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

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.

Application of X-ray Diffraction and Electron Crystallography for Solving Complex Structure Problems

All crystalline materials in nature, whether inorganic, organic, or biological, macroscopic or microscopic, have their own chemical and physical properties, which strongly depend on their atomic structures. Therefore, structure determination is extremely important in chemistry, physics, materials science, etc. In the past centuries, many techniques have been developed for structure determination. The most widely used one is X-ray crystallography (single-crystal X-ray diffraction (SCXRD) and powder X-ray diffraction (PXRD)), and it remains the most important technique for structure determination of crystalline materials. Although SCXRD and PXRD are successful in many cases, a number of reasons limit their applications, such as SCXRD for nanosized crystals, intergrowth, and defects and PXRD for complex structures, multiphasic samples, impurities, peak overlaps, etc. Another most valuable technique for structure determination is electron crystallography (EC). With the electron as a probe, EC alone can also be used for structure determination, especially for crystals that are too small to be studied by SCXRD or too complex for PXRD. As electrons interact much more strongly with matter than X-rays do, both electron diffraction (ED) patterns and high-resolution transmission electron microscopy (HRTEM) images can be obtained from nanosized crystals. However, collecting a complete set of ED patterns or recording a good HRTEM image requires considerable expertise on the operation of electron microscopes and crystallography. The strong interactions between electrons and materials can also lead to dynamical effects and beam damage. These difficulties make structure determination from ED patterns and HRTEM images not straightforward. Recently, two three-dimensional (3D) electron diffraction techniques, automated electron diffraction tomography (ADT) and rotation electron diffraction (RED), have been developed, which perform the data collection in an automated manner. Although the dynamical effects in the newly developed 3D electron diffraction techniques (ADT, RED) are reduced significantly, for some structures there are still problems with obtaining an initial model because of beam damage. The X-ray diffraction and EC methods discussed above are both powerful techniques but have their own limitations. In many complicated cases, one technique alone is not enough to solve the crystal structure, and different techniques that supply complementary structural information have to support each other for the complete structure determination. In this Account, we provide a summary of the advantages and disadvantages of X-ray diffraction (PXRD and SCXRD) and EC (HRTEM and ED) for structure determination and include a review of applications of X-ray diffraction and EC for solving complex structure problems such as peak overlap, impurities, pseudosymmetry and twinning, disordered frameworks, locating guests, aperiodic structures, etc. Some of the latest advances in structure determination are also presented briefly, namely, revealing hydrogen positions by ED, protein crystal structure solution by 3D electron diffraction, and structure determination using an X-ray free electron laser (XFEL).

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.

Precession electron diffraction - a topical review

In the 20 years since precession electron diffraction (PED) was introduced, it has grown from a little-known niche technique to one that is seen as a cornerstone of electron crystallography. It is now used primarily in two ways. The first is to determine crystal structures, to identify lattice parameters and symmetry, and ultimately to solve the atomic structure ab initio. The second is, through connection with the microscope scanning system, to map the local orientation of the specimen to investigate crystal texture, rotation and strain at the nanometre scale. This topical review brings the reader up to date, highlighting recent successes using PED and providing some pointers to the future in terms of method development and how the technique can meet some of the needs of the X-ray crystallography community. Complementary electron techniques are also discussed, together with how a synergy of methods may provide the best approach to electron-based structure analysis.

Atomic structure solution of the complex quasicrystal approximant Al77Rh15Ru8from electron diffraction data

The crystal structure of the novel Al77Rh15Ru8phase (which is an approximant of decagonal quasicrystals) was determined using modern direct methods (MDM) applied to automated electron diffraction tomography (ADT) data. The Al77Rh15Ru8E-phase is orthorhombic [Pbma,a= 23.40 (5),b= 16.20 (4) andc= 20.00 (5) Å] and has one of the most complicated intermetallic structures solved solely by electron diffraction methods. Its structural model consists of 78 unique atomic positions in the unit cell (19 Rh/Ru and 59 Al). Precession electron diffraction (PED) patterns and high-resolution electron microscopy (HRTEM) images were used for the validation of the proposed atomic model. The structure of the E-phase is described using hierarchical packing of polyhedra and a single type of tiling in the form of a parallelogram. Based on this description, the structure of the E-phase is compared with that of the ε6-phase formed in Al–Rh–Ru at close compositions.