3D Lattice Research Articles

A Halogen-Bonded Fluorescent Molecular Photoswitch: Transition from 3D Cubic Lattice to 1D Helical Superstructure for Polarization Inversion of Circularly Polarized Luminescence.

The fabrication of materials that can switch between circularly polarized luminescence (CPL) signals is both essential and challenging. Here, two new halogen-bonded fluorescent molecular photoswitches, namely, HB-switch 1 and HB-switch 2, containing α-cyano-substituted diarylethene compounds with different end groups were developed. Upon exposure to specific UV or visible light wavelengths, they exhibited controllable and reversible Z/E photoisomerization. When these switches were integrated into blue-phase liquid crystals (BPLCs), the temperature range of BP significantly expanded. Notably, the BP system incorporating HB-switch 1 exclusively achieved reversible polarization inversion of CPL signals under irradiation with specific UV/Visible light and during cooling/heating. The photo/thermal dual-response behavior of the CPL signals can be attributed to the phase transition from a high-symmetry 3D BP Icubic lattice to a low-symmetry 1D helical superstructure induced by the Z/E photoisomerization of HB-switch 1 and temperature changes. This study underscores the significance of employing halogen-bond assembly strategies to design materials with switchable CPL signals, opening new possibilities for CPL-active systems.

Is the Presence of Sn2+ a Crucial Factor for the Generation of Low Thermal Conductivity in Tin-Based Sulfides?

Comprehending the relationship between crystal structures and transport properties is crucial to develop materials with improved electrical and thermal properties for thermoelectric applications. In this article, we report on the complex crystal structure and physical properties of Cr2Sn3S7, a n-type magnetic semiconductor with a low energy band gap and low thermal conductivity. Importantly, we demonstrate that the high level of structural complexity is related to the coexistence of two sublattices: a host lattice, [Cr4Sn2S11]2-, characterized by a mixed Sn4+/Cr3+ occupancy of its cationic sites, and a guest lattice characterized by [Sn4S3]2+ chains, containing Sn2+ cations only, closely related to the ones encountered in the orthorhombic SnS compound. By combining experiments including X-ray diffraction with ab initio calculations of electrons and phonons, we succeeded to elucidate the origin of the low thermal conductivity in Cr2Sn3S7. We demonstrate that the low dimensionality of the [Sn4S3]2+ chains, which generates weak Sn···S interactions with the 3D host lattice, is induced by the lone pair stereochemical activity of Sn2+. This lattice softening favors strong anisotropic vibrations at low frequencies, highlighting the primordial role played by Sn2+ cations in both crystal structure dimensionality and low thermal conductivity in tin-based sulfides.

3D printed MXene/rGO hierarchical porous structure based on ultralow-concentration 2D nanomaterial inks for highly sensitive pressure sensing

3D direct ink writing technology based on two-dimensional (2D) MXene nanomaterial inks receives attention in the field of pressure sensing for simplicity of fabrication, programmable geometry with controllable function and performance. However, it is still a huge challenge to print excellent macro-structure with ultralow-concentration MXene inks, attributed to its weak gelation ability. Herein, we construct a MXene/reduced graphene oxide (MX/rGO) architecture (0.012 g cm−3) with macroscopic (hierarchical lattice) and microscopic (porous) structure by using ultralow-concentration emulsion-based inks of MXene (5.882 mg mL−1). The introduction of octadecylamine enhances the bonding between the MXene and GO, significantly improving the gelation ability of the ink with low-concentration 2D nanomaterials. More importantly, the MX/rGO pressure sensor achieves a high sensitivity (166.957 kPa−1), wide sensing range (0.028∼100 kPa), and excellent cyclic stability (10500 cycles) due to its 3D hierarchical lattice porous structure. These sensing capabilities enable the sensor to detect various human motions, such as pulse beating, vocal cord vibration, facial expressions, different joint movements and pressure distribution. Undoubtedly, this work provides a broad development prospect for the customized flexible pressure sensors based on MXene ink 3D printing technology.

Helicene Covalent Organic Frameworks for Robust Light Harvesting and Efficient Energy Transfers.

Helicenes represent a class of fascinating π compounds with fused yet folded backbones. Despite their broad structural diversity, harnessing helicenes to develop well-defined materials is still a formidable challenge. Here we report the synthesis of crystalline porous helicene materials by exploring helicenes to synthesize covalent 2D lattices and layered π frameworks. Topology-directed polymerization of [6]helicenes and porphyrin creates 2D covalent networks with alternate helicene-porphyrin alignment along the x and y directions at a 1.5-nm interval and develops [6]helicene frameworks through reversed anti-AA stack along the z direction to form segregated [6]helicene and porphyrin columnar π arrays. Notably, this π configuration enables the frameworks to be highly red luminescent with benchmark quantum yields. The [6]helicene frameworks trigger effieicnt intra-framework singlet-to-singlet state energy transfer from [6]helicene to porphyrin and facilitate intermolecular triplet-to-triplet state energy transfer from frameworks to molecular oxygen to produce reactive oxygen species, harvesting a wide range of photons from ultraviolet to near-infrared regions for light emitting and photo-to-chemical conversion. This study introduces a new family of extended frameworks, laying the groundwork for exploring well-defined helicene materials with unprecedented structures and functions.

Plasmon-mediated dynamics and lasing of nanoemitters enhanced by dispersing nanorings.

We investigate the plasmon-mediated nonlinear dynamics and the optics of a laser emission of random nanoemitters (NEs) embedded in a two-dimensional (2D) lattice of conducting nanorings (NRs) enhanced by plasmon-polariton (PP) excitations. The interaction of quantum NEs with the PP field in the NRs perturbs the dynamics of the electronic populations in NEs, leading to a significant dependence of laser generation (dynamics) on the plasma frequency ωp of PP. This results in a strong coupling of NE field emission with the PP field and sharp variations of the average current in the NR lattice. The phase transition in the system was found when the macroscopic structures of PP fields are excited simultaneously in different regions of the system if ωp (control parameter) reaches critical value ωc. We have established the analytical dependence of the PP current I = I(ωp/ωc) on the plasma frequency, which is in excellent agreement with the results of numerical simulations. This effect may allow the design of new types of PP active devices with the use of conducting NRs in modern nanoelectronics.

Thermoelectric Phenomena in a Magnetic Heterostructure with AAH Modulation: Charge and Spin Figure of Merits

ABSTRACT We put forward a prescription of getting a higher value of the spin-dependent figure of merit in comparison with its charge counterpart in the case of a 1D magnetic heterostructure (a ferromagnetic (FM) chain sandwiched between two non-magnetic 1D lattices) where all the site energies of the heterostructure follow cosine form of modulation defined in Aubry-Andre-Harper (AAH) model. It is shown that due to having a greater number of non-uniform peaks in its transmission spectra, the thermoelectric efficiency of this heterostructure becomes superior compared to that is obtained in a fully ferromagnetic 1D chain. It is also reported that the maximum value of the thermoelectric figure of merit (for both spin and charge-dependent cases) of the heterostructure in a specified energy range gets enhanced in a continuous manner as the disorder strength of the AAH modulation is increased. The Hamiltonian of the proposed quantum system is described within a tight-binding (TB) framework and after the evaluation of transmission probability by utilizing the non-equilibrium Green’s function (NEGF) technique, all the important thermoelectric quantities are determined on the basis of Landauer formalism. We believe that our study on this particular topic of spin caloritronics, a subject associated with temperature-dependent spin transmission through a quantum channel, may help to explore several fascinating ideas about spin-related thermoelectric efficiency in many other ferromagnetic quasicrystals.

Exceptional Nitrate Reduction to Ammonia Catalyst Enabled by BO2− Anion Induction Effects Combining Heterogeneous Branching Architecture‐Driven Mass Transport Enhancement

AbstractIn this paper, an exceptional nitrate reduction to ammonia catalyst is reported, enabled by BO2− anion induction effects combining heterogeneous branching architecture‐driven mass transport enhancement strategies. The implantation of the BO2− anion can inductively enhance the electron cloud density and electron transmission paths of intrinsic catalysts, makes electron more active to improve the conductivity, regulates the adsorption and desorption rates of intermediates by space barrier effect, reduces the binding energy of the electron and 3d orbital of Ni in NiFe(BO2)O(OH), thereby lowing the transform free energy of the determining *NO3 to *HNO3 step. 3D hollow sea urchin lattice heterogeneous branching structure can self‐drive generate differentiated micro convection intervals, which will be beneficial for improving mass transfer dynamics especially localized disturbance mass transfer effect of catalyst for nitrate reduction reaction (NO3RR) catalysis process. Amazingly, the as‐prepared 3D NiFe metaborate oxyhydroxide hollow bionic sea urchins lattice catalyst has a high NH3 rate 6.27mmol·h−1·cm−2 with 98.7% Faradaic efficiency at low ‐0.25V(vs RHE) NO3RR potential. Moreover, the catalytic activity of this highly stable catalyst decreases only slightly over 100 h at ultra‐high 1500mA·cm−2 current. This work breaks through the bottleneck that plagues the performance improvement of non Cu‐based high‐current NO3RR catalysts.

Lagrangian multiform structure of discrete and semi-discrete KP systems

A variational structure for the potential AKP system is established using the novel formalism of a Lagrangian multiforms. The structure comprises not only the fully discrete equation on the 3D lattice, but also its semi-discrete variants including several differential-difference equations asssociated with, and compatible with, the partial difference equation. To this end, an overview is given of the various (discrete and semi-discrete) variants of the KP system, and their associated Lax representations, including a novel `generating PDE' for the KP hierarchy. The exterior derivative of the Lagrangian 3-form for the lattice potential KP equation is shown to exhibit a double-zero structure, which implies the corresponding generalised Euler-Lagrange equations. Alongside the 3-form structures, we develop a variational formulation of the corresponding Lax systems via the square eigenfunction representation arising from the relevant direct linearization scheme.

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.

Twisted graphene superlattices: resonating valence bond states and magnetic properties

Resonating valence bond (RVB) states are fundamental for understanding quantum spin liquids in two-dimensional (2D) systems. The RVB state is a collective phenomenon in which spins are uncoupled. 2D lattices such as triangular, honeycomb, and dice lattices were investigated using the Hubbard model and exact diagonalization method. We analyzed the total spin, spin–spin correlation functions, local magnetic moments, and spin and charge gaps as a function of on-site Coulomb repulsion, electron concentration, and electronic hopping parameters. Phase diagrams showed that RVB states can live in half-filled and hole-doped anisotropic triangular lattices. We found two types of RVB states: one in the honeycomb sublattice and the other in the centered hexagons in the triangular lattices. Owing to the novel discovery of exotic magnetic ordering in triangular moiré patterns in twisted bilayer graphene and transition metal dichalcogenide systems, our results provide physical insights into the onset of magnetism and possible spin liquid states in these layered materials.

Discrete-continuum-discrete approach for the modeling of the dynamic behavior of 2D lattice systems

This work presents a new methodology to model elastic lattice systems through a two-step approach that permits to reliably capture its dynamic behavior with a lower computational cost than modeling the lattice explicitly. The first step consists of a non-standard continualization accounting for scale effects. Several methods are explored to derive new continuum models, whose dispersive and vibrational behaviors are compared to that of the lattice, considered as a reference. Non-classical models with micro-inertia reveal high accuracy, not presenting physical inconsistencies. The second step follows a FEM spatial discretization of the developed continua, accounting for micro inertia terms in the mass matrix. Finally, the FEM formulation allows the use of element sizes larger (up to four times) than the physical length scale of the lattice system, thus significantly reducing the computational cost while maintaining accuracy and enabling a versatile application to materials, geometries and boundary conditions. The methodology is tested here for a 2D system with displacements in the plane, but can be extended to other lattice typologies as well.

Laser direct fabrication and characterization of 3d lattice structures using continuous carbon fiber thermoset composites

Laser direct fabrication and characterization of 3d lattice structures using continuous carbon fiber thermoset composites

Flat bands in three-dimensional lattice models with non-trivial Hopf index

We report the presence of exactly and nearly flat bands with non-trivial topology in three-dimensional (3D) lattice models. We first show that an exactly flat band can be realized in a 3D lattice model characterized by a 3D topological invariant, namely Hopf invariant. In contrast, we find another distinct 3D model, exhibiting both 2D Chern and 3D Hopf invariant, namely Hopf-Chern insulator, that can host nearly or perfect flat bands across different 2D planes. Such a Hopf-Chern model can be constructed by introducing specific hopping along the orthogonal direction of a simple two-orbital 2D Chern insulator in the presence of in-plane nearest-neighbor and next-nearest hopping among different orbitals. While the Chern planes host nearly perfect flat bands, the orthogonal planes can host both perfect or nearly perfect flat bands with zero Chern number at some special parameter values. Interestingly, such a 3D lattice construction from 2D allows finite Hopf invariant too. Finally, we show that higher Chern models can also be constructed in the same lattice setup with only nearest and next-nearest hopping, but the appearance of flat bands along high-symmetric path in the Brillouin zone requires longer-range hopping. We close with a discussion on possible experimental platforms to realize the models.

Magnon bands and transverse transport in a proposed two-dimensional [formula omitted] ferrimagnet

The copper fluoride Cu2F5 is a proposed stable compound that can be seen as a layered lattice of S=1 and S=1/2 sites, corresponding to copper ions. Intending to cast light on the transport properties of ferrimagnetic magnons, we use the linear spin wave approach to study the magnon band structure of the 2D lattice in a ferrimagnetic off-plane order, as well as the transverse transport of magnons in the crystal bulk. A magnetic field or temperature gradient can induce transverse (Hall-like) transport within the linear response theory generated by the Berry curvature of the eigenstates. As in most cases involving magnons, the Berry curvature is related to Dzyaloshinskii–Moriya interactions between next-near-neighbors The band structure of the system is non-degenerate and the transport coefficients are non-null. The novel and interesting feature of the system is that, within certain conditions, the transport coefficients versus temperature curves are non-monotonic and present a sign change, opening the exciting possibility of controlling the transverse magnon flow direction and magnitude with the temperature change.

Enzyme induced polymer degradation as a pathway to create microbial habitats for biomanufacturing intensification

Polymer hydrogels are instrumental in cell immobilization for biomanufacturing, yet traditional hydrogel bioreactors often compromise cell viability, function, and mass transfer. This results in uncontrolled microbial proliferation and significant cell leakage, thereby impeding the continuous production of high-value products. To address these challenges, we introduce an innovative liquid microcavity technique employing a blend of Gelatin-methacryloyl (Gel-MA) and Pluronic F127diacrylate (F127-DA) for precision bioprinting, followed by selective enzymatic digestion of gelatin to create microbial habitats. Through tailoring of the hydrogel’s pore structure and integration of diverse networks, our approach facilitates controlled nutrient transfer, efficient waste removal, and stable mechanical support, all while maintaining a leak-free suspension culture of microorganisms. We validated the effectiveness of our method by fabricating yeast-infused Three-dimensional (3D) lattice constructs, successfully achieving continuous fermentation of glucose into ethanol in a flow reactor with minimal efficiency reduction (≥90 % yield) over five cycles. This research not only confronts the spatial limitations inherent in hydrogel-based systems but also demonstrates a foundational potential for revolutionary change in biomanufacturing practices.

Method for Generating Closely Packed Orbital Shells and Orbital Capacity Implications

Shell-wise orbital coordination in low Earth orbit can improve space safety, simplify space traffic coordination and management, and optimize orbital capacity. This work describes two methods to generate 2D lattice flower constellations (2D-LFCs) that are defined with respect to either an arbitrary zonal, or zonal, sectoral, and tesseral Earth geopotential. By generating orbital shells that are periodic with respect to the Earth geopotential, it is possible to safely stack shells with vertical separation distances smaller than the osculating variation in semimajor axis and radial distance of each shell, or a corresponding Keplerian 2D-LFC propagated under an aspherical geopotential. These methods exploit previous work on constellations based on time distributions and designs of closed 2D-LFCs under arbitrary Earth geopotentials using repeating ground track orbits. Factors that influence the widths and shapes of these shells are identified. Additionally, simplified formulas for estimating shell geometry and thickness are presented. Based on these results, it is shown that geopotential-aware periodic orbital shells significantly increase the number of admissible orbital shells while preserving shell separation. Finally, this work shows that sequencing shells to group similar or ascending inclinations can further improve capacity versus arbitrary inclination ordering, particularly for smaller shell separation distances.

Symmetry-Shaped Singularities in High-Temperature Superconductor H3S.

The superconducting critical temperature of H3S ranks among the highest measured, at 203 K. This impressive value stems from a singularity in the electronic density-of-states, induced by a flat-band region that consists of saddle points. The peak sits right at the Fermi level, so that it gives rise to a giant electron-phonon coupling constant. In this work, we show how atomic orbital interactions and space group symmetry work in concert to shape the singularity. The body-centered cubic Brillouin Zone offers a unique 2D hypersurface in reciprocal space: fully connecting squares with two different high-symmetry points at the corners, Γ and H, and a third one in the center, N. Orbital mixing leads to the collapse of fully connected 1D saddle point lines around the square centers, due to a symmetry-enforced s-p energy inversion between Γ and H. The saddle-point states are invariably nonbonding, which explains the unconventionally weak response of the superconductor's critical temperature to pressure. Although H3S appears to be a unique case, the theory shows how it is possible to engineer flat bands and singularities in 3D lattices through symmetry considerations.

Experimental and numerical studies on the chloride diffusion coefficient of calcium silicate hydrate gel

The chloride diffusivity of calcium silicate hydrate (C-S-H), as the main hydration product of cement paste, plays an important role for the durability of concrete structures, especially for low w/c ratio ones. In this paper, in order to measure the chloride diffusion coefficient of C-S-H, a diffusion path conversion method is proposed to convert the primary diffusion path of ions from capillary pores to gel pores. By combining diffusion path conversion method with steady-state migration test, the diffusion coefficients of C-S-H are obtained. Based on 3D nanostructure, which is generated by a hybrid scheme of Grand Canonical Monte Carlo and Molecular Dynamics, the chloride diffusion coefficient of C-S-H is predicted by a 3D diffusive lattice modelling. Results from the experiments and simulation are compared with the data in the literature. Our work contributes to the understanding of C-S-H diffusivity and is of great importance for predicting the long-term durability of concrete structure.

Ideas of lattice-basis reduction theory for error-stable Bravais lattice determination and abinitio indexing.

In ab initio indexing, for a given diffraction/scattering pattern, the unit-cell parameters and the Miller indices assigned to reflections in the pattern are determined simultaneously. `Ab initio' means a process performed without any good prior information on the crystal lattice. Newly developed ab initio indexing software is frequently reported in crystallography. However, it is not widely recognized that use of a Bravais lattice determination method, which is tolerant of experimental errors, can simplify indexing algorithms and increase their success rates. One of the goals of this article is to collect information on the lattice-basis reduction theory and its applications. The main result is a Bravais lattice determination algorithm for 2D lattices, along with a mathematical proof that it works even for parameters containing large observational errors. It uses two lattice-basis reduction methods that seem to be optimal for different symmetries, similarly to the algorithm for 3D lattices implemented in the CONOGRAPH software. In indexing, a method for error-stable unit-cell identification is also required to exclude duplicate solutions. Several methods are introduced to measure the difference in unit cells known in crystallography and mathematics.

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.