Complex Lattice Research Articles

Evaluation of the roughness of lattice structures of AISI 316 stainless steel produced by laser powder bed fusion

The present work evaluates the surface roughness of lattice structures produced in AISI 316 stainless steel, with laser powder bed fusion (LPBF). To this end, five lattice types were evaluated, namely cubic (C), truncated octahedron (TO), truncated cubic (TC), rhombicuboctahedron (RCO) and rhombitruncated cuboctahedron (RTCO) to determine the average roughness Sa by profilometry. For comparison, the surface roughness of a bulk specimen was also measured. The average roughness was Sa=7.3 mm for the bulk specimen, for the C and TC arrangements it was around 11 mm, while for configurations RCO, RTCO and TO it was in the range 18-22 mm, meaning that surface roughness increases for more complex structures. Values of Sa around 10-25 mm are reported in the literature for parts fabricated by LPBF for medical implants. If complex lattice arrangements are required, a study of the printing parameters is relevant, to achieve scaffolds with improved biomechanical performance.

Spectroscopic, structural characterization, along with DFT calculation, of a new cadmium(II) acetato meso-arylporphyrin: Theoretical study on NO2, CO2, N2, NO2, and SO2 gas-sensing and analysis of electrical conductance and dielectric properties

The paper presents a combined experimental and computational investigation of the cadmium(II) (acetato)‑meso-tetra(para-methoxyphenyl)porphyrin ion complex [Cd(TMPP)(OAc)]- (complex 1), which was prepared by the reaction of [Cd(TMPP)] with an excess of NaOAc and crysptand-222 in chloroform. This new Cd(II) meso‑arylporphyrin was characterized by elementary analysis and UV–Vis, IR, and 1H NMR spectroscopic techniques along with single crystal X-ray diffraction. This later study shows that the Cd2+center ion adopts a distorted square pyramidal geometry and is coordinated by the four nitrogens of the TMPP porphyrinate and the oxygen atom of the acetato axial ligand. The intermolecular interactions in the crystal lattice of [Cd(TMPP)(OAc)]-, determined using the PLATON program and Hirshfeld surfaces analysis, are of types O__H…O, C__H…H, C__H…Cl, C__H…Cg and C__Cl…Cg (Cg is the centroid of a phenyl or a pyrrole ring) involving the [Cd(TMPP)(OAc)]- ion complex, the [Na(crypt-222)]+ counterion, and the chloroform and water molecules found in the crystal lattice of complex 1. Using DFT calculations at the DFT/B3LYP-D3/lanL2DZ level of theory HOMO–LUMO orbitals of 1 and several global reactive parameters of this compound were calculated. The 3D-MEP plots of [Cd(TMPP)(OAc)]- were also determined. This theoretical study includes the sensing properties of complex 1 and the NO2, CO2, N2, and SO2 gas molecules. Furthermore, experimental tests have been carried out concerning the impedance and dielectric spectroscopy of the InGa/[Cd(TMPP)(OAc)]/InGa device.

A hybrid continuum-beam optimisation model: the virtual extensometer method for efficient optimisation of lattice materials

AbstractAdditive manufacturing (AM) enables the fabrication of complex lattice structures that are infeasible with traditional manufacturing processes. These structures are typically implemented with constant cross-sectional strut elements; this strategy is expedient but leads to sub-optimal structural efficiency. Numerical continuum models allow robust mechanical modelling of complex lattice geometry but provide equally complex data fields that are ill-suited for traditional optimisation techniques. By contrast, numerical beam models represent the fundamental tensile and bending stress states but are incapable of capturing nuanced geometrical effects that lead to local stress concentrations. In this research, a hybrid continuum-beam method is proposed for the systematic optimisation of strut cross section: a representative unit cell is simulated by continuum elements, and the local strut stress tensor is acquired by embedded beam elements that act as virtual extensometers. By integrating a computationally inexpensive beam model into a more robust continuum model, the volume and the quality of data returned are significantly increased whilst being provided in a readily usable format for optimisation techniques, for a trivial increase in computational cost. The presented method is generalised and can be applied to any strut-based lattice structure. Body-centred cubic (BCC) and BCC with z-strut (BCCZ) lattice structures optimised by the proposed method are fabricated using laser-based powder bed fusion (LB-PBF) in AlSi10Mg and are mechanically evaluated. On average, performance for BCC lattice structures improves by 33% and 26% for relative yield strength and relative Young’s modulus respectively. BCCZ lattice structures saw a performance improvement of 25% and 19% for relative yield strength and relative Young’s modulus respectively, thus confirming superior performance at lower relative densities when compared to incumbent designs.

Supramolecular Control of Helicene Circularly Polarized Luminescence Emitters in Molecular Solids and Bright Nanoparticles.

Circularly polarized luminescence (CPL) from chiral molecules is attracting much attention due to its potential use in optical materials. However, formulation of CPL emitters as molecular solids typically deteriorates photophysical properties in the aggregated state leading to quenching and unpredictable changes in CPL behavior impeding materials development. To circumvent these shortcomings, a supramolecular approach can be used to isolate cationic dyes in a lattice of cyanostar-anion complexes that suppress aggregation-caused quenching and which we hypothesize can preserve the synthetically-crafted chiroptical properties. Herein, we verify that supramolecular assembly of small-molecule ionic isolation lattices (SMILES) allows translation of molecular ECD and CPL properties to solids. A series of cationic helicenes that display increasing chiroptical response is investigated. Crystal structures of three different packing motifs all show spatial isolation of dyes by the anion complexes. We observe the photophysical and chiroptical properties of all helicenes are seamlessly translated to water soluble nanoparticles by the SMILES method. Also, a DMQA helicene is used as FRET acceptor in SMILES nanoparticles of intensely absorbing rhodamine antennae to generate an 18-fold boost in CPL brightness. These features offer promise for reliably accessing bright materials with programmable CPL properties.

Determination of the discreteness correction in dislocation equations for sphalerite crystals

Abstract The discreteness correction for simple lattices has been determined, however, there is still no detailed and rigorous derivation of the discreteness correction for compound lattices due to the relatively complex structure (simple lattices have only one set per slip system, while complex lattices have at least two sets). A lattice dynamics model which takes into account the energy increments caused by changes in bond length and bond angle is constructed for sphalerite crystals and the relationships between discreteness parameters and elastic constants are determined for the slip system. Compared to glide set, the discreteness correction for shuffle set is much larger due to it is mainly contributed by the interactions between nearest neighbor atoms. Based on the results obtained from the model, the dislocations in ZnS crystal are investigated. The theoretical prediction result of Peierls stress for shuffle dislocation closely matches the experimental critical shear stress. It is inferred that the initial plastic deformation of ZnS is closely related to the movement of shuffle dislocations.

Multiple Interaction Forces Construct Two‐Dimensional Self‐assembly Kagome Lattices on Au(111)

Comprehensive SummaryKagome lattices have garnered significant attention due to their promising applications in catalysis, electronics, and magnetics. Although many efforts have been paid to the design and synthesis of Kagome lattices, there is a limited focus on constructing this lattice by multiple interaction forces. In this work, we employ 2,7‐dibromo‐carbazole as precursors to successfully fabricate the two‐dimensional self‐assembly Kagome lattices stabled by multiple interaction forces on Au(111) substrate. Using low‐temperature scanning tunneling microscopy, non‐contact atomic force microscopy and density functional theory calculation, we visualize and identify the four interaction forces within Kagome lattices: Au—N coordination bonds, Au—H hydrogen bonds, Br—Br halogen bonds, and Br—H hydrogen bonds, respectively. This study provides a basic understanding for designing and constructing more complex Kagome lattices.

Diversity Analysis of Fungi Distributed in Inhalable and Respirable Size Fractions of Aerosols: A Report from Kuwait

Fungi are an important part of the atmospheric ecosystem yet an underexplored group. Airborne pathogenic fungi are the root cause of hypersensitive and allergenic states highly prevalent in Kuwait. Frequent dust storms in the region carry them further into the urban areas, posing an occupational health hazard. The fungal population associated with the respirable (more than 2.5 µm) and inhalable (2.5 µm and less) fractions of aerosols is negligibly explored and warrants comprehensive profiling to pinpoint tAhe health implications. For the present investigation, aerosol was collected using a high-volume air sampler coupled with a six-stage cascade impactor (Tisch Environmental, Inc) at a rate of 566 L min−1. The samples were lysed, DNA was extracted, and the internal transcribed regions were sequenced through targeted amplicon sequencing. Aspergillus, Penicillium, Alternaria, Cladosporium, Fusarium, Gleotinia and Cryptococcus were recorded in all the size fractions with mean relative abundances (RA%) of 17.5%, 12.9%, 12.9%, 4.85%, 4.08%, 2.77%, and 2.51%, respectively. A weak community structure was associated with each size fraction (ANOSIM r2 = 0.11; p > 0.05). The Shannon and Simpson indices also varied among the respirable and inhalable aerosols. About 24 genera were significantly differentially abundant, as described through the Wilcoxon rank sum test (p < 0.05). The fungal microbiome existed as a complex lattice of networks exhibiting both positive and negative correlations and were involved in 428 functions. All the predominant genera were pathogenic, hence, their presence in inhalable fractions raises concerns and poses an occupational exposure risk to both human and non-human biota. Moreover, long-range transport of these fungi to urban locations is undesirable yet plausible.

An Exploration of the Phonon Frequency Spectrum and Born–von Karman Periodic Boundary Conditions in 1D and 2D Lattice Systems Using a Computational Approach

Periodic boundary conditions (PBCs) are a pivotal concept in the treatment of ideal lattices of infinite extent as a finite lattice. Most undergraduate texts that delve into the analytical treatment of lattice dynamics solve the problem in the reciprocal space with an implicit assumption of PBCs. While the traditional approach centered in the reciprocal or [Formula: see text]-space is elegant for simple one-dimensional lattice structures, the method becomes mathematically cumbersome for more complex lattices with real-world applications, such as a honeycomb lattice involving a [Formula: see text] secular determinant. In this work, we have explored the solution of lattice dynamics in direct space numerically, by constructing unit cells through an explicit implementation of Born–von Karman PBCs and solving the lattice dynamical equations in the displacement–time domain using the fourth-order Runge–Kutta algorithm. The Fast Fourier Transform technique is then used to obtain the phonon frequency spectrum corresponding to the computed instantaneous displacements. The fidelity of the model is validated by the agreement of the computational results obtained for the phonon spectrum at high symmetry points in the Brillouin zone with the analytical values for the given problem. Initially, the dynamics and the phonon spectrum are explored for monatomic and diatomic linear lattices which serve to act as introductory cases for the approach before investigating the 2D monatomic square and honeycomb lattices using the nearest and next-nearest neighbor approximations. A short-range force constant model employing the central forces and angular forces is used for the monatomic square lattice to account for the interatomic interactions. Our computational approach is expected to be physically more intuitive for a student for visualizing the periodicity of a given lattice and understanding its related dynamics. The approach demonstrates the usage of Born–von Karman PBCs in constructing a unit cell that effectively captures the dynamics of a lattice system, complementing the traditional secular determinant formalism. The work also illustrates an instance of how the computer programming can be used as a tool to empower the students to explore abstract concepts in physics. A honing of programming and computational skills of students enables them to interact with dynamic models in physics and gain deeper insight into the real-world applications of physics principles. Target group of this work is the students and educators at undergraduate level who seek a thorough and didactic comprehension of lattice dynamics.

Design study of a low emittance complex bend achromat lattice

Light sources worldwide have experienced rapid growth in the last decades, pushing toward higher brightness with lower emittance to meet growing demands from the user community. The quest for higher brightness motivates the development of low-emittance ring lattices. At this point, all fourth-generation storage ring light sources employ variations of the multibend achromat (MBA) lattice. In this paper, we discuss an extension of this approach, known as complex bend achromat lattice in relation to the future NSLS-II upgrade. A detailed approach for the lattice design will be described and the developed lattice will be presented. The advantages of using our complex bend approach are evident in reaching a natural emittance as low as 23 pm at a beam energy of 3 GeV, providing a straight section of 8.4 m for long insertion devices, and acquiring a ratio of about 50% of free space with respect to the ring circumference. The design includes the use of permanent magnets largely reducing the need for power supplies. Our new approach provides an extension to the MBA concept for the next-generation light source lattice design. Published by the American Physical Society 2024

Thermal, Microstructural, and Mechanical Analysis of Complex Lattice Structures Produced by Direct Energy Deposition.

Lattice structures have gained attention in engineering due to their lightweight properties. However, the complex geometry of lattice structures and the high melting temperature of metals present significant manufacturing challenges for the large-scale fabrication of these structures. Direct Energy Deposition (DED) methods, such as the Wire Arc Additive Manufacturing (WAAM) technique, appear to be an interesting solution for overcoming these limitations. This study provides a detailed analysis of the manufacturing process of carbon steel lattice structures with auxetic geometry. The study includes thermal analysis using infrared thermography, microstructural characterization through metallography, and mechanical evaluation via hardness and mechanical testing. The findings reveal the significant impact of heat input, thermal cycles, and deposition sequence on the morphology and mechanical properties of the lattice structures. Fast thermal cycles are related to areas with higher hardness values, smaller strut diameters, and porous formations, which shows that controlling heat input and heat dissipation is crucial for optimizing the properties of lattice structures produced using WAAM.

Unprecedented Richness of Temperature- and Pressure-Induced Polymorphism in 1D Lead Iodide Perovskite.

Inherent features of metal halide perovskites are their softness, complex lattice dynamics, and phase transitions spectacularly tuning their structures and properties. While the structural transformations are well described and classified in 3D perovskites, their 1D analogs are much less understood. Herein, both temperature- and pressure-dependent structural evolutions of a 1D AcaPbI3 perovskitoid incorporating acetamidinium (Aca) cation are examined. The study reveals the existence of nine phases of δ-AcaPbI3, which present the most diverse polymorphic collection among known perovskite materials. Interestingly, temperature- and pressure-triggered phase transitions in the 1D perovskotoid exhibit fundamentally different natures: the thermal transformations are mainly associated with the collective translations of rigid polyanionic units and ordering/disordering dynamics of Aca cations, while the compression primarily affects inorganic polymer chains. Moreover, in the 1-D chains featuring the face-sharing connection mode of the PbI6 octahedra the Pb···Pb distances are significantly shortened compared to the corner-sharing 3D perovskite frameworks, hence operating in the van der Waals territory. Strikingly, a good correlation is found between the Pb···Pb distances and the pressure evolution of the bandgap values in the δ-AcaPbI3, indicating that in 1D perovskitoid structures, the contacts between Pb2+ ions are one of the critical parameters determining their properties.

Engineering colloidal crystals molecule by molecule.

DNA particles are programmed to assemble with precision into complex lattices.

Inverse design of a pyrochlore lattice of DNA origami through model-driven experiments.

Sophisticated statistical mechanics approaches and human intuition have demonstrated the possibility of self-assembling complex lattices or finite-size constructs. However, attempts so far have mostly only been successful in silico and often fail in experiment because of unpredicted traps associated with kinetic slowing down (gelation, glass transition) and competing ordered structures. Theoretical predictions also face the difficulty of encoding the desired interparticle interaction potential with the experimentally available nano- and micrometer-sized particles. To overcome these issues, we combine SAT assembly (a patchy-particle interaction design algorithm based on constrained optimization) with coarse-grained simulations of DNA nanotechnology to experimentally realize trap-free self-assembly pathways. We use this approach to assemble a pyrochlore three-dimensional lattice, coveted for its promise in the construction of optical metamaterials, and characterize it with small-angle x-ray scattering and scanning electron microscopy visualization.

Design of multi-topology lattice structures based on a high-quality unit cell library

Truss lattice structures have gained significant interest due to their exceptional performance across various applications. However, the design of complex lattices often relies on simple unit cells with limited capabilities, making it challenging to fulfill stringent design requirements. This paper proposes a novel strategy for generating high-performance multi-topology truss lattice structures using a diverse unit cell library. The proposed method leverages a hierarchical approach for candidate unit cell generation. A simple first-level unit cell forms the base, followed by the introduction of complexity and improved properties through a second-level cell creation process. Efficient screening and rapid homogenization calculations were used to estimate the physical characteristics of the generated candidates. Subsequently, suitable unit cells are identified for inclusion in the library, ensuring high quality and minimizing redundancy. Based on the density distribution obtained from topology optimization, the selection function chooses the optimal unit cell from the library for each element within the lattice structure. Finally, strut size optimization further enhances the design. The resulting optimized lattice structures demonstrated superior performance compared to those constructed from standard unit cells and results from the existing literature. This approach offers a powerful new pathway for designing complex high-performance lattice structures.

Synthetic molecular switches driven by DNA-modifying enzymes

Taking inspiration from natural systems, in which molecular switches are ubiquitous in the biochemistry regulatory network, we aim to design and construct synthetic molecular switches driven by DNA-modifying enzymes, such as DNA polymerase and nicking endonuclease. The enzymatic treatments on our synthetic DNA constructs controllably switch ON or OFF the sticky end cohesion and in turn cascade to the structural association or disassociation. Here we showcase the concept in multiple DNA nanostructure systems with robust assembly/disassembly performance. The switch mechanisms are first illustrated in minimalist systems with a few DNA strands. Then the ON/OFF switches are realized in complex DNA lattice and origami systems with designated morphological changes responsive to the specific enzymatic treatments.

A Systematic Approach to Optimize Parameters in Manufacturing Complex Lattice Structures of NiTi Using Electron Beam Powder Bed Fusion Process

Herein, the quality and accuracy to manufacture delicate parts from NiTi powder using electron beam powder bed fusion (EB‐PBF) technology is investigated. Therefore, benchmarks with thin cylinders and thin walls are designed and fabricated using two distinct scan strategies of EB‐PBF manufacturing (i.e., continuous melting and spot melting) with different process parameter sets. After these optimizations, four different lattice structures (i.e., octahedron, cell gyroid, sheet gyroid, and channel) are manufactured and characterized. It is shown both continuous melting and spot melting modes are able to manufacture lattices with relative densities over 97%. And as‐built lattice structures exhibit an excellent pseudoelasticity up to 8% depending on the design of the structure, e.g., the channel structure shows more deformation recoverability than the cell gyroid. This is attributed to the integrity of geometry as well as compressive mode of the mechanical loading. Of course, the compressive strength and ultimate compressive strength also increase with the increasing volume fraction. Moreover, the spot melting can be used as an engineering tool to customize a delicate beam‐shaped structure with a superior pseudoelasticity.

DLP printed 3D gyroid structure: Mechanical response at meso and macro scale

Rapid prototyping (RP) technology enables the fabrication of complex geometries, making lattice structures increasingly popular. Lattice structures, known as cellular materials, have garnered significant attention over the past two decades due to their ability to optimise mass distribution in components. These structures excel in mechanical properties, catering to energy absorption (bending-dominated structures) and structural performance (stretch-dominated structures). In this paper, we investigate the behaviour of stretch-dominated lattice structures using periodic surface models, specifically focusing on sheet-based Gyroid cells, to allow for a more efficient macroscale modelling. We study cells and scaffolds of different sizes, considering various triply periodic minimal surface thicknesses and relative densities ranging from approximately 0.2 to 0.65. We explore load applications in directions different from the unit cell's principal axes and analyse the strain rate effect on both bulk and cellular material. The lattice structures are manufactured using epoxy resin and digital light processing (DLP) technology. In the range of relative density investigated, both in quasi-static and dynamic conditions, a linear trend is observed for Young's modulus and compression yield strength. To extend the quasi-static results to the dynamic regime, we employ a more generalized normalization technique. This approach divides Young's modulus and compression yield strength by the behaviour of the base material at a specific strain rate, facilitating the correlation of mechanical properties across the two loading regimes. Based on experimental findings, we implemented and calibrated a bi-linear material model for describing, in macroscale, triply periodic minimal surface (TPMS) Gyroid structures. The model coefficients are parameterized with respect to relative density. In addition, the presented material law was compared with that proposed by Gibson-Ashby. Furthermore, we evaluated the anisotropy of both the base material and the unit cell. The first one is done by testing the 3D printed samples in directions different from the printing one, the latter by using the Zener factor. The anisotropy evaluation confirmed the isotropic behaviour of the unit cell within the range of relative density and test conditions investigated. Finally, we perform linear elastic 3D macroscopic and mesoscopic model simulations for combined shear-compression tests using the implemented bi-linear material model and the anisotropic stiffness matrix (obtained through the homogeneous formulation) for the macroscale, and the base material for the mesoscopic one. The results demonstrate the suitability of the proposed equivalent material model for studying the TPMS Gyroid structure in the elastic regime, both in quasi-static and dynamic states. This allows for an efficient FE modelling process of complex lattice structures.

Atomically precise engineering of spin–orbit polarons in a kagome magnetic Weyl semimetal

Atomically precise defect engineering is essential to manipulate the properties of emerging topological quantum materials for practical quantum applications. However, this remains challenging due to the obstacles in modifying the typically complex crystal lattice with atomic precision. Here, we report the atomically precise engineering of the vacancy-localized spin–orbit polarons in a kagome magnetic Weyl semimetal Co3Sn2S2, using scanning tunneling microscope. We achieve the step-by-step repair of the selected vacancies, leading to the formation of artificial sulfur vacancies with elaborate geometry. We find that that the bound states localized around these vacancies undergo a symmetry dependent energy shift towards Fermi level with increasing vacancy size. As the vacancy size increases, the localized magnetic moments of spin–orbit polarons become tunable and eventually become itinerantly negative due to spin–orbit coupling in the kagome flat band. These findings provide a platform for engineering atomic quantum states in topological quantum materials at the atomic scale.

Mechanical Response of Gradient Lattice Structures Based on Topology Optimization

Lattice structure has the characteristics of lightweight, crashworthiness, and better energy absorption capabilities. With the advancement of additive manufacturing technologies, preparing complex lattice structures has become possible. In this study, some novel lattice structures are designed by topology optimization based on the inspiration of the triply periodic minimum surface lattice structures. The different volume fraction lattice structures are combined into four gradient lattice structures (GLSs): unidirectional GLS, bidirectional increasing GLS, bidirectional decreasing GLS, and none GLS (NOGLS). Subsequently, selective laser melting is employed to manufacture the designed lattice structures. Experiments and finite‐element simulation analysis are utilized to evaluate the mechanical performance and collapse patterns of lattice structures. In the results, it is shown that NOGLS has a higher modulus of elasticity and greater load‐bearing capacity for the same relative density. Furthermore, the energy‐absorbing properties of the dot‐matrix structure are significantly improved by a rational density design strategy. This work is valuable for improving the energy absorption performance of structures.

Pair correlations of logarithms of complex lattice points

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