Continuous Lattice Research Articles

Manufacturing a TiO2-Based Semiconductor Film with Nanofluid Pool Boiling and Sintering Processes toward Solar-Cell Applications.

For the first time, nanofluid boiling was applied as a process for the creation of a semiconductor TiO2 nanoparticle film that can be deposited onto a conductive substrate (F-doped SnO2 glass: FTO). A steel-base device designed for pool boiling was used to deposit a TiO2-based nanofluid consisting of nanoparticles with an average size of about 20 nm. The boiling of the nanofluid directly on the FTO glass substrate allowed for the deposition of the nanoparticles onto the FTO surface. In principle, the surface responsible for transferring heat to the fluid can be covered with these nanoparticles when the nanofluid boils. Using the as-deposited films, crystal growth of the TiO2 nanoparticle was controlled by varying the strategies of the post-sintering profile. The maximum temperatures, periods, and ramping rates for the obtained samples were systematically changed. Scanning electron microscopy (SEM) revealed that a densely packed TiO2-nanoparticle layer was obtained for the as-deposited substrate via pool boiling. For the maximum temperature at 550 °C, the TiO2 grain sizes became larger (~50 nm) and more round-shaped TiO2 nanostructures were identified. Notably, we have demonstrated for the first time how the sintering of TiO2 nanoparticles proceeds for the nanoporous TiO2 films using high-resolution transmission electron microscopy (TEM) measurements. We found that the TiO2 nanoparticles fused with each other and crystal growth occurred through neighboring 2–4 nanoparticles for the 550 °C sample, which was proved by the TEM analysis that continuous lattice fringes corresponding to the (101) anatase phase were clearly observed through the entire area of some nanoparticles aligned horizontally. In addition, the loss of the TiO2 nanofluid (precursor solution) was completely avoided in our TiO2 deposition. Unlike the commonly used spin-coating method, nanofluid pool boiling would provide an alternative cost-effective approach to manufacture semiconductor layers for various applications, such as solar cells.

Comparing Microscopic and Macroscopic Dynamics in a Paradigmatic Model of Glass-Forming Molecular Liquid.

Glass transition is a most intriguing and long-standing open issue in the field of molecular liquids. From a macroscopic perspective, glass-forming systems display a dramatic slowing-down of the dynamics, with the inverse diffusion coefficient and the structural relaxation times increasing by orders of magnitude upon even modest supercooling. At the microscopic level, single-molecule motion becomes strongly intermittent, and can be conveniently described in terms of “cage-jump” events. In this work, we investigate a paradigmatic glass-forming liquid, the Kob–Andersen Lennard–Jones model, by means of Molecular Dynamics simulations, and compare the macroscopic and microscopic descriptions of its dynamics on approaching the glass-transition. We find that clear changes in the relations between macroscopic timescales and cage-jump quantities occur at the crossover temperature where Mode Coupling-like description starts failing. In fact, Continuous Time Random Walk and lattice model predictions based on cage-jump statistics are also violated below the crossover temperature, suggesting the onset of a qualitative change in cage-jump motion. Interestingly, we show that a fully microscopic relation linking cage-jump time- and length-scales instead holds throughout the investigated temperature range.

Moiré Pattern Dislocation in Continuous Atomic Lattice of Monolayer h-BN

Moiré Pattern Dislocation in Continuous Atomic Lattice of Monolayer h-BN

Quotients of L-domains

It is well known that the image of a bounded complete domain, respectively a continuous lattice T under a surjective map preserving infs of nonempty subsets and directed sups is a bounded complete domain, respectively a continuous lattice and a congruence relation on T is an equivalence relation on T and a subalgebra of T × T . In this paper, we propose some counterexamples to explain that these results do not persist in L -domains. The concepts of strong homomorphisms among L -domains and congruence relation on L -domains are introduced. We prove that the image of an L -domain under a surjective map which preserves infs of nonempty subsets bounded above and directed sups and satisfies an equation is an L -domain. Meanwhile, we obtain the quotients of L -domains. Moreover, we give the Isomorphism Theorem for L -domains.

On unbounded order continuous operators

Let $U$ and $V$ be two Archimedean Riesz spaces. An operator $S:U\rightarrow V$ is said to be unbounded order continuous ($uo$-continuous), if $r_{\alpha }\overset{uo}{\rightarrow }0$ in $U$ implies $Sr_{\alpha }\overset{uo}{% \rightarrow }0$ in $V$. In this paper, we give some properties of the $uo$% -continuous dual $U_{uo}^{\sim }$ of $U$. We show that a nonzero linear functional $f$ on $U$ is $uo$-continuous if and only if $f$ is a linear combination of finitely many order continuous lattice homomorphisms. The result allows us to characterize the $uo$-continuous dual $U_{uo}^{\sim }.$ In general, by giving an example that the $uo$-continuous dual $U_{uo}^{\sim }$ is not a band in $U^{\sim }$, we obtain the conditions for the $uo$% -continuous dual of a Banach lattice $U$ to be a band in $U^{\sim }$. Then, we examine the properties of $uo$-continuous operators. We show that $S$ is an order continuous operator if and only if $S$ is an unbounded order continuous operator when $S$ is a lattice homomorphism between two Riesz spaces $U$ and $V$. Finally, we proved that if an order bounded operator $S:U\rightarrow V$ between Archimedean Riesz space $U$ and atomic Dedekind complete Riesz space $V$ is $uo$-continuous, then $\left\vert S\right\vert $ is $uo$-continuous.

Thermodynamic Modeling of the Solid–Liquid Phase Transition in Polyethylene Copolymer–Solvent Systems Based on Continuous Thermodynamics and Lattice Cluster Theory

Thermodynamic Modeling of the Solid–Liquid Phase Transition in Polyethylene Copolymer–Solvent Systems Based on Continuous Thermodynamics and Lattice Cluster Theory

On Bilinear Narrow Operators

In this article, we introduce a new class of operators on the Cartesian product of vector lattices. We say that a bilinear operator T:E×F→W defined on the Cartesian product of vector lattices E and F and taking values in a vector lattice W is narrow if the partial operators Tx and Ty are narrow for all x∈E,y∈F. We prove that, for order-continuous Köthe–Banach spaces E and F and a Banach space X, the classes of narrow and weakly function narrow bilinear operators from E×F to X are coincident. Then, we prove that every order-to-norm continuous C-compact bilinear regular operator T is narrow. Finally, we show that a regular bilinear operator T from the Cartesian product E×F of vector lattices E and F with the principal projection property to an order continuous Banach lattice G is narrow if and only if |T| is.

A MULTI-COMPONENT IMPLANT FOR USE IN TIBIAL OSTEOTOMY TO CORRECT VARUS DEFORMITY IN THE MORBIDLY OBESE

Medial opening wedge high tibial osteotomy (OWHTO) offers an alternative to total knee arthroplasty (TKA) for patients with varus knee deformity. This report describes a novel, modular implant intended to occupy the wedge osteotomy space via a small medial incision to reduce surgical complications associated with patients having a BMI of 40 or greater (morbidly obese). The wedge-shaped, 3-D laser-sintered titanium alloy implant consists of interlocked components to be assembled in situ. Components were fabricated with a continuous laser-sintered surface lattice structure for bone ingrowth. The sliding resistance of a range of geometrically scaled lattices was assessed to determine the optimal lattice structure for initial implantation. The lattice structure had a 550mm surface opening (150mm internal pore size). Finite element models were created to evaluate three OWHTO scenarios including a medial restraining T-plate and implant combination, a T-plate alone as commonly seen clinically, and a model of only the implant within the osteotomy. Axially loaded models revealed implant stresses to be well below titanium fatigue strength, but the model of the T-plate alone indicated large plate and screw stresses comparable to the fatigue strength. Investigations are ongoing to assess multifunctional loading and experimental strain measurement. These results suggest this modular implant design may provide BMI > 40 patients an effective treatment option to early TKA.

Operators in pre-Riesz spaces: moduli and homomorphisms

We focus on two topics that are related to moduli of elements in partially ordered vector spaces. First, we relate operators that preserve moduli to generalized notions of lattice homomorphisms, such as Riesz homomorphisms, Riesz* homomorphisms, and positive disjointness preserving operators. We also consider complete Riesz homomorphisms, which generalize order continuous lattice homomorphisms. Second, we characterize elements with a modulus by means of disjoint elements and apply this result to obtain moduli of functionals and operators in various settings. On spaces of continuous functions, we identify those differences of Riesz* homomorphisms that have a modulus. Many of our results for pre-Riesz spaces of continuous functions lead to results on order unit spaces, where the functional representation is used.

Phase transition-enabled MnFe2O4 nanoparticles modulated by high-pressure with enhanced electrical transport properties

Pressure tuned structure-function relationship of MnFe2O4 nanoparticles is established for the first time by the mean of XRD, Raman and impedance spectra measurements. The application of external pressure results in a continuous lattice contraction of MnFe2O4. In the pressure range of 17.1–26.3 GPa, MnFe2O4 undergoes a cubic-to-orthorhombic structural phase transition. Meanwhile, increasing pressure from ambient state to 37.1 GPa leads to the continued improvement of conductivity of the sample. Further analysis shows that the hybridized enhancement between Fe-3d and O-2p orbits and the decrease in band gap upon compression are the major factors to affect the conductivity of MnFe2O4. With the release of pressure, the sample recovers to the cubic spinel structure, but the grain boundary resistance and dielectric constant are still decreased by nearly 3 orders of magnitude compared with the counterpart before compression. By analysis of Hall-effect and electron microscope on the recovered sample, the increased interfaces density and accordingly the enlarged carrier concentration account for the obvious improvement of electrical properties in MnFe2O4 nanoparticles. In this work, such a high enhancement in conductivity due to the annealing of pressure-cycle provides a newly feasible pathway to design ferrite materials with excellent electrical and electrochemical properties, and expands their application prospects in electronic devices and microwave industries, etc.

Growth of porous single-crystalline molybdenum nitrides microcubes with enhanced electrocatalysis performance

Porous single crystal has the characteristics of long-range order, continuous lattice and large specific surface area, which could reduce energy losses and keep high activity and stability in electrochemical systems. Here, we grow porous single-crystalline and polycrystalline molybdenum nitrides microcubes from MoO3 single crystals. These porous microcubes show superior HER and OER performance. The overpotential of Mo2N porous single crystal microcubes is only 73.13 mV at a current density of 10 mA cm−2, which is 150.53 mV, 192.76 mV and 255.87 mV lower than that of MoN single crystal, Mo2N polycrystal and MoN polycrystal, respectively. The advantages of Mo2N porous single crystals in electrocatalytic properties are also reflected in OER.

Room temperature Mott metal–insulator transition in V2O3 compounds induced via strain-engineering

Vanadium sesquioxide (V2O3) is an archetypal Mott insulator in which the atomic positions and electron correlations change as temperature, pressure, and doping are varied, giving rise to different structural, magnetic, or electronic phase transitions. Remarkably, the isostructural Mott transition in Cr-doped V2O3 between paramagnetic metallic and insulating phase observed in bulk has been elusive in thin film compounds so far. Here, via continuous lattice deformations induced by heteroepitaxy, we demonstrate a room temperature Mott metal–insulator transition in 1.5% Cr-doped and pure V2O3 thin films. By means of a controlled epitaxial strain, not only the structure but also the intrinsic electronic and optical properties of the thin films are stabilized at different intermediate states between the metallic and insulating phases, inaccessible in bulk materials. This leads to films with unique features such as a colossal change in room temperature resistivity (ΔR/R up to 100 000%) and a broad range of optical constant values as consequence of a strain-modulated bandgap. We propose a new phase diagram for pure and Cr-doped V2O3 thin films with the engineered in-plane lattice constant as a tunable parameter. Our results demonstrate that controlling phase transitions in correlated systems by epitaxial strain offers a radical new approach to create the next generation of Mott devices.

Nanoscale mechanical behavior of kaolinite under uniaxial strain conditions

Nanoscale mechanical behavior of kaolinite as a fundamental failure mechanism has been investigated under uniaxial tension and compression using Molecular Dynamics (MD) simulation methods. External deformation has been applied on kaolinite with a strain rate of 5 × 10−7fs−1 for tensile and compressive tests in the directions parallel (x-, y-direction)/perpendicular (z-direction) to clay mineral layers. Results showed that better mechanical performance was presented in the directions parallel to clay mineral layers than the other direction due to its continuous lattice in this plane. However, the elastic modulus of kaolinite in the z-direction was almost half of that in the other directions, which nearly equals the overall elastic modulus of kaolinite with a value of about 72.6 GPa. Compression in the x- and y-directions resulted in the separation of clay mineral layers then bending toward the octahedral sheet till crack. Compression in the z-direction resulted in slippage of clay mineral layers at the first fracture then resistance till the second fracture at the strain of about 0.2. Tension would cause cracks in the direction perpendicular to the strain direction, which may be a cleavage fracture or cracks in clay mineral sheets. Different failure modes under tension and compression were originated from the layered structure of kaolinite.

The categorical relationships between neighborhood spaces, ┬-neighborhood spaces and stratified L-neighborhood spaces

In this paper, for a complete residuated lattice L, we present the categorical properties of ?-neighborhood spaces and their categorical relationships to neighborhood spaces and stratified L-neighborhood spaces. The main results are: (1) the category of ?-neighborhood spaces is a topological category; (2) neighborhood spaces can be embedded in ?-neighborhood spaces as a reflective subcategory, and when L is a meet-continuous complete residuated lattice, ?-neighborhood spaces can be embedded in stratified L-neighborhood spaces as a reflective subcategory; (3) when L is a continuous complete residuated lattice, neighborhood spaces (resp., ?-neighborhood spaces) can be embedded in ?-neighborhood spaces (resp., stratified L-neighborhood spaces) as a simultaneously reflective and coreflective subcategory.

Edge localized Schrödinger cat states in finite lattices via periodic driving

Floquet states have been used to describe the impact of periodic driving on lattice systems, either using a tight-binding model, or by using a continuum model where a Kronig-Penney-like description has been used to model spatially periodic systems in one dimension. A number of these studies have focused on finite systems, and results from these studies are distinct from those of infinite lattice systems as a consequence of boundary effects. In the case of a finite system, there remains a discrepancy in the results between tight-binding descriptions and continuous lattice models. Periodic driving by a time-dependent field in tight-binding models results in a collapse of all quasienergies within a band at special driving amplitudes. In the continuum model, on the other hand, a pair of nearly-degenerate edge bands emerge and remain gapped from the bulk bands as the field amplitude increases. We resolve these discrepancies and explain how these edge bands represent Schr\"odinger cat-like states with effective tunneling across the entire lattice. Moreover, we show that these extended cat-like states become perfectly localized at the edge sites when the external driving amplitude induces a collapse of the bulk bands.

Microstructure and Mechanical Properties of Welded Joints in Austenitic Steel TP347HFG after Operation

The analysis involved a similar welded joint made of steel TP347HFG after operation at a temperature of 580°C. Tests revealed that the primary mechanisms responsible for the degradation of the microstructure in all areas of the joint subjected to analysis were precipitation processes within the grains and along the grain boundaries. The grain boundaries contained two morphologies forming a continuous lattice. Precipitation processes resulted in the high tensile strength of the joint and high hardness within the weld face area. After operation, the test joint was characterised by relatively high impact energy, which could be attributed to the fine-grained microstructure and the presence of numerous annealing twins.

Oxidation behavior and mechanism of aluminum oxynitride (AlON) at elevated temperatures

AbstractThe oxidation behavior and mechanism of aluminum oxynitride (AlON) powder exposed to air at elevated temperatures between 800°C and 1300°C was investigated by X‐ray diffractometry (XRD), scanning electron microscope (SEM), electron spin resonance (ESR), nuclear magnetic resonance (NMR), and simultaneous thermogravimetry, differential thermal analysis, and mass spectrometry techniques (TG‐DTA‐MS). The weight of AlON gradually increases to a maximum value at 1150°C and then decreases with further heating. Meanwhile, AlON powder undergoes chemical changes, as evidenced by lattice expansion, and turns eventually into alumina. ESR spectra reveal the occurrence of lone pair electrons in the oxidized products and the intensity of corresponding resonance signal increases before disappearing with the increase in temperature. Combined with the results of NMR and TG‐DTA‐MS, the measured data suggest that Al‐N in [AlO3N] tetrahedron and [AlO5N] octahedron are gradually oxidized into Al‐O‐N group with lone pair electrons, which causes continuous weight gain and lattice expansion. Further oxidation at higher temperatures results in alumina and N2.

Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories

We show that standard identities and theorems for lattice models with $U(1)$ symmetry get re-expressed discretely in the tensorial formulation of these models. We explain the geometrical analogy between the continuous lattice equations of motion and the discrete selection rules of the tensors. We construct a gauge-invariant transfer matrix in arbitrary dimensions. We show the equivalence with its gauge-fixed version in a maximal temporal gauge and explain how a discrete Gauss's law is always enforced. We propose a noise-robust way to implement Gauss's law in arbitrary dimensions. We reformulate Noether's theorem for global, local, continuous or discrete Abelian symmetries: for each given symmetry, there is one corresponding tensor redundancy. We discuss semi-classical approximations for classical solutions with periodic boundary conditions in two solvable cases. We show the correspondence of their weak coupling limit with the tensor formulation after Poisson summation. We briefly discuss connections with other approaches and implications for quantum computing.

Elastic wave and vibration bandgaps in planar square metamaterial-based lattice structures

In this work, a new type of planar square lattice structures for the attenuation of elastic wave propagation is proposed and designed. To obtain a high vibration attenuation in low frequency ranges, the internal resonance mechanism of the acoustic metamaterials (AMs) is introduced into the continuous square lattice system with a cross-type core consisting of two segments with a radius jump discontinuity in each unit-cell. The wave propagation and vibration bandgap properties of the AM-based lattice structures are studied by using a spectral element method (SEM) which can provide accurate dynamic characteristics of a lattice structure due to its analytical spectral element matrix. The band structures calculated show that the phononic bandgaps induced by the local resonance and destructive interference co-exist in the considered systems. The effects of the structural and material parameters on the bandgaps are investigated in detail by the frequency response analysis of a spectral element model subjected to a dynamic excitation. Finally, in order to obtain lower and wider frequency bandgaps, the mechanism to optimize the unit-cell of the AM-based lattice structures is illustrated and a composite lattice model is suggested.

Peculiarity of a magnetic structure in a quasi-one-dimensional columbite Co0.4Ni0.6Nb2O6

Quasi-one-dimensional (Q1D) spin chain systems have great potential applications in high-density information storage devices, quantum information and computers, because of their quantum magnetism properties. The low-dimensional magnetic behavior has been investigated in ANb2O6, (A = Mn, Fe, Co or Ni) compounds, the structural and magnetic properties are very interesting because the system presents weakly interacting Ising chains, which leads to this quasi-one-dimensional magnetic order. Our investigation combines specific heat and magnetic measurements; x-ray and neutron diffraction (ND). In this work, we present a Co/Ni orthorhombic structure, called columbite, which crystallizes with Pbcn space group, whose formula is Co0.4Ni0.6Nb2O6. Co for Ni substitution induces a continuous lattice volume decrease, preserving the orthorhombic crystal structure. Magnetic susceptibility and specific heat measurements reveal that antiferromagnetic order occurs at 3.4 K, as a consequence of weak interchain interactions. Partial substitution of the magnetic ion tends to change the magnetic ordering observed in the CoNb2O6 and NiNb2O6. Lastly, we present this magnetic structure changes with the Ni-Co substitution.