Aperiodic Structures Research Articles

Various Grids in Moiré Measurements

The moiré effect is typically observed in regular periodic structures and sometimes in random (aperiodic) structures. However, currently, only regular graphical objects are used in measurements. We propose using graphical objects that are not regular but not entirely random and that resemble rows, such as grids of dotted lines or matrixes of dots. The moiré effect in such objects may become similar to the moiré effect in regular graphical objects if a relatively simple modification of the image processing algorithm is applied. We demonstrated that the results of measurements with five different graphical objects arranged in rows (including text) are similar. Using such objects can be helpful for practical moiré measurements.

Tomographic and mechanical study of 3D printed porous polymer structure under compression

This study investigates the influence of open porosity rate and trabeculae diameter on the compressive behavior of structure printed by DLP technology. Three types of structures have been studied : two periodic structures (Cubic and Octet) and one aperiodic structure (Voronoi-based). Each of these structures are printed with a porosity of 40, 60 and 80 % and also with two different trabeculae diameters: 0.45 mm and 0.66 mm. We investigated porosity by micro-tomograpy with ImageJ for the data treatment. We determined the curing time by making a compressive test for different lengths of UV cure. The first results of the study show that Cubic structure has better Young’s Modulus and also better mechanical stress than Octet and Voronoi-based structures.

Comparison of elastic properties of periodic and aperiodic porous structures produced by additive methods

The aim of this work was to design, print, and examine elastic properties of porous structures with various parameters and beam distributions. These structures, generated using an algorithm, featured three types of lattices: octet, cubic, and Voronoi diagram-based, with different porosities (40 %, 60 %, 80 %) and beam sizes (0.45 mm, 0.66 mm). They were printed using Direct Light Processing and examined using X-ray computed microtomography. Compression tests were conducted to determine the Young’s modulus. The results were compared with computer simulations performed using Abaqus. The tools used, such as 3D printing and X-ray computed microtomography, were described, and the results and conclusions of the tests were presented. As a result, comparable outcomes were obtained for structures with higher beam diameter, while significantly different results were observed for structures with lower beam diameter.

Strain redistribution in stochastically perturbed single and dual-phase cellular materials under quasistatic compression

Inspired by the stochastic and dual-phase nature of spongy bone, this work examines the effect of the perturbation on the strain distribution in a single and dual-phase, surface-based cellular structure subjected to quasistatic compression. Each effect (perturbation and the introduction of a second phase) is studied in isolation, as well as in combination, using Digital Image Correlation (DIC) for the analysis of the resulting strain fields. Starting from a periodic, single-phase surface-based cellular structure, aperiodicity was introduced at three different levels, and specimens were designed with a second-phase introduced using a core–shell modeling approach. All designs were fabricated using multi-material extrusion, with ABS and TPU as the two materials used. The specimens were subjected to quasi-static compression until densification, with results showing that the addition of a second phase and aperiodicity were each found to delocalize strain, mitigate sympathetic cell collapse in continuous failure bands, thereby decreasing undulations in the stress plateau region. The dual-phase cellular structure was found to absorb more energy per unit mass and volume when normalized by the Maximum Transmitted Stress (MTS) but this trend was arrested at high levels of aperiodicity. While aperiodicity had a significant, and occasionally detrimental, effect on the behavior of the single-phase cellular structure, its effect on dual-phase cellular structures was far more muted, suggesting the benefits of adding a second-phase to aperiodic structures to improve isotropy without large sensitivities on account of local variations in the degree and nature of aperiodicity.

Nucleation and growth of quasicrystal-related precipitates within the Al-matrix of AlEr(Fe) alloys

Since the discovery of quasicrystals, their applications to industry have been interesting issues, among which attempts of introducing quasicrystal-related precipitates into the Al-matrix to enhance properties of Al alloys have been made without adequate understandings. Here, we report a formation pathway of quasicrystal-related precipitates in the Al-matrix of an AlEr(Fe) alloy. It is shown that upon thermal aging of the alloy, Al3Er precipitates form firstly in the Al-matrix, then quasicrystal-related (AlFe)-precipitates may nucleate heterogeneously within the Al3Er precipitates and grow large. As the quasicrystal-related precipitate grows large, the Al3Er-precipitate reform as the thin “skin” of the formed composite precipitate, keeping the quasicrystal-related portion well separated from the matrix. Atomic-resolution electron microscopy and spectroscopy reveal that these composite precipitates are the mixtures of the Al13Fe4 quasicrystal approximant structure and/or quasicrystal-related aperiodic structures, as well as their surrounding skin with Al3Er-structure. As such, Fe atoms as vexing impurity in Al alloys can be absorbed continuously into such composite precipitates. Our findings provide insights into the feasibility to form quasicrystal-related precipitates in the Al-matrix.

Superior damage tolerance observed in interpenetrating phase composites composed of aperiodic lattice structures

Interpenetrating Phase Composite (IPC) metamaterials, based on lattice topologies, have garnered significant attention as advanced materials for structural applications. However, conventional IPCs, which rely on periodic lattice unit cells, are prone to catastrophic failure due to their global deformation modes. To overcome this limitation, we present a novel IPC design utilizing aperiodic truss unit cells, inspired by the elusive “Einstein” monotile pattern. Our concept is demonstrated through IPC 3D printed via polymer jetting, using a hard polymer as the lattice filler and a soft polymer as the matrix. The distinctive mechanical properties of IPCs are characterized through single and cyclic quasi-static compression testing. Our findings demonstrate that aperiodic IPCs enable progressive deformation with gradual compression stress plateaus. Additionally, aperiodic IPCs exhibit remarkable damage tolerance, retaining 67.59 % of residual energy absorption and 73.83 % of ultimate strength after multiple cyclic compressions up to 30 % strain. These mechanisms are attributed to the synergistic deformation of interconnected unit cells, which lead to self-adjusting plastic collapse, progressive displacement evolution and delocalized deformation. This aperiodic concept paves the way for developing high-performance cushioning protection materials.

Low-dose electron microscopy imaging for beam-sensitive metal-organic frameworks.

Metal-organic frameworks (MOFs) have garnered significant attention in recent years owing to their exceptional properties. Understanding the intricate relationship between the structure of a material and its properties is crucial for guiding the synthesis and application of these materials. (Scanning) Transmission electron microscopy (S)TEM imaging stands out as a powerful tool for structural characterization at the nanoscale, capable of detailing both periodic and aperiodic local structures. However, the high electron-beam sensitivity of MOFs presents substantial challenges in their structural characterization using (S)TEM. This paper summarizes the latest advancements in low-dose high-resolution (S)TEM imaging technology and its application in MOF material characterization. It covers aspects such as framework structure, defects, and surface and interface analysis, along with the distribution of guest molecules within MOFs. This review also discusses emerging technologies like electron ptychography and outlines several prospective research directions in this field.

Monolithically integrated mode converter from terahertz substrateless silicon guide to conductive slotline

Although substrateless micro-scale silicon waveguides are a useful and versatile platform for terahertz waves, the fact that modal fields occupy the volume of the core limits the potential to dynamically manipulate guided waves. To address this, we introduce an aperiodic lattice structure to enable the monolithic co-integration of a Vivaldi antenna-like mode converter with a substrateless silicon waveguide. This broadband transition is experimentally confirmed to exhibit ∼2.5 dB average loss for two couplers, from 220 GHz to 330 GHz, and enables a photoexcited variable attenuator as proof-of-concept demonstration. This is an important enabling step to incorporate general-purpose dynamic reconfigurability, sensing, and modulation functionality into terahertz-range silicon-based integrated circuits, which are currently limited to primarily all-passive structures.

Prominent phonon transmission across aperiodic superlattice through coherent mode-conversion

In both particle and wave descriptions of phonons, the dense, aperiodically arranged interfaces in aperiodic superlattices are expected to strongly attenuate thermal transport due to phonon-interface scattering or broken long-range coherence. However, non-trivial thermal conductivity is still observed in these structures. In this study, we reveal that incoherent modes propagating in the aperiodic superlattice can be converted, through interference, into coherent modes defined by an approximate dispersion relation. This conversion leads to high transmission across the aperiodic superlattice structure, which contains hundreds of interfaces, ultimately resulting in non-trivial thermal conductivity. Such incoherent-to-coherent mode-conversion behavior is extensively observed in periodic superlattices. This work suggests an effective strategy to manipulate the phonon dispersion relation through layer patterning or material choice, enabling precise control of phonon transmission across aperiodic superlattices.

The research of vibration localization under strong disturbances using modal analysis methods

Abstract Vibration localization is a typical feature of aperiodic structures. This work investigates the vibration localization of framed cylindrical shells with a high disturbance degree. First, the spring oscillator system is considered an example to reveal the general law governing how high disturbance degree influences the vibration transmission in a structure. Then the strong localization coefficient is calculated using the modal analysis method. Finally, the conclusions of the one-dimensional systems are applied to the two-dimensional structures based on the passband approximation equivalent method to derive the strong localization coefficient of the aperiodic ring-ribbed cylindrical shell. This study realizes quantitative calculation of the vibration localization coefficient under high disturbance degree. The results of this work provide theoretical support for reducing the vibration transmission performance of a structure by increasing the degree of disturbance.

Complete photonic bandgap in a low-index two-dimensional quasicrystalline structure.

A bandgap in the continuum spectrum of photons in addition to its basic physical significance has strong potential for applications. Analogous to semiconductor crystals for electrons, periodic dielectric structures named photonic crystals were proposed to control photon flux propagation. In our search for low refractive index (RI) structures with a photonic bandgap, initial research efforts were focused on photonic crystal design, while aperiodic structures allow lower values of refractive index contrast to sustain a photonic bandgap. Here, we report on a two-dimensional quasicrystalline structure designed as a set of one-dimensional lattices merged into a single binary structure made of two materials with refractive index contrast 2|n1 - n2|/(n1 + n2) = 0.16 and even less in theory. We confirmed the theoretical prediction of bandgap exciting by measuring the radiation suppression of a dipole source placed in the center of the quasicrystalline structure. The full-wave numerical simulations and the experimental study appear to be in good agreement with the theoretical model.

Silicon artificial neurons for uniform signal transmission and amplification

Simulating the signal transmission process in neurons is crucial in computational neuroscience. However, much of the existing researches simplifies signal transmission in a single neuron to a basic mathematical process. In this article, we introduce an all-optical silicon artificial neuron incorporating an aperiodic gold monotile structure. This structure enables the simulation of uniform signal transmission within the axon. Furthermore, we propose a III-V quantum wells protocol to achieve the amplification function of nodes of Ranvier in neurons.

Influence of spatial coherence on phonon transmission across aperiodically arranged interfaces

In this study, we employ the atomistic wave-packet method to directly simulate coherent phonon transport and scattering dynamics in an aperiodic superlattice structure with aperiodically arranged interfaces. Our investigation reveals that interference dynamics, contingent upon the relative magnitudes of phonon wavelength, spatial coherence length, and average interface spacing, profoundly influence transmission spectra and mode-conversion behavior. Particularly, longer-wavelength phonons possessing larger coherence lengths exhibit more pronounced destructive interference and mode-conversion, leading to generally lower transmission. The insights gained into coherent phonon wave physics from this study can significantly augment the analysis and design of phononic devices.

Dynamic Stability of the Periodic and Aperiodic Structures of the Bernoulli-Euler Beams

The study analyzed the influence of periodic and aperiodic stiffness distribution for the four-element Bernoulli-Euler beam on the first two eigenfrequencies and the dynamic stability of the system. The influence of increasing the ratio of cross-sections of the analyzed elements was also analyzed. Significant differences were found in eigenfrequencies and dynamic stability. Using the variational Hamilton principle, the equation of motion was derived, on the basis of which the values of the eigenfrequencies were determined, and the transformation into the form of the Mathieu equation made it possible to determine the dynamic stability for the analyzed structures.

Omnidirectional mirror based on the aperiodic and hybrid-order aperiodic-periodic chirped multilayers

We propose an innovative design of highly reflective omnidirectional mirror based on chirped-type aperiodic and hybrid-order aperiodic-periodic multilayered structures in the spectral range from 400 nm to 3000 nm that contains a larger part of solar radiation. The aperiodic sequences considered are Fibonacci (FIB) and Thue-Morse (ThMo), while a power law function has been adopted to tune the thickness of layers. The chirping functions parameters were optimized to obtain maximum averaged reflectivity over the entire angular range. The numerical calculations were performed by a recursive formula via the scattering matrix method. For all the structures, the chirping effect improved the omnidirectional properties of multilayers in terms of average reflectivity and quasi omnidirectional spectral width (q-ODW). In detail, it was revealed that the ThMo based structures provide the best performance in terms of both averaged reflectivity and q-ODW. For ThMo chirped multilayer the q-ODW reached the value of 1605 nm with incident angular span 0-60°. On the other hand, the hybrid-order structure based on ThMo shows an q-ODW up to 2500 nm. Finally, for all the investigated structures the average reflectivity reaches a value larger than 0.93 using nearly 100 layers.

Generating zeolite crystals with mesoscopic aperiodic structure to promote catalytic hydroisomerization

Generating hierarchical zeolites provides an effective way to enhance their transport and catalytic properties. Several seminal methods have been reported to fabricate them with mesoscopically periodic order using surfactant-like structure...

High-performance narrowband thermal emitter based on aperiodic Tamm plasmon structures assisted by inverse design

Controlling the bandwidth and directionality of thermal emission is important for a broad range of applications, from imaging and sensing to energy harvesting. Here, we propose a new, to the best of our knowledge, type of long-wavelength infrared narrowband thermal emitter that is basically composed of aperiodic Tamm plasmon polariton structures. Compared to the thermal emitter based on periodic structures, more parameters need to be considered. An inverse design algorithm instead of traditional forward methodologies is employed to do the geometric parameter optimization. Both theoretical and experimental results show that the thermal emitter exhibits a narrowband thermal emission peak at the wavelength of 8.6 µm in the normal direction. The angular response of emission properties of the thermal emitter is dependent on the emission angle. We believe that our proposed thermal emitter provides an alternative for low-cost, high-effective narrowband mid-infrared light sources and would have a great potential in many applications.

Simulation of failure behavior of 2.5D SiC/SiC variable thickness dovetail joint structures based on mesoscale model

The application of ceramic matrix composites plays an important role in improving the performance of aero engines. However, mesoscopic aperiodicity causes excellent challenges for the performance analysis of ceramic matrix composite structures. It is no longer applicable to obtain the macroscopic properties of materials through experiments or RVE simulations for structural performance analysis. Here an attempt is made to develop a performance analysis method for mesoscopic aperiodic ceramic matrix composite structures based on mesoscale models and apply the method to the strength calculation of 2.5D SiC/SiC variable thickness dovetail joint structures. The established model reasonably approximates and accurately describes the structure’s real yarn geometries and orientations, reflecting the differences of yarn architectures in different regions. The yarn stress–strain curve is obtained through experiments, and the yarn constitutive model is established. The failure behavior of the 2.5D woven dovetail joint structure is simulated using the progressive damage analysis method and taking the yarn as the basic load-bearing unit. The simulated results are in good agreement with the experimental data in terms of failure load, load–displacement responses, macroscopic damage evolutions, and failure modes.

Ghost imaging based on Fermat spiral laser array designed for remote sensing.

We propose a Fermat spiral laser array as illumination source in ghost imaging. Due to the aperiodic structure, the Fermat spiral laser array generates illuminating light field without spatial periodicity on the normalized second-order intensity correlation function. A single-pixel detector is used to receive the signal light from object for image reconstruction. The effects of laser array parameters on the quality of ghost imaging are analyzed comprehensively. Through experimental demonstration, the Fermat spiral laser array successfully achieves ghost imaging with high quality by combining with the compressive sensing reconstruction algorithm. This method is expected to be applied in remote sensing by combining with phased and collimated fiber laser array equipped with the high emitting power and high-speed modulation frequency.

Effect of defects and doping on the transmission spectrum enhancement of photonic crystal based on 2D-MoS2

In this paper, we present the structural and photoluminescence (PL) spectra of 2D-MoS2 and we report a theoretical investigation of the influence of Ag- and Au-doping on the transmission in 2D-MoS2 photonic crystal structure (PCS). A finite-difference time-domain (FDTD) technique and plane wave expansion method (PWE) have been introduced and adapted for periodic and aperiodic structures to extract the PC-bandgap and study the behavior of the transmission spectrum. The impact of the size of defects, the Ag- and Au-doping on the 2D-PC band structure and transmission spectrum has been visualized under the inclusion of the distribution of electromagnetic fields and the associated field maps. It has been shown that the Au-doping changes significantly the 2D-MoS2 PCS and as a result the transmission spectrum increases considerably. We can predict that 2D-MoS2 PC doped with Au is more convenient than doped with Ag in most applications involving optical transmission and waveguides for optoelectronics devices.