phases allows regarding AT2Al10 composition as somewhat extension of the AT x Al12− x compositional range. Due to the unique magnetic properties of the AT x Al12− x phases, tunable as a function of crystallographic structure, study of structural stability and crystallographic relationships of related phases are of outmost importance.

Structure determination of a pseudo-decagonal quasicrystal approximant by the strong-reflections approach and rotation electron diffraction

The structure of a complicated pseudo-decagonal (PD) quasicrystal approximant in the Al–Co–Ni alloy system, denoted as PD1, was solved by the strong-reflections approach on three-dimensional rotation electron diffraction (RED) data, using the phases from the known PD2 structure. RED shows that the PD1 crystal is primitive and orthorhombic, with a = 37.3, b = 38.8, c = 8.2 Å. However, as with other approximants in the PD series, the superstructure reflections (corresponding to c = 8.2 Å) are much weaker than those of the main reflections (corresponding to c = 4.1 Å), so it was decided to solve the PD1 structure in the smaller primitive unit cell first, i.e. with unit-cell parameters a = 37.3, b = 38.8, c = 4.1 Å and space group Pnam. A density map of PD1 was calculated from only the 15 strongest unique reflections. It contained all 31 Co/Ni atoms and many weaker peaks corresponding to Al atoms. The structure obtained from the strong-reflections approach was confirmed by applying direct methods to the complete RED data set. Successive refinement using the RED data set resulted in 108 unique atoms (31 Co/Ni and 77 Al). This is one of the most complicated approximant structures ever solved by electron diffraction. As with other approximants in the PD series, PD1 is built of characteristic 2 nm wheel clusters with fivefold rotational symmetry, which agrees with results from high-resolution electron microscopy images. The simulated electron diffraction patterns for the structure model are in good agreement with the experimental electron diffraction patterns obtained by RED.

A complicated quasicrystal approximant epsilon16 predicted by the strong-reflections approach

The structure of the quasicrystal approximant ∊₁₆ was predicted by the strong-reflections approach based on the known approximant ∊₆.

The structure of a complicated quasicrystal approximant ∊₁₆ was predicted from a known and related quasicrystal approximant ∊₆ by the strong-reflections approach. Electron-diffraction studies show that in reciprocal space, the positions of the strongest reflections and their intensity distributions are similar for both approximants. By applying the strong-reflections approach, the structure factors of ∊₁₆ were deduced from those of the known ∊₆ structure. Owing to the different space groups of the two structures, a shift of the phase origin had to be applied in order to obtain the phases of ∊₁₆. An electron-density map of ∊₁₆ was calculated by inverse Fourier transformation of the structure factors of the 256 strongest reflections. Similar to that of ∊₆, the predicted structure of ∊₁₆ contains eight layers in each unit cell, stacked along the b axis. Along the b axis, ∊₁₆ is built by banana-shaped tiles and pentagonal tiles; this structure is confirmed by high-resolution transmission electron microscopy (HRTEM). The simulated precession electron-diffraction (PED) patterns from the structure model are in good agreement with the experimental ones. ∊₁₆ with 153 unique atoms in the unit cell is the most complicated approximant structure ever solved or predicted.

Electron crystallography: imaging and single-crystal diffraction from powders

The study of crystals at atomic level by electrons – electron crystallography – is an important complement to X-ray crystallography. There are two main advantages of structure determinations by electron crystallography compared to X-ray diffraction: (i) crystals millions of times smaller than those needed for X-ray diffraction can be studied and (ii) the phases of the crystallographic structure factors, which are lost in X-ray diffraction, are present in transmission-electron-microscopy (TEM) images. In this paper, some recent developments of electron crystallography and its applications, mainly on inorganic crystals, are shown. Crystal structures can be solved to atomic resolution in two dimensions as well as in three dimensions from both TEM images and electron diffraction. Different techniques developed for electron crystallography, including three-dimensional reconstruction, the electron precession technique and ultrafast electron crystallography, are reviewed. Examples of electron-crystallography applications are given. There is in principle no limitation to the complexity of the structures that can be solved by electron crystallography.