Unit Cell Structure Research Articles

Ordered structures in liquid water: Is cold water a genuine liquid?

AbstractOrdered structures in liquid water are discussed. Raman spectral changes of water in the temperature range −23°C to 45°C are analyzed with multivariate curve resolution with alternate least squares (MCR‐ALS) and hypothetical addition multivariate analysis with numerical differentiation (HAMAND). Three forms of water, destructured hydrogen bonded (DH) water, structured hydrogen bonded (SH) water, and nano‐ice, are identified. Formation of nano‐ice is shown to cause the density maximum anomaly of water at 4°C. The size of nano‐ice at −13°C is estimated to be 2–4 nm. SH water corresponds to one unit cell of hexagonal ice structure. The SH/DH ratio is an indicator of “structurality,” which is useful for microscopic understanding of liquid water. The existence of nano‐ice in cold water raises a fundamental question “Is cold water a genuine liquid?” Further study on the size of nano‐ice will give a clue to understand how water freezes or does not freeze.

Anisotropic yield models for lattice unit cell structures exploiting orthotropic symmetry

Numerical homogenization enables efficient computational analysis and design of multiscale structures made of micro-architected materials including lattice unit cells. However, predicting yield is nontrivial because it requires accurate and efficient predictions of the maximum stress inside the homogenized unit cells. To address this challenge, we develop a macroscale anisotropic yield function for micro-architected materials. The yield function depends on the three-dimensional macroscale stress state and the parameters describing a family of micro-architectures, such as the radii of the struts in a lattice unit cell. To ensure accuracy, we determine the maximum stress using three-dimensional continuum finite-element analysis. To ensure efficiency, we construct surrogate models from the aforementioned high-fidelity results for yield prediction. To reduce simulation costs and surrogate modeling complexity, we leverage orthotropic symmetry commonly found in lattice unit cells. In this paper, we provide a thorough presentation of group representations and the systematic procedure to exploit orthotropic domain symmetry in homogenization and surrogate modeling. We illustrate the use of linear homogenization results to predict yield in specific unit cells without further simulations. We furthermore show that surrogate modeling presents a viable option for anisotropic yield prediction in a continuously parametrized family of micro-architectures. More specifically, despite the dimensionality and degree of nonlinearity in the maximum micro von Mises stress within the unit cell, the surrogate models can predict it with less than 5% error at least 90% of the time. Moreover, the largest under-prediction error, which is more critical than the over-prediction error, is typically less than 10%.

Broadband efficient anomalous reflection using an aggressively discretized metasurface.

Aggressive discretization in metasurface design-using the least number of unit cells required-can dramatically decrease the phase coverage requirement, thus allowing the use of simple structure and avoiding unit cells with strong resonance, leading to a simple design with broadband performance. An aggressively discretized metasurface with two unit cells per period can realize efficient anomalous reflection. In this work, we investigate the power efficiency and bandwidth of an aggressively discretized metasurface featuring anomalous reflection. Through spectral domain considerations, we find that the theoretical upper limit for the bandwidth of this metasurface reflecting all the incident power into the desired mode is 67%. With aggressive discretization, we design a metasurface with a simple unit cell structure. By tuning the two unit cells, we achieve a metasurface design that reflects more than 80% of the incidence power into the desired anomalous reflection mode over a broad bandwidth of 53.6%. Such bandwidth is unprecedented for an anomalous reflection metasurface. Finally, we fabricate and experimentally demonstrate our anomalous reflection metasurface and obtain bandwidth and efficiency performances which agree well with simulation.

I-Shaped Metamaterial Using SRR for Multi-Band Wireless Communication

A novel I-shaped metamaterial (ISMeTM) using split-ring resonator (SRR) for multi-band wireless communication is presented in this paper. The proposed ISMeTM unit cell structure is designed using the three-square split-ring resonators (SSRRs) and I-shaped copper strip at the center. The size of the proposed ISMeTM is 10 × 10 × 1.6 mm3 while utilizing the FR-4 dielectric substrate material. The analysis of various array arrangements, variation in the ring gap, variation in strip length, and the variation in strip width is performed to achieve the optimum results for multi-band operation. The effective permittivity, permeability, and refractive index of the unit cell have been analyzed. The design and simulation of the ISMeTM unit cell and arrays are performed using the Computer Simulation Technology (CST) Studio Suite and MATLAB. The equivalent circuit of the ISMeTM is designed using the Advanced Design System (ADS) software. The split ring’s inner loop’s gap functions as a capacitor, while the metallic ring itself functions as an inductor. Electric resonance is created by the interaction between the split ring and the electric field. The interaction of magnetic fields with metallic loops during EM propagation in the structure causes the magnetic resonance. The variation in dimensions of the structure causes the variation in the inductance and capacitance, which causes the variation in resonant frequency. The proposed design is optimized after several parametric analyses. A comprehensive analysis of 1 × 2, 2 × 2, and 2 × 4 array is also investigated. The results confirm the multi-band operation of the proposed ISMeTM. The proposed ISMeTM is suitable for the multi-band C/X/Ku-band microwave applications.

Wide bandwidth enriched symmetric hexagonal split ring resonator based triple band negative permittivity metamaterial for satellite and Wi-Fi applications

Bandwidth is a vital factor for the transmission phase of satellite data that plays an important role in satellite performance. This paper presents a wide bandwidth enriched metamaterial consisting of symmetric hexagonal split ring resonator (SRR) with triple band negative permittivity and refractive index and near zero permeability for satellite and Wi-Fi applications. The electrical dimension of the designed metamaterial unit cell is 0.17λ × 0.17λ where wavelength (λ) is computed at a first resonance frequency and developed on a cheap dielectric material FR-4 (lossy) with a thickness of 1.6 mm. The proposed metamaterial contributes triple resonances for the transmission coefficient (S21) at the frequencies of 5 GHz, 6.88 GHz and 8.429 GHz with the magnitude of −33.79, −21.7 and −25.18 dB, respectively covering C and X bands through the numerical execution of CST microwave studio 2019. The effective bandwidth of the unit cell are 1.67 GHz (3.89 to 5.56 GHz), 0.52 GHz (6.59 to 7.11 GHz) and 0.98 GHz (7.98 to 8.96 GHz) where the value of S21 less than −10 dB. The first resonance frequency is used to high speed-bandwidth enriched Wi-Fi and satellite band. Wi-Fi is usually faster using 5 GHz frequency band. The rest of the resonance frequency can be used in satellite applications. A negative permittivity has been perceived at frequencies of 5 – 6.066 GHz, 6.88 – 7.409 GHz, 8.429 – 10.061 GHz using Nicolson-Ross-Weir (NRW) methods with MATLAB code. The dependence of the resonance frequencies on the design parameters, substrate thickness, dielectric materials, the influence of the different structure of unit cell has also been examined. The designed unit cell structure with equivalent circuit diagram are analyzed and validated using Advanced Design System (ADS) simulator that exhibits similar to the S21 of the proposed structure. Furthermore, measurement results and Ansys high-frequency structure simulator (HFSS) simulator results are also employed to verify the outcome. Due to the overall performance, such as wide bandwidth, excellent effective parameters of the designed structure, the proposed research can be very suitable for satellite and Wi-Fi applications.

Spin splitting in low-symmetry quantum wells beyond Rashba and Dresselhaus terms

Spin-orbit interaction in semiconductor structures with broken space inversion symmetry leads to spin splitting of electron and hole states even in the absence of magnetic field. We discover that, beyond the Rashba and Dresselhaus contributions, there is an additional type of the zero-field spin splitting which is caused by the interplay of the cubic shape of crystal unit cell and macroscopic structure asymmetry. In quantum wells grown along low-symmetry crystallographic axes, this type of spin-orbit interaction couples the out-of-plane component of carrier's spin with the in-plane momentum whereas the coupling strength is controlled by structure inversion asymmetry. We carry out numerical calculations and develop an analytical theory, which demonstrate that this interaction dominates $\mathbit{k}$-linear spin splitting of heavy-hole subbands in a wide range of parameters.

Investigation on impact resistance of hierarchical lightweight lattice structure

Abstract This paper is majorly discussing the impact resistance of hierarchical lightweight lattice structure. Firstly, the unit cells of hierarchical pyramidal lattice structure and traditional single-stage hollow pyramidal lattice structure are designed. At the same time, the concept of relative density is introduced to better demonstrate the impact resistance of hierarchical structure. In this paper, ABAQUS/Explicit software is used to simulate the drop hammer impact simulation of hierarchical structure and hollow structure. The result shows that the impact resistance of hierarchical structure is better than hollow structure. Meanwhile, the samples are prepared by 3D printing, and then quasi-static compression experiment and drop hammer impact experiment are carried out. It is concluded that the bearing and impact resistance performance of the hierarchical structure has obvious improvement than the hollow structure under both quasi-static compression and low-speed drop hammer impact.

Circumventing a challenging aspect of crystal structure determination from powder diffraction data.

Schmidt and co-workers [Acta Cryst. (2022), B78, 195–213], report a strategy for structure determination from powder XRD data in which unit-cell determination and structure solution are combined within a single process, rather than handling them as sequential stages on the structure determination pathway. This strategy offers the prospect to achieve successful structure determination in cases for which conventional approaches for indexing powder XRD data prove to be challenging.

Design of a polarization insensitive achromatic metalens with a high NA and uniform focusing efficiency based on a double layer structure of silicon and germanium

A polarization insensitive achromatic metalens (PIAML) was designed to realize a high NA of 0.5 and uniform focusing efficiency in the visible range based on a double layer structure of silicon (Si) and germanium (Ge). Due to their high refractive indices as well as the opposite characteristics of group delay in the visible wavelength, the combination of Si and Ge can contribute to the high NA and achromatic performances. In addition, an isotropic cylindrical unit cell structure was applied to confirm polarization sensitivity. From the finite difference time domain (FDTD) simulation results, it was confirmed that the designed PIAML shows good optical performance of both polarization insensitivity and achromatic performance with uniform focusing efficiency of 27% and high NA of 0.5 in the visible wavelength.

Polarization and angular insensitive bendable metamaterial absorber for UV to NIR range

Broadband absorbers are required for solar energy harvesting because they efficiently absorb the incident photon in the wide-ranging solar spectrum. To ensure high absorption of photons, metamaterial absorbers (MMAs) have been a growing area of interest in recent years. In this article, an MMA is proposed using a metal–insulator–metal (MIM) structure (Ni–SiO2–Ni) that shows a near-unity broadband absorption of wavelengths from 300 to 1600 nm, with a 95.77% average absorption and a peak absorption of 99.999% at 772.82 nm. The MMA is polarization insensitive as well as wide incident angle stable. Analysis of the effects of mechanical bending on the absorption of the proposed structure shows that absorption holds satisfactory values at different degrees of mechanical loading. The suggested MMA unit cell structure was computationally simulated using the Finite Integration Technique (FIT) and verified using the Finite Element Method (FEM). To analyze the feasibility of the proposed MMA as a solar cell, it is investigated with the universal AM 1.5 solar spectrum characteristics. Besides solar energy harvesting, the proposed MMA unit cell may be employed in a variety of diverse optical applications, including sensors, detectors, and imaging.

Electromagnetic parameter retrieval technique utilizing eigenvalue analysis and field averaging

In this paper, a fully numerical homogenization technique is presented for the retrieval of the effective constitutive parameters of a periodic composite medium. Based on the eigensolution returned by the utilized field-flux FEM formulation, a proper field averaging process of the field components is proposed over specific paths of the periodic unit cell of an arbitrary structure. Subsequently, the constitutive relations for every eigenmode supported by the medium are derived, forming a linear system of equations. The solution of this system returns a set of fifteen effective constitutive parameters, including the magnetoelectric coefficients, which account for possible cross-polarization effects, causing bianisotropy.

Triple band microwave metamaterial absorber based on double E-shaped symmetric split ring resonators for EMI shielding and stealth applications

In this paper, a double E-shaped symmetric split ring resonators metamaterial inspired triple band microwave metamaterial absorber (MA) for EMI shielding and stealth applications in C and X band is presented. The proposed absorber comprises double E shaped with two modified split ring resonators-based copper resonators separated by a FR-4 dielectric layer with a thickness of 1.6 mm and back annealed copper with 0.035 mm thickness and an electrical dimension of 0.179λ × 0.179λ, λ is computed at the frequency of 5.376 GHz. The simulated results derived from CST Microwave Studio simulator show that there are three absorption peaks at 5.376, 10.32 and 12.25 GHz with an absorption of 99.9%, 99.9% and 99.7%, respectively. An equivalent circuit model of the absorber is used to study the reflection coefficient characteristics and E-field, H-field and surface current distributions are investigated at absorption peaks in order to understand the electromagnetic wave absorption mechanism. Parametric analyses were also performed to select the appropriate absorption frequencies. In addition, the metamaterial absorber unit cell structure shows nearly perfect absorptions over a wide angle of incidences up to 60° for both TE and TM mode. The proposed MA has a triple band shielding behavior and provides the shielding effectiveness, greater than 40 dB for the entire band for both simulated and measured condition, which is a reasonable reduction in the RF signal to reduce the impact on devices susceptible to electromagnetic interference. The simulated, equivalent circuit model and experimental results for validation purposes showed that the complete results are mutually supportive. The proposed microwave metamaterial absorber is expected to be useful for EMI shielding and stealth applications.

Local structure and electron density distribution analysis of tin(II) sulfide using pair distribution function and maximum entropy method

Abstract Tin(II) sulfide (SnS) is a low symmetric orthorhombic double-layered dual bandgap semiconductor. It is low cost, toxic-free and highly abundant on Earth, with multifunctional optical, electronic, magnetic and light conversion applications when doped adequately with impurity. These physical properties can be understood only by the complete understanding of microstructural properties like average structure, electron density distribution inside the unit cell, bonding nature and local structure. In this work, the average and local structure, along with the electron density distribution of a nano crystallite sized single-phase sample of tin(II) sulfide is elucidated with the help of precise X-ray intensity data. The average structural information was extracted using Rietveld refinement analysis and the visual mapping of 3D, 2D and 1D electron density distribution inside the unit cell and its numerical contribution using maximum entropy method (MEM). The bonding between the first inter and intra bonding between Sn and S atoms is 2.65,105 Å and 3.2689 Å with mid bond electron density 0.907 e/Å3 and 0.1688 e/Å3 respectively. The inter-atomic correlations of 1st, 2nd and 3rd nearest neighbour atoms, their bond length, and the crystallite size are reported from pair distribution function (PDF) analysis using low Q-XRD data (Q ∼ 6.5 Å−1). The PDF analysis shows that the first and second nearest Sn–S bonding distance is 2.6064 Å and 3.4402 Å, first is between the Sn and S atoms of the same layer and the other between the Sn and S atoms of the adjacent layers respectively.

Elastic Molecular Crystals: Their Deformation-Induced Reversible Unit Cell Changes with Specific Poisson Effect

Abstract Detailed investigation of macroscopic deformation and nanoscopic structural changes in flexible organic crystals poses challenges for investigators. Herein, applied stress and subsequent relaxation of elastic organic crystals resulted in reversible macroscopic crystal deformation. X-ray diffraction with a curved stage-jig revealed reversible nanoscopic structural unit cell changes in the crystal structure under the bending stress and relaxation. The crystal lattice changed quantitatively under the applied macroscopic stress-strain (%). This method enables quantitative monitoring of the dynamic nanoscopic structural changes in detail associated with crystal deformation through the use of standard laboratory X-ray diffraction analysis. Importantly, the developed method offers a way of quantitatively measuring reversible structural changes, without synchrotron X-ray analysis. Moreover, the analysis derives Poisson’s ratio, i.e., the ratio of the change in the width per unit width of materials. It is important in materials science, and normally has a positive value in the range of 0.2–0.5. However, the crystals show not only the “Poisson effect” but also the unusual “negative Poisson effect”. This novel approach for investigation generates unprecedented opportunities for understanding dynamic nano-structural unit cell changes in flexible organic crystals.

A metamaterial absorber with centre-spin design and characteristic modes analysis

A novel wide band multilayer metamaterial absorber with unit cell of centre-spin structure is proposed, which has a high absorption rate of up to 90% in the 2.2 to 5.2 GHz frequency range. We use equivalent impedance matching theory and characteristic mode theory(CMA) to analyze the characteristics and mechanism of the absorber, and verify the correctness of the absorber design through experiments.With the advantages of thin thickness, simple structure, insensitivity to polarization, and good absorption in a wide-angle range, the absorber has a certain application value in antenna, military radar target stealth, electromagnetic compatibility, and other fields.

Wide-angle broadband polarization independent bend-able nano-meta absorber employed in optical wavelength

A new wide-angle, bend-able, three-layer nano-meta-absorber (NMA) unit cell structure, consisting of tungsten (W)-silicon dioxide (SiO2)-tungsten (W) for the entire visible spectrum (445 nm–780nm) has been proposed. The NMA has an average absorption of 97.58% and peak absorption of 99.99% has been achieved at 581.3194 nm under a normal incidence angle. This unit cell shows a good impedance match, good capacitive and inductive coupling along with plasmonic resonance features, as well as high electromagnetic (EM) fields with power loss distribution. The design was numerically simulated by the finite integration technique (FIT) and validated with the finite element method (FEM). The proposed NMA can be implemented as a solar energy harvester, optical sensor, light detector, or imaging application.

FDTD Simulations of Modulated Metasurfaces with Arbitrarily Shaped Meta-atoms by Surface Impedance Boundary Condition

In this paper, we propose a reduced-complexity finite difference time domain (FDTD) simulations of modulated metasurfaces with arbitrary unit cells. The three dimensional (3D) physical structure of the metasurface is substituted by a spatially varying surface impedance boundary condition (IBC) in the simulation; as the mesh size is not dictated by sub-wavelength details, considerable advantage in space- and time-step is achieved. The local parameters of the IBC are obtained by numerical simulation of the individual unit cells of the physical structure, in a periodic environment approximation, in the frequency domain. As the FDTD requires an appropriate time domain impulse-response, the latter is obtained by broad-band frequency simulations, and vector fitting to an analytic realizable time response. The approach is tested on metasurface structures with complex unit cells and extending over 10 ××10 wavelengths, using a standard PC with 64GB RAM.

Expanding the design space and optimizing stop bands for mechanical metamaterials

A predictive design, analysis, and optimization tool that quickly and accurately captures the frequency response of locally resonant metamaterials is presented. A reduced order model based on a discrete spring-mass system is used to relate the structural parameters of a unit cell to frequency response, intended for optimizing for the unit cell structure with the widest longitudinal stop band at a desired center frequency. Design maps that relate geometric parameters to performance metrics are assembled, from which optimized unit cells or paths for enhanced functionality can be identified. The method can be augmented to examine all vibration modes or extended to multi-dimensional wave propagation, such as shear or oblique waves. The practicality of the design maps is demonstrated through two examples. First, actual 3D printed size and material limitations are imposed onto the design maps to bound a physically realizable design space. The identified optimal geometry has the maximum gap width at the desired center frequency within the bounds. The second example utilizes tunable, filled resin systems to expand the design space through material variations. Multi-material unit cells fabricated with frames and resonators having different material properties are predicted to provide better performance than cells consisting of a single material.

A Novel Design of Multistable Metastructure With Nonuniform Cross Section

Abstract Multistable metastructure can be used as a reusable energy-absorbing structure which is usually accompanied by relatively low energy absorption capacity. In this work, a novel structure with variable cross-sectional width was designed to improve the energy dissipation efficiency of multistable structures. To this end, we theoretically obtained the specific optimization configuration of the bistable unit cell structure. Compared to the traditional bistable unit cell structure with uniform curved beam, the as-obtained optimized structure showed improved mechanical properties, while maximum strain remained relatively reduced during deformation. Systematic parameter analyses were carried out through theoretical analysis, finite element simulation, and experimental verification to determine the optimized range of the unit cell structure. Compared to the traditional structure with the same maximum strain during deformation, the mechanical properties like the maximum peak force, minimum negative force, and energy absorption efficiency of the optimized structure increased by at least 155%, 91%, and 136%, respectively.

Vibration reduction of cables with pendulum-type elastic metamaterials

Elastic metamaterials (EMMs) have been used to reduce the vibration of various mechanical structures. Recent studies have proposed methods to reduce the vibration of cables and space tethers by introducing pendulum-type EMMs. However, the vibration absorption characteristics in the bandgaps of pendulum-type EMMs need to be investigated in relation to the local resonances of the unit cell structure because only beams among the unit cell structure were considered. Furthermore, it is necessary to improve the vibration reduction performance of the pendulum-type EMMs by allocating as many bandgaps as possible in the frequency range of interest. In this study, the effect of the dynamic characteristics of the coupled structure with the same configuration as the unit cell structure including the ring or annular plate as well as the beam were investigated in depth. Further, based on these results, an improved pendulum-type EMM with multiple bandgaps in the frequency range of interest was developed, which is well suited for most practical applications in mechanical systems where the influence of low vibration modes is dominant. The vibration reduction performance and the effect of the bandgaps of the pendulum-type EMM with an annular plate were verified through comparison between the experimental and simulation results. The frequency response experiments and simulation results were consistent in terms of the resonant peak frequencies outside the bandgaps and the low response amplitude within the bandgaps. Moreover, the experimentally visualized and simulated operational deflection shapes showed that the cable hardly vibrates at the frequency within the bandgap; at this frequency, the operational deflection shape of the annular plate is very similar to the mode shape of the vibration mode of the coupled structure.