Three-dimensional Crystals Research Articles

A discrete crystal model in three dimensions: The line-tension limit for dislocations

Abstract We propose a discrete lattice model of the energy of dislocations in three-dimensional crystals which properly accounts for lattice symmetry and geometry, arbitrary harmonic interatomic interactions, elastic deformations and discrete crystallographic slip on the full complement of slip systems of the crystal class. Under the assumption of diluteness, we show that the discrete energy converges, in the sense of Γ-convergence, to a line-tension energy defined on Volterra line dislocations, regarded as integral vector-valued currents supported on rectifiable curves. Remarkably, the line-tension limit is of the same form as that derived from semidiscrete models of linear elastic dislocations based on a core cutoff regularization. In particular, the line-tension energy follows from a cell relaxation and differs from the classical ansatz, which is quadratic in the Burgers vector.

Reverse design and application of phononic crystals based on deep learning

Abstract This paper reverse-design phononic crystals with band gaps within a targeted frequency band using the trained conditional variational autoencoder (CVAE) and further studies the vibro-acoustic characteristics of a composite sandwich plate with a phononic crystal panel as the core layer. Firstly, a matrix composed of 0 s and 1 s, representing scatterers and substrates, is randomly generated by MATLAB to represent two-dimensional phononic crystals. The three-dimensional phononic crystals are obtained by stretching the two-dimensional phononic crystals along the average direction, and COMSOL Multiphysics is used to calculate the band gap. In order to maximize the production of phononic crystals with a band gap distribution, the convolutional neural network is trained to predict whether the generated phononic crystals have band gaps. Finally, using data on the structures of phononic crystals and their band gap distributions, the CVAE is trained to achieve the reverse design of artificial periodic structures based on the target band gap. To verify the effectiveness of the structures obtained through the reverse design method on vibration and noise reduction, the submerged vibro-acoustic characteristics of a composite sandwich plate are studied. The plate consists of a phononic crystal panel and carbon fiber panels. The model of the composite sandwich plate is fabricated, and its submerged vibro-acoustic characteristics are tested and compared with numerical results. Finally, the submerged vibro-acoustic response levels of composite sandwich plates with phononic crystal panels and honeycomb panels as core layers are compared using numerical methods. This comparison assesses the phononic crystal panel’s vibration and noise reduction effects.

Accurate and Fast Estimation of the Continuum Limit in Path Integral Simulations of Quantum Oscillators and Crystals.

Convergence of imaginary-time path integral results requires a substantial number of beads (n) when quantum effects are significant. Traditional Trotter scaling approaches estimate the continuum limit (n → ∞) through extrapolation; however, their validity is restricted to the asymptotic domain of large n. We introduce an efficient extrapolation approach for quantum oscillators and crystals with harmonic character. The fitting function is inspired by the analytic solution of the harmonic oscillator (HO), or the Einstein crystal for solids. While the formulation is designed for first derivative properties (energy and pressure), its extension to second derivative properties (e.g., heat capacity) is straightforward. We apply the method to a one-dimensional HO and anharmonic oscillator (AO), as well as a three-dimensional Lennard-Jones crystal. Configurations are sampled using path integral molecular dynamics simulations in the canonical ensemble, at a low temperature of T = 0.1 (simulation units). Compared to Trotter extrapolation approaches, the new method demonstrates a substantial accuracy in estimating the continuum limit, using only a few simulations of relatively small system sizes. This efficiency significantly reduces computational cost, providing a powerful tool to facilitate computations for more complex and challenging systems, such as molecules and crystals modeled using ab initio methods.

β-carotene and resveratrol loaded glycerol monostearate-based oleogels: Physicochemical characterization at low gelation concentrations

Oleogels are semi-solid systems that can function both as replacers of trans and saturated fats and/or as carriers of lipophilic bioactive compounds. However, bioactive compounds can affect the structure of the oleogel matrix and this effect depends on the properties of such compounds. Therefore, the aim of this study was to develop oleogels loaded with β-carotene (BC) or resveratrol (R), with low concentrations of glycerol monostearate (GMS, 2–5 wt%) and sunflower oil as organic solvent. The gels were characterized by polarized light microscopy, rheological measurements, differential scanning calorimetry, oil binding capacity and Fourier transform infrared spectroscopy. At higher GMS concentrations, stronger oleogels and higher temperatures associated with transitions (sol–gel/gel–sol and crystallization/melting) were observed. The incorporation of bioactive compounds modified the gelation behavior. BC weakened the oleogel structure during the transient molecular organization of GMS, whereas R increased the dynamic moduli. BC also caused slight oil release at lower concentrations, while R improved retention. The high hydrophobicity of BC may be disturbing the solubility balance of the system, while R has phenolic hydroxyl groups that may strengthen hydrogen bonds. However, there were no considerable changes in mechanical properties after storage. We hypothesize that the molecular organization of GMS over time may be masking the modifications that bioactive compounds cause in mechanical properties. In fact, changes in the structure were revealed, as the addition of BC or R changed the morphology of the three-dimensional network crystals. Thus, the results can contribute to the rational choice of system components using low concentrations of oleogelator, as the composition of the bioactive compound exerts influence on the modulation of lipid matrices.

A three-dimensional rubber-steel phononic crystal for broad and low-frequency vibration attenuation

Elastic metamaterials and phononic crystals have the potential for vibration isolation applications due to wave band gaps where elastic waves cannot propagate. However, their real-life application may be compromised by the narrow band gaps of the former and the high frequencies of the latter. In the current study, we present a three-dimensional frame structure made of steel and rubber elements that presents a wide complete band bag at low frequency. The structure provides extreme vibration isolation because it combines band gaps with high impedance mismatch between steel and rubber damping. The manufacturing process of the proposed frame structure is widely used in mounting pads, and its cost is relatively low. It provides reasonable structural strength, which makes its application in real life possible. The dynamic behavior predicted with spectral and finite element models is validated with experimental results.

Study of thermal behavior and crystallization kinetics of glass microspheres in the Y3Al5O12-Al2O3 system

Five types of glass microspheres with alumina and 40–80 mol.% Y3Al5O12 were prepared using solgel Pechini and flame synthesis techniques. Glass thermal behavior was analyzed using DSC/TG, XRD and SEM, and the JMAK model was applied to study crystallization kinetics and determine prevailing mechanisms. All samples, except the one with 80 mol.% YAG, had two exothermic effects in their DSC curves. The first appeared between 937 and 950 °C, while the second was observed between 958 and 1102 °C. XRD analysis of crystallized microspheres confirmed the presence of YAG and various forms of alumina phases in the samples with lower YAG/higher Al2O3 content (40 and 50 mol.%). The sample with the highest YAG content showed the strongest tendency to crystallize in the kinetics study. The value of apparent activation energy (Eapp) of this sample was 987.3 ± 13.0 kJ mol−1. For the remaining samples, the values of Eapp were higher and ranged from 1215.1 ± 10.6 to 1847.5 ± 9.3 kJ mol−1, indicating the lowest ability of these compositions to crystallization. The growth of three-dimensional (3-D) YAG crystals was predominant in glasses with the highest (80 mol.%) YAG content. One-dimensional (1-D) growth of γ-Al2O3 crystals and 3-D growth of YAG crystals was predominant in glasses with the lowest (40 mol.%) YAG content.

Optical Activities of Organic Crystals: Crystal Orbital Formulation of Anisotropic Gyration.

To describe the optical activities of crystals, gyration tensors are necessary for all wavelengths of incident light. To date, few studies on direct calculations of gyration tensors from Bloch states have been conducted. Herein, a practical procedure to obtain gyration tensors of organic crystals is presented using the crystal orbital method. The extended Hückel method was adopted to evaluate the gyration tensors, epitomizing the one-electron formulation. To confirm the validity of the formulation, the optical rotatory power of alanine and γ-glycine was examined. The reproduced profiles of the optical rotatory power were consistent with the results of recent experiments. This is a general formulation of the one-electron theory of optical activities for three-dimensional crystals. In principle, the optical rotatory strength tensor is not invariant with translation. For systems with small unit cells, however, the formalism is quasi-invariant with respect to translation. The quasi origin-independent formalism is sufficiently substantial to be applicable to modern crystal optics.

Global existence of strong solutions to the isentropic compressible nematic liquid crystal equations in a cuboid domain

In this paper, we study the initial-boundary value problem of three-dimensional compressible nematic liquid crystal equations in a cuboid domain. We prove that the strong solution exists globally in the time provided that both the initial L1-norm of the density ‖ρ0‖L1 and the initial L3-norm of the gradient of orientation field ‖∇d0‖L3 for nematic liquid crystal flow are small enough. The main tools of proving the global well-posedness are some time-weighted a priori estimates designed for the compressible nematic liquid crystal equations.

Nanotube spin defects for omnidirectional magnetic field sensing

Optically addressable spin defects in three-dimensional (3D) crystals and two-dimensional (2D) van der Waals (vdW) materials are revolutionizing nanoscale quantum sensing. Spin defects in one-dimensional (1D) vdW nanotubes will provide unique opportunities due to their small sizes in two dimensions and absence of dangling bonds on side walls. However, optically detected magnetic resonance of localized spin defects in a nanotube has not been observed. Here, we report the observation of single spin color centers in boron nitride nanotubes (BNNTs) at room temperature. Our findings suggest that these BNNT spin defects possess a spin S = 1/2 ground state without an intrinsic quantization axis, leading to orientation-independent magnetic field sensing. We harness this unique feature to observe anisotropic magnetization of a 2D magnet in magnetic fields along orthogonal directions, a challenge for conventional spin S = 1 defects such as diamond nitrogen-vacancy centers. Additionally, we develop a method to deterministically transfer a BNNT onto a cantilever and use it to demonstrate scanning probe magnetometry. Further refinement of our approach will enable atomic scale quantum sensing of magnetic fields in any direction.

Weyl superconductivity and quasiperiodic Majorana arcs in quasicrystals

Weyl superconductivity is a topological phase in three-dimensional crystals in which the Weyl equation describes quasiparticle excitation near band-touching points in momentum space called Weyl nodes. For quasicrystals which lack translational symmetry, a theory of Weyl superconductivity has not been established, in spite of recent extensive studies on quasicrystalline topological phases. Here, we demonstrate the occurrence of quasicrystalline Weyl superconductivity by extending the definition of Weyl superconductivity to periodically stacked, two-dimensional superconducting quasicrystals. We identify quasicrystalline Weyl nodes—topologically protected point nodes in one-dimensional momentum space corresponding to the stacking direction—in terms of a topological invariant given by a change in the Bott index in quasicrystalline layers. We find that these Weyl nodes exist in pairs and that Majorana zero-energy modes protected by the nonzero Bott index between a pair of quasicrystalline Weyl nodes appear on surfaces. These Majorana zero modes form an infinite number of arcs in momentum space, densely and quasiperiodically distributed as a function of momentum in the direction of surfaces within each quasicrystalline layer. In Ammann-Beenker (Penrose) quasicrystals, the quasiperiodicity of Majorana arcs is governed by the silver (golden) ratio associated with the quasicrystalline structure. Published by the American Physical Society 2024

Relationship between Salmonella enterica attachment and leaf hydrophobicity, roughness, and epicuticular waxes: a focus on 30 baby-leaf salads.

The first step in the contamination of leafy vegetables by human pathogens is their attachment to the leaf surface. The success of this is influenced strongly by the physical and chemical characteristics of the surface itself (number and size of stomata, presence of trichomes and veins, epicuticular waxes, hydrophobicity, etc.). This study evaluated the attachment of Salmonella enterica to 30 baby-leaf salads and tested whether the differences found among them were related to the following leaf traits: hydrophobicity, roughness, and epicuticular waxes. Differences in susceptibility to contamination by S. enterica were found between the 30 baby-leaf salads investigated. The lowest attachment was found in wild lettuce (Lactuca serriola L.) and lamb's lettuce 'Trophy F1' (Valerianella locusta [L.] Laterr.), with values of 1.63 ± 0.39 Log(CFU/cm2) and 1.79 ± 0.54 Log(CFU/cm2), respectively. Attachment was correlated with hydrophobicity (measured as contact angle) (r = -0.39) and epicuticular waxes (r = -0.81) but not with roughness (r = 0.24). The most important wax components for attachment were alcohols and, in particular, the three-dimensional (3D) wax crystals of C26 alcohol, but fatty acids probably also had a role. Both these compounds increased hydrophobicity. The presence of thymol, whose antimicrobial properties are well known, was found in lamb's lettuce. The findings of this study can help to predict and control the attachment and contamination of leafy salads by enterobacteria. They also provide useful information for breeding programs aiming to develop cultivars that are less susceptible to human pathogens, enhancing the food safety of vegetables. © 2024 The Author(s). Journal of the Science of Food and Agriculture published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry.

Prospects of a thousand-ion Sn2+ Coulomb-crystal clock with sub-10−19 inaccuracy

Optical atomic clocks are the most accurate and precise measurement devices of any kind, enabling advances in international timekeeping, Earth science, fundamental physics, and more. However, there is a fundamental tradeoff between accuracy and precision, where higher precision is achieved by using more atoms, but this comes at the cost of larger interactions between the atoms that limit the accuracy. Here, we propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn2+ ions confined in a linear RF Paul trap with the potential to overcome this limitation. Sn2+ has a unique combination of features that is not available in previously considered ions: a 1S0 ↔ 3P0 clock transition between two states with zero electronic and nuclear angular momentum (I = J = F = 0) making it immune to nonscalar perturbations, a negative differential polarizability making it possible to operate the trap in a manner such that the two dominant shifts for three-dimensional ion crystals cancel each other, and a laser-accessible transition suitable for direct laser cooling and state readout. We present calculations of the differential polarizability, other relevant atomic properties, and the motion of ions in large Coulomb crystals, in order to estimate the achievable accuracy and precision of Sn2+ Coulomb-crystal clocks.

Collimated beam formation in 3D acoustic sonic crystals

We demonstrate strongly collimated beam formation, at audible frequencies, in a three-dimensional acoustic phononic crystal where the wavelength is commensurate with the crystal elements; the crystal is a seemingly simple rectangular cuboid constructed from closely-spaced spheres, and yet demonstrates rich wave phenomena acting as a canonical three-dimensional metamaterial. We employ theory, numerical simulation and experiments to design and interpret this collimated beam phenomenon and use a crystal consisting of a finite rectangular cuboid array of 4×10×10 polymer spheres 1.38 cm in diameter in air, arranged in a primitive cubic cell with the centre-to-centre spacing of the spheres, i.e. the pitch, as 1.5 cm. Collimation effects are observed in the time domain for chirps with central frequencies at 14.2 kHz and 18 kHz, and we deployed a laser feedback interferometer or Self-Mixing Interferometer – a recently proposed technique to observe complex acoustic fields—that enables experimental visualisation of the pressure field both within the crystal and outside of the crystal. Numerical exploration using a higher-order multi-scale finite element method designed for the rapid and detailed simulation of 3D wave physics further confirms these collimation effects and cross-validates with the experiments. Interpretation follows using High Frequency Homogenization and Bloch analysis whereby the different origin of the collimation at these two frequencies is revealed by markedly different isofrequency surfaces of the sonic crystal.

Classification of electronic nematicity in three-dimensional crystals and quasicrystals

Classification of electronic nematicity in three-dimensional crystals and quasicrystals

Three-dimensional phononic crystals with self-similar structures

Acoustic metamaterials have the advantages of designability, strong pertinency, small size and good effect, and have good application value in solving the problem of sound insulation and noise reduction. Phononic crystals with wide bandgap and multi-bandgap can inhibit elastic wave propagation to some extent. In this study, a three-dimensional phononic crystal model with self-similar properties is designed by using fractal method. First, an initial unit is constructed, then the arm of the initial unit is replaced with the structure itself to form a self-similar structure. The self-similar model can block sound waves in the wide band and multi-band range. By changing the structure shape and size of phononic crystal, the sound wave blocking in different frequency range is also studied. At the same time of continuous optimization of the structure, the variation rules of the model band structure under different parameters are summarized. To find the good parameters of broadband and multi-band sound wave blocking, so as to achieve the effect of vibration isolation and noise reduction. The finite element method is used to simulate the vibration of the model to verify the existence of elastic wave bandgap. Phononic crystals have a good prospect in the field of sound insulation and noise reduction.

Coexistence of Defect Morphologies in Three-Dimensional Active Nematics.

We establish how active stress globally affects the morphology of disclination lines of a three-dimensional active nematic liquid crystal under chaotic flow. Thanks to a defect detection algorithm based on the local nematic orientation, we show that activity selects a crossover length scale in between the size of small defect loops and that of long and tangled defect lines of fractal dimension 2. This length scale crossover is consistent with the scaling of the average separation between defects as a function of activity. Moreover, on the basis of numerical simulation in a 3D periodic geometry, we show the presence of a network of regular defect loops, contractible onto the 3-torus, always coexisting with wrapping defect lines. While the length of regular defects scales linearly with the emerging active length scale, it verifies an inverse quadratic dependence for wrapping defects. The shorter the active length scale, the more the defect lines wrap around the periodic boundaries, resulting in extremely long and buckled structures.

Vibration attenuation and wave propagation analysis of 3D star-shaped resonant plate structures and their derivatives with ultra-wide band gap

Based on the local resonance effect of elastic waves, three single-phase acoustic metamaterials are proposed in this paper. Based on the finite element method and Bloch's theorem, the energy band structure diagrams and vibration modes are plotted, and the band gap properties and band gap opening mechanism of these structures are explored. New structures possessing lower frequency band gaps are obtained by topological optimization. The transmission curves verify the accuracy of the band gap and the vibration attenuation ability of the structure. Finally, the structural parameters were adjusted and the effect of each parameter change on the band gap characteristics was analyzed. The results show that the proposed structure has a maximum band gap coverage of 72.4 % and a strongest attenuation peak of less than −400 (dB) due to the occurrence of a local resonance. This paper provides a methodology for analyzing the vibration and noise reduction performance of single-phase material phononic crystals, as well as a three-dimensional phononic crystal with potential for practical applications.

Controlled creation of point defects in three-dimensional colloidal crystals.

Crystal defects crucially influence the properties of crystalline materials and have been extensively studied. Even for the simplest type of defect-the point defect-however, basic properties such as their diffusive behavior, and their interactions, remain elusive on the atomic scale. Here, we demonstrate in situ control over the creation of isolated point defects in a three-dimensional (3D) colloidal crystal allowing insight on a single-particle level. Our system consists of thermoresponsive microgel particles embedded in a crystal of nonresponsive colloids. Heating this mixed-particle system triggers the shrinking of the embedded microgels, which then vacate their lattice positions, creating vacancy-interstitial pairs. We use temperature-controlled confocal laser scanning microscopy to verify and visualize the formation of the point defects. In addition, by reswelling the microgels we quantify the local lattice distortion around an interstitial defect. Our experimental model system provides a unique opportunity to shed light on the interplay between point defects, on the mechanisms of their diffusion, on their interactions, and on collective dynamics.

Microswimmers Knead Nematics into Cholesterics.

The hydrodynamic stresses created by active particles can destabilize orientational order present in the system. This is manifested, for example, by the appearance of a bend instability in active nematics or in quasi-two-dimensional living liquid crystals consisting of swimming bacteria in thin nematic films. Using large-scale hydrodynamics simulations, we study a system consisting of spherical microswimmers within a three-dimensional nematic liquid crystal. We observe a spontaneous chiral symmetry breaking, where the uniform nematic state is kneaded into a continuously twisting state, corresponding to a helical director configuration akin to a cholesteric liquid crystal. The transition arises from the hydrodynamic coupling between the liquid crystalline elasticity and the swimmer flow fields, leading to a twist-bend instability of the nematic order. It is observed for both pusher (extensile) and puller (contractile) swimmers. Further, we show that the liquid crystal director and particle trajectories are connected: in the cholesteric state the particle trajectories become helicoidal.

Electron Localization and Mobility in Monolayer Fullerene Networks.

The novel 2D quasi-hexagonal phase of covalently bonded fullerene molecules (qHP C60), the so-called graphullerene, has displayed far superior electron mobilities, if compared to the parent van der Waals three-dimensional crystal (vdW C60). Herein, we present a comparative study of the electronic properties of vdW and qHP C60 using state-of-the-art electronic-structure calculations and a full quantum-mechanical treatment of electron transfer. We show that both materials entail polaronic localization of electrons with similar binding energies (≈0.1 eV) and, therefore, they share the same charge transport via polaron hopping. In fact, we quantitatively reproduce the sizable increment of the electron mobility measured for qHP C60 and identify its origin in the increased electronic coupling between C60 units.