Shape Of Unit Cell Research Articles

Exploring the Flexibility of MIL-47(V)-Type Materials Using Force Field Molecular Dynamics Simulations.

The flexibility of three MIL-47(V)-type materials (MIL-47, COMOC-2, and COMOC-3) has been explored by constructing the pressure versus volume and free energy versus volume profiles at various temperatures ranging from 100 to 400 K. This is done with first-principles-based force fields using the recently proposed QuickFF parametrization protocol. Specific terms were added for the materials at hand to describe the asymmetry of the one-dimensional vanadium-oxide chain and to account for the flexibility of the organic linkers. The force fields are used in a series of molecular dynamics simulations at fixed volumes but varying unit cell shapes. The three materials show a distinct pressure–volume behavior, which underlines the ability to tune the mechanical properties by varying the linkers toward different applications such as nanosprings, dampers, and shock absorbers.

Subwavelength three-dimensional frequency selective surface based on surface wave tunneling.

We propose a new type of three-dimensional frequency selective structure (3D-FSS) in form of subwavelength staggered metallic frames, and demonstrate a new design concept of confining and guiding surface wave propagation through the transmission tunnels for spacial filters. Both qualitative analysis by current loops and full-wave simulations show that the strong coupling along metallic frames can enhance the performance of frequency response, such as a sharper roll-off, clean out-of-band rejection, as well as angle and polarization insensitivity. Moreover, different unit cell shapes are introduced to confirm the universality of the design concept. Finally, a 3D-FSS with staggered rectangular frames was realized by experiment.

Extreme optical chirality of plasmonic nanohole arrays due to chiral Fano resonance

We study the physical origin of extreme optical chirality of subwavelength arrays of chiral holes in metal. We reconstruct the nanoscale relief of the hole arrays by the atomic-force microscopy and post-process the data to acquire an average unit-cell shape clear of noise and defects. For this shape, we perform the electromagnetic finite difference time domain simulations that reproduce all important features observed by the light-transmission experiments, including the notably strong circular dichroism and optical activity covering the whole range of possible values. To interpret the simulation results, we develop a chiral coupled-mode model which yields analytical expressions that fit accurately the numerical data in a broad wavelength range. Our conclusions undoubtedly link the extreme optical chirality to the plasmon resonances of chiral holes and the associated chiral Fano-type transmission resonance.

Achieving all-dielectric metamaterial band-pass frequency selective surface via high-permittivity ceramics

In this paper, we propose the design of all-dielectric metamaterial band-pass frequency selective surfaces (FSSs) using high-permittivity ceramics based on effective medium theory and dielectric resonator theory. The band-pass response can be determined by the permittivity of the dielectric material, the periodicity, and geometrical shape of the dielectric unit cell. As an example, a band-pass FSS composed of H shaped ceramic resonators is demonstrated. Both the simulation and experiment results show that the FSS can achieve a pass band in X-band. Since such FSSs are made of low-loss high-permittivity ceramics, they are of important application values, especially in high-temperature, high-power environments. The design method can be readily extended to the design of FSSs in other frequencies.

Analysis of radiation of antennas with a phase‐gradient partially reflective surface

This study presents a novel model for understanding the radiation phenomena and calculating the radiation pattern properties of uniform and phase-gradient partially reflective surface (PRS) antennas. This model is extracted for one- and two-dimensional antennas using array theory along with the dispersion analysis of the unit cells. The model can calculate the main lobe radiation pattern, scan angle and half-power beamwidth of uniform and phase-gradient PRSs with broadside, conical or tilted beams with an accuracy better than 5°. Two common PRS unit cell shapes (slotted patch and dipole) are used here.

Optimization of three-dimensional truss-like periodic materials considering isotropy constraints

In recent years, much attention has been directed to the study of ultralight periodic cellular materials, such as the so called Periodic Truss Materials (PTMs), which are made up of truss-like unit cells. Application of these materials has its best potential in structures subjected to multifunctional, and sometimes conflicting, engineering requirements. Hence, optimization techniques can be employed to help finding the shape of the optimal unit cell for a given multifunctional application. Although the result can be geometrically complex, this difficulty can be minored in view of modern additive manufacturing technologies. This work presents a parameter/topology optimization procedure to design the particular unit cell geometry (that is, finding the cross sections of the bars) that results in a macroscopic material with optimum homogenized elastic or/and thermal constitutive properties. Emphasis is devoted to analyze the effect of enforcing independently elastic or thermal isotropy in the macroscopic material behavior. Although isotropic behavior can be imposed through adequate cell symmetries, an equivalent effect can be achieved by satisfying equality constraints relating constitutive coefficients. A sequential quadratic programming algorithm (SQP) is adopted, thus enforcing equality constraints gradually and within a tolerance range. This results in an enlarged search space at intermediate stages, rendering an effective strategy to solve the optimization problem. Different 3D cases with engineering appeal are solved and the results discussed.

Subwavelength lattice optics by evolutionary design.

This paper describes a new class of structured optical materials—lattice opto-materials—that can manipulate the flow of visible light into a wide range of three-dimensional profiles using evolutionary design principles. Lattice opto-materials are based on the discretization of a surface into a two-dimensional (2D) subwavelength lattice whose individual lattice sites can be controlled to achieve a programmed optical response. To access a desired optical property, we designed a lattice evolutionary algorithm that includes and optimizes contributions from every element in the lattice. Lattice opto-materials can exhibit simple properties, such as on- and off-axis focusing, and can also concentrate light into multiple, discrete spots. We expanded the unit cell shapes of the lattice to achieve distinct, polarization-dependent optical responses from the same 2D patterned substrate. Finally, these lattice opto-materials can also be combined into architectures that resemble a new type of compound flat lens.

The phase problem for quasicrystals in reciprocal space

The phase problem is very well-known in crystallography and is particularly important for structure solution of quasicrystals. Structure solution ( initial phasing of the diffraction pattern) is the first step of atomic structure determination against the diffraction data. Many tools for solving the phase problem in crystallography were developed over the years. Besides the pioneer Patherson function method or direct methods, also the low density elimination method and, more recently, maximum entropy method or charge flipping algorithm are widely used. We propose another way of phase recovery, directly from the diffraction pattern. It has been shown, that diffraction patterns of aperiodic structures (quasicrystals and modulated structures) consists of periodic series of peaks [1,2]. The peaks are, of course, aperiodically distributed in reciprocal space. However, the envelopes of such peaks are strictly periodic. For Fibonacci sequence the shape of envelopes is given by a sinx/x – type function. In the centrosymmetric case all peaks belonging to a given series have the same phase (0 or π). Moreover, once we rescale peak positions to obtain the reduced envelope of structure factor (intensity), we can easily find the shape of the average unit cell, by applying the inverse Fourier transform. The functionality of such approach has been shown in [3] for d-AlNiCo quasicrystal. In this paper we show a few examples of model structures with recovered phases. Decorated Fibonacci sequence, Penrose tiling and Ammann tiling are used as model structures for 1D, 2D, and 3D quasicrystals respectively. We compare the results with conventionally used charge flipping method.

Evaluation of light-weight AlSi10Mg periodic cellular lattice structures fabricated via direct metal laser sintering

Aluminium alloy porous structures are highly demanded for many applications such as light-weight aerospace and heat exchanger products. Conventional manufacturing methods such as casting, however, faces difficulty in making aluminium alloy complex periodic cellular lattice structures with designed unit cell shape and size and volume fraction. This study evaluates the manufacturability and performance of AlSi10Mg periodic cellular lattice structures fabricated via direct metal laser sintering (DMLS). Various lattice structures at different volume fractions and unit cell sizes are designed by repeating a unit cell type called “diamond”. Due to the self-supported feature of the diamond unit cell, low volume fraction (7.5–15%) AlSi10Mg periodic cellular lattice structures can be fabricated by the DMLS process with the unit cell sizes ranging from 3mm to 7mm. A good geometric agreement is found between the original design structure models and the DMLS made structures, but the strut sizes of the DMLS made structures are slightly higher than the designed values and thus pore sizes decrease. There is clear relationship between the compressive modulus and strength of the structures and their volume fraction and unit size. Hence, this study shows that light-weight aluminium structures can be designed and made with the controlled unit size and volume fraction and the predicted mechanical properties.

Extended multiscale finite element method: its basis and applications for mechanical analysis of heterogeneous materials

Extended multiscale finite element method (EMsFEM) has been proved to be an efficient method for the mechanical analysis of heterogeneous materials. The key factor for efficiency and accuracy of EMsFEM is the numerical base functions (NBFs). The paper summarizes the general method for constructing NBFs and proposes a generalized isoparametric interpolation based on the rigid displacement properties (RDPs) of NBFs. We prove that the NBFs constructed by linear, periodic and rotational angle boundary conditions satisfy the RDPs, which is independent with the shape and material properties of unit cells. The properties of NBFs for oversampling technique are also comprehensively discussed. The algorithm complexity is discussed in theoretical and numerical aspects, which concludes that the computation quantity of EMsFEM is much smaller than the direct solutions. The algorithm is validated by linear analysis of the materials with random impurities and holes and the efficiency is improved further by parallel computing.

Measurement of a solid-state triple point at the metal–insulator transition in VO2

First-order phase transitions in solids are notoriously challenging to study. The combination of change in unit cell shape, long range of elastic distortion and flow of latent heat leads to large energy barriers resulting in domain structure, hysteresis and cracking. The situation is worse near a triple point, where more than two phases are involved. The well-known metal-insulator transition in vanadium dioxide, a popular candidate for ultrafast optical and electrical switching applications, is a case in point. Even though VO2 is one of the simplest strongly correlated materials, experimental difficulties posed by the first-order nature of the metal-insulator transition as well as the involvement of at least two competing insulating phases have led to persistent controversy about its nature. Here we show that studying single-crystal VO2 nanobeams in a purpose-built nanomechanical strain apparatus allows investigation of this prototypical phase transition with unprecedented control and precision. Our results include the striking finding that the triple point of the metallic phase and two insulating phases is at the transition temperature, Ttr = Tc, which we determine to be 65.0 ± 0.1 °C. The findings have profound implications for the mechanism of the metal-insulator transition in VO2, but they also demonstrate the importance of this approach for mastering phase transitions in many other strongly correlated materials, such as manganites and iron-based superconductors.

Sr-containing hydroxyapatite: morphologies of HA crystals and bioactivity on osteoblast cells

A series of Sr-substituted hydroxyapatites (HA), of general formula Ca(10−x)Srx(PO4)6(OH)2, where x=2 and 4, were synthesized by solid state methods and characterized extensively. The reactivity of these materials in cell culture medium was evaluated, and the behavior towards MG-63 osteoblast cells (in terms of cytotoxicity and proliferation assays) was studied. Future in vivo studies will give further insights into the behavior of the materials.A paper by Lagergren et al. (1975), concerning Sr-substituted HA prepared by a solid state method, reports that the presence of Sr in the apatite composition strongly influences the apatite diffraction patterns. Zeglinsky et al. (2012) investigated Sr-substituted HA by ab initio methods and Rietveld analyses and reported changes in the HA unit cell volume and shape due to the Sr addition.To further clarify the role played by the addition of Sr on the physico-chemical properties of these materials we prepared Sr-substituted HA compositions by a solid state method, using different reagents, thermal treatments and a multi-technique approach. Our results indicated that the introduction of Sr at the levels considered here does influence the structure of HA. There is also evidence of a decrease in the crystallinity degree of the materials upon Sr addition. The introduction of increasing amounts of Sr into the HA composition causes a decrease in the specific surface area and an enrichment of Sr-apatite phase at the surface of the samples. Bioactivity tests show that the presence of Sr causes changes in particle size and/or morphology during soaking in MEM solution; on the contrary the morphology of pure HA does not change after 14days of reaction. The presence of Sr, as Sr-substituted HA and SrCl2, in cultures of human MG-63 osteoblasts did not produce any cytotoxic effect. In fact, Sr-substituted HA increased the proliferation of osteoblast cells and enhanced cell differentiation: Sr in HA has a positive effect on MG-63 cells. In contrast, Sr ions alone, at the concentrations released by Sr-HA (1.21–3.24ppm), influenced neither cell proliferation nor differentiation. Thus the positive effects of Sr in Sr-HA materials are probably due to the co-action of other ions such as Ca and P.

Unified series solution for the anti-plane effective magnetoelectroelastic moduli of three-phase fiber composites

The anti-plane magnetoelectroelastic behavior of three-phase magnetoelectroelastic composites (fiber/interphase/matrix) with doubly periodic microstructures is dealt with. With the aid of the matrix notation, the anti-plane magnetoelectroelastic coupling problem is formulated as same as the anti-plane piezoelectric coupling problem. And then the eigenfunction expansion-variational method (EEVM) is extended to solve such a problem. Series solutions for the effective magnetoelectroelastic moduli are presented, which are in a unified form for generally periodic fiber arrays, different unit cell shapes as well as different constituent properties, and are applicable for high volume fraction of fibers. With the present solution, it is found that the effective magnetoelectric coefficient of a two-phase composite may have two local extrema rather than only one extremum predicted by the Mori-Tanaka method. By optimizing the volume fraction, permutation and the choice of the constituent phases, the maximum magnitude of the effective magnetoelectric coefficient of a three-phase composite can be much larger than that of any of the two-phase composites, and the sign of the magnetoelectric coefficient can be changed, which is not observed in a two-phase composite. For composites with a generally periodic array of fibers, the effective magnetoelectric moduli can be anisotropic.

Fatigue design of lattice materials via computational mechanics: Application to lattices with smooth transitions in cell geometry

A numerical method based on asymptotic homogenization theory is presented for the design of lattice materials against fatigue failure. The method is applied to study the effect of unit cell shape on the fatigue strength of hexagonal and square lattices. Cell shapes with regular and optimized geometry are examined. A unit cell is considered to possess a regular shape if the geometric primitives defining its inner boundaries are joined with an arc fillet, whose radius is 1% of the cell length. An optimized cell shape, on the other hand, is obtained by minimizing the curvature of its interior borders, which are conceived as continuous in curvature to smooth stress localization.For a given multi-axial cyclic loading, failure surfaces of metallic hexagonal and square lattices are provided along with their modified Goodman diagrams to assess the effect of mean and alternating stresses on the fatigue strength. In good agreement with the experimental data available in literature, the numerical results show that the shape of the unit cell has a major impact on the fatigue performance of the lattice material. For example under fully reversible tension, the fatigue strength of optimized square lattices of 10% relative density is shown to be 54% higher than that of their conventional counterparts with regular cell geometry.

Calculation of bulk madelung constants by direct summation without complications of conditional convergence

Calculation of bulk Madelung constants is not a straightforward process. In a direct summation, the infinite series is only conditionally convergent, and the value depends on the way the terms are grouped and truncated. For this reason, the traditional direct summation method taking an expanding sphere method cannot be generalized to an expanding cube method, and vice versa. We propose a straightforward method of calculating Madelung’s constants by direct summation of the screened Coulomb interaction that is applicable in both expanding modes. We demonstrate that the bulk Madelung constants of the sodium-chloride structure and the cesium-chloride crystal structure can be calculated regardless of the constraints on the unit cell shape or the expanding mode. Although the exponential factor in the screened potential generally slows down the convergence of the Madelung series, it is possible in many cases to accelerate the convergence with an appropriate choice of the unit cell. Since conditional convergence is eliminated by this simple method, we may choose any unit cell configuration to achieve a faster convergence of the Madelung constant.

Structure of Co-2 × 2 nanoislands grown on Ag/Ge(111)-√3 × √3 surface studied by scanning tunneling microscopy

We have found that Co-2 × 2 islands grown on an Ag/Ge(111)-√3 × √3 surface have hcp structure with the (11-20) orientation. The island evolution involves transformation of the unit cell shape from parallelogram into rectangular, which is accompanied by the island shape transformation from hexagonal into stripe-like. Identified are two crystallographic directions for the island growth, the pseudo-[0001] and the pseudo-[1-100]. We have observed the occurrence of a lateral shift between the topmost and the underlying bilayers in the case of the island growth along the pseudo-[0001] direction. In contrast, the topmost and the underlying bilayers are unshifted for the growth along the pseudo-[1-100] direction.

A finite-strain constitutive theory for electro-active polymer composites via homogenization

This paper presents a homogenization framework for electro-elastic composite materials at finite strains. The framework is used to develop constitutive models for electro-active composites consisting of initially aligned, rigid dielectric particles distributed periodically in a dielectric elastomeric matrix. For this purpose, a novel strategy is proposed to partially decouple the mechanical and electrostatic effects in the composite. Thus, the effective electro-elastic energy of the composite is written in terms of a purely mechanical component together with a purely electrostatic component, this last one dependent on the macroscopic deformation via appropriate kinematic variables, such as the particle displacements and rotations, and the change in size and shape of the appropriate unit cell. The results show that the macroscopic stress includes contributions due to the changes in the effective dielectric permittivity of the composite with the deformation. For the special case of a periodic distribution of electrically isotropic, spherical particles, the extra stresses are due to changes with the deformation in the unit cell shape and size, and are of order volume fraction squared, while the corresponding extra stresses for the case of aligned, ellipsoidal particles can be of order volume fraction, when changes are induced by the deformation in the orientation of the particles.

Multifunctional hybrids for electromagnetic absorption

Electromagnetic (EM) interferences are ubiquitous in modern technologies and impact on the reliability of electronic devices and on living cells. Shielding by EM absorption, which is preferable over reflection in certain instances, requires combining a low dielectric constant with high electrical conductivity, which are antagonist properties in the world of materials. A novel class of hybrid materials for EM absorption in the gigahertz range has been developed based on a hierarchical architecture involving a metallic honeycomb filled with a carbon nanotube-reinforced polymer foam. The waveguide characteristics of the honeycomb combined with the performance of the foam lead to unexpectedly large EM power absorption over a wide frequency range, superior to any known material. The peak absorption frequency can be tuned by varying the shape of the honeycomb unit cell. A closed form model of the EM reflection and absorption provides a tool for the optimization of the hybrid. This designed material sets the stage for a new class of sandwich panels combining high EM absorption with mass efficiency, stiffness and thermal management.

The X-Ray Studies on Amorphous Fe<sub>78</sub>Nb<sub>2</sub>B<sub>20</sub> Alloy

In this paper there are presented results of structure analyses of the Fe78Nb2B20 amorphous alloy after annealing. Basing on the initial analyses the “hypothetical” model structure was chosen as the combination of different kind of the Fe structure deformations: change of unit cell parameters (change of unit cell shape) and change of line broadening (change of crystallite size). The crystallite size (in meaning of the size of the ordered regions) for the amorphous state is in a range of 7 – 37 Å and for the crystalline state is about of 1100 Å. The comparison of the values of the unit cell parameters shows that the value of the basic – hypothetical unit cell in an amorphous state is bigger of 0.2 Å than in a crystalline state. After crystallisation there are detected Fe and Fe3B phases.

Plasmonic Crystals: A Platform to Catalog Resonances from Ultraviolet to Near‐Infrared Wavelengths in a Plasmonic Library

AbstractSurface plasmons are responsible for a variety of phenomena, including nanoscale optical focusing, negative refraction, and surface‐enhanced Raman scattering. Their characteristic evanescent electromagnetic fields offer opportunities for sub‐diffraction imaging, optical cloaking, and label‐free molecular sensing. The selection of materials for such applications, however, has been traditionally limited to the noble metals Au and Ag because there has been no side‐by‐side comparison of other materials. This feature article describes recent progress on manipulating surface plasmons from ultraviolet to near‐infrared wavelengths using plasmonic crystals made from 2D nanopyramidal arrays. A library of plasmon resonances is constructed in the form of dispersion diagrams for a series of unconventional and new composite plasmonic materials. These resonances are tuned by controlling both intrinsic factors (unit cell shape, materials type) and extrinsic factors (excitation conditions, dielectric environment). Finally, plasmonic crystals with reduced lattice symmetries are fabricated as another means to tailor resonances for broadband coupling.