Defect Engineering:Can it Mitigate Strong Coulomb Effect of Mg^(2+)in Cathode Materials for Rechargeable Magnesium Batteries?

Rechargeable magnesium batteries(RMBs)have been considered a promising“post lithium-ion battery”system to meet the rapidly increasing demand of the emerging electric vehicle and grid energy storage market.However,the sluggish diffusion kinetics of bivalent Mg^(2+)in the host material,related to the strong Coulomb effect between Mg^(2+)and host anion lattices,hinders their further development toward practical applications.Defect engineering,regarded as an effective strategy to break through the slow migration puzzle,has been validated in various cathode materials for RMBs.In this review,we first thoroughly understand the intrinsic mechanism of Mg^(2+)diffusion in cathode materials,from which the key factors affecting ion diffusion are further presented.Then,the positive effects of purposely introduced defects,including vacancy and doping,and the corresponding strategies for introducing various defects are discussed.The applications of defect engineering in cathode materials for RMBs with advanced electrochemical properties are also summarized.Finally,the existing challenges and future perspectives of defect engineering in cathode materials for the overall high-performance RMBs are described.

Supersymmetry and Shape Invariance of Hartmann Potential and Ring-Shaped Oscillator Potential in the γ and θ Dimensions of Spherical Polar Coordinates

This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator astwo important examples, thus in principle the energy eigenvalues and energy eigenfunctions of such the potentials in ther and θ dimensions can be obtained by the method of supersymmetric quantum mechanics. Here we use an alternativemethod to get the required results.

Buckling-controlled two-way shape memory effect in a ring-shaped bilayer

Shape memory polymers(SMPs)usually have a one-way shape memory effect.In this paper,an easy-operating method to realize a two-way shape memory effect was demonstrated in a ring-shaped bilayer structure where the two layers are SMPs with different thermal transition temperatures.By designing specific thermomechanical processes,the mismatched deformation between the two layers leads to a morphology change of ring-shaped bilayer structures from a smooth ring to a gear-like buckling shape under cooling and a reversible recovery to the smooth shape under heating.Such a morphology change is ascribed to occurrence and recovery of thermoelastic buckling.This method was validated by finite element simulation.We experimentally investigated the influence of pre-strain on buckling,and it was found that both the buckling occurrence and recovery temperature vary with pre-strain.Furthermore,considering a ring-shaped SMP-SMP bilayer structure,finite element analysis was conducted to study the influence of film thickness and modulus ratio of two layers on buckling behavior.The results showed that the critical buckling wavelength was greatly influenced by film thickness and modulus ratio.W e made a theoretical analysis that accorded well with the numerical results.

Numerical simulation and experimental verification of large-sized Zr-based bulk metallic glass ring-shaped parts in casting process

An outer ring of 29320 self-aliging roller bearing was used in an experimental study on the casting of Zr_(41)Ti_(14)Cu_(12.5)Ni_(10)Be_(22.5) amorphous alloy.Numerical simulations of mold filling and solidification processes were carried out to determine the velocity fields and temperature fields of the alloy melt during mold filling process as well as the temperature fields and temperature gradient fields in the course of the solidification.According to the results,a cast with a complete shape can be obtained at 1200℃under the condition that the cooling rate is greater than the critical cooling rate.The ring-shaped part with a thickness of 25 mm,an equivalent diameter of 22 mm,and a mass of 1.32 kg was prepared by gravity casting in a copper mold.X-ray diffraction and differential scanning calorimetry data revealed that the produced cast had the amorphous structure.

Solution of the Dirac Equation for Ring-Shaped Modified Kratzer Potential

We propose a new exactly solvable potential which is Formed by modified Kratzer potential plus a new ring-shaped potential η cot^2 θ/r^2 The solutions of the Dirac equation with equal scalar and vector ring-shaped modified Kratzer potential are found by using the Nikiforov-Uvarov method. The nonrelativistic limit of the energy spectrum has been discussed.

Solving Dirac Equation with New Ring-Shaped Non-Spherical Harmonic Oscillator Potential

A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 （2005） 94. The positive energy states of system are discussed and the conclusions are made properly.

Central corneal epithelium self-healing after ring-shaped glycerin-cryopreserved lamellar keratoplasty in Terrien marginal degeneration

Dear Sir, I am Dr Yan-Long Bi, from the Department of Ophthalmology, Tongji University Affiliated to Tongji University School of Medicine, Shanghai, China. I write to present a case report of total limbal stem cells deficiency after treatment with ring-shaped lamellar keratoplasty secondary to Terrien marginal degeneration. During 3 years

A Longitudinal Zeeman Slower Based on Ring-Shaped Permanent Magnets for a Strontium Optical Lattice Clock

We report a longitudinal Zeeman slower based on ring-shaped permanent magnetic dipoles used for the strontium optical lattice clock. The Zeeman slower is composed of 40 permanent magnets with the same outer diameter but different inner diameters. The maximum variation of the axial field from its target values is less than 2%. In most parts of the Zeeman slower, the intensity variations of the field in radial spatial distribution are less than 0.1 roT. With this Zeeman slower, the strontium atoms are slowed down to 95m/s, and approximately 2% of the total atoms are slowed down to less than 50m/s.

Decade Milestone Advancement of Defect-Engineered g-C_(3)N_(4) for Solar Catalytic Applications

Over the past decade, graphitic carbon nitride(g-C_(3)N_(4)) has emerged as a universal photocatalyst toward various sustainable carbo-neutral technologies. Despite solar applications discrepancy, g-C_(3)N_(4) is still confronted with a general fatal issue of insufficient supply of thermodynamically active photocarriers due to its inferior solar harvesting ability and sluggish charge transfer dynamics. Fortunately, this could be significantly alleviated by the “all-in-one” defect engineering strategy, which enables a simultaneous amelioration of both textural uniqueness and intrinsic electronic band structures. To this end, we have summarized an unprecedently comprehensive discussion on defect controls including the vacancy/non-metallic dopant creation with optimized electronic band structure and electronic density, metallic doping with ultraactive coordinated environment(M–N_(x), M–C_(2)N_(2), M–O bonding), functional group grafting with optimized band structure, and promoted crystallinity with extended conjugation π system with weakened interlayered van der Waals interaction. Among them, the defect states induced by various defect types such as N vacancy, P/S/halogen dopants, and cyano group in boosting solar harvesting and accelerating photocarrier transfer have also been emphasized. More importantly, the shallow defect traps identified by femtosecond transient absorption spectra(fs-TAS) have also been highlighted. It is believed that this review would pave the way for future readers with a unique insight into a more precise defective g-C_(3)N_(4) “customization”, motivating more profound thinking and flourishing research outputs on g-C_(3)N_(4)-based photocatalysis.

Generation of ring-shaped human iPSC-derived functional heart microtissues in a M?bius strip configuration

Although human-induced pluripotent stem cell-derived cardiomyocytes(hi PSC-CMs) have been used for disease modeling and drug discovery, clinically relevant three-dimensional(3D) functional myocardial microtissues are lacking. Here, we developed a novel ring-shaped cardiac microtissue comprised of chamber-specific tissues to achieve a geometrically non-orientable ventricular myocardial band, similar to a M?bius loop. The ring-shaped cardiac tissue was constructed of hi PSC-CMs and human cardiac fibroblasts(h CFs) through a facile cellular self-assembly approach. It exhibited basic anatomical structure,positive cardiac troponin T(c Tn T) immunostaining, regular calcium transients, and cardiac-like mechanical strength. The cardiac rings can be self-assembled and scaled up into various sizes with outstanding stability, suggesting their potential for precise therapy, pathophysiological investigation, and large-scale drug screening.

Deformation Analysis on Shear-Bending of Ring-Shaped Piezoelectric Actuator

Deformation of a simple single piezoelectric actuator is usually quite small.A ring-shaped piezoelectric actuator with large piezoelectrically generated displacement was proposed.The thickness of the actuator was1 mm,and the inner and outer diameters were 4 mm and 40 mm,respectively.The ring-shaped actuator was made of BiScO_3-PbTiO_3(BS-PT)ceramic and polarized in radial direction.An electric field was applied to thickness direction and a large shear-bending deformation emerged.Then Rayleigh-Ritz method and Bessel functions were adopted to analyze the shear-bending deformation.Results show that under an electric field of 7.5kV/cm,the maximum displacement at the inner edge of the actuator reached 5.07μm,which agreed well with the corresponding experimental results.

Exact solutions of the Klein-Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform

We present exact solutions for the Klein Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angulm＂ functions are expressed in terms of the hypergeometric functions. The radial eigenfunetions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial Klein-Gordon equation is reduced to a first-order differential equation.

Schrdinger Equation with Hulthen Potential Plus Ring-Shaped Potential

We present the solutions of the Schrodinger equation with the Hulthen potential plus ring-shape potential for l≠ 0 states within the framework of an exponential approximation of the centrifugal potential. Solutions to the corresponding angular and radial equations are obtained in terms of special functions using the conventional NikiforovUvarov method. The normalization constant for the Hulthen potential is also computed.

Adjustable transmission properties through ring-shaped nanotube arrays using finite-difference time-domain method

Metallic ring-shaped nanotube arrays are proposed and its optical transmission properties are studied by using finite-difference time-domain （FDTD） method. Compared with the transmission spectra of conventional circular nanotube arrays, two photonic band gaps are emerged in the transmission spectra offing-shaped nanotube arrays, the two band gaps and transmission spectra are adjusted by the length, inner radius, intertube spacing and the dielectric constants of the core and embedding medium, and magnitude modification, redshift and blueshift of the resonance modes are observed. A metallic ring-shaped nanotube arrays for subwavelength band-stop filter in the range of visible light can be achieved. To understand its physical origin, field-interference mechanism was suggested by the field distributions. The proposed nanostructures and results may have great potential applications in subwavelength near-field optics.

The relativistic bound states for a new ring-shaped harmonic oscillator

In this paper a new ring-shaped harmonic oscillator for spin 1/2 particles is studied, and the corresponding eigenfunctions and eigenenergies are obtained by solving the Dirac equation with equal mixture of vector and scalar potentials. Several particular cases such as the ring-shaped non-spherical harmonic oscillator, the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.

Heterointerface Engineering-Induced Oxygen Defects for the Manganese Dissolution Inhibition in Aqueous Zinc Ion Batteries

Manganese-based material is a prospective cathode material for aqueous zinc ion batteries(ZIBs)by virtue of its high theoretical capacity,high operating voltage,and low price.However,the manganese dissolution during the electrochemical reaction causes its electrochemical cycling stability to be undesirable.In this work,heterointerface engineering-induced oxygen defects are introduced into heterostructure MnO_(2)(δa-MnO_(2))by in situ electrochemical activation to inhibit manganese dissolution for aqueous zinc ion batteries.Meanwhile,the heterointerface between the disordered amorphous and the crystalline MnO_(2)ofδa-MnO_(2)is decisive for the formation of oxygen defects.And the experimental results indicate that the manganese dissolution ofδa-MnO_(2)is considerably inhibited during the charge/discharge cycle.Theoretical analysis indicates that the oxygen defect regulates the electronic and band structure and the Mn-O bonding state of the electrode material,thereby promoting electron transport kinetics as well as inhibiting Mn dissolution.Consequently,the capacity ofδa-MnO_(2)does not degrade after 100 cycles at a current density of 0.5 Ag^(-1)and also 91%capacity retention after 500cycles at 1 Ag^(-1).This study provides a promising insight into the development of high-performance manganese-based cathode materials through a facile and low-cost strategy.

Impact Analysis of Microscopic Defect Types on the Macroscopic Crack Propagation in Sintered Silver Nanoparticles

Sintered silver nanoparticles(AgNPs)arewidely used in high-power electronics due to their exceptional properties.However,the material reliability is significantly affected by various microscopic defects.In this work,the three primary micro-defect types at potential stress concentrations in sintered AgNPs are identified,categorized,and quantified.Molecular dynamics(MD)simulations are employed to observe the failure evolution of different microscopic defects.The dominant mechanisms responsible for this evolution are dislocation nucleation and dislocation motion.At the same time,this paper clarifies the quantitative relationship between the tensile strain amount and the failure mechanism transitions of the three defect types by defining key strain points.The impact of defect types on the failure process is also discussed.Furthermore,traction-separation curves extracted from microscopic defect evolutions serve as a bridge to connect the macro-scale model.The validity of the crack propagation model is confirmed through tensile tests.Finally,we thoroughly analyze how micro-defect types influence macro-crack propagation and attempt to find supporting evidence from the MD model.Our findings provide a multi-perspective reference for the reliability analysis of sintered AgNPs.

Solution of the Dirac equation with the ring-shaped oscillator potential

The ring-shaped oscillator potential, obtained by replacing the Coulomb part of the Hartmann potential by a harmonic oscillator term, was investigated. Under the equal vector potential and scalar potential, the Dirac equation was solved in spherical coordinate. The exact energy spectrum of the bound states was presented as a solution to the confluent hypergeometric equation by boundary conditions. Furthermore, the normalized angular and radial wave functions were presented.

The spin-one Duffin Kemmer Petiau equation in the presence of pseudo-harmonic oscillatory ring-shaped potential

The Duffin-Kemmer-Petiau equation （DKP） is studied in the presence of a pseudo-harmonic oscillatory ring-shaped potential in （1 ＋ 3）-dimensional space-time for spin-one particles. The exact energy eigenvalues and the eigenfunctions are obtained using the Nikiforov-Uvarov method.

Solution of Klein-Gordon Equation for Pseudo-Coulomb Potential Plus a New Ring-Shaped Potential

Under the condition of an equal mixing of vector and scalar potentials, exact solutions of bound states of theKlein-Gordon equation with pseudo-Coulomb potential plus a new ring-shaped potential are presented. Simultaneously,energy spectrum equations are also obtained. It is shown that the radial equation and angular wave functions areexpressed by confluent hypergeogetric and hypergeogetric functions respectively.