Related papers: Matching Crystal Structures Atom-to-Atom
Quasi-crystals are aperiodic structures that present crystallographic properties which are not compatible with that of a single unit cell. Their revolutionary discovery in a metallic alloy, less than three decades ago, has required a full…
Statistically sound crystallographic symmetry classifications are obtained with information theory based methods in the presence of approximately Gaussian distributed noise. A set of three synthetic patterns with strong Fedorov type…
The tree reconstruction problem is to find an embedded straight-line tree that approximates a given cloud of unorganized points in $\mathbb{R}^m$ up to a certain error. A practical solution to this problem will accelerate a discovery of new…
Diffraction is the most common method to solve for unknown or partially known crystal structures. However, it remains a challenge to determine the crystal structure of a new material that may have nanoscale size or heterogeneities. Here we…
We propose a geometrical characterization of amorphous liquid structures that suppress crystallization by competing locally with crystalline order. We introduce for this purpose the crystal affinity of a liquid, a simple measure of its…
A computer algorithm to search symmetries of crystal structures as implemented in the \texttt{spglib} code is described. An iterative algorithm is employed to robustly identify space group types tolerating a certain amount of distortion in…
Exact expressions for probability densities of conjugate pair separation in euclidean isometries are obtained, for the cosmic crystallography.These are the theoretical counterparts of the mean histograms arising from computer simulation of…
Amorphous solids such as glass are ubiquitous in our daily life and have found broad applications ranging from window glass and solar cells to telecommunications and transformer cores. However, due to the lack of long-range order, the…
Crystal material representation is the foundation of crystal material research. Existing works consider crystal molecules as graph data with different representation methods and leverage the advantages of techniques in graph learning. A…
Many real objects are modeled as discrete sets of points, such as corners or other salient features. For our main applications in chemistry, points represent atomic centers in a molecule or a solid material. We study the problem of…
The emerging field of on-chip integration of nanophotonic devices and cold atoms offers extremely-strong and pure light-matter interaction schemes, which may have profound impact on quantum information science. In this context, a…
Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in $R^d$. It is shown that natural parametrizations provide affine section…
We study the Euclidean minimum weight perfect matching problem for $n$ points in the plane. It is known that any deterministic approximation algorithm whose approximation ratio depends only on $n$ requires at least $\Omega(n \log n)$ time.…
Crystalline materials can form different structural arrangements (i.e. polymorphs) with the same chemical composition, exhibiting distinct physical properties depending on how they were synthesized or the conditions under which they…
Coherent crystalline interfaces form when a pair of joined crystals share lattice sites. Such interfaces are ubiquitous in materials, minerals, and compounds, with examples including grain boundaries in polycrystals and phase boundaries in…
Scientists use imaging to identify objects of interest and infer properties of these objects. The locations of these objects are often measured with error, which when ignored leads to biased parameter estimates and inflated variance.…
Liquid crystal is a typical kind of soft matter that is intermediate between crystalline solids and isotropic fluids. The study of liquid crystals has made tremendous progress over the last four decades, which is of great importance on both…
Crystal-structure phase mapping is a core, long-standing challenge in materials science that requires identifying crystal structures, or mixtures thereof, in synthesized materials. Materials science experts excel at solving simple systems…
The atomic displacements associated with the freezing of metals and salts are calculated by treating crystal growth as an assignment problem through the use of an optimal transport algorithm. Converting these displacements into time scales…
Determination of the symmetry profile of structures is a persistent challenge in materials science. Results often vary amongst standard packages, hindering autonomous materials development by requiring continuous user attention and educated…