Real Crystal Structure Research Articles

Crystal Structure Prediction Using Generative Adversarial Network with Data-Driven Latent Space Fusion Strategy.

Crystal structure prediction (CSP) is an important field of material design. Herein, we propose a novel generative adversarial network model, guided by a data-driven approach and incorporating the real physical structure of crystals, to address the complexity of high-dimensional data and improve prediction accuracy in materials science. The model, termed GAN-DDLSF, introduces a novel sampling method called data-driven latent space fusion (DDLSF), which aims to optimize the latent space of generative adversarial networks (GANs) by combining the statistical properties of real data with a standard Gaussian distribution, effectively mitigating the "mode collapse" problem prevalent in GANs. Our approach introduces a more refined generation mechanism specifically for binary crystal structures such as gallium nitride (GaN). By optimizing for the specific crystallographic features of GaN while maintaining structural rationality, we achieve higher precision and efficiency in predicting and designing structures for this particular material system. The model generates 9321 GaN binary crystal structures, with 16.59% reaching a stable state and 24.21% found to be metastable. These results can significantly enhance the accuracy of crystal structure predictions and provide valuable insights into the potential of the GAN-DDLSF approach for the discovery and design of binary, ternary, and multinary materials, offering new perspectives and methods for materials science research and applications.

On Chemical Bonding in ht-Ga3Rh and Its Effect on Structural Organization and Thermoelectric Behavior.

In the course of systematic studies of intermetallic compounds Ga3TM (TM─transition metal), the compound Ga3Rh is synthesized by direct reaction of the elements at 700 °C. The material obtained is characterized as a high-temperature modification of Ga3Rh. Powder and single-crystal X-ray diffraction analyses reveal tetragonal symmetry (space group P42/mnm, No. 146) with a = 6.4808(2) Å and c = 6.5267(2) Å. Large values and strong anisotropy of the atomic displacement parameters of Ga atoms indicate essential disorder in the crystal structure. A split-position technique is applied to describe the real crystal structure of ht-Ga3Rh. Bonding analysis in ht-Ga3Rh performed on ordered models with the space groups P1̅, P42nm, and P42212 shows, besides the omnipresent heteroatomic Ga-Rh bonds in the rhombic prisms ∞3[Ga8/2Rh2], the formation of homoatomic Ga-Ga bonds bridging the Rh-Rh contacts and the absence of significant Rh-Rh bonding. These features are essential reasons for the experimentally observed disorder in the lattice. In agreement with the calculated electronic density of states, ht-Ga3Rh shows temperature-dependent electrical resistivity of a "bad metal". The very low lattice thermal conductivity of less than 0.5 W m-1 K-1 at 300 K, being lower than those for most other Ga3TM compounds, correlates with the enhanced bonding complexity.

Regular relations of the composition, structure and properties of crystals of hydrogen-containing compounds

Research subject. Crystals of hydrogen-containing compounds belonging to the superprotonic family. Aim. To obtain knowledge about regular relations between composition, atomic structure, real structure and physical properties of materials, with the purpose of elucidating processes occurring in condensed state and forming the basis for modification of known or obtaining new compounds. Materials and methods. Experimental data were obtained using a set of complementary physical methods, including structural analysis using X-rays, synchrotron radiation and neutrons, optical microscopy, and atomic force microscopy. Results. Experimental data on the atomic structure, real structure, and physical properties of superprotonic crystals, including systems of hydrogen bonds and their changes, were obtained. Conclusions. The physical properties of superprotonic crystals are significantly affected by hydrogen bonding systems and their changes, primarily by the formation of dynamically disordered hydrogen bonds with energetically equivalent positions of hydrogen atoms. When carrying out diagnostics of crystalline samples, account should be taken of their real structure, including the structure of surface layers and the presence of crystallization water. These factors may affect the measured physical parameters, the boundaries of existence of phases, the formation of a multiphase state under variations in temperature.

Reduction of the Spin–Phonon Coupling of Quadrupole Nuclei in NaF Crystals under Magnetic Saturation

The rate of nuclear spin-lattice relaxation is determined by the efficiency of interaction between thermal phonons and nuclear spins. The results on reducing the efficiency of spin–phonon coupling by suppressing the contribution from paramagnetic centers to quadrupole nucleus relaxation are presented. The suppression has been performed by stationary magnetic effect at the Larmor frequency. It is shown that, as in the presence of an acoustic field, the rate of spin-lattice relaxation of 23Na nuclei in a sodium fluoride crystal at magnetic saturation of the NMR signal does not change in the region of a negative average spin temperature.In the region of positive spin temperature, the rate of relaxation of 23Na spins significantly decreases and nuclear magnetization recovery with time is described by the sum of two exponentials. The contribution from nuclear spins with a lower efficiency of spin–phonon coupling, corresponding to the exponential with a long relaxation time, increases with increasing saturating field intensity. It is demonstrated that the efficiency of spin–phonon coupling for 19F nuclei without quadrupole moment does not change under the saturation conditions.The results obtained can be used for analyzing the structure of real crystals.

Structural diversity in tetranuclear ytterbium-based metal–organic frameworks and their divided net analysis

Lanthanides such as ytterbium have high and various coordination numbers, which lead to the generation of versatile secondary building units (SBUs) for metal–organic framework (MOF) synthesis. However, the versatility also tends to impose relatively low symmetry and uncertainty on the structures, thus understanding the connectivity modes between the inorganic units and the linkers is essential. In this work, a ditopic linker with an α-amino group is employed to regulate the hydrolysis of Yb(III) to facilitate the generation of SBUs with [Yb4(μ3-OH)4] cores, which further reticulate with the linkers to afford three kinds of MOFs. Analysis of the coordination linkages reveals that the linkers can be divided into three different modes, and the arrangement of the linkers with different modes around the SBUs leads to the structures with completely different nets. Furthermore, linker vacancies are found and quantified in the real crystal structures. In addition, a divided net strategy is used to analyze the nets of the two 8-connected MOFs. By dividing each 8-connected node into a 6-connected node and a 2-connected node, the underlying nets of the two MOFs can be regarded as an integration of a pcu net with infinite zig-zag chains or straight rods.

Continuous chiral distances for two-dimensional lattices.

Chirality was traditionally considered a binary property of periodic lattices and crystals. However, the classes of two-dimensional lattices modulo rigid motion form a continuous space, which was recently parametrized by three geographic-style coordinates. The four non-oblique Bravais classes of two-dimensional lattices form low-dimensional singular subspaces in the full continuous space. Now, the deviations of a lattice from its higher symmetry neighbors can be continuously quantified by real-valued distances satisfying metric axioms. This article analyzes these and newer G-chiral distances for millions of two-dimensional lattices that are extracted from thousands of available two-dimensional materials and real crystal structures in the Cambridge Structural Database.

Comparative Study of the Crystal Structure and Simulated 3D Structure of the Hsp90N‐Inhibitor Complex

AbstractThe crystal structure of a target‐ligand plays an indispensable role in rational drug design, structural optimization, and understanding the molecular interaction mechanism. For drug targets without crystal structures, the simulated 3D structure will provide an alternative important reference. However, the credibility of the simulated structure and its difference from the real crystal structure deserve deep consideration. The complex crystal structures of the target Hsp90N and its four small molecular inhibitors has previously been successfully determined. Herein, computer‐aided molecular docking technology is applied to predict complex 3D structures, and the comparison between the simulated 3D structures and crystal structures is analyzed. Compared with the complex crystal structures, the simulated 3D structures of the four groups have higher consistency with the main chains, whereas the branch chains, binding modes of inhibitors, and molecular interactions are different in detail. Thus, the simulated 3D complex structure can provide useful information to guide drug design and structural optimization of inhibitors when the crystal structure is missing, but it cannot replace the crystal structure and should be used with caution.

Geographic style maps for two-dimensional lattices.

This paper develops geographic style maps containing two-dimensional lattices in all known periodic crystals parameterized by recent complete invariants. Motivated by rigid crystal structures, lattices are considered up to rigid motion and uniform scaling. The resulting space of two-dimensional lattices is a square with identified edges or a punctured sphere. The new continuous maps show all Bravais classes as low-dimensional subspaces, visualize hundreds of thousands of lattices of real crystal structures from the Cambridge Structural Database, and motivate the development of continuous and invariant-based crystallography.

Tetragonality and Real Crystal Structure of Martensite in the Carbon Steels

Tetragonality and Real Crystal Structure of Martensite in the Carbon Steels

Multiscale Modeling of Ion Dynamics in Memristive Elements

A multiscale computational scheme is proposed for ion dynamics that allows modeling based on primary information—data on the chemical composition of the material and its crystal structure. The scheme includes quantum mechanical and molecular dynamics modeling as well as Monte Carlo simulation of ion and electron dynamics taking into account the real crystal structure. Approbation of the proposed approach is carried out on a silicon oxide memristive element. The results of computational experiments are presented that demonstrate the stages of growth and destruction of a conductive filament under the action of a time-varying voltage.

Crystal structures.

A personal view is offered on various solved and open problems related to crystal structures: the present state of reconstructing the crystal electron density from X-ray diffraction data; characterization of atomic and molecular motion from a combination of atomic displacement parameters and quantum chemical calculations; Bragg diffraction and diffuse scattering: twins, but different; models of real (as opposed to ideal) crystal structures from diffuse scattering; exploiting unexplored neighbourhoods of crystallography to mathematics, physics and chemistry.

Taking into account convective heat and mass exchange in autoclave reactors when scaling hydrothermal and hydrometallurgical processes

The article presents the procedure of scaling the processes of hydrothermal synthesis for various dispersed inorganic materials and selection of an optimal technological mode for a given autoclave reactor on the base of a reaction kinetics experimental study with applying in situ heat flux calorimetry and developing the reaction mathematical model to simulate temperature and conversion fields inside a chosen apparatus for the selected mode. Natural convection is shown to be the main driving force for heat exchange and mass exchange in autoclave reactors without mechanical mixing and heating with a jacket. This may lead to a considerable non-homogeneity of temperature and concentration fields inside the reactor and be the reason of phase composition and particle size variations as well as real crystal structure of reaction products non-reproducibility. Applying an optimal heating mode with temperature linear programming on the wall results in forming stationary fields of temperature and concentrations inside the reactor and makes it possible to monitor the current conversion along the apparatus cross-section and minimize corresponding gradients in the final point. It is also possible to evaluate overheating of the reaction mixture for a hydrometallurgical process in the batch stirred reactor or continuous flow reactor. The proposed procedure makes it possible to select an optimal technological mode for producing a definite product in a definite apparatus on the base of a hydrothermal or hydrometallurgical reaction kinetic model with heat generation or heat absorbtion. The author would like to thank the leadership of the Saint Petersburg Mining University for their extensive support of the basic studies into hydrothermal synthesis of dispersed inorganic materials and that of mathematical modelling work.

The Intermetallic Semiconductor ht-IrGa3: a Material in the in-Transformation State.

The compound IrGa3 was synthesized by direct reaction of the elements. It is formed as a high-temperature phase in the Ir-Ga system. Single-crystal X-ray diffraction analysis confirms the tetragonal symmetry (space group P42 /mnm, No. 136) with a = 6.4623(1) Å and c = 6.5688(2) Å and reveals strong disorder in the crystal structure, reflected in the huge values and anisotropy of the atomic displacement parameters. A model for the real crystal structure of ht-IrGa3 is derived by the split-position approach from the single-crystal X-ray diffraction data and confirmed by an atomic-resolution transmission electron microscopy study. Temperature-dependent electrical resistivity measurements evidence semiconductor behavior with a band gap of 30 meV. A thermoelectric characterization was performed for ht-IrGa3 and for the solid solution IrGa3-x Zn x .

Crystal structure prediction of materials with high symmetry using differential evolution

Crystal structure determines properties of materials. With the crystal structure of a chemical substance, many physical and chemical properties can be predicted by first-principles calculations or machine learning models. Since it is relatively easy to generate a hypothetical chemically valid formula, crystal structure prediction becomes an important method for discovering new materials. In our previous work, we proposed a contact map-based crystal structure prediction method, which uses global optimization algorithms such as genetic algorithms to maximize the match between the contact map of the predicted structure and the contact map of the real crystal structure to search for the coordinates at the Wyckoff positions (WP), demonstrating that known geometric constraints (such as the contact map of the crystal structure) help the crystal structure reconstruction. However, when predicting the crystal structure with high symmetry, we found that the global optimization algorithm has difficulty to find an effective combination of WP that satisfies the chemical formula, which is mainly caused by the inconsistency between the dimensionality of the contact map of the predicted crystal structure and the dimensionality of the contact map of the target crystal structure. This makes it challenging to predict the crystal structures of high-symmetry crystals. In order to solve this problem, here we propose to use PyXtal to generate and filter random crystal structures with given symmetry constraints based on the information such as chemical formulas and space groups. With contact map as the optimization goal, we use differential evolution algorithms to search for non-special coordinates at the WP to realize the structure prediction of high-symmetry crystal materials. Our experimental results show that our proposed algorithm CMCrystalHS can effectively solve the problem of inconsistent contact map dimensions and predict the crystal structures with high symmetry.

Novel study on the electron density distribution projection maps calculated via the discrete cosine transform

It is already known that a curve estimated via the discrete cosine transform (DCT) always passes through all the measured points without using imaginary numbers in the DCT coefficients, unlike the discrete Fourier transform. Moreover, owing to its character, the DCT can be used instead of the nonlinear least-squares method to express various theoretical curves. Because the DCT is a kind of Fourier transform, there is a possibility that the DCT could be employed to draw electron density distribution maps of crystals. If so, the probability that the DCT could be used to investigate the internal structure of materials by analysing the theoretical curves would increase. This article reports an attempt to draw the electron density distribution maps of the Mg3BN3 low-pressure phase [Mg3BN3(L)] by using the DCT in order to confirm the utility of the DCT for analysing the internal structure of materials. It is found that the DCT can provide mirror-symmetric electron density distribution projection maps and a modified DCT can be used to calculate whole standard electron density distribution projection maps for the surface plane of the unit cell. Moreover, a real crystal structure that has a centre of symmetry can be determined by the DCT by transforming a 1/4 part of the mirror-symmetric electron density distribution projection map.

Simplicity Out of Complexity: Band Structure for W20O58 Superconductor.

The band structure, density of states, and the Fermi surface of a recently discovered superconductor, oxygen-deficient tungsten oxide WO that is equivalent to WO, is studied within the density functional theory (DFT) in the generalized gradient approximation (GGA). Here we show that despite the extremely complicated structure containing 78 atoms in the unit cell, the low-energy band structure is quite feasible. Fermi level is crossed by no more than 10 bands per one spin projection (and even 9 bands per pseudospin projection when the spin-orbit coupling is considered) originating from the t 5d-orbitals of tungsten atoms forming zigzag chains. These bands become occupied because of the specific zigzag octahedra distortions. To demonstrate the role of distortions, we compare band structures of WO with the real crystal structure and with the idealized one. We also propose a basis for a minimal low-energy tight-binding model for WO.

Double-Crystal X-Ray Diffractometry and Topography Methods in the Analysis of the Real Structure of Crystals

The high efficiency of double-crystal X-ray diffractometry and topography methods in the characterization of crystals during refinement of the crystal-growth technology is demonstrated for the example of diamond bulk crystals and films obtained by the high pressure, high temperature method and by chemical vapor deposition, respectively. Techniques and study schemes for analysis of the real crystal structure, assessment of the chemical composition and the period of the crystal lattice, and analysis of the distinctive features of the deformation and thickness of thin films are described. Major structural defects (dislocations, stacking defects, inclusions of a different phase, and others) that emerge during the production of synthetic diamond crystals are identified.

Tancaite-(Ce), ideally FeCe(MoO<sub>4</sub>)<sub>3</sub> ● 3H<sub>2</sub>O: description and average crystal structure

Abstract. Tancaite-(Ce), ideally FeCe(MoO4)3⚫3H2O, is a new mineral occurring within cavities in the quartz veins which cut the granite at Su Seinargiu, Sarroch (CA), Sardinia, Italy. It is a secondary mineral formed in the oxidation zone of a sulfide ore vein. Associated minerals are quartz, muscovite, molybdenite, pyrite, and a mendozavilite-like phase. Tancaite-(Ce) is red or pale brown in colour, with a vitreous to adamantine lustre. Electron microprobe analyses give (wt %) SiO2 0.34, CaO 0.09, Fe2O3 11.29, SrO 0.02, La2O3 5.04, Ce2O3 10.35, Pr2O3 1.07, Nd2O3 3.66, Sm2O3 0.19, ThO2 2.58, UO2 0.17, MoO3 58.62, and H2O (calculated) 7.43, with a sum of 100.85, from which the empirical formula is calculated. The empirical formula Fe1.033+(Ce0.46La0.23Nd0.16Pr0.05Sm0.01U0.01Th0.07)Σ=0.99(Mo2.96Si0.04)Σ=3.00O12⚫3H2O can be simplified as Fe3+(REE)(MoO4)3⚫3H2O and idealized as FeCe(MoO4)3⚫3H2O. The presence of H2O was confirmed by micro-Raman spectrometry (stretching and bending vibrations of O–H). The calculated density is 3.834 g cm−3. The X-ray diffraction pattern of tancaite-(Ce) is characterized by a set of strong reflections, which point to a cubic subcell with a=6.870(1) Å and space group Pm3¯m, plus a set of superstructure reflections. Tancaite-(Ce) displays a new structure type not previously reported in natural and synthetic molybdates. By considering only the strong reflections, it was possible to solve and refine its average structure (R1=0.038 for 192 unique reflections with I>2σ(I)). The crystal structure consists of FeO6 octahedra centred at the origin of the cubic subcell and linked together through MoO4 tetrahedra by corner sharing. The Mo-centred tetrahedra are statistically distributed in four symmetry-related positions, with one-fourth occupancy. In the centre of the cubic unit cell the REE cations exhibit a 6+3 coordination, bonding six oxygen atoms and three H2O molecules, each of them being disorderly distributed in four symmetry-related positions. One of the possible supercells, with a 48-fold volume with respect to the primitive cubic small subcell, corresponded to a rhombohedral lattice, with a≈19.43 and c≈47.60 Å in the hexagonal setting. Several unsuccessful trials were performed to solve the real crystal structure of tancaite, by indexing the additional superstructure reflections and using their intensities to refine an ordered structural model. The new mineral has been approved by the IMA CNMNC (no. 2009-097). The name comes from Giuseppe Tanca, an Italian amateur mineralogist, who discovered the mineral and gave it to us for studying.

General electron theory of reduction and oxidation of metals

The significance of the new theory of metal reduction from ores has been demonstrated. It was shown that all the existing versions of the theory are based on atomic-molecular representations of the early 20-th century where reduction is considered as a process of exchange of oxygen atoms between a reducing agent and oxide molecules. These representations do not take into account changes in the crystalline structure of oxides and in the state of a gas medium with change in temperature and pressure. The attention here was drawn to the absence of molecules in oxides, and atoms in metals. Inconsistency of a number of the theory conclusions with practice of reduction during operation of plants was revealed. Based on the assumptions of redox reactions as processes of exchange of reagents by the valence electrons, defective ionic structure of real crystals, changes in the state of the gaseous medium during heating and pressure increase using some statements of quantum mechanics on the distribution of electrons in solids, the authors have developed electron version of the reduction theory. This theory is based on the unity of the anionic sublattice of all crystals of the oxide phase and the collective electronic system of all valence electrons of metal cations in oxide. It is shown that in the reduction plants, due to the thermal ionization of gases and thermionic emission from the surface of the heated bodies, the gas medium is plasma. The presence of charged particles in the plasma ensures their interaction at a considerable distance and the course of chemical processes in the kinetic mode. The gaseous reduction products are removed from the reaction zone with exhaust gases, and the electrons released in the plasma are absorbed by the oxide surface and exist in the oxide together with the anionic vacancies that arise when oxygen is removed. In high-grade ores the vacancies merge and disappear on the oxide surface, and the free electrons of the vacancies combine the nearest cations with a metal bond to form a metal shell which later turns into carbides. The formation of carbide shells blocks the oxide surface and stops reduction. When temperature rises and the shells melt the reduction process resumes. Therefore, the carbon-thermal reduction produces cast iron and high-carbon ferroalloys. In low-grade and complex ores the vacancies are scattered in the oxide volume along the total anionic sublattice forming solution of vacancies and free electrons. The vacancies merge and disappear in places of increased concentration of cations where the Fermi level of atoms is less than the chemical potential of the free electrons. In the formed anionic void the free electrons rearrange metal cations with low Fermi energy and bind them with a metal bond bypassing the stage of atom formation. Crystal growth in an anionic void occurs without resistance from the parent oxide phase.

Voronoi‐Based Similarity Distances between Arbitrary Crystal Lattices

AbstractThis paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substantially speed up the crystal structure prediction, because the prediction of many target properties of crystal structures is computationally slow and is essentially repeated for many nearly identical simulated structures. The proposed distances between arbitrary periodic lattices of crystal structures are invariant under all rigid motions, satisfy the metric axioms and continuity under atomic perturbations. The above properties make these distances ideal tools for clustering and visualizing large datasets of crystal structures. All the conclusions are rigorously proved and justified by experiments on real and simulated crystal structures.