Zigzag Boundary Research Articles

Antenna Radiation Characteristics Optimization by a Hybrid Topological Method

A hybrid topology optimization method that integrates material distribution and level set methods (LSMs) is proposed. The topology of the antenna is optimized first by the material distribution method, and then, the derived structure, which has a zig-zag boundary, is further optimized by the LSM. By adopting this hybrid strategy, the powerful topology-searching ability of the material distribution method and the advantageous feature of producing structures with smooth and low sensitivity boundary of the LSM are fully exploited. To optimize antenna’s radiation characteristics, sensitivity analysis of the power density of the far-field is formulated. To demonstrate the capability of this hybrid topology optimization method and verify the sensitivity analysis formulation, three microstrip antennas with different desired polarizations, beam directions, and bandwidths are designed and tested. The measured results show that all the antennas not only achieve low reflection in the prescribed frequency band, but also give good performances in gain and polarization in the desired beam directions.

Formation of Widmanstätten Austenite in Strip Cast Grain-Oriented Silicon Steel

The formation of Widmanstatten austenite was studied in strip cast grain-oriented silicon steel. The microstructure was investigated by optical microscopy and scanning electron microscopy. The orientations of the ferrite, Widmanstatten austenite, and martensite were determined using electron backscatter diffraction. The Widmanstatten austenite exhibits a lath-like shape and nucleates directly on the ferrite grain boundaries. This differs significantly from earlier work on duplex stainless steels. The orientation relationship between the Widmanstatten austenite and the parent ferrite is closer to Kurdjumov–Sachs than to Nishiyama–Wassermann. The ferrite boundaries migrate so as to accommodate the habit planes of the laths, leading to the presence of zigzag boundaries in the as-cast strip. Carbon partitioning into the Widmanstatten austenite and silicon partitioning into the parent ferrite were observed.

Energetics and kinetics of phase transition between a 2H and a 1T MoS2 monolayer-a theoretical study.

Phase transitions between semiconducting 2H and metallic 1T (or 1T') molybdenum disulphides (MoS2) are explored comprehensively by first-principles calculations. The nucleation of a 1T (or 1T') nucleus in a 2H MoS2 lattice, the formation of the 2H-1T (1T') interfaces and the kinetics of interface propagation during phase transition were thoroughly investigated in this study. It was found that, among various potential interface structures between the two phases, Mo-rich and two S-rich zigzag (ZZ) boundaries are energetically more preferable than others. Therefore, triangular or hexagonal 1T MoS2 domains with the three types of ZZ boundaries are expected to be the equilibrium structures of the 1T nucleus in a 2H lattice. Further exploration reveals a very high nucleation energy of the 1T phase which suggests that the nucleation may start from a defect site or the edge of the 2H phase. Besides, the kinetics of 2H-1T (1T') boundary propagation show that the growth rate of the ZZ boundaries is significantly slower than the armchair (AC) ones'. Therefore, the ZZ-boundary dominated domains are expected to be observed during the growth of the 1T phase while the rounded domains with various high-index edges are expected to be seen throughout shrinkage. This study reveals both the energetics and the kinetics of the phase transition of transition metal dichalcogenide materials and also sheds light on other 2D materials.

Tunable spin–orbit coupling and symmetry-protected edge states in graphene/WS2

We demonstrate clear weak anti-localization (WAL) effect arising from induced Rashba spin–orbit coupling (SOC) in WS2-covered single-layer and bilayer graphene devices. Contrary to the uncovered region of a shared single-layer graphene flake, WAL in WS2-covered graphene occurs over a wide range of carrier densities on both electron and hole sides. At high carrier densities, we estimate the Rashba SOC relaxation rate to be and show that it can be tuned by transverse electric fields. In addition to the Rashba SOC, we also predict the existence of a‘valley-Zeeman’ SOC from first-principles calculations. The interplay between these two SOC’s can open a non-topological but interesting gap in graphene; in particular, zigzag boundaries host four sub-gap edge states protected by time-reversal and crystalline symmetries. The graphene/WS2 system provides a possible platform for these novel edge states.

Magnetic-flux-driven topological quantum phase transition and manipulation of perfect edge states in graphene tube

We study the tight-binding model for a graphene tube with perimeter N threaded by a magnetic field. We show exactly that this model has different nontrivial topological phases as the flux changes. The winding number, as an indicator of topological quantum phase transition (QPT) fixes at N/3 if N/3 equals to its integer part [N/3], otherwise it jumps between [N/3] and [N/3] + 1 periodically as the flux varies a flux quantum. For an open tube with zigzag boundary condition, exact edge states are obtained. There exist two perfect midgap edge states, in which the particle is completely located at the boundary, even for a tube with finite length. The threading flux can be employed to control the quantum states: transferring the perfect edge state from one end to the other, or generating maximal entanglement between them.

A unified growth model of the secondary grain boundary α phase in TA15 Ti-alloy

The growth mechanisms of the flat, zig-zag and mixed secondary grain boundary α (αGB) phase in TA15 Ti-alloy were investigated through heat treat experiment (cooled from β-phase field at a constant rate combined with interrupted water quenching). A unified growth model was proposed by introducing the relationship between the critical length of flat αGB (Lc) and β grain boundary (GB) length. The Lc is related to the characteristic and energy of the host GB, possible variants and habit plane of αGB, and chemical driving force. αGB preferentially nucleates at a triple junction (TJ) and extends on one side of β GB to form the flat morphology. Deviated growth of the heterogeneously and separately nucleated αGB on a high-angle grain boundary results in zia-zag morphology. The driving force and time available for αGB growth on the undecorated β GB determines its type, connected or unconnected. The flat and zig-zag αGB showed a competitive growth, and if αGB nucleated at the TJs and in the middle of the β GB simultaneously, the mixed αGB would appear.

Perfect Spin-filtering in graphene monolayer-bilayer superlattice with zigzag boundaries.

We show that the spontaneous magnetization is formed at the zigzag boundary between monolayer and bilayer graphene by the self-consistent calculation based on Hubbard model. In a monolayer- bilayer graphene superlattice with zigzag boundaries, it is surprising that nearly 100% spin polarization is achieved in the energy window around the Dirac point, no matter the magnetization configuration at two boundaries is parallel or antiparallel. The reason is that the low-energy transport is only influenced by the magnetization at one edge, but not by that at the other. The underlying physics is unveiled by the spin-split band structure and the distribution of the wave-function pertaining to the lowest (highest) subband of electron (hole).

Energy levels of hybrid monolayer-bilayer graphene quantum dots

Often real samples of graphene consist of islands of both monolayer and bilayer graphene. Bound states in such hybrid quantum dots are investigated for (i) a circular single-layer graphene quantum dot surrounded by an infinite bilayer graphene sheet and (ii) a circular bilayer graphene quantum dot surrounded by an infinite single-layer graphene. Using the continuum model and applying zigzag boundary conditions at the single-layer--bilayer graphene interface, we obtain analytical results for the energy levels and the corresponding wave spinors. Their dependence on perpendicular magnetic and electric fields are studied for both types of quantum dots. The energy levels exhibit characteristics of interface states, and we find anticrossings and closing of the energy gap in the presence of a bias potential.

Strain-tunable half-metallicity in hybrid graphene-hBN monolayer superlattices

As research in 2-D materials evolves toward combinations of different materials, interesting electronic and spintronic properties are revealed and may be exploited in future devices. A way to combine materials is the formation of spatially periodic domain boundaries in an atom-thick monolayer: as shown in recent reports, when these domains are made of graphene and hexagonal boron nitride, the resulting superlattice has half-metallic properties in which one spin component is (semi)metallic and the other is semiconductor. We explore here the range of spin-dependent electronic properties that such superlattices can develop for different type of domain boundaries, domain widths, and values of tensile strain applied to the monolayer. We show evidence of an interplay between strain and domain width in determining the electronic properties: while for armchair boundaries the bandgap is the same for both spin components, superlattices with zigzag boundaries exhibit rich spin-dependent behavior, including different bandgaps for each spin component, half-metallicity, and reversal of half-metallicity. These findings can lead to new ways of controlling the spintronic properties in hybrid-domain monolayers, which may be exploited in devices based on 2-D materials.

Bottom-up fabrication of graphene nanostructures on Ru

Investigations on the bottom-up fabrication of graphene nanostructures with 10, 10’-dibromo-9, 9’-bianthryl (DBBA) as a precursor on Ru were carried out using scanning tunnelling microscopy (STM) and density functional theory (DFT) calculations. Upon annealing the sample at submonolayer DBBA coverage, N = 7 graphene nanoribbons (GNRs) aligned along the direction form. Higher DBBA coverage and higher annealing temperature lead to the merging of GNRs into ribbon-like graphene nanoflakes with multiple orientations. These nanoflakes show different Moiré patterns, and their structures were determined by DFT simulations. The results showed that GNRs possess growth preference on the Ru substrate with a rectangular unit cell, and GNRs with armchair and zigzag boundaries are obtainable. Further DFT calculations suggest that the interaction between graphene and the substrate controls the orientations of the graphene overlayer and the growth of graphene on Ru.

Microstructural Characteristics of Plasma Nitrided Layer on Hot-Rolled 304 Stainless Steel with a Small Amount of α-Ferrite

The hot-rolled 304 stainless steel with γ-austenite and approximately 5 pct α-ferrite elongated along the rolling direction was plasma-nitrided at a low temperature of 693 K (420 °C). X-ray diffraction results revealed that the nitrided layer was mainly composed of the supersaturated solid solution of nitrogen in austenite (γN). Transmission electron microscopy (TEM) observations showed that the microstructure of the γN phase exhibited “fracture factor contrast” reflective of the occurrence of fine pre-precipitations in γN by the continuous precipitation. The occurrence of a diffuse scattering effect on the electron diffraction spots of γN indicated that the pre-precipitation took place in γN in the form of strongly bonded Cr-N clusters or pairs due to a strong attractive interaction of nitrogen with chromium. Scanning electron microscopy and TEM observations indicated that the discontinuous precipitation initiated from the γ/α interfaces and grew from the austenite boundaries into austenite grains to form a lamellar structure consisting of CrN and ferrite. The orientation relationship between CrN and ferrite corresponded to a Baker-Nutting relationship: (100)CrN//(100)α; [011]CrN//[001]α. A zigzag boundary line following the banded structure of alternating γ-austenite and elongated α-ferrite was presented between the nitrided layer and the substrate to form a continuous varying layer thickness, which resulted from the difference in diffusivities of nitrogen in α-ferrite and γ-austenite, along the γ/α interfaces and through the lattice. Microstructural features similar to the γN were also revealed in the ferrite of the nitrided layer by TEM. It was not excluded that a supersaturated solid solution of nitrogen in ferrite (αN) formed in the nitrided layer.

Remotely Sensing Image Fusion Based on Wavelet Transform and Human Vision System

Wavelet transform has many good characteristics, used extensively in image fusion. In recent years, many algorithms have been developed, but there exist some inherent defects such as image blur, burr phenomenon, zigzag boundaries and image discontinuity. In this theory, without considering disadvantages of HVS, especially fused image should preserve brightness and texture features which are the most sensitive to eye, so a new algorithm combining them is proposed. Firstly, by calculating brightness and texture metrics in different wavelet decomposition subimages. And then, by using root mean square rule to get fused low frequency and high frequency coefficients respectively. Finally, performing inverse wavelet transform by the concatenation of low frequency and high frequency to gain fused image. In order to evaluate different algorithms, the assessment metric based on HVS is adopted, which is a more comprehensive and effective measure. Experiments merging IKONOS Pan image(resolution is 1 meter) with multispectral image (resolution is 4 meter) show that the proposed algorithm is the best on brightness, contrast, texture, definition, resolution, object edge regardness of visual effect and objective metric, also verifing human visual characteristic to be considered in image fusion.

Mechanical manipulations on electronic transport of graphene nanoribbons

We study the effects of uniaxial strains on the transport properties of graphene nanoribbons (GNRs) connected with two metallic leads in heterojunctions, using the transfer matrix method. Two typical GNRs with zigzag and armchair boundaries are considered and the tension is applied either parallel or perpendicular to the ribbon axis. It turns out that the electron–hole symmetry is missing in the gate voltage dependence of the conductance data of the armchair GNRs, while it persists in the zigzag ribbons under any strains. For an armchair GNR with a vertical tension applied, a sharp drop of conductance is found near the critical value of the strain inducing a quantum phase transition, which allows one to determine the critical strain accurately via measuring the conductance. In the zigzag ribbon, there exists a range of gate voltage around zero, where the conductance is insensitive to the small horizontal strains. The band structures and low-energy properties are calculated to elucidate the mechanism on the strain effects in GNRs. We expect that our results can be useful in developing graphene-based strain sensors.

An improved particle method for simulation of the non-isothermal viscoelastic fluid mold filling process

A non-isothermal molding filling process for a non-Newtonian viscoelastic fluid is investigated in this work. An extended smoothed particle hydrodynamics with diffusive term and kernel gradient correction (extended SPH_DTKGC) method is first presented to simulate the non-isothermal molding filling for the viscoelastic fluid based on the coupled eXtended Pom-Pom (XPP) and thermal power-law model. Meanwhile, a suitable discrete temperature scheme in the SPH frame is proposed. And a new way to treat the zig-zag boundary is given and expected to deal with arbitrary shaped rigid wall. Subsequently, the merits of the proposed boundary treatment are demonstrated by a spin-down problem and the filling process in a C-shaped mould. The ability of the extended SPH_DTKGC to simulate the viscoelastic free surface flow is verified by the several classical problems. Two benchmark problems are presented to display the reliability of the proposed temperature scheme. The non-isothermal filling process for a power-law fluid is performed to show the feasibility of the extended SPH_DTKGC to simulate the non-isothermal mold filling process. Then the extended SPH_DTKGC method combined with other improvements is applied to the non-isothermal filling processes based on the coupled XPP and power-law model. Especially, the influences of the parameters of the XPP model on the physical quantities, such as the first normal stress difference and the temperature field, are numerically predicted.

Synthesis and electrical properties of In2O3(ZnO)m superlattice nanobelt**Project supported by the National Natural Science Foundation of China (Grant No. 51172058), the Key Project of the Science Technology and Research Project of Education Bureau, Heilongjiang Province, China (Grant No. 12521z012), and the Natural Science Foundation of Heilongjiang Province for Returned Chinese Scholars, China (Grant No. LC2013C17).

One-dimensional (1D) In2O3(ZnO)m superlattice nanobelts are synthesized by a chemical vapor deposition method. The formation of the In2O3(ZnO)m superlattice is verified by the high-resolution transmission electron microscopy images. The typical zigzag boundaries could be clearly observed. An additional peak at 614 cm−1 is found in the Raman spectrum, which may correspond to the superlattice structure. The study about the electrical transport properties reveals that the In2O3(ZnO)m nanobelts exhibit peculiar nonlinear I–V characteristics even under the Ohmic contact measurement condition, which are different from the Ohmic behaviors of the In-doped ZnO nanobelts. The photoelectrical measurements show the differences in the photocurrent property between them, and their transport mechanisms are also discussed.

Electromechanical response at polar zigzag boundaries in hybrid monolayers

First-principles calculations are used to demonstrate electromechanical control of charge and spin at zigzag-edged interfaces between graphene and boron-nitride domains in hybrid monolayers. We show how, through a direct piezoelectric effect, the interfacial bound charges and associated electric fields can be tuned by application of an external mechanical force (stress) on the system. This results in mechanical control of the edge magnetization (piezomagnetic effect), and the possibility to transform a semiconducting heterostructure into a half-metal. The inverse effect (application of an external electric field to induce a mechanical deformation) goes together with a magnetoelectric response, which under ideal conditions we estimate to be comparable to that of prototypical ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$. These effects originate from the magnetic properties of graphene's zigzag edges and the dielectric properties of the boron-nitride domain, and can also be expected in any other coplanar heterostructures with polar discontinuities.

Conductance Spectra in Graphene-Superconductor Junctions

The conductance spectra of a graphene ribbon and graphene-superconductor (G-S) junctions are investigated, using the tight-binding model and non-equilibrium Green' function formalism. It is found that the quantized conductance related to graphene' edge-states is robust against perturbations in the model parameters for a graphene monolayer ribbon with the zigzag boundary. With appropriate model parameter of the spin-orbit interaction strength, a new bound state with odd-frequency symmetry is found in the G-S junction. An enhancement in the zero-energy conductance amplitude is followed.

Spectra of graphene nanoribbons with armchair and zigzag boundary conditions

We study the spectral properties of the two-dimensional Dirac operator on bounded domains together with the appropriate boundary conditions which provide a (continuous) model for graphene nanoribbons. These are of two types, namely, the so-called armchair and zigzag boundary conditions, depending on the line along which the material was cut. In the former case, we show that the spectrum behaves in what might be called a classical way; while in the latter, we prove the existence of a sequence of finite multiplicity eigenvalues converging to zero and which correspond to edge states.

Quasi-Freestanding Monolayer Heterostructure of Graphene and Hexagonal Boron Nitride on Ir(111) with a Zigzag Boundary

In-plane heterostructure of hexagonal boron nitride and graphene (h-BN-G) has become a focus of graphene research owing to its tunable bandgap and intriguing properties. We report herein the synthesis of a quasi-freestanding h-BN-G monolayer heterostructure on a weakly coupled Ir(111) substrate, where graphene and h-BN possess distinctly different heights and surface corrugations. An atomically sharp zigzag type boundary has been found to dominate the patching interface between graphene and h-BN, as evidenced by high-resolution Scanning tunneling microscopy investigation as well as density functional theory calculation. Scanning tunneling spectroscopy studies indicate that the graphene and h-BN tend to exhibit their own intrinsic electronic features near the patching boundary. The present work offers a deep insight into the h-BN-graphene boundary structures both geometrically and electronically together with the effect of adlayer-substrate coupling.

Energy levels of double triangular graphene quantum dots

We investigate theoretically the energy levels of the coupled double triangular graphene quantum dots (GQDs) based on the tight-binding Hamiltonian model. The double GQDs including the ZZ-type, ZA-type, and AA-type GQDs with the two GQDs having the zigzag or armchair boundaries can be coupled together via different interdot connections, such as the direct coupling, the chains of benzene rings, and those of carbon atoms. It is shown that the energy spectrum of the coupled double GQDs is the amalgamation of those spectra of the corresponding two isolated GQDs with the modification triggered by the interdot connections. The interdot connection is inclined to lift up the degeneracies of the energy levels in different degree, and as the connection changes from the direct coupling to the long chains, the removal of energy degeneracies is suppressed in ZZ-type and AA-type double GQDs, which indicates that the two coupled GQDs are inclined to become decoupled. Then we consider the influences on the spectra of the coupled double GQDs induced by the electric fields applied on the GQDs or the connection, which manifests as the global spectrum redistribution or the local energy level shift. Finally, we study the symmetrical and asymmetrical energy spectra of the double GQDs caused by the substrates supporting the two GQDs, clearly demonstrating how the substrates affect the double GQDs' spectrum. This research elucidates the energy spectra of the coupled double GQDs, as well as the mechanics of manipulating them by the electric field and the substrates, which would be a significant reference for designing GQD-based devices.