Related papers: Statistical Distribution of Crystallographic Group…
A routine crystallography technique, crystal structure analysis, is rarely performed in computational condensed matter research. The lack of methods to identify and characterize crystal structures reliably in particle simulation data…
The prediction of material structure from chemical composition has been a long-standing challenge in natural science. Although there have been various methodological developments and successes with computer simulations, the prediction of…
Inorganic crystals are periodic, highly-symmetric arrangements of atoms in three-dimensional space. Their structures are constrained by the symmetry operations of a crystallographic \emph{space group} and restricted to lie in specific…
Recognition of structure prototypes from tremendous known inorganic crystal structures has been an important subject beneficial for material science research and new materials design. The existing databases of inorganic crystal structure…
We describe a statistical method to avoid biased estimation of the content of different particle species. We consider the case when the particle identification information strongly depends on some kinematical variables, whose distributions…
In crystallography, a structure is typically represented by the arrangement of atoms in the direct space. Furthermore, space group symmetry and Wyckoff site notations are applied to characterize crystal structures with only a few variables.…
Machine learning techniques have successfully been used to extract structural information such as the crystal space group from powder X-ray diffractograms. However, training directly on simulated diffractograms from databases such as the…
A wide range of synthesized crystalline inorganic materials exhibit compositional disorder, where multiple atomic species partially occupy the same crystallographic site. As a result, the physical and chemical properties of such materials…
Crystals are the foundation of numerous scientific and industrial applications. While various learning-based approaches have been proposed for crystal generation, existing methods seldom consider the space group constraint which is crucial…
Crystals which have a uniform distribution of defects are endowed with a Lie group description which allows one to construct an associated discrete structure. These structures are in fact the discrete subgroups of the ambient Lie group. The…
Crystallographic groups describe the symmetries of crystals and other repetitive structures encountered in nature and the sciences. These groups include the wallpaper and space groups. We derive linear and nonlinear representations of…
Crystal Structure Prediction (CSP) is crucial in various scientific disciplines. While CSP can be addressed by employing currently-prevailing generative models (e.g. diffusion models), this task encounters unique challenges owing to the…
Evolutionary crystal structure prediction proved to be a powerful approach for studying a wide range of materials. Here, we present a specifically designed algorithm for the prediction of the structure of complex crystals consisting of…
We provide a procedure for generating the irreducible representations of crystallography groups in any dimension. We also furnish a strategy to investigate the topology of the unitary dual of a crystallography group using sequences of…
This paper was motivated by the articles "Same or different - that is the question" in CrystEngComm (July 2020) and "Change to the definition of a crystal" in the IUCr newsletter (June 2021). Experimental approaches to crystal comparisons…
By the method of Poissonization we confirm some existing results concerning consistent estimation of the structural distribution function in the situation of a large number of rare events. Inconsistency of the so called natural estimator is…
Whereas knowledge of a crystalline material's unit cell is fundamental to understanding the material's properties and behavior, there are not obvious analogues to unit cells for disordered materials despite the frequent existence of…
The prediction of energetically stable crystal structures formed by a given chemical composition is a central problem in solid-state physics. In principle, the crystalline state of assembled atoms can be determined by optimizing the energy…
Geometric information such as the space groups and crystal systems plays an important role in the properties of crystal materials. Prediction of crystal system and space group thus has wide applications in crystal material property…
Motivated by the concept of partial ergodicity, we present an alternative description of covalent and ionic glassy solids as statistical ensembles of crystalline local minima on the potential energy surface. We show analytically that the…