Periodic Lattice Research Articles

Pressure drop measurements over anisotropic porous substrates in channel flow

Previous theoretical and simulation results indicate that anisotropic porous materials have the potential to reduce turbulent skin friction in wall-bounded flows. This study experimentally investigates the influence of anisotropy on the drag response of porous substrates. A family of anisotropic periodic lattices was manufactured using 3D printing. Rod spacing in different directions was varied systematically to achieve different ratios of streamwise, wall-normal, and spanwise bulk permeabilities (κxx\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa _{xx}$$\\end{document}, κyy\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa _{yy}$$\\end{document}, and κzz\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa _{zz}$$\\end{document}). The 3D printed materials were flush-mounted in a benchtop water channel. Pressure drop measurements were taken in the fully developed region of the flow to systematically characterize drag for materials with anisotropy ratios κxxκyy∈[0.035,28.6]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{\\kappa _{xx}}{\\kappa _{yy}} \\in [0.035,28.6]$$\\end{document}. Results show that all materials lead to an increase in drag compared to the reference smooth wall case over the range of bulk Reynolds numbers tested (Reb∈[500,4000]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Re}_b \\in [500,4000]$$\\end{document}). However, the relative increase in drag is lower for streamwise-preferential materials. We estimate that the wall-normal permeability for all tested cases exceeded the threshold identified in previous literature (κyy+>0.4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{\\kappa _{yy}}^+> 0.4$$\\end{document}) for the emergence of energetic spanwise rollers similar to Kelvin–Helmholtz vortices, which can increase drag. The results also indicate that porous walls exhibit a departure from laminar behavior at different values for bulk Reynolds numbers depending on the geometry.Graphical abstract

Cleaning of laser-induced periodic surface structures on copper by gentle wet chemical processing

Laser-induced periodic surface structures (LIPSS) attract considerable attention due to the manifold applications enabled by these self-organised structures ranging from optical colouring to bio-mimicking or wetting effects. The mechanism of LIPSS-formation at metal surfaces includes laser-ablation processes that results in phase transitions, explosive material removal and partial redeposition of the ablation products in the form of nanoscopic debris or even sub-micrometre-sized spherical particles in case of melt ejection. For some applications, these particulates, debris, and microscopic features on top of the periodic surface structures are disadvantageous. We studied wet-chemical cleaning approaches to remove redeposited material from LIPSS to enhance their applicability. LIPSS on copper with a lateral periodicity of ∼ 365 nm, that were fabricated by ultrashort pulse laser exposure(λ: 515 nm, tp: 260 fs), were cleaned with different liquids ranging from solvents to microemulsions. The surface morphologies were characterised by scanning electron microscopy (SEM), atomic force microscopy (AFM) and transmission electron microscopy(TEM) to study the surface topography, the size and density of surface particulates as well as other surface contaminations before and after wet cleaning. The LIPSS surface composition was analysed by X-ray photoelectron spectroscopy (XPS), Raman spectroscopy and Energy-dispersive x-ray spectroscopy (EDX) at the FIB-cross sections. The different cleaning approaches are classified with respect to their capability to remove particles and contaminations as well as to their influence on the morphology and shape of LIPSS pattern, whereby substantial differences are found. At least two wet-chemical solutions enable the removal of nanoparticles with only minor modification of the LIPSS topography. The main effect of wet cleaning is the detachment of particulates including sub-micrometre-sized spheres due to a gentle and selective etching of the interface region between the LIPSS and the redeposited material that comprise of modified copper and copper oxides.

Femtosecond trimer quench in the unconventional charge-density-wave material 1T′−TaTe2

Ultrafast optical switching of materials properties promises future technological applications, enabled by fundamental insights about microscopic couplings and nonequilibrium phenomena. Transition-metal dichalcogenides (TMDCs) combine photosensitivity with strong correlations, furthering rich phase diagrams and enhanced tunability. The compound 1T′−TaTe2 exhibits an electronically and structurally unique set of charge density waves (CDWs), featuring an unusual increase in conductivity and amplitude modes of low prominence. Compared to other charge-ordered TMDCs, only very few studies addressed the ultrafast response of this material to optical excitation. In particular, the question whether such unconventional properties translate to unusual quench dynamics remains largely unresolved. Here, we investigate the structural dynamics in 1T′−TaTe2 by means of ultrafast nanobeam electron diffraction at an unprecedented repetition rate of 2MHz. We reveal a strongly directional cooperative atomic motion during the one-dimensional quench of the low-temperature trimer lattice. These dynamics are completed within less than 500fs, substantially faster than reported previously. In striking contrast, the periodic lattice distortion of the room-temperature phase is unusually robust against high-density electronic excitation. In conjunction with the known sensitivity of 1T′−TaTe2 to chemical doping, we thus expect the material to serve as a versatile platform for tunable structural control by optical stimuli. Published by the American Physical Society 2024

Effect of residual stress on mechanical properties of Triply periodic minimal surface lattice structures in Additive manufacturing

Due to its special porous structure with smooth continuous surface and high specific surface area, the triply periodic minimal surface (TPMS) lattice structure exhibits excellent properties such as strong bearing capacity, high energy absorption rate and good fatigue performance. The residual stresses generated during the additive manufacturing (AM) process can have a significant impact on the mechanical properties of the TPMS structure. In this paper, the AM process of four typical TPMS structures are investigated by the thermal–mechanical coupling model. The mechanism of residual stress generation is analyzed, and an optimized preparation process scheme is proposed to reduce the residual stress. Furthermore, the effects of residual stresses on the mechanical properties of TPMS structures are investigated for different types, volume fractions and compression directions. Results show that the influences of scanning speed and hatch spacing on the residual stress are not significant with constant laser power, but the deposition thickness should be adjusted according to the characteristics of the structure. The residual stress will reduce the elastic modulus and yield strength, while no obvious effect on the plastic behavior is observed. Importantly, the residual stress has the greatest influence on the mechanical properties of I-WP-type among the four investigated types, which becomes more pronounced with the increase of volume fraction. Moreover, the influence of residual stress on the mechanical properties of TPMS structures depends on the compression direction. Our results give a comprehensive understanding of the residual stress distribution and impact on the mechanical properties of TPMS structures, providing guidance to the rational design and optimization of TPMS structures in engineering applications.

Comparative analysis of double and single porosity effects on SH-wave induced vibrations in periodic porous lattices

The manuscript presents a novel study comparing the impact of single and double porosity on horizontally polarized shear wave (SH-wave) propagation in corrugated elastic void materials. The considered mathematical model comprises two cases; the first one depicts SH-wave propagation through a void porous layer having creased boundaries and resting over a heterogeneous anisotropic fluid-saturated fractured porous half-space, whereas according to the second case, heterogeneous anisotropic fluid-saturated porous semi-infinite medium without fractures has been considered. In both cases, rigidity and density of the half-space vary quadratically with depth. The separable variable method is used to attain the complex frequency equation for each case that leads to two different dispersion relations associated with two distinct wave fronts. The first wave front depends on the void parameters, whereas the second wave front defines the propagation of SH-waves in an elastic layer without void pores. In each case, the complex dispersion relation has been separated into two equations that illustrate the dispersion and attenuation properties of SH-waves. Using the variations in the inhomogeneity, position, fluctuation, flatness, total porosity, and anisotropy parameters, case I and case II have been compared in each graphical execution. In addition, the surface response of shear stress and displacement have been implemented graphically.

Fabrication of Inconel 718 composites reinforced with TiCN via laser powder bed fusion: Integration of triply periodic minimal surface lattice structures

The integration of TiCN particles into superalloy composites for laser powder bed fusion (LPBF) and the construction of Triply Periodic Minimal Surface (TPMS) lattice structures have been understudied. This research systematically examines the microstructure and mechanical properties of LPBF-processed 10 vol% micron sized TiCN particle reinforced Inconel 718 (IN718) composites. The compressive behavior of the resultant TPMS lattice structures, derived from the TiCN-IN718 composite, was scrutinized through a combination of experimental testing and Finite Element (FE) simulation. The micro-sized TiCN reinforcement is demonstrated to notably augment the hardness, tensile strength, and wear resistance of the LPBFed TiCN-IN718 composite. Furthermore, the application of homogenization-solution-aging (HSA) heat treatment is shown to provide additional enhancements to the composite's mechanical behavior. Both the TiCN reinforcement and the HSA heat treatment are identified as pivotal factors influencing the compressive response of the TPMS lattice structures. Experimental findings indicate that the HSA-treated D-structure attains the highest compressive strength, reaching 122 MPa, outperforming both the G- and P-structures. During quasi-static compression testing, the D- and G-structures undergo a layer-by-layer collapse, while the P-structure exhibits tilt shear band behavior. The congruence between FE simulation results and experimental data substantiates the simulation's reliability and its capacity to accurately evaluate the mechanical behavior of TPMS lattice structures.

Optimal design and performance evaluation of grinding wheels with triply periodic minimal surface lattice structure

High-performance grinding wheels are critical tools for precision surface generation. In precision grinding processes, the coolant supply at the wheel-workpiece interface is critical for reducing grinding temperature and detrimental friction. For better lubrication and chip removal performance, the cavities or pores need to be generated throughout the grinding wheel. The ideal morphology of pores in grinding wheels should be inter-connected and capable of providing sufficient coolant. Conventional grinding wheel design and fabrication methods can only passively generate closed circular pores by using pore-forming agents. Increasing the percentage of pores in this way generally leads to an uncontrollable reduction in mechanical strength, while the closed pores are insufficient in cooling performance. In this paper, the grinding wheels with triply periodic minimal surface lattice structure are designed and fabricated, which achieves the regulable and inter-connected internal structure of grinding wheels. Meanwhile, to balance the relationship between the structural properties and performance indicators of porous grinding wheels, an optimal design method for the porous structure of grinding wheels is proposed. Finally, the grinding performance of the novel grinding wheels in comparison to electroplated diamond grinding wheels is investigated in terms of grinding force, specific grinding energy and ground surface roughness.

High-transmission dual-tunable structural color based on an all-dielectric medium

In this paper, we propose a three-layer all-dielectric structure capable of dynamic tunability by varying the lattice period and incident angle, thereby facilitating the production of high-quality colors. By integrating three dielectric layers with outer rings and inner cylinders, we effectively suppress multimodal spectra, leading to significantly improved transmission rates for the CMY primary colors. The high transmission efficiency for magenta reaches 96 %, yellow reaches 89 %, and cyan attains an outstanding 99 %. The materials utilized in this design possess characteristics conducive to practical fabrication, thereby offering extensive possibilities for practical applications. Furthermore, our findings provide new insights and potential avenues for future research and applications of structural colors in all-dielectric materials.

Structural Analysis of Periodic Trusses and Lattice Materials: States of Self-Stress, Mechanisms, and Mechanical Properties

Abstract In the realm of low relative density, a rigid-jointed lattice material exhibits a mechanical response analogous to that of a pin-jointed periodic truss with an identical micro-architecture. This correspondence simplifies the evaluation of the lattice's structural performance. While established matrix methods in linear algebra are capable of determining the states of self-stress, infinitesimal mechanisms, and mechanical properties of pin-jointed periodic trusses, they lack a systematic approach to deriving closed-form expressions for these properties. This paper presents a straightforward approach to address this gap. Furthermore, we introduce an inventive finite element framework that directly yields self-stress states and infinitesimal mechanisms in periodic trusses subjected to specific uniform macroscopic loading conditions. This framework allows for the determination of mechanical properties for periodic trusses by solving straightforward boundary value problems, such as uniaxial tension/compression or simple shear. The developed finite element framework offers greater simplicity compared to the matrix methods, with its benefits becoming more pronounced for complex micro-architectures. To demonstrate the effectiveness of the two newly developed methods, we conduct structural analyses on five different lattice materials, achieving successful outcomes.

A social monitoring mechanism for third-party judges promotes cooperation in evolutionary games

Corruption of third-party judges seriously undermines the level of cooperation. Without intervention, more corruptors and defectors would emerge, disrupting social harmony. Therefore, introducing an anti-corruption mechanism is crucial for the evolution of cooperation. In this paper, we propose a social monitoring mechanism to monitor third-party judges so that their payoffs are affected by the proportions of cooperators. Monte Carlo simulations on periodic boundary lattices. The results show that the social monitoring mechanism is effective in promoting cooperation and inhibiting corruption, and enhances the effectiveness of zealots in promoting cooperation. This facilitation effect is not only manifested in the Prisoner's Dilemma Game but also in the Snowdrift Game, which confirms the robustness of the results. Our research provides new insights for solving social dilemmas and curbing corruption.

Dispersion Analysis of Plane Wave Propagation in Lattice-Based Mechanical Metamaterial for Vibration Suppression

Phononic crystals based on lattice structures provide important wave dispersion characteristics as band structures, showing excellent compatibility with additive manufacturing. Although the lattice structures have shown the potential for vibration suppression, a design guideline to control the frequency range of the bandgap has not been well established. This paper studies the dispersion characteristics of plane wave propagation in lattice-based mechanical metamaterials to realize effective vibration suppression for potential aerospace applications. Triangular and hexagonal periodic lattice structures are mainly studied in this paper. The influence of different geometric parameters on the bandgap characteristics is investigated. A finite element approach with Floquet–Bloch’s principles is implemented to effectively evaluate the dispersion characteristics of waves in lattice structures, which is validated numerically and experimentally with a 3D-printed lattice plate. Based on numerical studies with the developed analysis framework, the influences of the geometric parameters of lattice plate structures on dispersion characteristics can mainly be categorized into three patterns: change in specific branches related to in-plane or out-of-plane vibrations, upward/downward shift in frequency range, and drastic change in dispersion characteristics. The results obtained from the study provide insight into the design of band structures to realize vibration suppression at specific frequencies for engineering applications.

Statistical description of interacting multistream quantum systems

In this research, the electrostatically coupled multistream quasiparticle excitations are studied in the framework of the Wigner distribution function. It is remarked that the Wigner distribution of coupled multistream collective quantum excitations satisfies a simple Liouville-like evolution equation from which a generalized distribution function for multistream quasiparticle excitations is deduced. The phase-space structure of collective quantum excitations in counter-stream electron and two-stream electron–positron gas with their evolution is calculated and electron/positron hole formation due to the onset of quantum stream instability is studied in connection with the energy band structure of the multistream quantum system, for the first time. The quantum stream instabilities in symmetric and asymmetric stream systems are studied and compared. It is found that the presence of opposite-charge streams leads to overall stability due to lowering the interaction potential effect. The generalized Wigner theory is also applied to study the electron transport in a one-dimensional periodic lattice using the concept of virtual streams. Current generalized statistical formalism may be used to model different quantum phenomena in the linear excitations limit with collective electrostatic interactions. The applications extend to the stream instability in quantum charge transport in metals, semiconductors, plasmonic devices, phase-space structure of charge carriers in periodic lattices interacting with the external potential of arbitrary shape and the dynamic evolution of dense electron–positron jets in active galactic nuclei or within the extremely dense astrophysical objects.

Hierarchical triply periodic minimal surface shell lattices with superior isotropic elasticity: Design guidelines, fabrication, and validation

Hierarchical triply periodic minimal surface (TPMS) shell lattices exhibit a wide range of tailorable properties that can be fine-tuned by lattice design. Recent advances in additive manufacturing towards high resolution enable the precise fabrication of hierarchical TPMS lattices. However, the isotropic behavior of hierarchical TPMS lattices has received little attention. In this study, we focus on the design of hierarchical TPMS lattices to explore their superior isotropic elasticity. By considering three unique geometric parameters of hierarchical TPMS: cell length ratio, relative density, and order number, multiple representative isotropic hierarchical TPMS lattices can be achieved at the same given relative density, which significantly expands its design space. The resultant lattices retain a minimal mid-surface and exhibit a large range of tailorable stiffness. To validate their isotropic elasticity, high-precision laser powder bed fusion was adopted to fabricate representative isotropic lattices and their anisotropic counterparts. Morphology observation and micro-CT scan show that the fabricated samples are dense, and their geometries are highly consistent with the designed models. Quasi-static compression tests further confirm the isotropic elasticity in the new designs. Moreover, a prediction rule was proposed to assess whether an isotropic hierarchical TPMS lattice can be obtained from two selected single-level lattices, which significantly enhances the design efficiency. As a result, the design method and principles can be summarized in this study to provide effective design guidelines to swiftly create hierarchical shell lattices with superior isotropic elasticity.

Bound impurities in a one-dimensional Bose lattice gas: Low-energy properties and quench-induced dynamics

We study two mobile bosonic impurities immersed in a one-dimensional optical lattice and interacting with a bosonic bath. We employ the exact diagonalization method for small periodic lattices to study stationary properties and dynamics. We consider the branch of repulsive interactions that induce the formation of bound impurities, akin to the bipolaron problem. A comprehensive study of ground-state and low-energy properties is presented, including an examination of the interaction strengths which induce the formation of a bound dimer of impurities. We also study the dynamics induced after an interaction quench to examine the stability of the bound dimers. We reveal that after large interaction quenches from strong to weak interactions the system can show large oscillations over time with revivals of the dimer states. We find that the oscillations are driven by selected eigenstates with phase-separated configurations.

Thin film resonant metasurface absorbers using patch-based arrays on liquid crystal polymer substrates for centimeter-wave applications

This paper reports the design and development of thin-film resonant absorbers for narrowband and multiband operation in the frequency regions centered at 10 GHz. The structure of the resonant metasurface absorber (RMA) is based on a liquid crystal polymer (LCP) thin-film spacer with a copper patch array on the front surface and un-patterned copper film on the back surface of the LCP film. The design and simulation works were carried out using full-wave analysis of the RMA characteristics. The copper-based periodic patch array acts as a metasurface. The perfect RMA for a given LCP film thickness can be obtained through impedance optimization by adjustment of the dimensions of the lattice periods. The electric and magnetic field distributions were studied. The resonant film absorber based on a 100 μm thick LCP film has an electrical thickness of λ/300 at 10 GHz. The experimental work was conducted using a narrowband RMA prototype consisting of 11×11 cells. The measured result of the resonant absorption is at 10.1 GHz, which is in close agreement with the design frequency of 10 GHz. For multiband functionality, double- and quad-band film resonant absorbers have been designed based on a coplanar supercell utilizing the superposition of the resonance effect. The LCP film-based absorbers have the potential to be used in EM shielding and sensing applications in centimeter-wave applications.

Chemically Nanostructured Organogel Monoliths from Cross-Linked Block Copolymers for Selective Infusion Templating.

Soft gels with spatially defined mesoscale distributions of chemical activity that guide and accelerate reactions by chemical nanoconfinement are found ubiquitously in nature but are rare in artificial systems. In this study, we introduce chemically nanostructured bulk organogels with periodically ordered morphologies from self-assembled block copolymer monoliths with a single selectively cross-linked block (xBCP). Ordered bulk organogels are fabricated with various distinct morphologies including hexagonally packed cylinders and two gyroidal three-dimensionally periodic network structures that exhibit macroscopic and nanoscopic structural integrity upon swelling. Small-angle X-ray scattering and transmission electron microscopy confirm that the periodic arrangement of the chemically distinct blocks in the self-assembled xBCP is retained at polymer fractions as low as 15 vol %. Our results reveal that the swelling equilibrium is not exclusively determined by the cross-linked block despite its structural role but is strongly influenced by the weighted interactions between solvent and the individual nanophases, including the non-cross-linked blocks. Therefore, substantial swelling can be obtained even for solvents that the cross-linked block itself has unfavorable interactions with. Since these ordered organogels present a class of solvent-laden bulk materials that exhibit chemically distinct nanoenvironments on a periodic mesoscale lattice, we demonstrate their use for selective infusion templating (SIT) in a proof-of-concept nanoconfined synthesis of poly(acrylonitrile) from which a monolithic ordered gyroidal mesoporous carbon is obtained. Going forward, we envision using xBCP gels and SIT to enable the fabrication of traditionally hard-to-template materials as periodically nanostructured monoliths due to the extensive tunability in their physicochemical parameter space.

Transmetalation in Surface-Confined Single-Layer Organometallic Networks with Alkynyl-Metal-Alkynyl Linkages.

Transmetalation represents an appealing strategy toward fabricating and tuning functional metal-organic polymers and frameworks for diverse applications. In particular, building two-dimensional metal-organic and organometallic networks affords versatile nanoarchitectures of potential interest for nanodevices and quantum technology. The controlled replacement of embedded metal centers holds promise for exploring versatile material varieties by serial modification and different functionalization. Herein, we introduce a protocol for the modification of a single-layer carbon-metal-based organometallic network via transmetalation. By integrating external Cu atoms into the alkynyl-Ag organometallic network constructed with 1,3,5-triethynylbenzene precursors, we successfully realized in situ its highly regular alkynyl-Cu counterpart on the Ag(111) surface. While maintaining a similar lattice periodicity and pore morphology to the original alkynyl-Ag sheet, the Cu-based network exhibits increased thermal stability, guaranteeing improved robustness for practical implementation.

Interfacial Charge-Transfer Excitonic Insulator in a Two-Dimensional Organic-Inorganic Superlattice.

Excitonic insulators are long-sought-after quantum materials predicted to spontaneously open a gap by the Bose condensation of bound electron-hole pairs, namely, excitons, in their ground state. Since the theoretical conjecture, extensive efforts have been devoted to pursuing excitonic insulator platforms for exploring macroscopic quantum phenomena in real materials. Reliable evidence of excitonic character has been obtained in layered chalcogenides as promising candidates. However, owing to the interference of intrinsic lattice instabilities, it is still debatable whether those features, such as the charge density wave and gap opening, are primarily driven by the excitonic effect or by the lattice transition. Herein, we develop an intercalation chemistry strategy for obtaining a novel charge-transfer excitonic insulator in organic-inorganic superlattice interfaces that serves as an ideal platform to decouple the excitonic effect from the lattice effect. In this system, we observe a narrow excitonic gap, formation of a charge density wave without periodic lattice distortion, and metal-insulator transition, providing visualized evidence of exciton condensation occurring in thermal equilibrium. Our findings identify self-assembly intercalation chemistry as a new strategy for developing novel excitonic insulators.

Nonlinear wave propagation in homogenized strain gradient 1D and 2D lattice materials: Applications to hexagonal and triangular networks

AbstractThis work aims to analyze the propagation of fully nonlinear waves, encompassing shear, extension, and bending deformation modes, within homogenized periodic nonlinear hexagonal and triangular networks, successively considering 1D and 2D situations. The wave analysis is conducted from the expression of the effective strain energy density of periodic hexagonal and triangular lattices in the nonlinear regime by a continualization of the discrete lattice equations, considering all forms of energy. We incorporate strain gradient effects into the continuous model to account for the wave‐dispersive nature. The resulting second‐gradient nonlinear continuum exhibits subsonic and supersonic propagation modes. We first examine in a 1D situation the dynamical response of the hexagonal and triangular lattices, considering varying levels of nonlinearity quantified by a single scalar valued parameter. We further evaluate the impact of a fully nonlinear analysis compared to an analysis solely based on the shear energy, regarding both supersonic and subsonic modes. The nonlinear wave propagation analysis is then extended to a 2D situation for the same two lattices. It is shown that the longitudinal mode exhibits a higher frequency at a low degree of nonlinearity; however, as the degree of nonlinearity increases, the shear mode surpasses the longitudinal mode in terms of frequency. As the wavenumber increases, the nonlinearity has a lesser impact on the frequency behavior, and the phase velocity is more influenced by other factors, such as the second gradient contributions of the effective constitutive law. Such a behavior indicates a transition from a highly nonlinear behavior at lower wave numbers to a more linear behavior at higher wave numbers.

Cu Regulating the Bifunctional Activity of Co-O Sites for the High-Performance Rechargeable Zinc-Air Battery.

The rational design of cost-effective and highly active electrocatalysts becomes the crucial energy storage technology to boost the kinetics of the oxygen reduction reaction (ORR) and the oxygen evolution reaction (OER), which hinders the large-scale application of metal-air batteries under the situation of increasingly pressing energy anxiety. Herein, the Co-based ZIF introduced the moderate amount of Cu2+-derived Cu/Co metal nanoparticles (NPs) embedded in carbon frameworks after high-temperature calcination. The Co-O bond on the surface of Co nanoparticles is modulated by adjacent Cu nanoparticles with the surface Cu-O bonds. The resulted increase of the Co2+/Co3+ ratio in 0.1CuCo-NC enhances the ORR/OER bifunctional catalytic kinetics along with the ΔE of 0.639 V. In situ Raman spectra of the catalyst on the three-electrode system as well as in the driven zinc-air battery (ZAB) show that the Co-O active sites regulated by Cu nanoparticles with Cu-O bonds maintain a periodic lattice expansion and compression during discharging and charging. The zinc-air battery based on 0.1CuCo-NC has a peak power density of up to 198.3 mW cm-2, a mass-specific capacity of 798.2 mAh g-1, and a cycling stability of 923 h at room temperature. This work makes up the research gap of a Co-based metal-organic framework (MOF)-derived catalyst regulated by a transition metal.