Crystal Theory Research Articles

Mathematical Modeling of Multiple-Li-Dendrite Growth in Li-ion Battery Electrodes

Lithium dendrite growth in Li-ion batteries is one of the most dangerous phenomena because it can cause inner short circuits and thermal runaways. However, the nucleation and growth of the dendrites are difficult to predict because of their complex behaviors, which depend on several factors such as the charging conditions and electrode-design parameters. In this study, a comprehensive mathematical model has been developed for Li-deposition on Li-ion battery electrodes. The model is based on the Single Particle model (to evaluate the Li-ion concentration fields) combined with dendrite-growth models based on the electrochemical and crystal growth theory. The effect of the SEI thickness distribution, the charging C-rate and cut-off voltage on the growth of dendrite tips have been statistically evaluated, and the risk of short circuit is discussed. The study focuses on the effects of the SEI-thickness distribution on the timing of the SEI breaking and density of the dendrite formation.

Wave control of a flexible space tether based on elastic metamaterials

AbstractThis study proposes a spider‐web elastic metamaterial to suppress vibrations in space slender structures, such as flexible space tethers. The metamaterial consists of unit cells that are periodically distributed on the space tether to obtain band gaps. The finite element model of the unit cell is established by employing the absolute nodal coordinate formulation (ANCF) due to the large deformation of the structure. The eigenfrequencies and corresponding vibration modes of the unit cell are obtained by ANCF. Moreover, the band gap of the unit cell is calculated based on the phonon crystal theory. The relationship between the vibration modes and the band gaps is analyzed. Finally, an experiment is conducted to verify the vibration transmission characteristics of finite period cells. The results show the effectiveness of the spider‐web elastic metamaterial for vibration suppression of a flexible tether. This study provides insights into the use of elastic metamaterials for vibration isolation in space tether systems.

Cooperative Pseudo Jahn Teller distortion derives phase transitions in bismuth oxide

Bismuth oxide exhibits a complex array of structures with a broad range of properties of various technological importance. We derive the phase transition pathway using the in-situ heating X-ray diffraction data, evidencing four polymorphs of α, β, δ, and γ. We prove that the observed phase transitions are due to the cooperative pseudo-Jahn-Teller distortion in the crystal originating from mixing the ground state Bi6s and excited Bi6p states. Using the electron localization function and crystal orbital theory, we explore the role of the Bi3+ lone pair in the second-order phase transition. It is found that the O2p states have a critical role in stabilizing the lone pair activity, which leads to a pseudo-Jahn Teller distortion cooperatively inducing the phase transition.

Competitive growth of Sb2Se3 and GeSe2 crystals in pseudobinary (GeSe2)x(Sb2Se3)1-x glass-forming materials

The present study deals with crystal growth in undercooled melts in the GeSe2-rich region of the (GeSe2)x(Sb2Se3)1-x system. Two different crystalline phases (Sb2Se3 and GeSe2) were identified and directly investigated using infrared microscopy. In the case of GeSe2 crystals, the crystal growth rates depended only on the temperature and did not change with the composition of the system. The competitive growth of Sb2Se3 and GeSe2 was described in terms of current crystal growth theories. To complete the viscosity behavior in (GeSe2)x(Sb2Se3)1-x system, new viscosity data were obtained for the (GeSe2)0.9(Sb2Se3)0.1 composition. The combination of growth and viscosity data provides useful information on crystal growth and enables the prediction of crystal growth rates in the (GeSe2)x(Sb2Se3)1-x system over a wide temperature range.

Contact guidance of mesenchymal stem cells by flagellin-modified substrates: Aspects of cell-surface interaction from the point of view of liquid crystal theory

A major challenge for the tissue engineering is the regulation of cell behavior using topographical cues of the artificial biomaterials without biochemical stimuli. In this study, micropatterned substrates with ridge/groove topography (pitch size of 6–80 µm) and upper adhesive layer from non-animal origin RGD peptide flagellin were created on the basis of polydimethylsiloxane (PDMS). The obtained flagellin(FL)-modified PDMS microstructures revealed both physicochemical and biological anisotropic properties. Mesenchymal stem cells (MSCs) sensed and reshaped in response to the ridge/groove patterned surface similar to water microdroplets behavior. Cultivation of MSCs on the micropatterned FL-PDMS substrates led to cell polarization in a direction parallel to the pattern and the degree of MSCs orientation increased with the enhance in the pitch size from 8 to 20 µm, and then decreased. The MSCs orientation on micropatterned FL-PDMS substrates was explained from the point of view of nematic liquid crystal theories assuming that stem cells can be considered as active nematic phase and their orientation order can be evaluated by P2 parameter. In accordance with the theory, an enhanced orientation effect of the surface profile can be reached by providing a strong polar interaction between the cells and the patterned surface of the substrate. Surface modification by FL layer increased the polar interaction between the MSCs and the surface resulting in stimulation of the isotropic-to-nematic transition. In summary, our data make a significant contribution to understanding the fundamentals of the influence of substrate topographical features on MSCs topology and can be useful for the rational design of scaffolds intended to manipulate cell behavior without exogenous stimuli.

Heterogeneous Nucleation in Protein Crystallization.

Protein crystallization was first discovered in the nineteenth century and has been studied for nearly 200 years. Protein crystallization technology has recently been widely used in many fields, such as drug purification and protein structure analysis. The key to successful crystallization of proteins is the nucleation in the protein solution, which can be influenced by many factors, such as the precipitating agent, temperature, solution concentration, pH, etc., among which the role of the precipitating agent is extremely important. In this regard, we summarize the nucleation theory of protein crystallization, including classical nucleation theory, two-step nucleation theory, and heterogeneous nucleation theory. We focus on a variety of efficient heterogeneous nucleating agents and crystallization methods as well. The application of protein crystals in crystallography and biopharmaceutical fields is further discussed. Finally, the bottleneck of protein crystallization and the prospect of future technology development are reviewed.

A Critical Review of von Mises Criterion for Compatible Deformation of Polycrystalline Materials

A von Mises criterion for compatible deformation states that five independent slip systems must operate for polycrystals to deform uniformly and without failure at the grain boundaries, which is supported by the Taylor–Bishop–Hill theory or simply the Taylor model, defining the laws of plastic deformation of polycrystalline aggregates and being one of the key cornerstones of crystal plasticity theory. However, the criterion has fundamental flaws as it is based on an unfounded correlation between phenomenological material flow behaviour in continuum mechanics and crystal structure dependent dislocation slip, and there has been no experimental evidence to show simultaneous operation of five independent slip systems. In this paper, the Von Mises criterion and the Taylor model are revisited and examined critically, and the fundamental issues related to the requirement of independent slip systems for compatible deformation and the selection of the active slip systems are addressed. Detailed analysis is performed of the stress state that eliminates the possibility of the simultaneous operation of five independent slip systems, and of the relative displacement vector due to the dislocation slip which defines the quantity of the strain that can be expressed by a strain tensor, instead of individual strain components. Discussions are made to demonstrate that although three linearly independent slip systems are essentially sufficient for compatible deformation, one slip system, being selected according to Schmidt law, dominates at a time in a characteristic domain as deformation accommodation occurs between grains or characteristic domains rather than at each point.

Theory of dielectric photonic crystals sandwiched between parallel metal plates

Photonic crystals based on silicon-air-geometries sandwiched between parallel metal plates are studied theoretically. Compared with in-plane propagation in corresponding infinite-height photonic crystals, modes with one of the two possible polarizations are eliminated for small plate separations. Consequently, 2D photonic crystals that usually do not have a band gap for both polarizations possess a complete band gap in the sandwich geometry. A procedure for obtaining the maximum allowed photonic-crystal height between plates that preserves the in-plane band gap is described. The effect on the band gap of adding an air-gap or a silicon substrate to the photonic crystal structure between plates is also studied. Finally, it is shown that, for terahertz frequencies, a useful distance between metal plates is comparable to the thickness of thin silicon wafers, and that propagation losses are sufficiently small that the structures are of practical interest. We briefly discuss the numerical method that was used for calculating band diagrams and band gaps, which is based on a modification to the plane-wave-expansion method [R. D. Meade et. al., Phys. Rev. B 48, 8434 (1993)10.1103/PhysRevB.48.8434] based on an iterative search algorithm exploiting Fast Fourier Transforms for fast calculations.

Process-performance-prediction integration for fatigue life improvement technologies: An implementation in cold expansion of hole structures

In this work, the process-performance-prediction integration (3P integration) is developed to improve the fatigue life and reveal the strengthening mechanisms of holed structures after a novel cold expansion process (CEP), where a specific dual-scale modelling approach is proposed to refine the close-loop system. In macro-scale simulation, the cyclic deformation behavior is addressed by an isotropic constitutive model, where the residual stress distribution extracted from CEP simulation is set as initial stress field. The local deformation histories in weak region calculated from the macro-scale simulation are supplied to micro-scale simulation as boundary conditions. The micro-scale simulation solves the local damage evolution of holed structures after CEP by using a modified crystal plasticity theory that grain size effect is considered. Excellent agreements between experimental data and predicted results in terms of fatigue life and damage mechanisms prove the robustness and accuracy of the proposed dual-scale modelling approach. Finally, a feedback link in 3P integration is established by the proposed approach combined with different residual stresses and plastic layers. The significant fatigue life improvement is mainly ascribed to residual stress, while plastic layer plays a synergistic role in life performance.

Landau theory and self-assembly of spherical nanoclusters and nanoparticles with octahedral symmetry

Spherical nanoclusters and nanoparticles are rising materials whose functional design provides many useful applications ranging from catalysis, molecular sensing, gas storage to drug targeting and delivery. Here, we develop phenomenological crystallization theory of such spherical structures with octahedral symmetries O and O_h. Within the developed theory, we propose a method, which is based on constructing irreducible octahedral density functions and allows to predict the positions of structural units in the spherical nanoobjects. The proposed theory explains the structures of the simplest known metal nanoclusters, some metal-organic polyhedra and membrane protein polyhedral nanoparticles, and also predicts more complex chiral spherical structures and achiral assemblies characterized by the geometry of semiregular polyhedra. A relationship between the constructed irreducible octahedral functions and spherical lattices, obtained by mapping a plane hexagonal order onto a spherical surface through an octahedron net, is discussed as well.

Ultrasonic constitutive model and its application in ultrasonic vibration-assisted milling Ti3Al intermetallics

Ultrasonic vibration-assisted technology is widely utilized in the performance research and manufacturing process of metallic materials owing to its advantages of introducing high-frequency acoustic systems. However, the acoustic plasticity constitutive model and potential mechanism, involving Ti3Al intermetallic compounds, have not yet been clarified. Therefore, the Ultrasonic-K-M hybrid acoustic constitutive model of Ti3Al was established by considering the stress superposition, acoustic thermal softening, acoustic softening and acoustic residual hardening effects according to the dislocation density evolution theory and crystal plasticity theory. Meanwhile, the mechanical behavior of ultrasonic vibration-assisted tension (UVAT) and microstructure of ultrasonic vibration-assisted milling (UVAM) for Ti3Al was investigated. Dislocation density to be overcome from initial deformation to failure of Ti3Al was calculated in UVAT and was verified in UVAM. The results indicated that the Ultrasonic-K-M model showed a good agreement with the experimental data. There was an obviously softening phenomenon after introducing the ultrasonic energy field in the Ti3Al whole deformation region, and the degree of softening was positively correlated with amplitude. Furthermore, the maximum reduction ratio in yield strength of Ti3Al was 16 % and the maximum reduction value in ultimate tensile strength was 206.91 MPa. The elongation rose first and then fell as amplitude enlarged, but only as the vibration was applied in the whole deformation region, the elongation was always greater than 14.58 %. In addition, The UVAM process significantly reduced the dislocation density increment to be overcome for Ti3Al material removal by 1.37 times, and promoted dislocation motion and cancellation to make twisted dislocations evolve into parallel dislocations. As the amplitude increased to 4 μm, the depth of the disturbed area of the plastic deformation layer increased by a maximum of 2.5 times.

Continuum theory of a nematic liquid crystal with a nonideal physical surface and the surfacelike elasticity

ABSTRACT The nematic surface violates the translational symmetry of unrestricted medium and induces novel elastic effects. An ideal surface, where the nematic order parameter and density vanish abruptly, induces the surface elastic term that cancels out the Nehring-Saupe divergence term. A more realistic, nonideal surface is represented by a thin layer where the order parameter and density smoothly vary from their bulk values to zero. This surface is shown to induce additional contributions to the effective surface elastic and terms. These terms are no longer total divergences which is employed to incorporate them in the elastic theory. It is shown how the higher order elasticity and the finite surface layer provide the lower free energy bound both for nonzero term and for term violating Ericksen’s stability condition for the uniform director ground state. The effective boundary condition and procedure of the free energy minimisation for arbitrary and are derived. It is shown how Ericksen’s condition is modified by the presence of the term, anchoring, and spatial boundedness. An example of the surfacelike-elasticity-induced spontaneous modulations of the uniform director ground state is presented.

Physics of crystal lattices and plasma; analytical and numerical simulations of the Gilson–Pickering equation

In this study, we use cutting-edge analytical and numerical approaches to the Gilson–Pickering (GP) problem in order to get precise soliton solutions. This model explains wave propagation in plasma physics and crystal lattice theory. A variety of evolution equations have been developed from the GP model, including the Fornberg–Whitham (FW) equation, the Rosenau–Hyman (RH) equation, and the Fuchssteiner-Fokas-Camassa–Holm (FFCH) equation, to name a few. The GP model has been studied using these evolution equations. To investigate the characterizations of new waves, crystal lattice theory and plasma physics use the Khater II, and He’s variational iteration approaches. Many alternative responses may be achieved by utilizing various formulae; each of these solutions is shown by a distinct graph. The validity of such methods and solutions may be demonstrated by assessing how well the relevant techniques and solutions match up. The results of this study suggest that the technique is preferred for successfully resolving nonlinear equations that emerge in mathematical physics.

Estimation of pressure effect on the crystallization process control based on a generalized theoretical model of a crystallizing metal

It is installed, that on aspects such as automation and control, liquid and/or crystallizing metal is a complex dynamic object, whose properties correspond to rheological body properties. Conclusions were made that the casting structure formation during crystallization proceeds under the influence of two main factors — heat removal to the mold wall and metallostatic pressure. Theoretical studies shown that the deformation of cast metal is carried out in order to correct defects but does not give this metal greater strength. It is established, by using the results of computational and theoretical studies that for efficient control of the crystallization process, it is necessary to calculate the solidification rate, and crystallization control can be reduced to control the metastable state interval. Keywords aluminum alloys, control, pressure, crystallization theory, mathematical model, heat flow, cooling rate

On symmetry of energy minimizing harmonic-type maps on cylindrical surfaces

<abstract><p>The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional in the class of $ \mathbb{S}^2 $-valued maps defined in cylindrical surfaces. The model naturally arises as a curved thin-film limit in the theories of nematic liquid crystals and micromagnetics. We show that minimal configurations are $ z $-invariant and that energy minimizers in the class of weakly axially symmetric competitors are, in fact, axially symmetric. Our main result is a family of <italic>sharp</italic> Poincaré-type inequality on the circular cylinder, which allows for establishing a nearly complete picture of the energy landscape. The presence of symmetry-breaking phenomena is highlighted and discussed. Finally, we provide a complete characterization of in-plane minimizers, which typically appear in numerical simulations for reasons we explain.</p></abstract>

Патофизиологические аспекты гиперестезии зубов и пути ее устранения у пожилых пациентов после перенесенной новой коронавирусной инфекции COVID-19

Currently, there is no scientifically substantiated information on the occurrence of dental hyperesthesia and its causes in patients who have undergone a new coronavirus infection COVID-19. Objective: to study the occurrence of dental hyperesthesia, to analyze the causes and to find ways to eliminate it in elderly patients after a new coronavirus infection COVID-19. Material and methods. The incidence of dental hyperesthesia was studied in 175 elderly people (from 61 to 75 years old) who had a new coronavirus infection COVID-19 2-4 months ago. As a control group, 125 elderly people were examined, who had not suffered from a new COVID-19 coronavirus infection before their examination. Functional resistance of hard tissues of teeth was assessed using the index of enamel resistance test (TER-test) according to V.R. Okushko and oral hygiene using the simplified index of oral hygiene of Green-Vermillion OHI-S. Results. It has been established that in the postcovid period, dental hyperesthesia is more common in elderly patients, the cause of which is the demineralization of tooth enamel due to the deterioration of individual oral hygiene. Generally accepted oral hygiene in elderly people suffering from dental hyperesthesia contributes to the normalization of the TER-test indicators with a period of 3 to 6 months of regular dental and oral care. The additional use of remineralizing ASEPTА gel for teeth by patients during dental care made it possible to achieve high structural and functional resistance of tooth enamel during the quarter. Conclusion. In people who have undergone a new coronavirus infection COVID-19, due to the deterioration of the hygienic condition of the oral cavity, there is a decrease in the mineralization of hard tooth tissues, which is a factor in the occurrence of dental hyperesthesia and confirms the crystal chemical theory of this pathology. The additional use of remineralizing ASEPTА dental gel for individual dental and oral care makes it possible to achieve high caries resistance of tooth enamel in a shorter time.

Molecular dynamics simulations of GaAs crystal growth under different strains

The high-quality growth of GaAs crystals is extremely essential for the fabrication of high-performance high-frequency microwave electronic devices and light-emitting devices. In this work, the molecular dynamics (MD) simulation is used to simulate the induced crystallization of GaAs crystal along the [110] orientation. The effects of strain on the growth process and defect formation are analyzed by the largest standard cluster analysis, the pair distribution function, and visualization analysis. The results indicate that the crystallization process of GaAs crystal changes significantly under different strain conditions. At the initial stage, the crystal growth rate of the system decreases after a certain tensile strain and a large compressive strain have been applied, and the greater the strain, the lower the crystallization rate is. In addition, as the crystal grows, the system forms a zigzag interface bounded by the {111} facet, and the angle between the growth plane and the {111} facet affects the morphology of the solid-liquid interface and further affects the formation of twins. The larger the applied tensile strain and the smaller the angle, the more twin defects will form and the more irregular they will be. At the same time, a large proportion of the dislocations in the system is associated with twins. The application of strain can either inhibit or promote the nucleation of dislocations, and under an appropriate amount of strain size, crystals without dislocations can even grow. The study of the microstructural evolution of GaAs on an atomic scale provides a reference for crystal growth theory.

Hydrothermal topotactic epitaxy of SrTiO3 on Bi4Ti3O12 nanoplatelets: understanding the interplay of lattice mismatch and supersaturation.

The engineering of epitaxial, two-dimensional (2D) nano-heterostructures has stimulated great interest owing to an expectation of better functional properties (e.g., photocatalytic, piezoelectric). Hydrothermal topotactic epitaxy is one of the promising synthetic approaches for their preparation, particularly the formation of a highly ordered, epitaxial interface and possibilities for the preparation of anisotropic nanostructures of symmetrical materials. The present study highlights the key parameters when steering the alkaline, hydrothermal, topochemical conversion process from Bi4Ti3O12 nanoplatelets to the intermediate, epitaxial, SrTiO3/Bi4Ti3O12 nano-heterostructures and the final SrTiO3 nanoplatelets by balancing the lattice mismatch and the supersaturation. An atomic-scale examination revealed the formation of an ordered epitaxial SrTiO3/Bi4Ti3O12 interface with the presence of dislocations. The SrTiO3 grows in islands for a stoichiometric amount of Sr (Sr/Ti = 1) and the growth resembles a layer-by-layer mode for surplus Sr content (Sr/Ti ≥ 12). The latter enables SrTiO3 overgrowth of the Bi4Ti3O12 basal surface planes, protecting them against dissolution from the top and consequently ensuring the preservation of the platelet morphology during the entire transformation process, the kinetics of which is controlled by the base concentration. A developed understanding of this particular transformation provides the guiding principles and ideas for designing other defined or complex epitaxial heterostructures and structures under low-temperature hydrothermal conditions.

Classifying compact 4-manifolds via generalized regular genus and G-degree

$(d+1)$-colored graphs, i.e., edge-colored graphs that are $(d+1)$-regular, have already been proved to be a useful representation tool for compact PL $d$-manifolds, thus extending the theory (known as crystallization theory) originally developed for the closed case. In this context, combinatorially defined PL invariants play a relevant role. The present paper focuses in particular on generalized regular genus and G-degree: the first one extending to higher dimension the classical notion of Heegaard genus for 3-manifolds, the second one arising, within theoretical physics, from the theory of random tensors as an approach to quantum gravity in dimension greater than two. We establish several general results concerning the two invariants, in relation with invariants of the boundary and with the rank of the fundamental group, as well as their behaviour with respect to connected sums. We also compute both generalized regular genus and G-degree for interesting classes of compact $d$-manifolds, such as handlebodies, products of closed manifolds by the interval and $\mathbb D^2$-bundles over $\mathbb S^2.$ The main results of the paper concern dimension 4, where we obtain the classification of all compact PL manifolds with generalized regular genus at most one, and of all compact PL manifolds with G-degree at most 18; moreover, in case of empty or connected boundary, the classifications are extended to generalized regular genus two and to G-degree 24.

Synthesis of energetic coordination polymers based on 4-nitropyrazole by solid-melt crystallization in non-ionization condition

Based on the theory of crystallization, a solvent-free solid-liquid phase crystallization method called solid-melt crystallization was designed to prepare energetic coordination polymers. Two target compounds [Cu(NPyz)4NO3]·NO3 (ECPs-1) and Cu(NPyz)4(ClO4)2 (ECCs-2) were prepared through programmed heating and cooling by using 4-nitropyrazole (NPyz), (Cu(NO3)2·5H2O and Cu(ClO4)2·5H2O as raw materials. In addition, crystallization pre-experiments and annealing experiments also verified the feasibility of the method. Their structures were confirmed by IR, elemental analysis, single-crystal X-ray diffraction and powder X-ray diffraction. The physicochemical properties and sensitivity test results showed that ECCs-2 has better thermal stability (Td = 221 °C), while ECPs-1 is less sensitive to mechanical stimuli (IS = 12 J, FS = 240 N). Calculations based on EXPLO5 and the Kamlet-Jacobs equation showed that ECCs-2 has more considerable detonation performance (P = 25.2 GPa, D = 7.5 km/s). In comparison, the more intuitive results from the HN test, flame test, thermal resistance test and lead plate explosion test revealed that ECCs-2 has an “ acceptable” detonation performance. The laser detonation test also showed that ECCs-2 is a promising excellent laser detonation material (E = 408 mJ, P = 24 W, τ = 17 ms).