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Using density functional theory with the generalized gradient approximation, we explored the geometric and electronic structure of polymerized spiro [4,4]nonatetraene (spiro-graphene) as a possible two-dimensional carbon allotrope comprising sp2 and sp3 C atoms. By reflecting a shape of the hydrocarbon molecule, this two-dimensional allotrope has a covalent network of fused pentagons with nanometer-scale structural rippling. The covalent network is thermally and dynamically stable with a relatively high total energy, higher than graphene by 0.6 eV/atom. The spiro-graphene is a metal where two linear dispersion bands cross each other at the Fermi level. In addition to these linear dispersion bands, the covalent network possesses the Dirac nodal line just above the Fermi level and along the Brillouin zone boundary. Accordingly, the ribbons with zigzag edges derived from spiro-graphene possess edge states like those of graphene nanoribbons with zigzag edges.

Graphical abstract Device model based on zigzag magnetic MoS2 nanotube and the calculated spin-dependent currents through the device., Bipolar magnetic semiconductors (BMSs) are a new member of spintornic materials. In BMSs, one can obtain 100% spin-polarized currents by means of the gate voltage. However, most of previous studies focused on their applications in spintronics instead of spin caloritronics. Herein, we show that BMS is an intrinsic model for spin Seebeck effect (SSE). Without any gate voltage and electric field, currents with opposite spin orientation are generated and flow in opposite directions with almost equal magnitude when simply applying a temperature bias. This is also due to the special electronic structure of BMS where the conduction and valence bands near the Fermi level belong to opposite spin orientation. Based on density function theory and non-equilibrium Green’s function methods, we confirm the thermal-induced SSE in BMS using a case of magnetic MoS2 nanotube. The magnitude of spin current in zigzag tube is almost four times higher than that in armchair tube. BMS is promising candidates for spin caloritronic applications.

In this research, two novel folded lattice-core sandwich cylinders were designed, manufactured, and tested. The lattice core has periodic zigzag corrugations, whose ridges and valleys are directed axially or circumferentially. Free vibration and axial compression experiments were performed to reveal the fundamental frequency, free vibration modes, bearing capacity, and failure mode of the cylinder. A folded lattice core effectively restricts local buckling by reducing the dimension of the local skin periodic cell, and improves the global buckling resistance by enhancing the shear stiffness of the sandwich core. The cylinders fail at the mode of material failure and possess excellent load-carrying capacity. An axially directed folded sandwich cylinder has greater load-carrying capacity, while a circumferentially directed folded sandwich cylinder has higher fundamental frequencies. These two types of folded lattices provide a selection for engineers when designing a sandwich cylinder requiring strength or vibration. This research also presents a feasible way to fabricate a large-dimensional folded structure and promote its engineering application. Keywords: Folded lattice-core sandwich cylinder, Fabrication, Mechanical testing

A fringe pattern normalization algorithm is proposed using the smoothing Kalman filter. The background intensity and the fringe amplitude are estimated consecutively. These estimates are subsequently utilized to obtain the normalized fringe pattern. The fringe pattern normalization can be performed by scanning it either in a row-column-wise or in a zigzag manner. The simulation and experimental results are provided to substantiate the practical applicability of the proposed method.

The miniaturization of transistors and the high density of integrated circuits makes conventional transistors reach a size limit, causing leakage currents, unstable performance, and increasing production cost. Spin field effect transistors (SFETs) based on spintronics use electron spin as an information carrier and regulate electron spin degree of freedom for storing and processing information. As a class of spintronics, Rashba spin–orbit coupling (SOC) effect attracts increasing attention because of its electric tunability. SFETs based on Rashba SOC and two-dimensional materials will make a qualitative leap in future semiconductor devices. Based on first-principles calculations, it is found that the applied strains along zigzag (ZZ), armchair (AC), and biaxial direction make the bandgaps of SnS and SnSe monolayers (ML) have an indirect-direct-zero transition. SnS and SnSe ML have a more stable electron spin and stronger Rashba spin splitting than InGaAs/InAlAs heterojunction and Au(1 1 1) surface. For SnS ML, 6% tensile strain along ZZ direction not only stabilizes the electron spin but also strengthens Rashba spin splitting to a maximum of 0.76 eV A. For SnSe ML, 2% tensile strain along biaxial direction makes Rashba spin splitting strength reach a maximum of 1.33 eV A.

Edges of single-walled carbon nanotubes (SWCNTs) have unique electronic structure and chemical reactivity that have not been fully explored yet. With help of the DFT and GFN2-xTB electronic structure calculations, we demonstrate for the first time that the zigzag edges of carbon nanotubes are capable of forming direct interlinking covalent bonds between the SWCNTs. The interlinking bond formation is predicted to be feasible for SWCNTs of different length, diameter, and chirality vectors. Covalent linking of SWCNTs might have implications in chemical and mechanical applications of SWCNTs.

Organic molecular devices are promising candidates for thermoelectric applications. By using density functional theory combined with non-equilibrium Green’s function method, we have investigated the thermoelectric properties of a single-molecule junction, which is constructed by 2,7-dialkyl [1] benzothieno [3,2-b] [1] benzothiophene derivatives (Cn-BTBT) connected with zigzag graphene nanoribbon electrodes. It is found that the phonon thermal conductance decreases with the increase of alkyl edge branches due to the local resonance. And the thermoelectric performance can be enhanced significantly by substituting bithiophene or biphosphole bridge anchor groups. A good thermoelectric figure of merit about 0.56 can be obtained near Fermi level. Moreover, we also found that the molecular device can be changed from p-type into n-type by changing the contact points, resulting in the transformation of Seebeck coefficient from positive to negative.

Strong heterogeneity, poor pay reservoir connectivity, and complex micro-pore structure are the reasons behind the high difficulty and low accuracy in the productivity evaluation of tight sandstone gas reservoirs. This paper utilized various well logging and mud logging curve data, summarizes the typical curve type, and made use of a mathematical method to form quantitative characterization. Additionally, a logging curve evaluation method is proposed based on the test of production capacity. The total hydrocarbon curve can be divided into six types as shown by the results: box shape, half box shape, upright triangle, inverted triangle, sawtooth shape, single peak, etc. The above is closely related to the level of oil and gas in the reservoir layer. Six types of total hydrocarbon curve can be quantified by amplitude, relative centroid, relative sawtooth, variance, and the parameter value of the autocorrelation function. The box-shaped total hydrocarbon gas logging curve is full and has a large scale. The half box-shaped total hydrocarbon gas logging curve peak scale is significantly smaller than that of the reservoir thickness. The triangularly-shaped total hydrocarbon gas logging curve may either be an upright or inverted triangle. The sawtooth-shaped total hydrocarbon gas logging curve has high and low tendencies that show a number of spikes. Single peak-shaped total hydrocarbon gas logging curve is small with a single peak. There is a good relationship between the six kinds of total hydrocarbon gas logging curve and the tight sandstone gas reservoir production capacity. The high and middle gas pay layers are mainly box-shaped and triangular, whereas the lower production layer is half box-shaped, triangular, and has a zigzag pattern. However, the low gas pay layers mainly possess a sawtooth pattern, while the non-production layer is mainly single peak in shape. The comprehensive interpretation of the total hydrocarbon gas logging curve and log resistivity curve can more accurately distinguish the production capacity of tight sandstone gas reservoirs. Finally, the quantitative model is used for automatic interpretation. Through data verification and analysis, it is found that the coincidence rate of the production gas pay layer is 80.95%, whereas the coincidence rate of production capacity is 78.05%. It is proven by practice that the gas formation capacity of tight sandstone gas reservoirs can be predicted based on the logging and mud logging well curve shapes. Keywords: Method of total hydrocarbon gas mud logging curve, Tight sandstone gas, Reservoir, Fracturing production well capacity

The consumption of electronic products has grown considerably in the last decades. These products become obsolete in a short period of time, generating electronic waste, which presents loads of materials harmful to health and metals of great value to industries. In this work, an innovative metal concentration technique for PCBs was applied aiming at the valuable metals recovery from ground printed circuit boards (PCBs) of computers that would be discarded. The PCBs were comminuted, classified by sieving and the metallic materials were processed in a zig-zag classifier type. The Schytil's phase diagram was developed to estimate the air flow rate to be used in the classifier. The product of each step was characterized. The copper content rose from 13.8% (w/w) to 48.8% (w/w) after the passage of the PCBs powder through the classifier. Its recovery and Newton's efficiency were above 89.4% and 0.91, respectively. The total content of metals was increased from 39.5% (w/w) to 89% (w/w) with a recovery of more than 82% and Newton's efficiency of 0.67 for the particle size in the range from 0.2 to 0.1 mm. The gold content has increased from 200 ppm to more than 8000 ppm after segregation by a simple manual concentration. Results shown that the use of zig-zag classifier to separate and concentrate metals was fairly effective, do not generate liquid and gaseous effluents and eliminates a number of pyrometallurgical or hydrometallurgical steps for metals obtaining. Keywords: Printed circuit boards, Recycling, Copper, Zig-zag classifier, Schytil's phase diagram

The dynamic behavior of two-dimensional nanostructures is important to the future application of nano devices. The vibrational behaviors of single-layered hexagonal boron nitride (h-BN) are studied by molecular dynamics simulation and continuum plate model. The bending stiffness and Poisson's ratios of h-BN along zigzag direction and armchair direction are calculated. H-BN is softer compared with graphene. The continuum plate model can predict the vibration of h-BN with four edge-clamped boundary conditions well. The electric fields in different directions have obvious influence on the vibration of h-BN. The natural frequency of h-BN changes linearly with the electric field intensity along the polarization direction. The natural frequency of h-BN decreases with the increase of electric field intensity along both positive and negative non-polarization direction. While the natural frequency of h-BN increases with the increase of electric field intensity along both positive and negative transverse electric field. Keywords: Hexagonal boron nitride, Molecular dynamics, Natural frequency, Electric field

Additively manufactured (AM) metamaterials with unparallel mechanical and biological properties have been of interest for many biomedical, aerospace, and defense applications. In this study, new findings on the structure-property relationships of a specific class of AM meta-biomaterials based on minimal surfaces which have not been well understood previously (i.e., Primitive and Schoen-IWP (IWP)) are presented. Biocompatible Ti-6Al-4V meta-biomaterials based on Primitive and IWP topologies, with three different morphological properties for each, were designed and fabricated via laser powder bed fusion technique. The microstructure, morphological, quasi-static compressive, flexural properties, and fracture mechanisms of the designed meta-biomaterials are thoroughly evaluated. Studied meta-biomaterials exhibited distinct fracture mechanisms under flexural loading depending on their topology; crack growth path was either zigzag (i.e., deflected) or straight. Additionally, Primitive meta-biomaterials exhibited ductile material behavior, under both compressive and flexural loading conditions, with pore size, porosity, and elastic gradient similar to the trabecular bone (850–1020 μm, 40–64%, and 3200–6000 MPa). However, IWP meta-biomaterials showed brittle behavior with porosity and elastic gradient closer to cortical bone (20–42% and 7000–13,000 MPa). These outcomes indicate that both mechanical behavior and fracture mechanisms of meta-biomaterials can be controlled based on topology and morphology.

In this study, the inverse finite element method (iFEM) is experimentally applied to real-time displacement reconstruction of a moderately thick wing-shaped sandwich structure via a network of strain sensors. For this purpose, the iFEM algorithm is incorporated to the kinematic relations of refined zigzag theory (RZT) by considering laminate mechanics of the woven-fabric reinforcement. After a twill-woven wing-shaped structure is manufactured with embedded fiber Bragg grating sensors and surface mounted strain gauges/rosettes, the discrete real-time experimental strains are acquired from these sensors concurrently during a flexural test of the structure. This data is then processed by iFEM algorithm for full-field displacement and strain monitoring. Moreover, the displacement fields at the one edge of the sandwich structure is monitored by digital image correlation (DIC) system simultaneously. Furthermore, the reference displacement solutions are established by performing high-fidelity FEM analysis. Finally, the three-dimensional real-time deformations and strains obtained through iFEM approach show very good consistency when compared to the results of DIC/FEM analysis and experimental strains, respectively. Overall, the present study serves as a comprehensive experimental guidance of iFEM-based shape and strain sensing for its realistic implementation on large-scale composite structures and notably increases technology readiness level of the iFEM methodology.

In this study, we propose a new I so G eometric formulation based on Refined Zigzag Theory (RZT), abbreviated as IG-RZT, for static analysis of laminated plates and sandwich panels with curvilinear fiber paths for the first time in literature. The original RZT formulation defines constant, linear, and zigzag deformation contributions of thickness coordinate to the in-plane displacements. This kinematic relation can accurately predict in-plane displacement of composite with straight fibers. However, estimating a realistic variation of in-plane displacements in a variable angle tow (VAT) composite is a more challenging problem as compared to the straight fiber composites. This difficulty has been addressed herein by including a quartic (fourth-order) polynomial thickness expansion that includes the transverse normal strain effects to the kinematic displacement fields of RZT. Moreover, the modelling of VAT composites results in the RZT zigzag functions to depend not only on the thickness coordinate but also on the in-plane positions. The present IG-RZT methodology is free of shear-locking and shear correction factors due to the integration of RZT with Non-Uniform Rational B-Splines (NURBS) functions of isogeometric analysis. The use of NURBS functions also enable the exact geometry data to be taken directly from a computer aided design (CAD) software, e.g., Rhinoceros, into an in-house Mathematica code. The accuracy and efficiency of the present IG-RZT formulation is assessed and validated by solving various examples of curvilinear fiber laminated plates with different aspect and span-to-thickness ratios. Comparison of IG-RZT results with reference solutions available in literature and generated by a commercial software (ANSYS) using 3D finite elements have demonstrated the remarkable benefits of the proposed IG-RZT method for predicting highly accurate both displacement and stress distributions of VAT composite structures.

We theoretically investigate the photonic band structure of layered photonic crystals composed of alternating layers of right- and left-handed materials (RHMs and LHMs). The dispersion curves are mainly studied by assuming that the dielectric permittivity and magnetic permeability are constant in each layer. It is shown that such structures can exhibit new types of electromagnetic modes and dispersion curves that do not exist in usual photonic crystals composed only of RHMs. In particular, we emphasize the possibility of bands that originate from the interface modes localized at the boundary between an LHM and RHM or from confined modes in one type of layers. These waves are evanescent in both or in one constituent of the photonic crystal. One of the passbands may lie below the light lines of the constituting material and go down to the static limit of a vanishing frequency ω, even at a value of the wavevector k|| (parallel to the layers) that is different from zero. For a given value of the wavevector k||, the dispersion curves ω versus k3 (where k3 is the Bloch wavevector of the periodic system along the axis of the photonic crystal) may exist only in a limited part of the photonic crystal Brillouin zone and exhibit a zigzag behavior instead of a monotonic behavior as in usual photonic crystals. With an appropriate choice of the parameters, we show that it is possible to realize an absolute (or omnidirectional) bandgap for either transverse electric (TE) or transverse magnetic (TM) polarization of the electromagnetic waves. A combination of two multilayer structures composed of RHMs and LHMs is proposed to realize, in a certain range of frequency, an omnidirectional reflector of light for both polarizations.

Graphenenanosheet (GNS), armchair graphenenanoribbon (AGNR), and zigzag graphenenanoribbon (ZGNR) systems were investigated by first principle calculations using the density functional theory (DFT). The DFT calculations explored the potential of utilization of these materials as gas sensors to detect hydrogen sulfide (H2S) gas. H2S gas adsorption was explored using: the adsorption energy (Eads), adsorption distance (D), charge transfer (ΔQ), density of states (DOS), and band structure of the generated systems before and after adsorption of H2S. The results showed that Eads of bare ZGNR was the highest of −0.171 eV as compared with GNS and AGNR. The surfaces of GNS, AGNR, and ZGNR have been modified with epoxy and then with a hydroxyl groups. The adsorption capacity of the three systems has been enhanced after the modifications with both the epoxy and hydroxyl groups. Based on the adsorption energy and charge transfer results, hydroxyl modified ZGNR system can be used effectively for detection applications of H2S since it exhibits the highest charge transfer and large adsorption energy. Open Access funding provided by the Qatar National Library.

We analytically and numerically investigated the dynamics of the Hermite–Gaussian (HG) beams in linear and nonlocal nonlinear fractional Schrodinger equations (SEs), in both one and two dimensions. In the linear regime, HG beams on the order of n > 1 were observed to undergo an initial compression phase before they split into two sub-beams. The sub-beams were saddle-shaped; the separation between them linearly increased with the propagation distance. Due to their nonlinear propagation dynamics, HG beams quite unexpectedly followed a zigzag trajectory in the real space, which corresponds to a modulated anharmonic oscillation in the momentum space. Although the beam was well localized during propagation, it still broadened and may become unstable. In the two-dimensional case, a superposition of HG beams showed a linear evolution similar to that in the one-dimensional case; however, because of orbital angular momentum, the beams in two dimensions exhibited incomplete rotation during propagation. In the nonlinear regime, the superposed HG input beam first evolved in the real space into a filiform structure and then into an annular structure, with periodic inversion and variable rotation.

Ferromagnetism in 2D materials has attracted extensive interest due to its possible applications for spintronics devices. Zigzag edges and defects, such as vacancies, can induce ferromagnetism in 2D materials. Alternatively, doping with a magnetic element can also introduce ferromagnetism in 2D materials. In this chapter, we introduce the research of magnetism in different 2D materials, such as graphene, boron nitride, SnO, black phosphors, and transition-metal dichalcogenide (TMD) by both theoretical calculations and experimental investigations. From the theoretical results, the ground state of pure 2D materials and the ferromagnetism after doping with a nonmagnetic element or magnetic element is discussed and introduced. In addition, the effect of defects is also discussed in detail. By introducing vacancies, the formation energy of magnetic element doping is strongly reduced and by the control of defects, the ferromagnetism in 2D materials can be manipulated. Experimentally, room-temperature ferromagnetism has been observed in magnetic element-doped TMD 2D materials by ion implantation.

The paper presents a locking-free four-node element for laminated composite and sandwich plates based on Refined Zigzag Theory (RZT). Initially, two RZT-based plate elements are derived using four-node and eight-node configurations, achieved by way of standard C0 isoparametric shape functions. In addition, with a view on improving the modelling of extremely thin plates, an anisoparametric four-node element is developed in which the transverse deflection variable is interpolated using quadratic polynomial shape functions, whereas the remaining kinematic variables are bilinear. A straightforward transverse-shear edge-constraint procedure gives rise to a four-node anisoparametric element. A further enhancement is achieved using an Element Shear Correction (ESC) factor that is derived from a strain-energy matching procedure. The resulting four-node element (ZQ4c) uses full Gauss quadrature, consistent load vector, and mass matrix. Furthermore, the ZQ4c stiffness matrix has no spurious zero-energy modes, and the element is extremely robust when modelling ultra-thin plates. Several numerical studies are carried out to demonstrate the predictive capabilities of the four elements examined in this investigation. It is concluded ZQ4c is a highly accurate element over a wide range of material systems and span-to-thickness ratios, and is the best performing element of the four elements examined in this study.

The initiation and propagation of uncertainties in structural behavior of complex anisotropic sandwich structures have significant computational challenges. Owing to limitations of experimental data, probabilistic descriptions of uncertain parameters are not practically feasible to expedite. This chapter presents the prediction capability of a surrogate model (polynomial neural network [PNN]) to estimate the stochastic buckling behavior of sandwich plates. The PNN is used to construct the surrogate. The computational time and cost is significantly reduced by using the proposed model in conjunction to finite element model using higher order zigzag theory. Both material and geometric uncertainties are considered to obtain the statistical quantity of interest. The computational efficacy of PNN is validated by means of scatter plot and probability density function plot. The constructed PNN model is found to be convergent with the results obtained by direct Monte Carlo simulation techniques. The proposed model can be used for more complex structures in future.

We analyze a method of regulating spin dynamics of the so-called magnetic graphene. Magnetic moments can be incorporated into graphene flakes and graphene ribbons through defects, such as adatoms and vacancies. Local spins can also be attached to graphene at hydrogenated zigzag edges. Spin flips can be produced by transverse pulses and by connecting the sample to a resonance electric coil. The action of the resonator feedback field strongly accelerates spin reversal. The possibility of fast spin reversal is important for spintronics and for quantum information processing allowing for an efficient functioning of spin registers.

Different scales of ribbon-like micelle presentation visualizing the linear propagation of hydrophilic (white circles) and hydrophobic (black zigzag lines) bands (top). The central picture visualizes the amyloid Aβ(15–40) containing 50 polypeptides. The long fragment of fibril Aβ(15–40) containing 200 peptides (bottom). The structures generated as the multiplication of short fragments available in PDB. The intensity of gray color is proportional to hydrophobicity level.

Because of the lack of information regarding the reliability of stretchable electronic circuits (SECs), this chapter presents the stress analysis of these circuits using a polymer material of polydimethylsiloxane (PDMS) as the substrate and a new formulated Ag flakes blends with PDMS (Ag-PDMS) conductive ink. The mechanical properties were characterized using the Neo-Hookean model for substrate and the multilinear plastic model for conductive ink. Different geometries of an SEC such as rectangular, zigzag, and horseshoe shape were modeled and analyzed under static structural analysis in simulation. The structural analyses were conducted on a real prototype of a thermal sensor circuit application. The structural integrity of the circuit under different geometries, loadings, and materials was assessed by investigating the deformation behavior of the circuit. The obtained results show that the critical area for stress concentration depends on the loading direction either parallel or perpendicular to the circuit printing. The high stress concentration produced at the inner side of the crest and through for both horseshoe and zigzag design. The yield stress for the conductive ink was 0.20 MPa. The stress–strain results of the entire model showed that the maximum equivalent stress was below the yield stress for a simple circuit that was limited to 10% strain applied at 0.19 MPa. However, the maximum equivalent stresses for a thermal sensor circuit exceed the yield stress for uniaxial vertical and biaxial loading at 8% strain and 1.3% strain plastic deformation, respectively. The horizontal loading gives no plastic deformation for a thermal sensor circuit at maximum equivalent stress 0.16 MPa.

A new family of rigid periodically zigzag structure of TiN1 + x and columnar TiN1 + x rods were synthesized by a vapor–liquid–solid deposition method, using iron as the catalyst and milled TiO2/Al powders as the starting material. Fundamental mechanism studies based on interface thermodynamics and surface tension were conducted in order to understand the formation of the near-perfect periodically zigzag structure. Four-terminal electrical measurements showed that the single crystalline rods yielded very different resistances due to their nonstoichiometric characteristics. The conductivity of the TiN1 + x rods could be affected by insulating-type electric field. The results indicated that TiN-based nano-rods have a big potential for application in electric scopes. Keywords: TiN, Zigzag structure, Growth mechanism, Electrical, Transportation properties

This study presents an isogeometric plate element, IG-RZT based on the refined zigzag theory (RZT) to model bending behavior of blade stiffened and unstiffened thick or thin laminates. This element is free of shear-locking and shear correction factors due to the use of Non-Uniform Rational B-Splines (NURBS) functions which satisfy the requirement of C 1 continuity in the computation of transverse shear stresses. Comparison of the predictions with IG-RZT element with the previous benchmark solutions reveals fast convergence and high accuracy for general laminate layups under different loading and boundary conditions. Thus, the IG-RZT element can be adopted for computationally efficient and accurate analysis of unstiffened and stiffened flat laminates.

International audience; The present work deals with the simulation of heat transfer in zigzag millimetric channels with square crosssection of 2mm width in the laminar flow regime. They consist of periodic zigzag units composed of straight sections and 90° bends with a curvature radius of 1.5 mm. The influences of fluid velocity and straight section length on the thermo-hydraulic performances are investigated. The results showed that by increasing the flow velocity or decreasing the straight section length between two bends, a transition from periodic flow to nonperiodic flow can be observed. A thermo-hydraulic performance factor based on heat transfer enhancement and pressure drop penalty compared with a straight channel is then discussed. It is observed that the ratio of the Nusselt number in the zigzag channels to that in the straight channel is always higher than one. This ratio increases with increasing Reynolds number and values up to 6.4 are reached in the cases studied (Pr=6.13). When the pressure drop penalty is considered in the performance factor, an enhancement is still observed with a factor up to 2.5. It is shown that non-periodic flow is not particularly interesting in terms of thermo-hydraulic performance compared with periodic flow.

Solids exhibit transverse shrinkage when they are stretched, except auxetics that abnormally demonstrate lateral expansion instead. Graphene possesses the unique normal-auxeticity (NA) transition when it is stretched along the armchair direction but not along the zigzag direction. Here we report on the anisotropic temperature-dependent NA transitions in strained graphene using molecular dynamics simulations. The critical strain where the NA transition occurs increases with respect to an increase in the tilt angle deviating from armchair direction upon uniaxial loading. The magic angle for the NA transition is 10.9°, beyond which the critical strain is close to fracture strain. In addition, the critical strain decreases with an increasing temperature when the tilt angle is smaller than the NA magic angle. Our results shed lights on the unprecedented nonlinear dimensional response of graphene to the large mechanical loading at various temperatures.

The stability and electronic properties of hexagonal and triangular silicene quantum dots are investigated under the effect of edge passivation by different elements and molecular groups. The structures experience a considerable alternation in shape depending on the attached elements or groups. The most noticeable alternations occur in zigzag triangular flakes passivated with sulfur and in all the selected flakes when OH groups are attached to their edge atoms. The resulting structure has a spherical shape with a large total dipole moment. All the studied clusters have been proven to be stable by the calculated positive binding energies. A flexible structure transformation from insulator (conductor) to conductor (insulator) is obtained in zigzag hexagonal-H (zigzag triangular-H) and zigzag hexagonal-S (zigzag triangular-OH), respectively. The magnetic properties of the triangular zigzag depend on the parity of the total number of Si atoms such that flakes with an even number of Si atoms will have antiferromagnetic properties while flakes with an odd number of Si atoms can have ferromagnetic or antiferromagnetic properties depending on the attached element or group. Thus, a proper choice of the attached functional groups or elements to silicene flakes allows tailoring of their properties to different application. In particular, hydrogenated or fluorinated flakes are highly interactive with the surrounding and can be used for sensor applications while clusters passivated with S or OH are insensitive to edge defects and have tunable electronic properties that make them promising in semiconductor device applications. Stability and electronic properties of edge functionalized silicene quantum dots: A first principles study © 2018. This is the authors’ accepted and refereed manuscript to the article. Locked until 18 July 2020 due to copyright restrictions. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

The paper presents an application of the extended Refined Zigzag Theory (eRZT) in conjunction with the Ritz method to the analysis of bending, free vibration and buckling of functionally graded carbon nanotube-reinforced (FG-CNTR) sandwich plates. Two stacking sequences are taken into consideration: sandwich panels with a homogeneous core and functionally graded face-sheets and sandwich panels with homogeneous face-sheets and a functionally graded core. After validating the convergence characteristics and the numerical accuracy of the developed approach using orthogonal and non-orthogonal admissible functions, a detailed parametric numerical investigation is carried out. Bending under bi-sinusoidal and uniform transverse pressure, free vibration and buckling loads under uniform in-plane uniaxial, biaxial and shearing loadings of FG-CNTR sandwich plates are studied. Numerical results for square and rectangular FG-CNTR sandwich plates under various combinations of geometry (core-to-face sheet thickness ratio and side to thickness ratio), different set of boundary conditions, CNTs volume fraction and grading laws are presented and discussed in detail. It is concluded that the eRZT predicts the response for static, stability and free vibration problems more accurately than first-order (FSDT) and third-order (TSDT) shear deformation theories, also for FG-CNTR sandwich plates.

We report the controlled growth of single crystals of intercalated layered Lu$ _{1+n} $Fe$ _{2+n} $O$ _{4+3n-\delta} $ ($ n $=1,2) with different oxygen stoichiometries ${\delta}$. For the first time crystals sufficiently stoichiometric to exhibit superstructure reflections in X-ray diffraction attributable to charge ordering were obtained. The estimated correlation lengths tend to be smaller than for not intercalated LuFe$ _2 $O$ _4$. For Lu$ _2 $Fe$ _3 $O$ _7 $, two different superstructures were observed, one an incommensurate zigzag pattern similar to previous observations by electron diffraction, the other an apparently commensurate pattern with ($\frac{1}{3}\frac{1}{3}0$) propagation. Implications for the possible charge order in the bilayers are discussed. Magnetization measurements suggest reduced magnetic correlations and the absence of an antiferromagnetic phase., Comment: 7pages, 7figures

Multilayer structures often present a challenge for equivalent single layer theories which are based on single displacement approximation through the thickness. This chapter first discusses the need for a different approach and then discusses two types of discrete layer approaches: layerwise theories and zigzag theories. In layerwise theories, separate displacement fields are assumed in each layer and displacement continuity conditions are enforced at each interface. This results in a number of variables to be determined that increases with the number of plies and discontinuities in the transverse normal and shear stresses at the interfaces. Zigzag theories reduce the number of variables by enforcing continuity of the transverse stresses and by discribing the kinematics of the deformation in terms of both global and ply-level variables. This results in a fixed number of unknowns regardless of the number of layers in the laminate. Both layerwise and zigzag theories treat each layer the same which can be a problem when there is a sharp contrast between plies in terms of material properties and/or thicknesses. This is the case for sandwich structures and, as a result, many theories have been developed with different assumptions for the facings and the core. The last section presents a comprehensive view of existing theories for analyzing sandwich structures.

The method for production of atomic chains by heating of graphene nanoribbons (GNRs) is proposed and studied by molecular dynamics simulations. The Brenner potential is revised to adequately describe formation of atomic chains, edges and vacancy migration in graphene. A fundamentally different behaviour is observed for zigzag-edge GNRs with 3 and 4 atomic rows (3 and 4-ZGNRs) at 2500 K: formation of triple, double and single carbon chains with the length of hundreds of atoms in 3-ZGNRs and edge reconstruction with only short chains and GNR width reduction in 4-ZGNRs. The chain formation mechanism in 3-ZGNRs is revealed by analysis of bond reorganization reactions and is based on the interplay of two processes. The first one is breaking of bonds between 3 zigzag atomic rows leading to triple chain formation. The second one is bond breaking within the same zigzag atomic row, which occurs predominantly through generation of pentagons with subsequent bond breaking in pentagons and results in single or double chain formation. The DFT calculations of the barriers for relevant reactions are consistent with the mechanism proposed. The possibility of chain-based nanoelectronic devices with a controllable number of chains is discussed., ASS, AMP and AAK acknowledge the Russian Foundation for Basic Research, Russia (Grant 18-02-00985). IVL acknowledges Grupos Consolidados del Gobierno Vasco, Spain (IT-578-13) and EU-H2020 project "MOSTOPHOS" (n. 646259).

In this chapter, different concepts from production to the characterization of carbon nanotubes (CNTs) are described. The construction of the actual chapter mainly starts with the description and comparison of the common synthesis techniques i.e. arc discharge, laser ablation, chemical vapour deposition (CVD), flame synthesis, and silane solution methods for the production of the CNTs, followed by the purification process and application potentials of these nanomaterials. Then, a fundamental demonstration and insight in the atomic structure of main CNT configurations (armchair, zigzag and chiral) is provided. In the subsequent subsection, various defect types, classified into two general groups of macroscopic disorders (curvature, twist and hetero-junction kink) and atomic scale defects (vacancies, impurities, perturbation and Stone-Wales defect), and their influence on the properties of CNTs as well as functionalization of CNTs and harvesting these defects for various applications are elucidated. Finally, the experimental and theoretical CNT characterization approaches are discussed and the pertaining results in the literature are presented. The results from literature reveals the fact that these nanostructures, not only involve different defect and disorder types from their synthesis process which reduce their individual mechanical stabilities and often necessitate purification process for their redundant impurities and by-products removal, but also from their functionalization process in which particular defects i.e. adatom doping and multi-CNT welding through hetero-junctions are intentionally employed for enhancing the properties and functionality of the CNTs for various applications from energy storing, gas detection and materials reinforcement to drug delivery and molecules transportation.

In this paper we study the effect of absorption peak correlation in finite length carbon nanotubes and graphene nanoribbons. It is shown, in the orthogonal {\pi}-orbital tight-binding model with the nearest neighbor approximation, that if the ribbon width is a half of the tube circumference the effect takes place for all achiral ribbons (zigzag, armchair and bearded), and corresponding tubes, starting from lengths of about 30 nm. This correlation should be useful in designing nanoribbon-based optoelectronics devices fully integrated into a single layer of graphene., Comment: 20 pages, 4 figures

A new spin-chain representation of the Temperley-Lieb algebra $TL_n(\beta=0)$ is introduced and related to the dimer model. Unlike the usual XXZ spin-chain representations of dimension $2^n$, this dimer representation is of dimension $2^{n-1}$. A detailed analysis of its structure is presented and found to yield indecomposable zigzag modules., Comment: 23 pages. Comments and references added

This chapter gives an overview of natural carbon and graphite and establishing some similarities with the properties of carbonaceous nanomaterials. A description of carbon's electronic properties and atomic structure is reviewed, including s- and p-orbitals, bonds, and hybridization. The discussion puts particular emphasis on the edge sites of graphite (primarily armchair and zigzag) and surfaces, and the dangling bonds associated with the edge sites relating their importance in applications.

The cross-sectional behaviour of laminated glass (LG) is characterised by a significant zigzag effect owing to the large stiffness mismatch between the glass and polymer layers. The approach incorporated in current glass design standards is based on the use of a monolithic model with an effective thickness, which suffers several sources of inaccuracy and limitations. In this paper, laminated shell elements with an alternating stiff/soft lay-up are enhanced and used to model LG structures, so as to accurately reproduce the through-thickness behaviour of LG with a minimal number of zigzag displacement parameters per node. In order to consider the influence of loading rate and temperature on the response of LG, a linear viscoelastic material model is adopted to simulate the polymer interlayer, which is formulated based on a recursive formula for stress calculation. Finally, several applications of the proposed modelling approach for two-ply and multi-ply LG structures are presented, considering typical deflection, stability and creep problems, where the benefits of the proposed approach are demonstrated through comparisons against monolithic shell models based on an effective thickness as well as 3D continuum models.

This chapter focuses on dynamic features of the helicoidal strip sensors with internal and external damping. We study the internal friction asymmetry and vibration parameters of these helicoidal systems. We also discuss the specifics of bifurcation in the helicoids, small and large impedance relations in vibrating contours, zigzag deflections in their frequency functions, three ways of frequency function linearization, and the advantage of differential transmission. These developments may be useful for modeling DNA dynamic functions, particularly, in single-protein spin resonance spectroscopy under ambient conditions.

Using hybrid density functional theory methods, we investigate the second hyperpolarizabilities (γ) of hexagonal shaped finite graphene fragments, which are referred to as hexagonal graphene nanoflakes (HGNFs), with two types of edge shapes: zigzag (Z) and armchair (A) edges. It is found that Z-HGNF, which gives intermediate diradical characters (y), exhibits about 3.3 times larger orthogonal components of γ (γxxxx = γyyyy in this case) than A-HGNF, which gives zero y value (closed-shell system). The γ density analysis reveals that this enhancement originates in the significant contribution of γ densities on edge regions in Z-HGNF. These observations strongly indicate that Z-HGNF is a promising candidate of open-shell singlet NLO systems.

Using spin-unrestricted density functional theory methods, the second hyperpolarizabilities, γ , of square nanographenes presenting different diradical characters are investigated from the viewpoint of open-shell singlet nonlinear optical systems. For nanographenes with intermediate diradical character, the γ component along the armchair edges is enhanced and amounts to about four times the γ component along the zigzag edges, whereas these γ components are of similar amplitudes when the system displays nearly pure diradical character. These observations are in conformity with the diradical character dependence of γ predicted in our previous studies.

This paper proposes a multi-layer formulation for the nonlinear analysis of laminated shells with an alternating stiff/soft lay-up. The zigzag variation of planar displacements is taken into account by adding to the Reissner–Mindlin formulation a specific set of zigzag function which is effective for the considered lay-up. Furthermore, a piecewise linear through-thickness distribution of the material transverse shear strain is assumed, which agrees well with the real distribution. The proposed lamination model with a low-order nonlinear strain–displacement relationship is incorporated within a co-rotational framework for geometric nonlinear analysis, thus upgrading the low-order local element formulation to large displacement analysis with relative ease. In addition, a local shell system is employed for direct definition of the additional zigzag displacement fields and associated parameters, which are thus excluded from the large displacement co-rotational transformations. The application of the proposed laminated shell modelling approach is illustrated in this paper for a 9-noded co-rotational shell element, which utilises the Mixed Interpolation of Tensorial Components (MITC) method in the local system for overcoming locking effects. Several linear and nonlinear numerical examples of multi-layer shell structures with alternating stiff/soft lay-ups are used to illustrate the effectiveness and efficiency of the proposed modelling approach.

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A mixed-field Refined Zigzag Theory (RZT(m)) for laminated plates is presented. The theory is developed using Reissner’s Mixed Variational Theorem (RMVT) and employs the kinematic assumptions of the displacement-based Refined Zigzag Theory (RZT). In addition, a robust set of assumed transverse-shear stresses is implemented. The stresses, initially derived by integration of the three-dimensional elasticity equations, satisfy a priori the continuity conditions along the layer interfaces and on the bounding surfaces. With the aid of the strain-compatibility variational statement of RMVT, the transverse-shear stresses are expressed in terms of first-order derivatives of the kinematic variables. The RZT(m) retains a fixed number of kinematic variables (seven) regardless of the number of material layers. To ascertain the importance of transverse-shear stress assumptions, the layer-wise polynomial approximation scheme is also implemented. Numerical results concerning the elasto-static and vibration problems of simply supported and clamped plates, demonstrate that RZT(m) is more accurate than RZT, both in terms of local and global responses. These results also reveal that the transverse-shear stresses achieved by a layer-wise polynomial scheme are considerably less accurate, particularly for highly heterogeneous laminates. Furthermore, the RZT(m) is well suited for developing C 0 -continuous finite elements, thus resulting attractive for large-scale analysis of laminated structures.

A third-order Refined Zigzag Theory for multilayered composite and sandwich beams is developed based on the Reissner Mixed Variational Theorem. The assumed kinematics enriches the Timoshenko’s beam Theory: a second- and a third-order smeared polynomial terms along with a piece-wise linear contributions are added to the axial displacement, whereas the transverse displacement is approximated with a power-series expansion up to the second-order term. Transverse shear and normal stress, continuous and able to satisfy the boundary stress conditions on the outer beam surfaces, are assumed by the model: the transverse shear stress is derived with the aid of the Elasticity equations, whereas a third-order power-series expansion is adopted for the transverse normal stress. Based on the proposed model, an efficient C 0 -continuous beam element is formulated by adopting the anisoparametric interpolation strategy to avoid the shear locking phenomenon. The accuracy of the proposed model and the finite element implementation is assessed by solving problems concerning the elasto-static behavior of generally laminated beams, both simply supported and clamped at the ends. Comparison with reference solution (Elasticity or high-fidelity FE model) demonstrates the remarkable accuracy of the proposed model, both in terms of displacements and stresses distributions, as well as the finite element implementation efficiency.

Inkjet printing of functional materials is the key technology toward ultra-low-cost, large-area electronics. Low-temperature 3D micro-metal structure fabrication was developed by direct inkjet printing of metal nano-particles (NPs) as a versatile, direct 3D metal structuring approach representing an alternative to conventional vacuum deposition and photolithographic methods. Metal NP ink was inkjet printed to exploit the large melting temperature drop of the nano-material and the ease of the NP ink formulation. Parametric studies on the basic conditions for stable 3D inkjet printing of NP ink will be explained. Furthermore, diverse 3D metal micro-structures, including micro-metal pillar arrays, helical, zigzag, and micro-bridges were demonstrated and electrical characterization will be given as examples. Since the process requires low temperature, it carries substantial potential for fabrication of electronics on a plastic substrate.

The Refined Zigzag Theory (RZT) has been recently developed for the analysis of homogeneous, multilayer composite and sandwich plates. The theory has a number of practical and theoretical advantages over the widely used First-order Shear Deformation Theory (FSDT) and other types of higher-order and zigzag theories. Using FSDT as a baseline, RZT takes into account the stretching, bending, and transverse shear deformations. Unlike FSDT, this novel theory does not require shear correction factors to yield accurate results for a wide range of material systems including homogeneous, laminated composite, and sandwich laminates. The inplane zigzag kinematic assumptions, which compared to FSDT add two additional rotation-type kinematic variables, give rise to two types of transverse shear strain measures – the classical average shear strain (as in FSDT) and another one related to the cross-sectional distortions enabled by the zigzag kinematic terms. Consequently, with a fixed number of kinematic variables, the theory enables a highly accurate modeling of multilayer composite and sandwich plates even when the laminate stacking sequence exhibits a high degree of transverse heterogeneity. Unlike most zigzag formulations, this theory is not affected by such theoretical anomalies as the vanishing of transverse shear stresses and forces along clamped boundaries. In this paper, six- and three-node, C 0 -continuous, RZT-based triangular plate finite elements are developed; they provide the best compromise between computational efficiency and accuracy. The element shape functions are based on anisoparametric (aka interdependent) interpolations that ensure proper element behavior even when very thin plates are modeled. Continuous edge constraints are imposed on the transverse shear strain measures to derive coupled-field deflection shape functions, resulting in a simple and efficient three-node element. The elements are implemented in ABAQUS – a widely used commercial finite element code – by way of a user-element subroutine. The predictive capabilities of the new elements are assessed on several elasto-static problems, which include simply supported and cantilevered laminated composite and sandwich plates. The numerical results demonstrate that the new RZT-based elements provide superior predictions for modeling a wide range of laminates including highly heterogeneous sandwich laminations. They also offer substantial improvements over the existing plate elements based on FSDT as well as other higher-order and zigzag-type elements.

In this paper, we propose to use the Murakami’s zig-zag theory for the static and vibration analysis of laminated plates, by local collocation with radial basis functions in a finite differences framework. The equations of motion and the boundary conditions are obtained by the Carrera’s Unified Formulation, and further interpolated by a local collocation with radial basis functions and finite differences. This paper considers the analysis of static deformations, free vibrations and buckling loads on laminated composite plates.

The chapter presents a crystallogeometrical analysis of the geometry of micro- and macrocracks in a Ti3Al single crystal with an orientation where the basal slip is operative. The basal and {1 0 1¯ 1}, {1 0 1¯ 2}, {1¯1¯ 2 3} pyramidal planes are the planes of micro- and macrocracks facets. The coalescence of shear microcracks in the basal plane leads to the zigzag crack formation on the fracture surface. A model for shear microcrack nucleation with screw a-superdislocations interacting in the slip band of the basal planes is described. The macrocracks path behaviour in the Ti3Al single crystal is discussed based on the model.

Chiral hollow tubule with chiral mesoporous channels was observed for the first time. The chiral tubule possessing a hexagonal cross section, with outer diameter of about 300 nm, and inter diameter of about 50 nm, was synthesized from a two-phase acidic system using achiral surfactant cetyltrimethylammonium bromide (CTAB). Furthermore, the helical meso-channels in the tubule exhibited zigzag lattice fringes along the tubule axis in TEM micrographs.

This chapter discusses electronic and magnetic properties of nanographites. Nanometer-sized systems with open boundaries called nanographites display unusual features where the presence of edges of various shapes determines the electronic states. It is found that the electronic states are strongly influenced by the existence and shape of graphite edge. Zigzag edges produce the localized edge states, which give a sharp peak in the density of states at the Fermi energy. The orbital magnetic susceptibility of nanographites has the intermediate values between those of aromatic molecules and bulk graphites. The orbital magnetic susceptibility can be scaled as a function of the Fermi energy, temperature, and ribbon width. Zigzag ribbons show the large Pauli paramagnetic response at low-temperature due to the existence of the sharp peak in the density of states at the Fermi energy, whereas, in armchair ribbons, the Pauli paramagnetic susceptibility is negligible. It is found that in the activated carbon fiber and graphitized nanodiamonds, the dangling bonds are terminated by other elements. Their magnetic susceptibility shows the Curie–Weiss behavior originating from localized spins. Results suggest that in nanographite systems, the paramagnetic response due to the nonbonding edge states are crucial, resulting in the nonographites assigning completely different systems from bulk graphites and aromatic molecules in the viewpoint of the magnetic properties.