Periodic Lattice Research Articles

Angle-Resolved Lattice Population Density Plots: A Novel Approach for Fast 2D Unit Cell Determination from HAADF STEM Images

This study presents a new efficient method for determining the 2D unit cell size from HAADF STEM images using angle-resolved lattice population density (ALPD) plots. The approach uses the maxima in these plots, which represent the lines with the highest atom peak density, to determine the cell angle of the primitive 2D unit cell. Lattice types and 2D unit cell sizes that comply with crystallographic standards can easily be obtained by introducing angle constraints for the selection of the ALPD maxima. The method is very flexible and can be applied to images with fewer than 20 atom peaks, making it valuable for the automated analysis of periodic lattices in both large and small crystalline regions. The method has been evaluated for ideal and disordered lattices and is compared in terms of processing speed and the quality of results with the recently proposed real-space motif extraction method and with the well-established Fourier-based crystallographic image processing method commonly used for this task.

On quantifying dynamic behavior of architected metal/polymer TPMS/lattices-based interpenetrating phase composites.

This article presents the numerical analysis of architected metal/polymer-based interpenetrating phase composites (IPCs) to study their effective mechanical properties and dynamic behavior using finite element (FE) simulation. In this, we considered four types of Triply periodic minimal surfaces (TPMS) and lattice architectures, including gyroid, primitive, cubic, and octet, to form architected IPCs. The aluminum alloy is used for the TPMS/lattice reinforcing phase, and epoxy as a reinforced phase. The periodic boundary conditions were applied using FE analysis to compute the effective properties, while these properties were utilized to investigate the dynamic analysis of composite structures considering free vibration, wherein actual and homogenized models are compared. Our results reveal that the effective properties of IPCs increase with respect to the volume fraction of respective architectures in conjunction with enhanced natural frequency and less deformation. Moreover, we conducted a comparative study between these newly architected metal/polymer IPCs and conventional composites.

Hyperuniformity in mass transport processes with center-of-mass conservation: some exact results

Abstract We characterize the steady-state static and dynamic properties in a broad class of mass transport processes on a periodic hypercubic lattice of volume Ld , where both the mass and center-of-mass (CoM) remain conserved and the detailed balance is violated in the bulk; we specifically consider the models in the d = 1 and 2 dimensions. Using a microscopic approach, we exactly determine the decay (or growth) exponents for various dynamic and static correlation functions. We show that despite constrained dynamics due to CoM conservation (CoMC), the density relaxation is indeed diffusive. However, the fluctuation properties are strikingly different from those in diffusive systems with a single (mass) conservation law as dynamic and static fluctuations are more suppressed in systems with CoMC, resulting in an extreme (‘class-I’) hyperuniformity in certain cases. In the thermodynamic limit, the steady-state variance ⟨ Q 2 ( T ) ⟩ c of time-integrated bond current Q ( T ) across a bond in the time interval T exhibits the following long-time behavior: ⟨ Q 2 ( T ) ⟩ c ≃ A 1 T + A 2 + A 3 T − d / 2 . The exponents governing the small-frequency behavior of the power spectra S J ( f ) ≃ A 1 + Const . f ψ J for bond current are exactly determined as ψ J = 3 / 2 and 2 in d = 1 and 2 dimensions, respectively; the corresponding unequal-time current-current correlation function decay as t − 5 / 2 and t −3 as a function of time t in d = 1 and 2 dimensions, respectively. Remarkably, depending on the dimensions and microscopic details, the prefactor A 1 can vanish, causing the variance to eventually saturate, implying a class-I ‘dynamic hyperuniformity’. We also compute the static structure factor S(q), which varies as the square of the wave number q in the small-q limit, i.e. S ( q ) ∼ q 2 , implying a class-I spatial hyperuniformity.

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

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

Discrete Euler–Bernoulli beam lattices with beyond nearest connections

Abstract The propagation of elastic waves on discrete periodic Euler-Bernoulli mass-beam lattices is characterised by the competition between coupled translational and rotational degrees-of-freedom at the mass-beam junctions. We influence the dynamics of this system by coupling junctions with beyond-nearest-neighbour spatial connections, affording freedom over the locality of dispersion extrema in reciprocal space, facilitating the emergence of interesting dispersion relations. A generalised dispersion relation for an infinite monatomic mass-beam chain, with any integer order combination of non-local spatial connections, is presented. We demonstrate that competing power channels, between mass and rotational inertia, drive the position and existence of zero group velocity modes within the first Brillouin zone.

Acoustic lattice resonances and generalised Rayleigh–Bloch waves

The intrigue of waves on periodic lattices and gratings has resonated with physicists and mathematicians alike for decades. In-depth analysis has been devoted to the seemingly simplest array system: a one-dimensionally periodic lattice of two-dimensional scatterers embedded in a dispersionless medium governed by the Helmholtz equation. We investigate such a system and experimentally confirm the existence of a new class of generalised Rayleigh–Bloch waves that have been recently theorised to exist in classical wave regimes, without the need for resonant scatterers. Airborne acoustics serves as such a regime and we experimentally observe the first generalised Rayleigh–Bloch waves above the first cut-off, i.e., in the radiative regime. We consider radiative acoustic lattice resonances along a diffraction grating and connect them to generalised Rayleigh–Bloch waves by considering both short and long arrays of non-resonant 2D cylindrical Neumann scatterers embedded in air. On short arrays, we observe finite lattice resonances under continuous wave excitation, and on long arrays, we observe propagating Rayleigh–Bloch waves under pulsed excitation. We interpret their existence by considering multiple wave scattering theory and, in doing so, unify differing nomenclatures used to describe waves on infinite periodic and finite arrays and the interpretation of their dispersive properties.

Nonlinear Airy beam propagation in defected photonic lattices.

This work theoretically investigates the interplay of nonlinear Airy beams (AB) propagation and optically induced waveguide arrays in a photorefractive (PR) crystal. By introducing defect guides within the photonic lattice, we control the trajectory and self-bending properties and mostly the complex photoinduced waveguiding structures of these unconventional beams. Positive defects within the lattice induce the formation of solitary-like waves, while negative defects result in strong repulsion effects. In the nonlinear regime, these phenomena are further enhanced, with higher solitonic wave intensity in the case of a positive defect. Our simulations further demonstrate that at a lattice period of 20 µm, a specific defect guide modulation depth, and proper nonlinearity strength, a single laser beam injected in a negatively defected waveguide splits into up to seven distinct output channels. By judiciously adjusting the parameters, we can generate output channels that are spatially separated by up to 19 times the beam waist, thereby offering precise control over both the position and intensity of the output channels.

Atomic-Scale Tracking of Topological Defect Motion and Incommensurate Charge Order Melting

Charge order pervades the phase diagrams of quantum materials where it competes with superconducting and magnetic phases, hosts electronic phase transitions and topological defects, and couples to the lattice generating intricate structural distortions. Incommensurate charge order is readily stabilized in manganese oxides, where it is associated with anomalous electronic and magnetic properties, but its nanoscale structural inhomogeneity complicates precise characterization and understanding of its relationship with competing phases. Leveraging atomic-resolution variable-temperature cryogenic scanning transmission electron microscopy, we characterize the thermal evolution of charge order as it transforms from its ground state in a model manganite system. We find that mobile networks of discommensurations and dislocations generate phase inhomogeneity and induce global incommensurability in an otherwise lattice-locked modulation. Driving the order to melt at high temperatures, the discommensuration density grows, and regions of order locally decouple from the lattice periodicity. Published by the American Physical Society 2025

Direct Evidence of Anomalous Peierls Transition-Induced Charge Density Wave Order at Room Temperature in Metallic NaRu2O4.

In the field of quantum materials, understanding anomalous behavior under charge degrees of freedom through bond formation is of fundamental importance, with two key concepts: Dimerization and charge order at different cation sites. The coexistence of both dimerization and charge ordering is unusually found in NaRu2O4, even in its metallic state at room temperature. Our work unveils the origin of the interplay of these effects within metallic single-crystalline NaRu2O4. Employing advanced transmission electron microscopy techniques, we probe the lattice order of NaRu2O4 as a function of temperature and provide direct microscopic evidence of a Peierls-type transition. This transition is accompanied by a pronounced dimerization of the ruthenium chains, resulting in a distinctive twofold superstructure along the b axis below the critical transition temperature of ∼535 K, coinciding with a charge order. In situ heating experiments confirm the reversibility of this first-order phase transition, and periodic lattice displacement maps depict atomic-scale displacements linked to dimerization.

Triply periodic minimal surfaces for thermo-mechanical protection

Triply periodic minimal surface (TPMS) metamaterials show promise for thermal management systems but are challenging to integrate into existing packaging with strict mechanical requirements. Composite TPMS lattices may offer more control over thermal and mechanical properties through material and geometric tuning. Here, we fabricate copper-plated, 3D-printed triply periodic minimal surface primitive lattices and evaluate their suitability for battery thermal management systems. We measure the effects of lattice geometry and copper thickness on pressure drop, mechanical properties, and thermal conductivity. The lattices as internal filling structures in a multichannel cold plate exhibited pressure drops under 6.5 kPa at a 1 LPM flow rate. Pressure drop decreased when the number of channels (width of the cold plate) was increased. With a 0.43% copper volume loading, the lattice more than tripled in thermal conductivity but still retained a polymer-like compliance. A higher lattice relative density did not affect the thermal conductivity but caused a higher elastic modulus and compressive strength, and a stiffer cyclic loading response. The lattice design demonstrates that the structural parameters that control pressure drop, mechanical, and thermal conductivity can be decoupled, which can be used to achieve a wide range of disparate properties in complex multiphysics systems.

Effect of Elementary Unit Configurations on the Mechanical Performance of Periodic Lattice Structures to Architect Porous Scaffolds by FEM-Driven Additive Manufacturing

Effect of Elementary Unit Configurations on the Mechanical Performance of Periodic Lattice Structures to Architect Porous Scaffolds by FEM-Driven Additive Manufacturing

Multiphoton and Harmonic Imaging of Microarchitected Materials.

Microadditive manufacturing has revolutionized the production of complex, nano- to microscale components across various fields. This work investigates two-photon (2P) and three-photon (3P) fluorescence imaging, as well as third-harmonic generation (THG) microscopy, to examine periodic microarchitected lattice structures fabricated using multiphoton lithography (MPL). By immersing the structures in refractive index matching fluids, we demonstrate high-fidelity 3D reconstructions of both fluorescent structures using 2P and 3P microscopy as well as low-fluorescence structures using THG microscopy. These results show that multiphoton fluorescence (MPF) imaging offers reduced signal decay with respect to depth compared to single-photon techniques in the examined structures. We further demonstrate the ability to nondestructively identify intentional internal modifications of the structure that are not immediately visible with scanning electron microscope (SEM) images and compression-induced fractures, highlighting the potential of these techniques for quality control and defect detection in microadditively manufactured components.

Mechanisms of interlayer friction in low-dimensional homogeneous thin-wall shell structures and its strain effect.

Due to the multi-factor coupling effect, the rule of interlayer friction in low-dimensional homogeneous thin-wall shell structures is still unclear. Double walled carbon nanotubes (DWCNTs) having a typical low-dimensional homogeneous thin-wall shell structure are selected for this study. The interlayer friction of numerous chiral DWCNTs is investigated using molecular dynamics simulations to systematically analyze and understand the coupling mechanisms of various factors in interlayer friction. To eliminate the influence of the edge effect, a high-speed pure rotation model is used. The results demonstrate that DWCNTs with varying mismatch angle, interlayer distance, and interfacial radius exhibit distinct interlayer frictions and strain effects, due to the differences in interlayer interaction, atomic vibrational amplitudes, and lattice periods. Theoretical analysis is conducted on the interlayer friction and its strain effect based on the theoretical model. Based on phonon spectrum analysis, the vibrational modes and energy dissipation of DWCNTs with different chiral combinations under various strains are demonstrated. Based on the analysis, physical insight into the variation in friction forces is provided. The findings of this work deepen the understanding of the interlayer friction and strain mechanism and provide a theoretical basis for further exploitation of the strain effect to realize the regulation of nanoelectromechanical devices.

Mechanical responses of triply periodic minimal surface gyroid lattice structures fabricated by binder jetting additive manufacturing

Mechanical responses of triply periodic minimal surface gyroid lattice structures fabricated by binder jetting additive manufacturing

Localized strengthening of triply periodic minimal surface lattice structures via tuning the internal material distribution at the grain level

Localized strengthening of triply periodic minimal surface lattice structures via tuning the internal material distribution at the grain level

Topological Moiré Polaritons.

The combination of an in-plane honeycomb potential and of a photonic spin-orbit coupling (SOC) emulates a photonic or polaritonic analog of bilayer graphene. We show that modulating the SOC magnitude allows us to change the overall lattice periodicity, emulating any type of moiré-arranged bilayer graphene with unique all-optical access to the moiré band topology. We show that breaking the time-reversal symmetry by an effective exciton-polariton Zeeman splitting opens a large topological gap in the array of moiré flat bands. This gap contains one-way topological edge states whose constant group velocity makes an increasingly sharp contrast with the flattening moiré bands.

THE CRYSTAL STRUCTURE OF THE BASIC LAYERS OF CADMIUM TELLURIDE IN PLANAR ELEMENTS FOR PROTECTING MICROWAVE EQUIPMENT FROM ELECTROMAGNETIC PULSES

To create the physical basis of the industrial technology of planar protection elements, base layers of cadmium telluride, which were obtained by the method of thermal vacuum evaporation at different substrate temperatures on polycore plates with a molybdenum interlayer, were investigated using the X-ray diffractometric method. Temperature intervals corresponding to a qualitative change in the crystal structure of cadmium telluride films were determined. It is shown that the cadmium telluride films obtained at a substrate temperature that does not exceed 100°C contain only the hexagonal metastable phase, have a predominant orientation in the [002] direction, the level of microdeformation is 0.088 - 0.110, the size of the coherent scattering regions is 15.6 - 21.5 nm. The determined periods of the hexagonal crystal lattice a = 4.586 Å and c = 7.505 Å indicate the presence of significant tensile macrodeformations. An increase in the deposition temperature to 200°C leads to the appearance of a stable cubic phase oriented in the [111] direction along with the metastable hexagonal phase of cadmium telluride. At the same time, the orientation of the hexagonal phase in the [002] direction decreases from GH = 1.74 to GH = 1.45. The appearance of the cubic phase also leads to a decrease in microdeformations and the dimensions of the coherent scattering regions of the hexagonal phase to 0.029 - 0.043 nm and 12.1 - 15.8 nm, respectively. A further increase in the temperature of the substrate leads to the formation of cadmium telluride films in which there is only a stable cubic phase without a preferred orientation. At the same time, an increase in the temperature of the substrate to 300°C leads to a decrease in the macrodeformations of the cubic phase, which is evidenced by the approach of the period of the crystal lattice to the theoretical value: from a = 6.4870 Å to a = 6.4858 Å. Thus, it was experimentally shown that in order to ensure stable initial parameters of protection elements, the production of cadmium telluride films must be carried out at a substrate temperature of 300°C, as this prevents the presence of degradation processes due to the thermodynamically activated transformation of the metastable hexagonal phase into a stable cubic phase.

Nonconventional thermal states of interacting bosonic oligomers

There has recently been a growing effort to understand the physics and intricate dynamics of many-body and many-state (multimode) interacting bosonic systems in a comprehensive manner. For instance, in photonics, nonlinear multimode fibers are being intensely investigated nowadays due to their promise for ultrahigh-bandwidth and high-power capabilities. Similar prospects are being pursued in connection with magnon Bose-Einstein (BE) condensates, and ultracold atoms in periodic lattices for room-temperature quantum devices and quantum computation, respectively. While it is practically impossible to monitor the phase space of such complex systems (classically or quantum mechanically), thermodynamics has succeeded in predicting their thermal state: the Rayleigh-Jeans (RJ) distribution for classical fields and the BE distribution for quantum systems. These distributions are monotonic and promote either the ground state or the most excited mode. Here, we demonstrate the possibility to advance the participation of other modes in the thermal state of bosonic oligomers. The resulting nonmonotonic modal occupancies are described by a microcanonical treatment, while they deviate drastically from the RJ/BE predictions of canonical and grand-canonical ensembles. Our results provide a paradigm of ensemble equivalence violation and can be used for designing the shape of thermal states. Published by the American Physical Society 2024

Symmetry Breaking in Supramolecular Gel Condensation.

Supramolecular condensation during cooling cycles often transitions through multiple metastable phases before achieving a stable crystalline state. Metastability arises from various competing parameters like symmetrical arrangement, and supramolecular bonding and manifests at different temperatures. Symmetrical physical arrangements can minimize vibrational energy and stabilize the systems at higher temperatures. Further cooling promotes directional supramolecular bonding, such as charge-assisted hydrogen bonding, resulting in molecular periodicity within metastable structures. Frustration occurs when weaker van der Waals bonds form during further cooling, propagating perpendicularly to stronger one-dimensional charge-assisted hydrogen bonds and disrupting lateral periodicity in certain solvents. This makes parallel 1D fibers slidable, adding flexibility to the gel fiber. Eventually, some supramolecular systems attain thermodynamically stable crystalline states by perfectly arranging all the molecules. Throughout the process, metastability results from different symmetrical arrangements, and each rearrangement alters the supramolecular structure's symmetry, generating new physicochemical properties. Different supramolecular gels uniquely break symmetry, which can be monitored through various techniques. This perspective analyzes supramolecular thermoreversible, reverse thermal, liquid crystalline, thixotropic, and antisolvent-induced gels to illustrate spontaneous symmetry reduction processes. Reaching a suprasymmetry condensate can classify big data and be applied in unconventional analogue computing or data storage.

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.