Related papers: Solution of the crystallographic phase problem by …

In analysis of X-ray diffraction data, identifying the crystalline phase is important for interpreting the material. The typical method is identifying the crystalline phase from the coincidence of the main diffraction peaks. This method…

We propose efficient algorithms based on a band-limited version of 2D synchrosqueezed transforms to extract mesoscopic and microscopic information from atomic crystal images. The methods analyze atomic crystal images as an assemblage of…

The design of crystal materials plays a critical role in areas such as new energy development, biomedical engineering, and semiconductors. Recent advances in data-driven methods have enabled the generation of diverse crystal structures.…

Sub-angstrom spatial resolution of electron density coupled with sub-femtosecond temporal resolution is required to directly observe the dynamics of the electronic structure of a molecule after photoinitiation or some other ultrafast…

Like many other advanced imaging methods, x-ray phase contrast imaging and tomography require mathematical inversion of the observed data to obtain real-space information. While an accurate forward model describing the generally nonlinear…

Atom arrangement plays a critical role in determining material properties. It is, therefore, essential for materials science and engineering to identify and characterize distinct atom configurations. Currently, crystal structures can be…

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…

In this work we consider the problem of reconstruction of a signal from the magnitude of its Fourier transform, also known as phase retrieval. The problem arises in many areas of astronomy, crystallography, optics, and coherent diffraction…

The diffraction technique is widely used in the determination of crystal structures and is one of the bases for the modern science and technology. All related structure determination methods are based on the assumption that perfect single…

Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to…

X-ray Bragg coherent diffraction imaging has been demonstrated as a powerful three-dimensional (3D) microscopy approach for the investigation of sub-micrometer-scale crystalline particles. It is based on the measurement of a series of…

The application of powder diffraction methods in two-dimensional crystallography is regarded as intractable because of the uncertainties associated with overlapping reflections. Here, we report an approach that resolves these ambiguities…

Quasicrystals are one kind of space-filling structures. The traditional crystalline approximant method utilizes periodic structures to approximate quasicrystals. The errors of this approach come from two parts: the numerical discretization,…

We present the first phase retrieval algorithm guaranteed to solve the multidimensional phase retrieval problem in polynomial arithmetic complexity without prior information. The method successfully terminates in O(N log(N)) operations for…

Accurate molecular crystal structure prediction is a fundamental goal in academic and industrial condensed matter research and polymorphism is arguably the biggest obstacle on the way. We tackle this challenge in the difficult case of the…

The use of machine learning methods for accelerating the design of crystalline materials usually requires manually constructed feature vectors or complex transformation of atom coordinates to input the crystal structure, which either…

The fast algorithms in Fourier optics have invigorated multifunctional device design and advanced imaging technologies. However, the necessity for fast computations has led to limitations in the widely used conventional Fourier methods,…

Mathematical crystal chemistry views crystal structures as the optimal solutions of mathematical optimization problem formalizing inorganic structural chemistry. This paper introduces the minimum and maximum atomic radii depending on the…

In this paper, based on the analysis of the formula (2.2) for calculating the elastic scattering diagrams of microparticles on a multilayer crystal surface, derived by the author in the article [3], it is shown that the stochastic approach…

We suggest new modification (we call it a noise reduction procedure) for Steinhardt parameters which are often used for detecting crystalline structures in computer simulation of solids and soft matter systems. We have also developed a new…