Sublattice Points Research Articles

Sr-doped CuFe2O4 nanoparticles: Exploring structural, magnetic, and blood compatibility characteristics

The aim of this study is to investigate the structural, magnetic, and blood compatibility properties of Sr2+ substituted for Cu2+ in Cu1−xSrxFe2O4 (x = 0.0 to 1 with a 0.25 increment) nanoparticles synthesized via the sol-gel auto-combustion technique. Regardless of the substitution rate, the sol-gel auto-combustion method consistently yields powders with sizes ranging from 20 to 40 nm. The specific surface area of the produced powders is determined as 12 m2/g. X-ray diffraction analysis reveals that CuFe2O4 exhibits a singular phase; however, as the Sr2+ ion substitution increases, the emergence of various secondary phases becomes apparent, with their proportions increasing with the substitution rate. The magnetic characteristics of the synthesized powders exhibit variations in magnetization, correlating with the distribution of cations in the sublattice points. Coercivities are influenced by both anisotropy and secondary phases. Saturation magnetization decreases from 31.3 (CuFe2O4) to 7.6 (SrFe2O4) emu/g with Sr replacement. The lowest observed coercivity is 429.5 Oe in powders prepared with CuFe2O4 composition, while the highest is measured at 583.8 Oe in nanopowders prepared with Cu0.5Sr0.5Fe2O4 composition. Moreover, blood compatibility experiments indicate significantly low hemolysis ratios for Cu1−xSrxFe2O4 nanoparticles. Additionally, all examined samples exhibit an increase in Soret band intensity compared to the negative control test, suggesting potential biocompatibility.

Indirect characterization of point defects in proton irradiated ceria

A rate theory model informed by multimodal characterization is used to evaluate the concentration of point defects in irradiated materials. Cerium dioxide (CeO2) is used as a model ionic compound, whose cation and anion sublattice point defects evolve independent of each other, but extended defects in the form of dislocation loops retain stoichiometry of the compound. To demonstrate this, we performed extensive measurement of defect evolution in CeO2 exposed to energetic protons at elevated temperature. Two sintered polycrystalline CeO2 samples were irradiated with protons having energies up to 2.5 MeV. Both samples were irradiated at 600°C to a dose of 0.14 dpa, but with different dose rates. These irradiation conditions produced a rich microstructure with resolvable extended defects and a significant concentration of point defects. Dislocation loop density revealed by electron microscopy and lattice constant changes measured by X-ray diffraction (XRD), and mesoscale thermal conductivity measurements were used to parameterize the rate theory model. The model, which includes point defect generation, recombination, and clustering into stoichiometric interstitial loops, suggests a large concentration of cerium vacancies and interstitials is present under these irradiation conditions. This work lays the foundation for expanded multimodal characterization of microstructure, including more direct characterization of point defects using optical spectroscopies.

Predictive side decoding for human-centered multiple description image coding

Multiple description coding (MDC) provides a favorable solution for human-centered image communication, which takes into account people’s varying watching situations as well as people’s demand for real-time image display. As an effective technique for MDC, three-description lattice vector quantization (3D-LVQ) is considered for image coding in this paper. Based on intra- and inter-correlation in the 3D-LVQ index assignment as well as wavelet intra-subband correlation, a novel predictive decoding method for 3D-LVQ-based image coding is proposed to enhance side decoding performance, which attempts to predict lost descriptions (sublattice points) in a good way for better reconstructions of wavelet vectors (fine lattice points) in the side decoding. Experimental results validate effectiveness of the proposed decoding scheme in terms of rate-distortion performance.

Tunable in-plane topologically protected edge waves in continuum Kagome lattices

In this paper, we report the evidence of topologically protected edge waves (TPEWs) in continuum Kagome lattice. According to the bulk edge correspondence principle, such edge states are inherently linked with the topological characteristics of the material band structure and can, therefore, be predicted evaluating the associated topological invariant. Due to the non-trivial band structures shown in the context of quantum valley Hall effect, TPEWs are supported at the interface between two lattices characterized by different valley Chern numbers. The break of lattice symmetry is obtained here, in contrast with other similar works in continuum elastic structures, biasing in the stiffness properties of the unit cell, instead of manipulating mass at sublattice points. This opens new promising possibilities related to waveguide tunability and wave propagation control, exploiting the established techniques for stiffness modulation in elastic structures. A sensitivity analysis of robustness of the supported energy transport is provided, showing the amount of de-localized disorder the waveguide is immune to, and how performances are affected by perturbations in the nominal parameters of the lattice.

RKKY interaction in graphene with a line defect

A kind of extended line defect is currently an experimentally available one-dimensional topological structure in graphene lattice. It modifies the electronic properties of graphene in many aspects. For example, it induces an even-parity boundary state which has linear dispersion and breaks the electron–hole symmetry of the graphene electronic structure. In addition, the line defect possesses much stronger adsorption ability to the metal adatoms than the ordinary graphene lattice point. In the present work, by developing an analytical lattice Green's function technique, we theoretically study the RKKY interaction in graphene when two magnetic impurities are adsorbed near the line defect. We find that R−3 decay rate of the RKKY interaction unique to graphene still holds true in the presence of the line defect. But another feature of the RKKY interaction in graphene, referred to as the Saremi's rule, which claims the RKKY interactions between the same or opposite sublattice points are ferro- or antiferromagnetic respectively, is no longer preserved due to the influence of the boundary state around the line defect. More importantly, the RKKY interaction on the line defect is greater than its counterpart in the pristine graphene by about one or two orders of magnitude. The local lattice distortion around the line defect can bring about the transition of the RKKY interaction between ferro- and antiferromagnetic orders. Such a result implies that the presence of the extended line defect provides a feasible platform in graphene to realize the long-range magnetic order even at a high temperature.

Thermodynamic modeling of native defects in ZnO

ZnO is an important optical material and is an ideal candidate for light emitting diode applications. The optical property of ZnO is determined by its native defects. In this study, the concentrations of native defects and carriers in ZnO are investigated by a four sublattice point defect thermodynamic model. The intrinsic carrier concentration calculated by this model showed a good consistency with the estimation from Maxwell–Boltzmann function. This demonstrates the feasibility of this model. The concentrations of native defects, zinc vacancy, oxygen vacancy and zinc interstitial, are calculated as a function of temperature under different growth conditions such as zinc-rich and oxygen-rich. The calculation results show that ZnO is an intrinsic n-type material and has a slight zinc excess at the congruent melting point due to oxygen vacancies. This model provides a methodology to obtain the information of defect and dopant chemistry in ZnO from a quantitative thermodynamic analysis.

Designing band gap of graphene by B and N dopant atoms

Ab-initio calculations have been performed to study the geometry and electronic structure of boron (B) and nitrogen (N) doped graphene sheet. The effect of doping has been investigated by varying the concentrations of dopants from 2 % (one atom of the dopant in 50 host atoms) to 12 % (six dopant atoms in 50 atoms host atoms) and also by considering different doping sites for the same concentration of substitutional doping. All the calculations have been performed by using VASP (Vienna Ab-initio Simulation Package) based on density functional theory. By B and N doping p-type and n-type doping is induced respectively in the graphene sheet. While the planar structure of the graphene sheet remains unaffected on doping, the electronic properties change from semimetal to semiconductor with increasing number of dopants. It has been observed that isomers formed differ significantly in the stability, bond length and band gap introduced. The band gap is maximum when dopants are placed at same sublattice points of graphene due to combined effect of symmetry breaking of sub lattices and the band gap is closed when dopants are placed at adjacent positions (alternate sublattice positions). These interesting results provide the possibility of tuning the band gap of graphene as required and its application in electronic devices such as replacements to Pt based catalysts in Polymer Electrolytic Fuel Cell (PEFC).

RKKY interaction in AB-stacked multilayer graphene

The RKKY interaction between two magnetic impurities absorbed on the surface layer of half-filled AB-stacked multilayer graphene (ABSMLG) is theoretically studied based on the lattice Green’s function technique. In comparison with the case of monolayer graphene, the RKKY interaction in such multilayer graphene presents distinct properties in some aspects. Firstly, from the numerical results, we find that the thickness of the ABSMLG influences the RKKY interaction in a complicated manner, depending on the odd/even parity of the number of layers and the sublattice attribution of the positions of the two magnetic impurities. Then, we derive the asymptotic expressions of the RKKY interactions in ABSMLG in the long-distance limit. For even-layered ABSMLG, we find that the RKKY interactions of the 1A–1A, 1B–1A and 1B–1B couplings fall off as 1/R2, 1/R4 and 1/R6 (1A and 1B stand for, respectively, the sublattice points in the surface layer, which are positioned directly on the plaquette and on a lattice point of the layer underneath). On the other hand, in odd-layered ABSMLG, the decays of these interactions follow the 1/R2, 1/R3 and 1/R3 power laws respectively. In addition, we also find that these analytical expressions are quantitatively valid to describe the RKKY interaction in ABSMLG when the distance between the two magnetic impurities is larger than the lattice constant of graphene by one order of magnitude.

Effects of structurally deformed sub-lattice points on the dispersion properties of 2D hybrid triangular–graphite photonic crystal

We investigate a hybrid two dimensional (2D) photonic crystal which is constructed by merging triangular and graphite lattices in air background. Different geometries of scatterers such as circular rods, circular rods with elliptical holes, circular hollow rods and elliptical rods with circular holes in the triangular sub-lattice are considered and effects of shape on their dispersion properties are discussed. Photonic band gaps (PBGs) for TM- and TE-polarized modes are found to exist for these symmetry-reduced graphite structures. The TE PBGs are found to contribute to produce complete photonic band gaps (CBGs) up to high values of filling fraction and rod diameter ratios. We show that TM and TE PBGs display opposite behaviors as the structure is transformed from graphite to symmetry-reduced graphite (hybrid triangular–graphite lattice) and from symmetry-reduced graphite to hollow centered symmetry-reduced graphite. Concerning the PBGs, inner structural deformation is found to be more beneficial in comparison to outer structural deformation. Small group velocities are observed at the same frequency for both polarizations near the edges of PBGs for the configurations of circular rods, circular rods with elliptical holes and circular hollow rods. These observations seem valuable for optical gain enhancement and low-threshold lasing.

Theory of Electron Scattering by Lattice Defects in Monolayer Graphene

Electron scattering by defects consisting of several strong and short-range impurities at A and B sublattice points lying close to each other is studied within a k · p scheme in monolayer graphene. In a defect consisting of a single impurity, a quasi-bound state like donor or acceptor state emerges near the Dirac point when the potential becomes extremely strong. In the case of AB pair impurities, the quasi-bound state splits into two and the resonance appears near the Dirac point for small scattering potential. In the case of defects consisting of many atoms, the number of resonances is given by that of AB pairs.

Tunable band gap and magnetic ordering by adsorption of molecules on graphene

We have studied the electronic and magnetic properties of graphene and their modification due to the adsorption of water and other gas molecules. Water and gas molecules adsorbed on nanoscale graphene were found to play the role of defects which facilitate the tunability of the bandgap and allow us to control the magnetic ordering of localized states at the edges. The adsorbed molecules push the wavefunctions corresponding to $\alpha$-spin (up) and $\beta$-spin (down) states of graphene to the opposite (zigzag) edges. This breaks the sublattice and molecular point group symmetry that results in opening of a large bandgap. The efficiency of the wavefunction displacement depends strongly on the type of molecules adsorbed

Sublattice enumeration. IV. Equivalence classes of plane sublattices by parent Patterson symmetry and colour lattice group type

The Dirichlet generating functions for the number of sublattices fixed under each symmetry operation of the parent Patterson group may be combined to count the number of crystallographically nonequivalent sublattices, in total, by sublattice point group and by colour lattice group type. The combinatorial formulae used imply the existence of various congruences among the corresponding arithmetic functions.

Index assignment for 3-description lattice vector quantization based on A2 lattice

Multiple description lattice vector quantization (MDLVQ) is an effective technique to realize multiple description coding. In this paper, we investigate a 3-description lattice vector quantization (LVQ) design using A 2 lattice, which finds a 3-tuple combination of sublattice points to represent each fine lattice point, based on two principles that each edge of the triangle formed by the 3-tuple points needs to be as short as possible, and the gravity center of the triangle is as close as possible to the fine lattice point. Following a delicate sublattice partition, a well-designed construction and mapping of each fine lattice point to a 3-tuple of sublattice points is developed to minimize the side distortion. The proposed index assignment is shown to achieve smaller distortion (up to 0.58 dB for Gaussian source) than some other 3-description index assignments. Compared with a 2-description LVQ, the 3-description LVQ achieves better expected rate-distortion performance in most cases of high description loss rates, while it also exhibits more graceful coding results with significantly smaller side distortions. Numerical analysis on Gaussian source and the simulations on image source validate the effectiveness of our proposed index assignment scheme.

Integrable lattices and their sublattices: From the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme

We present the sublattice approach, a procedure to generate, from a given integrable lattice, a sublattice which inherits its integrability features. We consider, as illustrative example of this approach, the discrete Moutard 4-point equation and its sublattice, the self-adjoint 5-point scheme on the star of the square lattice, which are relevant in the theory of the integrable discrete geometries and in the theory of discrete holomorphic and harmonic functions (in this last context, the discrete Moutard equation is called discrete Cauchy-Riemann equation). Therefore an integrable, at one energy, discretization of elliptic two-dimensional operators is considered. We use the sublattice point of view to derive, from the Darboux transformations and superposition formulas of the discrete Moutard equation, the Darboux transformations and superposition formulas of the self-adjoint 5-point scheme. We also construct, from algebro-geometric solutions of the discrete Moutard equation, algebro-geometric solutions of the self-adjoint 5-point scheme. In particular, we show that the corresponding restrictions on the finite-gap data are of the same type as those for the fixed energy problem for the two-dimensional Schrödinger operator. We finally use these solutions to construct explicit examples of discrete holomorphic and harmonic functions, as well as examples of quadrilateral surfaces in R3.

Magnetization Processes in Dilute Metamagnets with Ferro- and Antiferromagnetic Exchange Interactions

Using the Green function method there has been presented the mathematical description of dilute two sub-lattice metamagnets with ferroand antiferromagnetic exchange interactions. The Green function averaging procedure is based on the Cumulant Expansion Technique and includes any localized Green function irrespectively of the decoupling algorithm making the chain system of equations self-consistent. The derived form of the averaged Green function is the base for the analysis of magnetization processes and phase transitions occurring in the system under the influence of external magnetic field. It has been found in particular that the tricritical point and the second-order phase transition vanish when concentrations of magnetic atoms coupled with different sub-lattice points become different.

Ga sublattice defects in (Ga,Mn)As: thermodynamical and kinetic trends.

We have used positron annihilation spectroscopy and infrared absorption measurements to study the Ga sublattice defects in epitaxial Ga(1-x)MnxAs with Mn content varying from 0% to 5%. We show that the Ga vacancy concentration decreases and As antisite concentration increases with increasing Mn content. This is in agreement with thermodynamical considerations for the electronic part of the formation energy of the Ga sublattice point defects. However, the absolute defect concentrations imply that they are determined rather by the growth kinetics than by the thermodynamical equilibrium. The As antisite concentrations in the samples are large enough to be important for compensation and magnetic properites. In addition, the Ga vacancies are likely to be involved in the diffusion and clustering of Mn at low annealing temperatures.

Lattice points in lattice polytopes

It is shown that, for any lattice polytope P ⊂ℝ d the set int ( P )∩lℤ d (provided that it is non-empty) contains a point whose coefficient of asymmetry with respect to P is at most 8 d · (8 l +7) 2 2 d +1 . If, moreover, P is a simplex, then this bound can be improved to 8 · (8 l +7 ) 2 d +1 . As an application, new upper bounds on the volume of a lattice polytope are deduced, given its dimension and the number of sublattice points in its interior.

Structure of conduction channels in superionic conductors: Crystallochemical modeling

The experimental and theoretical studies of the structure of conduction channels of superionic conductors are analyzed. A crystallochemical method of modeling the conduction channels is proposed in which they are treated as sets of polyhedron Vorono-Dirichlet sections outside of impenetrable spheres of the rigid sublattice. The allowance for both weak flexibility of the spheres and their mean-square displacements relative to the sublattice points yields a channel structure that “wraps” around the Vorono-Dirichlet polyhedron edges. Modeling the interionic potential for α-AgI with the help of equipotential surfaces suggests that the mobile-ion motion slips along the conduction channel walls. For α-AgI, the set of the equipotential surfaces specifies “the minimum energy trajectory” of transition into a superionic state, while the crystallochemical “wrapping” structure corresponds to a saddle point of a multidimensional potential surface. Symmetry selection rules are used for predicting mechanical trajectories as allowed oscillation modes for the tetrahedral and octahedral fragments of α-CuI.

Conductance quantization in the presence of huge and short-range potential in carbon nanotubes

Conductance of carbon nanotubes (CNs) with a pair of impurities having a huge and short-range potential is studied within a tight-binding model. When a pair occupies different sublattices, the conductance is given by 2 e 2/πℏ same as in ideal CNs for a small distance and approaches either e 2/πℏ or 0 with the increase of the distance depending on types of their sites. When a pair occupies same sublattice points, the conductance is either e 2/πℏ or 0 independent of the distance.

Preparation and CO2Methanation Activity of an Ultrafine Ni(II) Ferrite Catalyst

Ultrafine Ni(II) ferrite (UNF) with 36% Ni2+substitution for Fe2+in magnetite has been synthesized in order to study its catalytic activity and selectivity toward CO2methanation at 300°C. Ni(II) ferrites were prepared by two different methods: (1) coprecipitation of Ni2+, Fe2+, and Fe3+at 60°C followed by heating to 300°C and (2) oxidation of aqueous suspension of Fe2+and Ni2+hydroxides at 65°C (oxidation method). The BET surface area of the initial UNF synthesized by coprecipitation was 73 m2g−1, eight times as large as that of the Ni(II) ferrite obtained by the oxidation method (NF; 9 m2g−1). It rapidly decreased to 26 m2g−1by sintering in the initial stage of methanation. The yield of CH4obtained on the UNF catalyst was 1.5–6.0 times larger than that on the NF catalyst in a 2-h run of the methanation, depending on a flow rate of reactant H2/CO2mixed gas. It was found that the selectivity for CH4was much improved in UNF (96%) in comparison with NF. XRD and chemical analysis showed that the UNF and NF were transformed to oxygen-deficient ferrite forms during the methanation. The specific activity (mol m−2s−1) of UNF for CH4formation was rather lower than that of NF, about half the activity of NF, which could be explained assuming that oxygen sublattice points on the catalyst surface formed by H2reduction serve as active sites for methanation. On the other hand, the activity for CO formation significantly decreased on UNF, due to the change in the nature of the active site.