Related papers: Identifying and Indexing Icosahedral Quasicrystals…

Automatic crystal orientation determination and orientation mapping are important tools for research on polycrystalline materials. The most common methods of automatic orientation determination rely on detecting and indexing individual…

Pinwheel patterns and their higher dimensional generalisations display continuous circular or spherical symmetries in spite of being perfectly ordered. The same symmetries show up in the corresponding diffraction images. Interestingly, they…

We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochner's theorem from Fourier analysis. This clarifies a common…

Orientation mapping is a widely used technique for revealing the microstructure of a polycrystalline sample. The crystalline orientation at each point in the sample is determined by analysis of the diffraction pattern, a process known as…

Quasicrystals are aperiodically ordered solids that exhibit long-range order without translational periodicity, bridging the gap between crystalline and amorphous materials. Due to their lack of translational periodicity, information on…

In this paper, we propose a general mechanism for the existence of quasicrystals in spatially extended systems (partial differential equations with Euclidean symmetry). We argue that the existence of quasicrystals with higher order…

The large amount of powder diffraction data for which the corresponding crystal structures have not yet been identified suggests the existence of numerous undiscovered, physically relevant crystal structure prototypes. In this paper, we…

Determining the atomic-level structure of crystalline solids is critically important across a wide array of scientific disciplines. The challenges associated with obtaining samples suitable for single-crystal diffraction, coupled with the…

Electron backscatter diffraction (EBSD) is a technique used to measure crystallographic features in the scanning electron microscope. The technique is highly automated and readily accessible in many laboratories. EBSD pattern indexing is…

The increasing scientific and technological interest in nanoparticles has raised the need for fast, efficient and precise characterization techniques. Powder diffraction is a very efficient experimental method, as it is straightforward and…

We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the…

Two novel (and proprietary) strategies for the structural identification of a nanocrystal from either a single high-resolution (HR) transmission electron microscopy (TEM) image or a single precession electron diffraction pattern are…

We propose a unified framework for dealing with matching rules of quasiperiodic patterns, relevant for both tiling models and real world quasicrystals. The approach is intended for extraction and validation of a minimal set of matching…

Quasicrystals, realized in metal alloys, are a class of lattices exhibiting symmetries that fall outside the usual classification for periodic crystals. They do not have translational symmetry and yet the lattice points are well ordered.…

Optical reflectivity as a simple diagnostic method for testing structural quality of icosahedral quasicrystals 2 The optical reflectivity of Al-based and Ti-based quasicrystalline and approximant samples were investigated versus the quality…

Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side, pinwheel patterns and their higher dimensional…

Using a strategy that may be applied in theory or in experiments, we identify the regime in which a model binary soft matter mixture forms quasicrystals. The system is described using classical density functional theory combined with…

A major challenge in materials science is the determination of the structure of nanometer sized objects. Here we present a novel approach that uses a generative machine learning model based on diffusion processes that is trained on 45,229…

A simple model of 1D structure based on a Fibonacci sequence with variable atomic spacings is proposed. The model allows for observation of the continuous transition between periodic and non-periodic diffraction patterns. The diffraction…

Topological properties of crystals and quasicrystals is a subject of recent and growing interest. This Letter reports an experiment where, for certain quasicrystals, these properties can be directly retrieved from diffraction. We directly…