Periodic Lattice Research Articles

3D Printing of Graphene Aerogel Microspheres to Architect High-Performance Electrodes for Hydrogen Evolution Reaction.

The hydrogen evolution reaction (HER) efficiency is highly dependent on the electrocatalysts microstructure and the macrostructure of the electrodes. Herein, the graphene aerogel microspheres loaded with well-dispersed ultrafine Ni/Co nanoparticles catalyst is prepared through electro-spraying, in-situ crosslinking, freeze-drying, and pyrolysis, and then is utilized to print the HER electrode via direct ink writing (DIW). The obtained graphene-based aerogel microspheres possess peculiar cabbage-like mesoporous structures which allow ready access of reaction species to active sites, optimal mass transfer, and proton diffusion within the microspheres. DIW 3D printing achieves the ordered control on the periodic lattice macro-geometry and thus facilitates the fast gas bubble evolution and release from the electrode surface. The as-fabricated 3D electrode possesses a low overpotential of 341 mV at 10 mA cm-2, a decrease by 31.5% compared to 3D printed electrode directly from 2D graphene, and a low Tafel slope of 119.1 mV dec-1, 40% lower than that of the electrodes fabricated via directly casting the aerogel microspheres. Furthermore, the 3D-printed electrode of aerogel microspheres displays good HER stability. This work provides a good approach for constructing high-performance HER electrodes through 3D printing of graphene aerogel microspheres.

Extended Dummy Node Rule for analysis and characterization of pin-jointed periodic cellular materials: An approach based on Bloch-wave method

Micro-truss lattice materials are a class of hybrid periodic cellular solids that consist of a combination of solids and voids. The material is partitioned into cells structured in a given cell topology tessellated to form an almost unbounded micro-truss framework. The Bloch-wave method is one technique that can describe the propagation of a wave function over a periodic infinite lattice. It demonstrated the effectiveness of modeling the static and dynamic responses of lattices of various topologies. However, the Bloch-wave method presents limitations when applied to unit cell topologies whose structural elements extend across their envelopes to adjacent unit cells, as a given unit cell may not contain the full nodal parameters and periodicity information necessary to describe the kinematic and static wave propagations across the periodic lattice. The first part of this paper presents the Dummy Node Rule (DNR), which overcomes this limitation. The rule introduces dummy nodes at the intersection points between cell envelopes and elements extending between the adjacent unit cells, which are initially treated as part of the finite unit cell structure. Then, the rule establishes mathematical relationships between the static and kinematic wave functions propagating across dummy nodes and those propagating across the connected cell elements. The second part of the paper describes DNR for specific applications such as (a) the development of static and kinematic systems of the unit cell finite structure, which aids in the determinacy analysis of periodic lattice structures, and (b) the development of the Cauchy–Born kinematic boundary condition that is used to homogenize the kinematic response of the infinite periodic structure to an assumed macroscopic strain field, which in turn, forms the effective properties of the lattice material. Furthermore, the last part of the paper shows examples where the scheme is applied for the stiffness characterization of selected lattice topologies.

Crystalline Assemblies of DNA Nanostructures and Their Functional Properties

AbstractSelf‐assembly presents a remarkable approach for creating intricate structures by positioning nanomaterials in precise locations, with control over molecular interactions. For example, material arrays with interplanar distances similar to the wavelength of light can generate structural color through complex interactions like scattering, diffraction, and interference. Moreover, enzymes, plasmonic nanoparticles, and luminescent materials organized in periodic lattices are envisioned to create functional materials with various applications. Focusing on structural DNA nanotechnology, here, we summarized the recent developments of two‐ and three‐dimensional lattices made purely from DNA nanostructures. We review DNA‐based monomer design for different lattices, guest molecule assembly, and inorganic material coating techniques and discuss their functional properties and potential applications in photonic crystals, nanoelectronics, and bioengineering as well as future challenges and perspectives.

Alignment of polarization volume gratings using semi-circular arc patterns via nanofabrication technology

Polarization volume gratings have the potential for future applications such as AR due to their high single-order diffraction efficiency and large angular and wavelength response range. However, the preparation method of photo alignment, which is currently employed, presents challenges to the application of PVGs due to issues of poor uniformity and difficulty in preparing large sizes. To promote the application, a scheme for fabricating the alignment layer of PVGs by nanofabrication technology is proposed. The alignment structure, where the basic unit is a semicircular arc, was designed. We prepared the structure using EBL and spin-coated a layer of chiral liquid crystals (CLC) on top of it. The dispersion effect in white light indicates that the designed alignment structure imparts lateral periodicity to the CLC. The device could efficiently reflect specific right-polarized light and efficiently transmit specific left-polarized light. Therefore, the diffraction performance of the device can be considered to be consistent with the photo-alignment PVGs within the error allowance. This work provides what we believe to be a novel scheme for the alignment of PVGs, creating a new platform for mass production and multifunctional integrated design of PVGs.

Hierarchical sheet triply periodic minimal surface lattices: Design, performance and optimization

Hierarchical sheet triply periodic minimal surface lattices: Design, performance and optimization

Mapping the nonequilibrium order parameter of a quasi-two dimensional charge density wave system

The driving force of a charge density wave (CDW) transition in quasi-two dimensional systems is still debated, while being crucial in understanding electronic correlation in such materials. Here we use femtosecond time- and angle-resolved photoemission spectroscopy combined with computational methods to investigate the coherent lattice dynamics of a prototypical CDW system. The photo-induced temporal evolution of the periodic lattice distortion associated with the amplitude mode reveals the dynamics of the free energy functional governing the order parameter. Our approach establishes that optically-induced screening rather than CDW melting at the electronic level leads to a transiently modified potential which explains the anharmonic behaviour of the amplitude mode and discloses the structural origin of the symmetry-breaking phase transition.

Design of very-large area photonic crystal surface emitting lasers with an all-semiconductor photonic crystal

We report on the design of a photonic crystal surface emitting laser (PCSEL) with an all-semiconductor (InGaP/GaAs) photonic crystal suitable for very-large-area emission and high-power operation. Using coupled-wave theory for PCSELs we model infinite- and finite-size cavity PCSELs and show that a photonic crystal unit cell with square lattice periodicity and a rotated and stretched triangular feature is suitable for the realization of PCSELs with very large areas (1 mm<L < 3 mm for a square cavity of size L × L) while maintaining high mode discrimination between the fundamental laser mode and higher order cavity modes as well as high external efficiency. This was achieved by exploiting a single-lattice photonic crystal unit cell design that minimizes one-dimensional coupling in the photonic crystal, providing a promising alternative to double-lattice PCSELs.

Crystalline Assemblies of DNA Nanostructures and their Functional Properties.

Self-assembly presents a remarkable approach for creating intricate structures by positioning nanomaterials in precise locations, with control over molecular interactions. For example, material arrays with interplanar distances similar to the wavelength of light can generate structural color through complex interactions like scattering, diffraction, and interference. Moreover, enzymes, plasmonic nanoparticles, and luminescent materials organized in periodic lattices are envisioned to create functional materials with various applications. Focusing on structural DNA nanotechnology, here, we summarized the recent developments of two- and three-dimensional lattices made purely from DNA nanostructures. We review DNA-based monomer design for different lattices, guest molecule assembly, and inorganic material coating techniques and discuss their functional properties and potential applications in photonic crystals, nanoelectronics, and bioengineering as well as future challenges and perspectives.

Engineering the Coherent Phonon Transport in Polar Ferromagnetic Oxide Superlattices.

Artificial superlattices composed of perovskite oxides serves as an essential platform for engineering coherent phonon transport by redefining the lattice periodicity, which strongly influences the lattice-coupled phase transitions in charge and spin degrees of freedom. However, previous methods of manipulating phonons have been limited to controlling the periodicity of superlattice, rather than utilizing complex mutual interactions that are prominent in transition metal oxides. In this study onoxide superlattices composed of ferromagnetic metallic SrRuO3 and quantum paraelectric SrTiO3, phonon modulation by controlling the geometry of superlattice in atomic-scale precision is realized, demonstrating the coherent phonon engineering using structural and magnetic phase transitions. By modulating the interface density, coherent-incoherent crossover of the phonon transport at room temperature is observed, which is coupled with a change in interfacial structural continuity. Upon cooling, the close relation between phonon transport and multiple phase transitions is identified. In particular, the enhancement of the polar state in SrTiO3 layer at ≈200K leads to the weakening of phonon coherence and a further reduction of thermal conductivity in superlattices compared to the bulk limit. These findings provide a guide to developing future thermoelectric nanodevices by engineering the coherence of phonons via the design of complex oxide heterostructures.

Stacking of charge-density waves in 2H−NbSe2 bilayers

We employ electronic-structure calculations to investigate the charge-density waves and periodic lattice distortions in bilayer 2H−NbSe2. We demonstrate that the vertical stacking can give rise to a variety of patterns that may lower the symmetry of the charge-density waves exhibited separately by the two composing 1H−NbSe2 monolayers. The general tendency to a spontaneous symmetry breaking observed in the ground state and the first excited states is shown to originate from a non-negligible interlayer coupling. Simulated images for scanning tunneling microscopy as well as geometric structure factors show signatures of the different stacking orders. This may not only be useful to reinterpret past experiments on surfaces and thin films, but it may also be exploited to devise ad hoc experiments for the investigation of the stacking order in 2H−NbSe2. We anticipate that our analysis not only applies to the 2H−NbSe2, but is also relevant for thin films and bulk, whose smallest centrosymmetric component is indeed the bilayer. Finally, our results illustrate clearly that the vertical stacking is not only important for 1T structures, as exemplified by the metal-to-insulator transition observed in 1T−TaS2, but seems to be a general feature of metallic layered transition metal dichalcogenides as well. Published by the American Physical Society 2024

High topological charge lasing in quasicrystals.

Photonic modes exhibiting a polarization winding akin to a vortex possess an integer topological charge. Lasing with topological charge 1 or 2 can be realized in periodic lattices of up to six-fold rotational symmetry-higher order charges require symmetries not compatible with any two-dimensional Bravais lattice. Here, we experimentally demonstrate lasing with topological charges as high as -5, +7, -17 and +19 in quasicrystals. We discover rich ordered structures of increasing topological charges in the reciprocal space. Our quasicrystal design utilizes group theory in determining electromagnetic field nodes, where lossy plasmonic nanoparticles are positioned to maximize gain. Our results open a new path for fundamental studies of higher-order topological defects, coherent light beams of high topological charge, and realizations of omni-directional, flat-band-like lasing.

Local monodromy of Drinfeld modules

Compared with algebraic varieties the local monodromy of Drinfeld modules appears to be hopelessly complex: the image of the wild inertia subgroup under Tate module representations is infinite save for the case of potential good reduction. Nonetheless, we show that Tate modules of Drinfeld modules are ramified in a limited way: the image of a sufficiently deep ramification subgroup is trivial. This leads to a new invariant, the local conductor of a Drinfeld module. We establish an upper bound on the conductor in terms of the volume of the period lattice. As an intermediate step we develop a theory of normed lattices in function field arithmetic including the notion of volume. We relate normed lattices to vector bundles on projective curves. With the aid of Castelnuovo–Mumford regularity this implies a volume bound on norms of lattice generators, and the conductor inequality follows. Last but not least we describe the image of inertia for Drinfeld modules with period lattices of rank $1$ . Just as in the theory of local $\ell$ -adic Galois representations this image is commensurable with a commutative unipotent algebraic subgroup. However, in the case of Drinfeld modules such a subgroup can be a product of several copies of $\mathbf {G}_a$ .

Multianalyte Detection with Metasurface-Based Midinfrared Microspectrometer.

Midinfrared (2.5-25 μm) spectroscopy is an ideal tool for identifying chemicals in a nondestructive manner. The traditional platform is a Fourier transform infrared (FTIR) spectrometer, but this is too bulky, expensive, and power-hungry for many applications. There is therefore a growing demand for small, lightweight, and cost-effective microspectrometers for use in the field. One emerging platform is the filter-array detector-array microspectrometer. It pairs a broadband detector array with a thin and rigid array of spectral filters to offer a robust, compact platform for real-time in situ sensing. However, most demonstrations have only focused on identifying a single chemical against a null sample, even though many applications would involve multianalyte detection. In this work, we show a rare attempt at simultaneously tracking multiple analytes with a metasurface filter-array microspectrometer. The metasurface consists of periodic lattices of subwavelength circular apertures in an aluminum layer to create an array of bandpass filters. The filter array is imaged with an off-the-shelf microbolometer via a reverse-lens imaging setup to simultaneously monitor the concentration of ethanol and methanol in gasoline. This represents an important application of fuel quality monitoring. Chemometric models (PLS and SVR) are trained and tested on gasoline blends with ethanol and methanol contents, both ranging from 0% to 20% v/v. A support vector machine regression (SVR) model with a cubic kernel was found to have the lowest combined prediction errors. The root-mean-square-error of prediction (RMSEP) for ethanol and methanol are 1.23% and 1.84% v/v; the corresponding pseudounivariate limit of detection is found to be 4.22% and 6.86% v/v, respectively. This work takes the emerging field of metasurface-based mid-infrared spectrometers from single- to multianalyte detection, thereby considerably expanding their range of potential applications.

Standing Solitons Tuned by Impurities in Damped Nonlinear Lattices under External Excitation.

Periodic chains of nonlinear oscillators are known to support solitonic solutions within a specific range of physical parameters when damping effect is considered. This Letter investigates the dynamics of stationary solitons in damped nonlinear lattices under external excitation, focusing on the influence of impurities related to the natural frequency of the oscillators. We demonstrate experimentally and numerically that incorporating impurities into externally driven periodic lattices can expand the solitonic stability diagram under high-damping areas and near the Hopf bifurcation of periodic structures. A mathematical description that closely aligns with experimental realities is presented through the disordered damped nonlinear Schrödinger equation. Specifically, we prove how impurities along the chain can spontaneously nucleate the lattice solitons. The obtained results open the way toward the functionalization of disorder to control nonlinear energy localization in damped nonperiodic structures.

Stable Au(111) Hexagonal Reconstruction Induced by Perchlorinated Nanographene Molecules.

Surface reconstructions play a crucial role in surface science because of their influence on the adsorption and arrangement of molecules or nanoparticles. On the Au(111) surface, the herringbone reconstruction presents favorable anchoring at the elbow sites, where the highest reactivity is found. In this work, we deposited large organic perchlorinated molecules on a Au(111) surface via high-vacuum electrospray deposition. With noncontact atomic force microscopy measurements at room temperature, we studied the molecular structures formed on the surface before and after annealing at different temperatures. We found that a supramolecular layer is formed and that a hexagonal reconstruction of the Au(111) surface is induced. After high-temperature annealing, the molecules are removed, but the hexagonal Au(111) surface reconstruction is preserved. With the hexagonal Au(111) surface reconstruction, a periodic lattice of anchoring sites is formed.

The dynamical Ising-Kac model in 3D converges to $$\Phi ^4_3$$

AbstractWe consider the Glauber dynamics of a ferromagnetic Ising-Kac model on a three-dimensional periodic lattice of size $$(2 N + 1)^3$$ ( 2 N + 1 ) 3 , in which the flipping rate of each spin depends on an average field in a large neighborhood of radius $$\gamma ^{-1}<\!\!< N$$ γ - 1 < < N . We study the random fluctuations of a suitably rescaled coarse-grained spin field as $$N \rightarrow \infty $$ N → ∞ and $$\gamma \rightarrow 0$$ γ → 0 ; we show that near the mean-field value of the critical temperature, the process converges in distribution to the solution of the dynamical $$\Phi ^4_3$$ Φ 3 4 model on a torus. Our result settles a conjecture from Giacomin et al. (1999). The dynamical $$\Phi ^4_3$$ Φ 3 4 model is given by a non-linear stochastic partial differential equation (SPDE) which is driven by an additive space-time white noise and which requires renormalisation of the non-linearity. A rigorous notion of solution for this SPDE and its renormalisation is provided by the framework of regularity structures (Hairer in Invent Math 198(2):269–504, 2014. https://doi.org/10.1007/s00222-014-0505-4). As in the two-dimensional case (Mourrat and Weber in Commun Pure Appl Math 70(4):717–812, 2017), the renormalisation corresponds to a small shift of the inverse temperature of the discrete system away from its mean-field value.

Strain regulation retards natural operation decay of perovskite solar cells

Perovskite solar cells (pero-SCs) have undergone rapid development in the past decade. However, there is still a lack of systematic studies investigating whether the empirical rules of working lifetime assessment used for silicon solar cells can be applied to pero-SCs. It is believed that pero-SCs show enhanced stability under day/night cycling owing to the reported self-healing effect in the dark1,2. Here we find that the degradation of highly efficient FAPbI3 pero-SCs is much faster under a natural day/night cycling mode, bringing into question the widely accepted approach to estimate the operational lifetime of pero-SCs based on continuous-mode testing. We reveal the key factor to be the lattice strain caused by thermal expansion and shrinking of the perovskite during operation, an effect that gradually relaxes under the continuous-illumination mode but cycles synchronously under the cycling mode3,4. The periodic lattice strain under the cycling mode results in deep trap accumulation and chemical degradation during operation, decreasing the ion-migration potential and hence the device lifetime5. We introduce phenylselenenyl chloride to regulate the perovskite lattice strain during day/night cycling, achieving a certified efficiency of 26.3 per cent and a 10-fold improvement in the time required to reach 80% of peak efficiency (T80) under the cycling mode after the modification.

Sub-THz and THz Cherenkov radiation source with two-dimensional periodic surface lattice and multistage depressed collector

We present the theory, concept and design of an efficient, megawatt coherent Cherenkov radiation source based on a two-dimensional periodic surface lattice (2D-PSL) cavity combined with a novel energy recovery system for the generation of highly efficient (> 50%) single-frequency radiation. We demonstrate the scalability of the transverse dimension of the 2D-PSL cavity of the Cherenkov source and thus the potential for efficient, continuous-wave, high-power (> 1 MW) operation; fundamental to the eventual realization of clean, fusion energy. These new sources, with the capacity to operate in the 0.1-10THz range, hold strong promise to address the long-standing “Terahertz gap”. By combining a Cherenkov oscillator driven by a non-gyrating beam with an innovative four-stage depressed collector energy recovery system, the overall device efficiency can be increased to be competitive with gyrotrons in the requirements for heating and current drive in fusion plasma. In these Cherenkov devices, the frequency independence of the magnetic guide field enables advantageous frequency scaling without deployment constraints, making them especially attractive for high-impact applications in fusion science, turbulence diagnostics, non-destructive testing and biochemical spectroscopy. The novel energy recovery techniques presented in this paper have broad applicability to many electron-beam driven devices, bringing revolutionary potential to future THz source technologies.

Multi-objective topology optimization and numerical investigation of heat sinks based on triply periodic minimal surface lattices

In thermal management applications, such as heat sinks (HSs) for electronic devices, cellular materials have extensively been employed. In recent years, there has been a growing attention towards employing topology optimization for enhancing hydraulic and heat transfer performance of HSs by optimizing their topology. The utilization of triply periodic minimal surface (TPMS) based structures presents distinctive prospects for customizing the design and performance of HSs. However, their potential remains unexplored in the context of customizing additively manufactured porous optimized HSs. Consequently, there is a need for research aimed at examining their coupled hydraulic and thermal performance. Density mapping approaches are used to build a variable density TPMS-based HSs from the output of topology optimization by applying the TPMS level-set equations that relate relative density and the level-set constant. In this work, a relative density mapping methodology is applied to thermo-fluid optimization problem to design a TPMS-based convective cooling system. An in-house MATLAB code was developed to perform a multi-objective topology optimization. After that, uniform and variable density (mapped from topology optimization results) TPMS-based HSs are analyzed using Star-CCM + CFD software to investigate their hydraulic and heat transfer performance. An experimental setup was established, and the numerical results were validated using uniform TPMS-based heat sinks. Results showed that incorporating TPMS with topology optimization has a great potential in thermal management applications as pressure drop across the heat sink was reduced while maintaining the performance.

Numerical study of dispersion characteristics of cylindrical spiral lines and periodic gratings based on them

Numerical studies of the dispersion characteristics of cylindrical spiral lines have been carried out. One-dimensional and two-dimensional periodic lattices formed by such lines are also considered. The eigenvalue method was used in combination with periodic boundary conditions. The dispersion characteristics are calculated in the range of parameters for which the conditions of applicability of the known approximate numerical-analytical methods for analyzing spiral lines are not met. The dispersion characteristics of the first two eigen-waves in one-dimensional and two-dimensional periodic lattices of spirals are obtained for different values of phase shifts between lattice periods. It is shown that the main type of wave in them is a wave slowed down relative to the axes of the lines with the direction of rotation of the field vector determined by the direction of winding of the spiral.