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We introduce a phase-field crystal model that creates an array of complex three- and two-dimensional crystal structures via a numerically tractable three-point correlation function. The three-point correlation function is designed in order…

Kinematic diffraction is well suited for a mathematical approach via measures, which has substantially been developed since the discovery of quasicrystals. The need for further insight emerged from the question of which distributions of…

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…

Atomic form factors are widely used for the characterization of targets and specimens, from crystallography to biology. By using recent mathematical results, here we derive an analytical expression for the atomic form factor within the…

We present detailed elaboration and first generally applicable linearization routines of the \textit{Parameter Space Concept} (PSC) for determining 1-dimensionally projected structures of $m$ independent scatterers. This crystal…

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…

Nuclear matter at large number of colors is necessarily in a solid phase. In particular holographic nuclear matter takes the form of a crystal of instantons of the flavor group. In this article we initiate the analysis of the…

It is show that in group representation by non-traditionally determining by the Maxwell equations, instead of wave, linear differential operator of momentous type from the common point of view the transformation of electromagnetic and…

Determining the stability of chemical compounds is essential for advancing material discovery. In this study, we introduce a novel deep neural network model designed to predict a crystal's formation energy, which identifies its stability…

Crystal structure modeling with graph neural networks is essential for various applications in materials informatics, and capturing SE(3)-invariant geometric features is a fundamental requirement for these networks. A straightforward…

For a very long time, computational approaches to the design of new materials have relied on an iterative process of finding a candidate material and modeling its properties. AI has played a crucial role in this regard, helping to…

Amorphous, glass, and glass-ceramic materials practically always include a significant number (more than eight) of crystalline phases, with the contents of the latter ranging from a few wt.% to several hundredths or tenths of wt.%. The…

We introduce CrystalFormer, a transformer-based autoregressive model specifically designed for space group-controlled generation of crystalline materials. By explicitly incorporating space group symmetry, CrystalFormer greatly reduces the…

In this paper the problem of the theory of a quasicrystal structures - the determination of coordinates of each atom of quasicrystal in analytical form - is solved. Within the framework of the proposed model a periodic crystal can be…

The mathematics of crystalline structures connects analysis, geometry, algebra, and number theory. The planar crystallographic groups were classified in the late 19th century. One hundred years later, B\'erard proved that the fundamental…

We demonstrate a strategy for simulating wide-range X-ray scattering patterns, which spans the small- and wide scattering angles as well as the scattering angles typically used for Pair Distribution Function (PDF) analysis. Such simulated…

We explain how the action of the Heisenberg algebra on the space of q-deformed wedges yields the Heisenberg crystal structure on charged multipartitions, by using the boson-fermion correspondence and looking at the action of the Schur…

We show that one can employ well-established numerical continuation methods to efficiently calculate the phase diagram for thermodynamic systems. In particular, this involves the determination of lines of phase coexistence related to first…

Weyl group multiple Dirichlet series and metaplectic Whittaker functions can be described in terms of crystal graphs. We present crystals as parameterized by Littelmann patterns and we give a survey of purely combinatorial constructions of…

Dynamical diffraction effects always play a role when working with perfect single crystals. The penetration of X-rays respect to the surface normal during diffraction (extinction depth, $1/\sigma_e$) in perfect single crystals does not have…