Imperfect Lattice Research Articles

Mechanical characterization of lattice structures fabricated by selective laser melting via an image-based finite cell method with a damage model

Lattice structures fabricated by the selective laser melting (SLM) additive manufacturing process hold great potential for diverse applications. However, their actual mechanical behaviors often deviate from their counterparts with the as-designed geometries due to manufacturing defects. In this study, we presented an in-depth mechanical characterization of imperfect octet lattice structures via an image-based finite cell method (FCM) in combination with the multi-level hp refinement scheme for resolving the local defects and a Lemaitre damage model to conduct the damage analysis. Micro-computed tomography scanning was utilized to scan six SLM-fabricated octet lattice cells to obtain their as-built geometries. Based on the obtained geometry, the force-displacement curves and the damage distribution of the octet lattice cells and struts under given loads were predicted. The numerical results indicate that external defects significantly affect the struts' damage distribution, while internal voids have a lesser influence due to their low volume fraction. It is identified that the SLM-fabricated octet lattice cell presents better elastoplastic behavior along the loading direction perpendicular than parallel to its build direction. These insights into the mechanical performance of imperfect octet lattice cells underscore the defects' adverse effects and advance the understanding of their significance in SLM components.

3D Nanocrystallography and the Imperfect Molecular Lattice.

Crystallographic analysis relies on the scattering of quanta from arrays of atoms that populate a repeating lattice. While large crystals built of lattices that appear ideal are sought after by crystallographers, imperfections are the norm for molecular crystals. Additionally, advanced X-ray and electron diffraction techniques, used for crystallography, have opened the possibility of interrogating micro- and nanoscale crystals, with edges only millions or even thousands of molecules long. These crystals exist in a size regime that approximates the lower bounds for traditional models of crystal nonuniformity and imperfection. Accordingly, data generated by diffraction from both X-rays and electrons show increased complexity and are more challenging to conventionally model. New approaches in serial crystallography and spatially resolved electron diffraction mapping are changing this paradigm by better accounting for variability within and between crystals. The intersection of these methods presents an opportunity for a more comprehensive understanding of the structure and properties of nanocrystalline materials.

Self‐assembled monolayers for perovskite solar cells

AbstractIn metal‐halide perovskite solar cells (PSCs), various carrier recombination losses occur at the interface between metal oxides (MOs) and perovskite (PVK) due to the imperfect lattice structure of the crystal surface. Additionally, the nonoptimal energy levels of MOs and PVK, as well as ion diffusion and chemical corrosion between the two materials, severely hinder carrier transport at the interface. Therefore, there is an urgent need to introduce multifunctional materials between MOs and PVK to mitigate interface defects, carrier transport limitations, chemical corrosion, and other related issues. In recent years, self‐assembled monolayers (SAMs) have emerged as essential organic interfacial materials for effectively bridging MOs and PVK, playing a pivotal role in enhancing cells’ performance. Based on this, we provide a detailed overview of the origin and development of SAMs in PSCs and summarize the importance and potential of SAMs from various aspects, including their chemical structure, interface passivation, energy level tuning, and interface corrosion. We finally discuss the prospects of SAMs in terms of molecular structure, deposition methods, and their application in narrow‐band gap PSCs. With these insights, it is anticipated that SAMs will assist in realizing larger, highly efficient, stable, and cost‐effective PSCs, thereby enhancing the competitiveness of PSCs in the solar photovoltaics market.

TomoNet: A streamlined cryogenic electron tomography software pipeline with automatic particle picking on flexible lattices.

Cryogenic electron tomography (cryoET) is capable of determining in situ biological structures of molecular complexes at near-atomic resolution by averaging half a million subtomograms. While abundant complexes/particles are often clustered in arrays, precisely locating and seamlessly averaging such particles across many tomograms present major challenges. Here, we developed TomoNet, a software package with a modern graphical user interface to carry out the entire pipeline of cryoET and subtomogram averaging to achieve high resolution. TomoNet features built-in automatic particle picking and three-dimensional (3D) classification functions and integrates commonly used packages to streamline high-resolution subtomogram averaging for structures in 1D, 2D, or 3D arrays. Automatic particle picking is accomplished in two complementary ways: one based on template matching and the other using deep learning. TomoNet's hierarchical file organization and visual display facilitate efficient data management as required for large cryoET datasets. Applications of TomoNet to three types of datasets demonstrate its capability of efficient and accurate particle picking on flexible and imperfect lattices to obtain high-resolution 3D biological structures: virus-like particles, bacterial surface layers within cellular lamellae, and membranes decorated with nuclear egress protein complexes. These results demonstrate TomoNet's potential for broad applications to various cryoET projects targeting high-resolution in situ structures.

The Correlation between the Microstructure and the Characteristic Luminescence in the High Crystalline α-Ga2O3 Grown on the Thin-Wall Single Crystal Al2O3

A high-quality alpha-Ga2O3 thin film was grown on an Al2O3 single-crystal thin-wall channel structure. Alpha-Ga2O3 crystals are grown with a 3-fold symmetry template provided by the Al2O3 surface, which forms domain boundaries from the small rotation of the mosaic structure. The anti-phase domain (APD) was confirmed by convergent-beam electron diffraction (CBED), and it is believed to be developed at the stage of nucleation based on the unstable, or uneven Al-O bonding on the Al2O3 surface. The in-phase domain and the APD boundaries exhibit bright contrast in ADF, which originates from a local strain of crystallographic rotation and not from the local elemental fluctuations of gallium. As confirmed by CL measurement in TEM, the bandgap energy of alpha-Ga2O3 is inferred to be 5.56 eV with a near band edge transition of ~ 223 nm. Even though the heights and positions of peaks vary slightly from area to area, 4 distinct luminescence peaks and a long tail of wavelength are commonly observed throughout the crystal. 2-dimensional mapping with the specific wavelength window reveals a clear difference between the inside domain, in-phase domain boundary, and APD boundary. A luminescence peak of distinct 350 nm was observed at the APD boundary. Misorientation between domains was found, which leads to an in-plane mismatch in crystallographic lattices at the boundary when the two misoriented domains grow and the growth front merges. The imperfect lattice structure at the boundary is believed to create strain and intermediate states.

Nonepitaxial Wafer-Scale Single-Crystal 2D Materials on Insulators.

Next-generation nanodevices require 2D material synthesis on insulating substrates. However, growing high-quality 2D-layered materials, such as hexagonal boron nitride (hBN) and graphene, on insulators is challenging owing to the lack of suitable metal catalysts, imperfect lattice matching with substrates, and other factors. Therefore, developing a generally applicable approach for realizing high-quality 2D layers on insulators remains crucial, despite numerous strategies being explored. Herein, a universal strategy is introduced for the nonepitaxial synthesis of wafer-scale single-crystal 2D materials on arbitrary insulating substrates. The metal foil in a nonadhered metal-insulator substrate system is almost melted by a brief high-temperature treatment, thereby pressing the as-grown 2D layers to well attach onto the insulators. High-quality, large-area, single-crystal, monolayer hBN and graphene films are synthesized on various insulating substrates. This strategy provides new pathways for synthesizing various 2D materials on arbitrary insulators and offers a universal epitaxial platform for future single-crystal film production.

Topological measures of order for imperfect two-dimensional Bravais lattices.

Motivated by patterns with defects in natural and laboratory systems, we develop two quantitative measures of order for imperfect Bravais lattices in the plane. A tool from topological data analysis called persistent homology combined with the sliced Wasserstein distance, a metric on point distributions, are the key components for defining these measures. The measures generalize previous measures of order using persistent homology that were applicable only to imperfect hexagonal lattices in two dimensions. We illustrate the sensitivities of these measures to the degree of perturbation of perfect hexagonal, square, and rhombic Bravais lattices. We also study imperfect hexagonal, square, and rhombic lattices produced by numerical simulations of pattern-forming partial differential equations. These numerical experiments serve to compare the measures of lattice order and reveal differences in the evolution of the patterns in various partial differential equations.

Resonant absorption of light by a two-dimensional imperfect lattice of spherical particles.

The light absorption and scattering by an infinite two-dimensional array with an imperfect lattice of identical spherical particles is considered based on the statistical approach to a description of electromagnetic wave interaction with particulate media. Absorption resonances due to the coherent component of scattered light (zeroth order of diffraction) and resonances arising from the excitation of a flux of incoherently scattered light (higher diffraction orders) propagating at grazing angles to the array plane are studied. The dependence of absorption on the degree of positional ordering of particles is considered. It is shown that with an increase in ordering, the spatial coherence of the light flux along the array plane increases and the absorption resonance becomes more pronounced. Data are presented for silver wavelength-sized particles for s- and p-polarized incident waves. It is shown that at small angles of incidence, the first diffraction order can arise at the wavelength of zeroth-order resonance. In this case, the contributions to absorption created by the coherent and incoherent components of scattered light are summed up. The value of the absorption coefficient can be close to 0.95. A comparison with data for a partially ordered array is carried out.

Constructing of superhydrophobic and intact crystal terminal: Interface sealing strategy for stable perovskite solar cells with efficiency over 23%

The numerous nonstoichiometric imperfections on the perovskite crystal terminal are usually resulting in unwished nonradiative recombination as well as high risk of lead leakage. Herein, the terminal sealing strategy by using pseudo-halide ammonium salts was developed to seal lattice defects via ion-exchange reaction and interact with uncoordinated Pb2+ at the terminal of the perovskite films. The superhydrophobic ammonium cations can bond to undercoordinated Pb2+ and I−/Br− on crystal terminal, impeding erosion from the environment. Furthermore, the terminal sealing layer modulated the energy level alignment between perovskite and holes transport layer to promote efficient extraction of the hole. The optimal device attained a power conversion efficiency (PCE) over 23% without obvious hysteresis. The unencapsulated devices maintained 90% of the original PCE after operation at 60 ± 10% RH for 1200 h and exhibited a 20% loss in PCE after 500 h light soaking aging. More importantly, immersion operation further showed their superior structure stability against water. This work provides a unique perspective towards reconstructing the imperfect lattice defects and reducing lead leakage venture of perovskite crystal terminals.

Effective passivation of perovkiste grain boundaries by a carboxylated polythoiphene for bright and stable Pure-Red perovskite light emitting diodes

High luminance and operative stability are essential parameters for realizing the commercialization of perovskite-based light-emitting diodes (PLEDs). However, the optoelectronic properties of PLEDs are still limited owing to the un-optimized charge transport behavior of perovskite films arising from severe defect densities and imperfect lattice structure at grain boundaries. To retrieve the morphological imperfection, we herein suggest a carboxylated polythiophene (P3CT) as a novel passivating agent of perovskite films in PLEDs. The carboxylic acid groups of P3CT enable Lewis acid-base interactions with the defective surface of perovskites such as under-coordinated Pb2+ sites or halide deficiencies, leading to efficient defect passivation and stabilization of the perovskite film surface. The P3CT-passivation successfully fabricates pinhole-free perovskite films with diminished defects at grain boundaries, bringing enhanced optoelectronic properties of red electroluminescence EL emission with a peak current efficiency and external quantum efficiency (EQE) values up to 11.15 % and 4 %, respectively. Moreover, the operative stability of the passivated PLEDs is markedly improved due to the stabilization and increased hydrophobicity of perovskite films by the inclusion of P3CT. The present findings provide a new perspective for developing stable red-PLEDs with efficient luminescence.

Statistically equivalent surrogate material models: Impact of random imperfections on the elasto-plastic response

Manufactured materials usually contain random imperfections due to the fabrication process, e.g., the 3D-printing, casting, etc. These imperfections affect significantly the effective material properties and result in uncertainties in the mechanical response. Numerical analysis of the effects of the imperfections and the uncertainty quantification (UQ) can be often done by use of digital stochastic surrogate material models. In this work, we present a new flexible class of surrogate models depending on a small number of parameters and a calibration strategy ensuring that the constructed model fits to the available observation data, with special focus on two-phase materials. The surrogate models are constructed as the level-set of a linear combination of an intensity field representing the topological shape and a Gaussian perturbation representing the imperfections, allowing for fast sampling strategies. The mathematical design parameters of the model are related to physical ones and thus easy to interpret. The calibration of the model parameters is performed using progressive batching sub-sampled quasi-Newton minimization, using a designed distance measure between the synthetic samples and the data. Then, employing a fast sampling algorithm, an arbitrary number of synthetic samples can be generated to use in Monte Carlo type methods for prediction of effective material properties. In particular, we illustrate the method in application to UQ of the elasto-plastic response of an imperfect octet-truss lattice which plays an important role in additive manufacturing. To this end, we study the effective material properties of the lattice unit cell under elasto-plastic deformations and investigate the sensitivity of the effective Young’s modulus to the imperfections.

Аbsorption of diffuse light by 2D arrays of spherical particles

The problem of absorption of diffuse light by a 2D array of identical spherical particles is considered. The equations to solve this problem are derived on the basis of statistical approach. They can be used to match parameters of the array and the illumination system to get maximum absorption. The numerical results are presented for absorption coefficients of arrays with the imperfect triangular lattice and partially ordered structures of crystalline silicon and silver particles embedded in nonabsorbing medium, in the wavelength range 0.35 μm – 0.80 μm. The size of particles and their concentration are chosen so as to illustrate the dependence of light absorption on the angle of incidence under conditions of resonances due to the high spatial ordering of particles. The absorption coefficients of the arrays at diffuse and directional light illumination are compared.

An image-based multi-level hp FCM for predicting elastoplastic behavior of imperfect lattice structure by SLM

An image-based multi-level hp FCM for predicting elastoplastic behavior of imperfect lattice structure by SLM

Two-dimensional numerical model of Marangoni surfers: From single swimmer to crystallization.

We numerically study the dynamics of an ensemble of Marangoni surfers in a two-dimensional and unconfined space. The swimmers are modeled as Gaussian sources of surfactant generating surface tension gradients and are shown to follow the Marangoni flow filtered at their spatial scale in the lubrication regime, an unstable situation leading to spontaneous motion as soon as the Marangoni effect is intense enough. As the system is fully unconstrained, it is possible to study the various dynamical regimes from single swimmer, two-body interaction, to the many-particles case characterized by an efficient particle dispersion. We show that, although the present model is very simple, it reproduces the experimentally observed transition between a regime of dispersion by random agitation when the number of swimmers is moderate to the regime of crystallization with imperfect hexagonal lattice at high density.

On the role of carboxylated polythiophene in defect passivation of CsPbI 2 Br surface for efficient and stable all‐inorganic perovskite solar cells

Improved film surface is a prerequisite to achieve high photovoltaic performance of inorganic perovskite solar cells because defective (under-coordinated) lead ions derived from imperfect lattice structure of the film surface or grain boundaries the principal nonradiative recombination centers in the inorganic perovskite absorber. In this study, we suggest poly[3-(4-carboxybutyl)thiophene-2,5-diyl] (P3CT), a carboxylated p-type conjugated polymer, as a passivating agent of the CsPbI2Br layer to tailor electronic properties of a perovskite absorber. With the P3CT passivation, the defective sites of the perovskite film surface were improved and stabilized, which can suppress nonradiative recombination to promote charge transport of CsPbI2Br-based all-inorganic perovskite solar cells. Consequently, the P3CT passivation delivers a power conversion efficiency (PCE) of 12.25% and decent long-term stability of CsPbI2Br perovskite solar cells, which surpasses the pristine device without the passivation. The electricity generation capability under indoor light source of the passivated device is also studied, demonstrating a promising PCE of 27.47%. This work unveils the role of P3CT as a passivating agent to passivate the defective sites of CsPbI2Br perovskite film surface and grain boundaries, which facilitates charge transport and reduced carrier recombination of CsPbI2Br absorber in solar cell devices.

Support vector machines for predicting the compressive response of defected 3D printed polymeric sandwich structures

Purpose This study aims to investigate the prediction of the nonlinear response of three-dimensional-printed polymeric lattice structures with and without structural defects. Unlike metallic structures, the deformation behavior of polymeric components is difficult to quantify through the classical numerical analysis approach as a result of their nonlinear behavior under mechanical loads. Design/methodology/approach Geometric models of periodic lattice structures were designed via PTC Creo. Imperfections in the form of missing unit cells are introduced in the replica of the lattice structure. The perfect and imperfect lattice structures have the same dimensions – 10 mm × 14 mm × 30 mm (w × h × L). The fused deposition modelling technique is used to fabricate the parts. The fabricated parts were subjected to physical compression tests to provide a measure of their transverse compressibility resistance. The ensuing nonlinear response from the experimental tests is deployed to develop a support vector machine surrogate model. Findings Results from the surrogate model’s performance, in terms of correlation coefficient, rose to as high as 99.91% for the nonlinear compressive stress with a minimum achieved being 98.51% across the four datasets used. In the case of deflection response, the model accuracy rose to as high as 99.74% while the minimum achieved is 98.56% across the four datasets used. Originality/value The developed model facilitates the prediction of the quasi-static response of the structures in the absence and presence of defects without the need for repeated physical experiments. The structure investigated is designed for target applications in hierarchical polymer packaging, and the methodology presents a cost-saving method for data-driven constitutive modelling of polymeric parts.

Localization and coalescence of imperfect planar FCC truss lattice metamaterials under multiaxial loadings

This study investigates the effect of stress triaxiality on the failure mechanisms of an-isotropic perfect and imperfect planar FCC (Face Centred Cubic) truss lattice metamaterials. Three types of imperfection have been considered in the numerical modelling, namely, distorted struts, missing struts, and strut diameter variation. In order to maintain constant stress triaxiality during the simulations, a novel numerical framework was developed to overcome computational difficulties within the existing numerical approaches beyond elastic region. Three modes of microscopic localization were observed in perfect and imperfect lattices before failure: crushing band, shear band and void coalescence. A clear separation exists between the three modes of localization depending upon the type and level of defects, as well as the stress triaxiality. Under compressive loading, all lattices fail owing to crushing band; the distorted lattices are prone to shear band localization with increase in distortion, whereas missing lattices majorly fail due to void coalescence at high missing struts defect. Strut diameter variation, within the range of the strut diameters selected, shows no significant influence on the macroscopic mechanical response and strain localization. This work may open the door for predicting failure mechanisms of imperfect lattices under variety of loading conditions.

Topology optimization of imperfect lattice materials built with process-induced defects via Powder Bed Fusion

Abstract Lattice materials built via additive manufacturing feature process-induced defects that impact their mechanical properties and optimum design. This work presents a methodology to integrate geometric defects in a density-based formulation for topology optimization of additively built lattice materials. The method combines imperfect unit cell models capturing their geometric defects with a homogenization scheme upscaling their effective properties, into a topology optimization formulation. The method is of general application, and it is here demonstrated through the application to two cell topologies, the Tetrahedron-based and the Octet-truss unit cells, called to satisfy specific geometric constraints. Verification is performed through the solution of two well-known benchmark problems in 3D: the fixed-beam and the L-shaped beam, assumed to consist of either defect-free or imperfect lattice materials. The impact of process-induced defects, and cell orientation is demonstrated on the elastic anisotropy of the unit cell, the optimized gradients of relative density and the global compliance of the beams. The results highlight the significance of accounting for geometric defects in topology optimization of additively built lattice materials.

Effects of vacancies on high-order harmonic generation in a linear chain with band gap

In this paper, high-order harmonic generation (HHG) in imperfect lattices with one or several point defect vacancies either being evenly distributed, or localized at neighboring lattice points, is studied by two different realizations of linear chain systems. The authors search for detectable signatures of finite structure in the HHG spectra and also investigate the role of vacancy-induced defect-state orbitals in the HHG process.

Borophene-graphene heterostructures.

Integration of dissimilar two-dimensional (2D) materials is essential for nanoelectronic applications. Compared to vertical stacking, covalent lateral stitching requires bottom-up synthesis, resulting in rare realizations of 2D lateral heterostructures. Because of its polymorphism and diverse bonding geometries, borophene is a promising candidate for 2D heterostructures, although suitable synthesis conditions have not yet been demonstrated. Here, we report lateral and vertical integration of borophene with graphene. Topographic and spatially resolved spectroscopic measurements reveal nearly atomically sharp lateral interfaces despite imperfect crystallographic lattice and symmetry matching. In addition, boron intercalation under graphene results in rotationally commensurate vertical heterostructures. The rich bonding configurations of boron suggest that borophene can be integrated into a diverse range of 2D heterostructures.