Special Lattice Research Articles

Superconducting Boride Nb2IrB2 with Variable and Tunable Stacking Behaviors of Two-Dimensional [Nb-Ir-Nb] Triangular Lattices.

In structures with special geometry lattices, variations in stacking sequences are ubiquitous, yielding many novel structures and functionalities. Despite a wealth of intriguing properties and wide-ranging applications, there remains a considerable gap in understanding the correlation between special geometry lattices and functionalities in borides. Here, we design and synthesize a new superconducting boride Nb2IrB2, with a body-centered orthorhombic structure, consisting of alternating two-dimensional [Nb-Ir-Nb] triple-triangular-lattice-layers and B fragment layers. Advanced aberration-corrected scanning transmission electron microscopy observations show variable stacking configurations between [Nb-Ir-Nb] triple-triangular-lattice layers that can be tuned through synthesis conditions. Density functional theory calculations reveal that the coherent low-energy boundary interface plane of {101} between [11̅1] and [010] domains is responsible for the variable stacking behaviors. Energetically favorable structures are thereby reasonably proposed, based on nanoscale imperfect structure units. These findings provide valuable insights for designing and exploring new structures and functionalities within boride systems involving special geometry lattices.

Investigation of the Crystallographic Evolution Sequence of Nano-Precipitation via HRTEM in Cu-Bearing Ultra-Low Carbon Steel.

The precipitation behavior of Cu-bearing ultra-low carbon steel after step quenching and tempering at 923 K for 0.5-2.5 h was investigated. The size, quantity, and characteristic distribution of nano-precipitates were analyzed using transmission electron microscopy, and the microstructure of B2 (an ordered structure belonging to the body-centered cubic structure), 9R (a special triclinic lattice that has characteristics of rhombohedral structure), 3R (a special triclinic lattice like 9R), and FCT (face-centered tetragonal lattices) were accurately determined. The relationship between nano-precipitates and mechanical properties under different heat treatment processes was obtained, revealing that nano-precipitates effectively enhanced the yield strength of Cu-bearing ultra-low carbon steel. There were two forms of crystal structure evolution sequence of precipitation: B2→multi twin 9R→detwined 9R→FCT→FCC and B2→multi-twin 9R→detwinned 9R→3R→FCT→FCC. The morphology of the precipitated particles during the growth process changed from spherical to ellipsoidal and finally to rod-shaped. It was proven that a stable 3R structure existed due to the coexistence of 9R, 3R, and FCT structures in the same precipitate particle.

Some algebras and logics from quasiorder-generated covering-based approximation spaces

In A. Kumar, & M. Banerjee [(2012). Definable and rough sets in covering-based approximation spaces. In T. Li. (eds.), Rough sets and knowledge technology (pp. 488–495). Springer-Verlag], A. Kumar, & M. Banerjee [(2015). Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae, 141(1), 37–55], authors proposed a pair of lower and upper approximation operators based on granules generated by quasiorders. This work is an extension of algebraic results presented therein. A characterisation has been presented for those quasiorder-generated covering-based approximation spaces whose corresponding collections of definable and rough sets form Stone algebras. The notion of rough lattice was proposed in A. Kumar, & M. Banerjee [(2015). Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae, 141(1), 37–55], A. Kumar [(2020). A Study of Algebras and Logics of Rough Sets Based on Classical and Generalized Approximation Spaces. In Transactions on Rough Sets XXII, LNCS (Vol. 12485, pp. 123–251). Springer]. Some special rough lattices are introduced in this work, viz. rough Stone algebra, ∼ 1 -complemented and ∼ 2 -complemented rough lattices. Representations of these algebras in terms of rough sets are obtained. Moreover, logics for these algebras are shown to be sound and complete with respect to rough set semantics.

Target-oriented inverse optimization design of phononic crystals with variable constraints for vibration attenuation

Previous research on phononic crystals (PnCs) design mostly focused on the maximum band gap (BG) between adjacent orders and could not optimize the desired target frequency based on actual engineering problems. In order to achieve an arbitrarily specified BG structure of PnCs near the target frequency, a new topology design method for PnCs is proposed using a special triangular lattice PnC as the object. In the genetic algorithm (GA) optimization framework, two variable constraint optimization strategies, fixed-step and adaptive, are proposed to form a variable constraint genetic algorithm (VC-GA), which enables the non gradient optimization process to be continuous and uninterrupted. This optimization model also divides optimization into two stages, which can search for target individuals and maximize BG under the constraints of the target BG. Combining the optimization model with the improved fast plane wave expansion method (IFPWEM) for optimizing the single and multi-objective BGs in the in-plane and out-of-plane modes, and the weight coefficient is introduced to broaden its scope of application. The effectiveness of the method is verified through experiments, and the vibration reduction optimization design is carried out within a specific frequency range for the engineering structure corrugated plate as an example.

Anomalous electrons in a metallic kagome ferromagnet

Ordinary metals contain electron liquids within well-defined ‘Fermi’ surfaces at which the electrons behave as if they were non-interacting. In the absence of transitions to entirely new phases such as insulators or superconductors, interactions between electrons induce scattering that is quadratic in the deviation of the binding energy from the Fermi level. A long-standing puzzle is that certain materials do not fit this ‘Fermi liquid’ description. A common feature is strong interactions between electrons relative to their kinetic energies. One route to this regime is special lattices to reduce the electron kinetic energies. Twisted bilayer graphene1–4 is an example, and trihexagonal tiling lattices (triangular ‘kagome’), with all corner sites removed on a 2 × 2 superlattice, can also host narrow electron bands5 for which interaction effects would be enhanced. Here we describe spectroscopy revealing non-Fermi-liquid behaviour for the ferromagnetic kagome metal Fe3Sn2 (ref. 6). We discover three C3-symmetric electron pockets at the Brillouin zone centre, two of which are expected from density functional theory. The third and most sharply defined band emerges at low temperatures and binding energies by means of fractionalization of one of the other two, most likely on the account of enhanced electron–electron interactions owing to a flat band predicted to lie just above the Fermi level. Our discovery opens the topic of how such many-body physics involving flat bands7,8 could differ depending on whether they arise from lattice geometry or from strongly localized atomic orbitals9,10.

Iodide Vacancy Defects Clustering in Pairs Rather Than in Isolation in a Lead Iodide Perovskite: Identification, Origin, and Implications.

Iodide (I-) vacancy defects are strongly related to the stability of perovskite optoelectronic devices. The I- vacancy in lead iodide perovskites is normally considered to exist in the form of a single isolated defect. However, we determined that the I- vacancies cluster in pairs in specific ways in the typical perovskite of tetragonal CsPbI3. This I- vacancy-vacancy dimer is energetically more favorable than two isolated I- monovacancies. It breaks the symmetry of the Pb-I octahedron, resulting in lattice distortion. Its origin lies in the special lattice distortion effect caused by the electron orbital interaction of the perovskite material. Furthermore, the I- vacancy-vacancy dimer and the associated lattice distortion increase the carrier lifetime by 1.3 times compared to that of the system with two isolated I- monovacancies, but they also compromise its structural stability. This new insight into the I- vacancy defect will enhance our understanding of perovskite optoelectronic devices.

Air Pollution Modeling of UNI-DEM Model by using Innovative Stochastic Approaches

In this paper we develop advanced multidimensional sensitivity analysis, based on some innovative stochastic approaches for performing air pollution modelling on a large-scale model of long-range transport of air pollutants. The Unified Danish Eulerian Model (UNI-DEM) is a very important mathematical model, and can be applied in many different studies related to damaging effects caused by high air pollution levels. We shall use it in this paper to get a reliable answer to a some very important questions regrading environmental protection. We develop some advanced Monte Carlo and quasi-Monte Carlo methods, based on special lattice and digital sequences. In this paper we will improve the digital ecosystem modeling by improving the existence stochastic approaches. The computational efficiency (in terms of relative error and computational time) of the advanced Monte Carlo algorithms for multidimensional numerical integration has been studied to analyze the sensitivity of UNI-DEM model output to variation of input emissions of the anthropogenic pollutants and of rates of several chemical reactions. The algorithms will be applied to compute global Sobol sensitivity measures corresponding to the influence of several input parameters on the concentrations of important air pollutants. The study will be done for the areas of several European cities with different geographical locations.

Condensation of preformed charge density waves in kagome metals

Charge density wave (CDW) is a spontaneous spatial modulation of charges in solids whose general microscopic descriptions are yet to be completed. Kagome metals of AV3Sb5 (A = K, Rb, Cs) provide a chance to realize CDW intertwined with dimensional effects as well as their special lattice. Here, based on a state-of-the-art molecular dynamics simulation, we propose that their phase transition to CDW is a condensation process of incoherently preformed charge orders. Owing to unavoidable degeneracy in stacking charge orders, phases of preformed orders on each layer are shown to fluctuate between a limited number of states with quite slower frequencies than typical phonon vibrations until reaching their freezing temperature. As the size of interfacial alkali atom increases, the fluctuations are shown to counterbalance the condensation of orderings, resulting in a maximized transition temperature for RbV3Sb5. Our results resolve controversial observations on their CDWs, highlighting a crucial role of their interlayer interactions.

Stereochemically Active Lone-Pair Containing Metal Substitution in Polar Axis toward a Giant Phase-Matchable Optical Nonlinear Silicate Crystal Li3(OH)PbSiO4.

Atoms in special lattice sites can play a crucial role in realizing materials properties, which is long pursued but difficult to control. Herein, by adopting a stereochemically active lone-pair-containing metal substitution strategy, a nonlinear-optical (NLO) silicate crystal Li3(OH)PbSiO4 was successfully synthesized, featuring [PbSiO4]∞ layers with the perfect orientation of the stereochemically active lone-pair Pb(II) cation in the polar-axis lattice. Li3(OH)PbSiO4 overcomes the long-standing problem of silicates, that is, poor nonlinear properties because it exhibits both the largest birefringence of 0.082 and the largest phase-matchable second-harmonic-generation (SHG) efficiency of 21 × KDP among the known silicates. The successful polar-axis lattice substitution could offer a new direction for realizing the rational control of materials structures and properties.

Grain boundary engineering activated by residual stress during the laser powder bed fusion of Inconel 718 and the electrochemical corrosion performance

Conventional grain-boundary engineering (GBE) is not directly compatible with the complicated geometric parts fabricated via laser powder bed fusion (LPBF) owing to the multiple thermomechanical processes involved therein. In this study, GBE was activated by the inherent residual stress of an Inconel 718 superalloy produced via LPBF. The grain boundary character distribution and corresponding electrochemical corrosion behaviors were systematically investigated in a 3.5 wt% NaCl solution. The results indicate that numerous Σ3 boundaries (twin boundary, 64.89%) can be obtained via a simple heat treatment, and a favorable grain size can be maintained owing to the segmentation effect of the twin boundary. The corrosion resistance is closely related to the fraction of low special low-coincidence site lattices because the random boundary networks are broken. In addition, samples fabricated using GBE with the highest fraction of the twin boundary exhibited more compact and stronger passive films. The main components (oxide and metallic states) of thicker passive films provided intrinsic protection for the matrix. This study demonstrates a feasible method for GBE in additive-manufactured superalloys for fabricating complicated geometric parts with unique properties.

Bismuth layer-structured Bi4Ti3O12-CaBi4Ti4O15 intergrowth ferroelectric films for high-performance dielectric energy storage on Si substrate

Bismuth layer-structured ferroelectrics (BLSFs) have shown a great design capability for electrical energy storage, due to a highly anisotropic lattice and dielectric property. In this work, we add another notch to their qualifications as high energy density dielectrics, by demonstrating an ultrahigh recyclable energy density (Wrec ∼ 151.1 J/cm3 @ 4 MV/cm) and a good energy efficiency (η ∼ 72.0%) in Bi4Ti3O12-CaBi4Ti4O15 intergrowth ferroelectric films integrated on Si. This performance was achieved by the combination of a high spontaneous polarization (Ps) of the intergrown superlattice, and a polycrystalline nanograin microstructure. The high Ps is obtained through design of a special lattice, which determines the up limit of the energy density. On the other hand, the nanograin structure corresponds to a reduce remnant polarization, an intermediate dielectric constant and a delayed polarization saturation, all are ideal features for achieving a high recyclable energy density and energy efficiency. Such a structure is the consequence of a limited grain growth under the effect of a buffer layer. Lastly, a remarkable fatigue-resistance and an excellent charge-retaining ability were exhibited by these lead-free BLSF films. We expect this work will pave the way for designing high performance bismuth layer-structured ferroelectric films targeted for dielectric energy storage applications.

A versatile model with three-dimensional triangular lattice for unconventional transport and various topological effects.

The finite Berry curvature in topological materials can induce many subtle phenomena, such as the anomalous Hall effect (AHE), spin Hall effect (SHE), anomalous Nernst effect (ANE), non-linear Hall effect (NLHE) and bulk photovoltaic effects. To explore these novel physics as well as their connection and coupling, a precise and effective model should be developed. Here, we propose such a versatile model-a 3D triangular lattice with alternating hopping parameters, which can yield various topological phases, including kagome bands, triply degenerate fermions, double Weyl semimetals and so on. We reveal that this special lattice can present unconventional transport due to its unique topological surface states and the aforementioned topological phenomena, such as AHE, ANE, NLHE and the topological photocurrent effect. In addition, we also provide a number of material candidates that have been synthesized experimentally with this lattice, and discuss two materials, including a non-magnetic triangular system for SHE, NLHE and the shift current, and a ferromagnetic triangular lattice for AHE and ANE. Our work provides an excellent platform, including both the model and materials, for the study of Berry-curvature-related physics.

Strain‐Mediated Lattice Rotation Design for Enhancing Thermoelectric Performance in Bi2S2Se

AbstractA unique strain‐mediated lattice rotation strategy is introduced via nanocompositing to upsurge the optimized limits in the composition‐to‐structural pathway on rationally engineering the efficient thermoelectric material. In this study, a special lattice rotation via strain engineering is realized to optimize the desired electronic and chemical environment for enhancing thermoelectric properties in n‐type Bi2S2Se. This approach results in a unique transport phenomenon to assist high‐energy electrons in transferring through the optimized transport channels, and appropriate structure disparity to significantly localize phonons. As a result, Sb over Cl doping in Bi2S2Se gently reduces Eg and introduces defect states in bandgap with shifting down the Fermi level, thus causing increase in carrier concentration, which contributes to a higher power factor of ≈7.18 µW cm−1 K−2 (at T = 773 K). Besides, a lower thermal conductivity of ≈0.49 W m−1 K−1 is driven through lattice strain and defect engineering. Consequently, an ultra‐high ZTmax = 1.13 (at T = 773 K) and a high ZTave = 0.54 (323 K‐773 K) are realized. This study not only leads to an extraordinary thermoelectric performance but also reveals a unique paradigm for electron transportation and phonon localization via lattice strain engineering.

Duals of Cesàro sequence vector lattices, Cesàro sums of Banach lattices, and their finite elements

In this paper, we study the ideals of finite elements in special vector lattices of real sequences, first in the duals of Cesàro sequence spaces {text {ces}}_p for pin {0}cup [1,infty ) and, second, after the Cesàro sum {text {ces}}_{p}{(mathfrak {X})} of a sequence of Banach spaces is introduced, where p=infty is also allowed, we characterize their duals and the finite elements in these sums if the summed up spaces are Banach lattices. This is done by means of a remarkable extension of the corresponding result for direct sums.

A special two-dimensional lattice by Blaszak and Szum: Solitons, breathers, lump solutions, and their interactions and dynamics

In this paper, we study a special two-dimensional lattice equation proposed by Blaszak and Szum. Upon utilizing the bilinear method, we derive solitons, breathers and rational solutions to the lattice equation both on the constant and periodic background. These solutions are given in terms of determinants whose matrix elements have simple algebraic expressions. In particular, we find three types of breather solutions, including Kuznetsov-Ma breather, Akhmediev breather and general one. By introducing two differential operators applied to the soliton solutions, we obtain rational solutions in terms of Schur polynomials. We demonstrate that rational solutions can exhibit algebraic solitons and lump solitons. We explore the asymptotic analysis to the algebraic solitons and find asymptotic algebraic solitons localized in the straight. By taking higher-order differential operators, we present multiple and higher-order rational solutions. The dynamical behaviors of these obtained solutions are illustrated and analyzed.

Discrete unified gas kinetic scheme for continuum compressible flows.

In this paper, a discrete unified gas kinetic scheme (DUGKS) is proposed for continuum compressible gas flows based on the total energy kinetic model [Guo et al., Phys. Rev. E 75, 036704 (2007)1539-375510.1103/PhysRevE.75.036704]. The proposed DUGKS can be viewed as a special finite-volume lattice Boltzmann method for the compressible Navier-Stokes equationsin the double distribution function formulation, in which the mass and momentum transport are described by the kinetic equationfor a density distribution function (g), and the energy transport is described by the other one for an energy distribution function (h). To recover the full compressible Navier-Stokes equationsexactly, the corresponding equilibrium distribution functions g^{eq} and h^{eq} are expanded as Hermite polynomials up to third and second orders, respectively. The velocity spaces for the kinetic equationsare discretized according to the seventh and fifth Gauss-Hermite quadratures. Consequently, the computational efficiency of the present DUGKS can be much improved in comparison with previous versions using more discrete velocities required by the ninth Gauss-Hermite quadrature.

Spline function generating Gabor systems on the half real line

Recently, Gabor analysis on locally compact abelian (LCA) groups has interested some mathematicians. The half real line is an LCA group under multiplication and the usual topology. This paper addresses spline Gabor frames for , where is the corresponding Haar measure. We introduce the concept of spline functions on by ‐convolution and estimate their Gabor frame sets, that is, lattice sets such that spline generating Gabor systems are frames for . For an arbitrary spline Gabor frame with special lattices, we present its one dual Gabor frame window, which has the same smoothness as the initial window function. For a class of special spline Gabor Bessel sequences, we prove that they can be extended to a tight Gabor frame by adding a new window function, which has compact support and same smoothness as the initial windows. And we also demonstrate that two spline Gabor Bessel sequences can always be extended to a pair of dual Gabor frames with the adding window functions being compactly supported and having the same smoothness as the initial windows.

Regular Partial Residuated Lattices and Their Filters

To express wider uncertainty, Běhounek and Daňková studied fuzzy partial logic and partial function. At the same time, Borzooei generalized t-norms and put forward the concept of partial t-norms when studying lattice valued quantum effect algebras. Based on partial t-norms, Zhang et al. studied partial residuated implications (PRIs) and proposed the concept of partial residuated lattices (PRLs). In this paper, we mainly study the related algebraic structure of fuzzy partial logic. First, we provide the definitions of regular partial t-norms and regular partial residuated implication (rPRI) through the general forms of partial t-norms and partial residuated implication. Second, we define regular partial residuated lattices (rPRLs) and study their corresponding properties. Third, we study the relations among commutative quasi-residuated lattices, commutative Q-residuated lattices, partial residuated lattices, and regular partial residuated lattices. Last, in order to obtain the filter theory of regular partial residuated lattices, we restrict certain conditions and then propose special regular partial residuated lattices (srPRLs) in order to finally construct the quotient structure of regular partial residuated lattices.

Experimental realization of tunable finite square optical arrays

Recently optical lattices containing optical vortices (OVs), which carry phase singularities and possess exotic optical properties, have attracted increasing attention due to their potential applications in optical trapping or light-matter interaction systems. Here, we propose a kind of arbitrary order alternated OV lattices with positive and negative topological charges ±n, which are named as the nth-order alternated OV lattices (NAOVLs), and we experimentally demonstrate their propagation properties. We find that such NAOVLs can generate finite square optical arrays with interesting patterns or defects near the focal plane or far-field Fraunhofer region. We further find a general law (although with some exceptions) about the number N of bright spots in finite optical arrays as the value n increases. The interference experiments confirm optical properties of such finite arrays close to the focal plane. Our results may have potential applications in particle trapping and experimental realizations of novel optical arrays for the interaction between special optical lattices and atoms (or molecules, ions, micro- or nano-particles).

МРТ- ТРУЗИ фьюжн-биопсия в диагностике рака предстательной железы

Introduction. Significant improvement in the quality of visualization of the prostate using magnetic resonance imaging (MRI), as well as the development of technologies for virtual combination of MRI and ultrasound images opens new horizons in the diagnosis of prostate cancer. The introduction of the PI-RADS system has allowed the standardization of MRI findings, and the development of fusion biopsy systems seeks to make diagnostics more accurate and less operator-dependent. Materials and methods. In this literature review, we evaluate the effectiveness of various biopsy approaches and discuss the prospects for targeted biopsies. The search for publications was carried out in the databases PubMed, e-library, Web of Scince et al. For citation, 55 literature sources were selected that met the search criteria for the keywords, «prostate cancer», «biopsy», «MRI», «TRUS», «fusion». Results. Diagnosis of prostate cancer using MRI. Modern technologies for radiological diagnosis of prostate cancer using magnetic resonance imaging (MRI) are based on the standardized PI-RADS protocol, using different modes (T2, diffusion-weighted images and contrast enhancement), which provides the best visualization of tumor-suspicious nodes in the prostate gland, allowing determination of lesion localization and size for subsequent targeted biopsy. Options for performing a prostate biopsy to diagnose prostate cancer. A description of the methods and effectiveness of transrectal and transperineal biopsy under ultrasound guidance is carried out - due to the fact that ultrasound diagnostics of prostate cancer has a rather low sensitivity due to small differences in the ultrasound structure of normal and tumor tissue of the prostate, an extended template biopsy technique was proposed, which involves puncture of the prostate through a special lattice. It also describes the technology of fusion biopsy and also provides literature data comparing the diagnostic accuracy of standard TRUS and fusion prostate biopsy, as well as the importance of transrectal / transperineal access. Questions for further study. Given the desire to reduce the number of biopsies while maintaining or even increasing the accuracy of diagnosing prostate cancer, data from studies investigating the feasibility of combining polyfocal (non-targeted) and targeted (targeted) biopsies are presented. Conclusion. The existing methods of non-targeted biopsy (polyfocal, saturation, template) and targeted (fusion biopsy) have their advantages and disadvantages, which currently do not allow making certain recommendations for their use, but a significant number of authors prefer MRI-as sisted, fusion -biopsy.