Three-dimensional Sn Research Articles

An optimized sweeping solution method for the three-dimensional Sn equations of neutron transport on hexahedral meshes

• An optimized sorting algorithm is proposed to remove deadlock without searching for global dependent cycles. • The effective face method is applied in the spatial discretization to deal with the integrals on the non-planar cell faces. • The convergence of the splitting iterative algorithm is proved rigorously. • The new method is verified to be conducive to the convergence of the iteration by numerical experiments. • Numerical results show the effectiveness and high efficiency of the new algorithm on general hexahedral meshes. We propose a new sweeping solution method for the three-dimensional (3D) discrete ordinates (Sn) equations of neutron transport on general hexahedral meshes, with particular focus on handling the surface integrals and sweeping deadlocks. The main contributions of this paper include three aspects. Firstly, the surface integrals on the non-planar cell faces are well discretized by virtue of the effective face method, which successfully addresses the reentrance problem without the decomposition of the cell faces. Secondly, based on the effective face method, we devise a new sorting algorithm which works for any hexahedral meshes. In this algorithm, the identification for dependent cycles is avoided and the physical characteristics of transport problems are taken into account in the choice of lagged cells used to decouple the sweeping deadlocks. Combining the above advancements, a splitting sweeping iterative method is proposed for the solution of the Sn equations on general hexahedral meshes. Finally, we prove theoretically that this sweeping iterative method always converges, and the decoupling method affects little on iterative convergence rate. Numerical experiments are presented to demonstrate the effectiveness of the proposed methods on both cubic and spherical domains. The ideas presented in this paper are also applicable to the polyhedral meshes or two-dimensional polygonal meshes.

Development of an improved quasi-static transient analysis code based on three-dimensional Sn nodal transport theory for fast reactor

Abstract A transient analysis code based on three-dimensional Sn nodal transport theory was developed for accurate transient analysis of the fast reactor. The time-dependent flux is factorized into the amplitude function and the shape function by the improved quasi-static approximation. The direct extension of the Sn nodal transport theory leads to the angular-dependent source term and requires much computer memory. To avoid direct treatment of angular-dependent source term, a new treatment was derived for the source term. The results of steady-state calculations were compared with that obtained by NSHEX for the verification of transport solver. For the verification of reactivity calculation based on perturbation theory, the reactivity was compared with that obtained from the multiplication factor by using the adiabatic approximation. The result with Sn transport calculation was compared with that with the diffusion calculation in Monju core. The results show the discrepancy of reactivity mainly comes from the absorption term.

Effects of the standing accretion-shock instability and the lepton-emission self-sustained asymmetry in the neutrino emission of rotating supernovae

Rotation of core-collapse supernovae (SNe) affects the neutrino emission characteristics. By comparing the neutrino properties of three three-dimensional SN simulations of a 15 M_sun progenitor (one non-rotating model and two models rotating at different velocities), we investigate how the neutrino emission varies with the flow dynamics in the SN core depending on the different degrees of rotation. The large-amplitude sinusoidal modulations due to the standing accretion-shock instability (SASI) are weaker in both the rotating models than in the non-rotating case. The SN progenitor rotation reduces the radial velocities and radial component of the kinetic energy associated with convection interior to the proto-neutron star. This effect seems to disfavor the growth of the hemispheric neutrino-emission asymmetries associated with the lepton-emission self-sustained asymmetry (LESA). An investigation of the multipole expansion of the neutrino luminosity and the electron neutrino lepton number flux shows a dominant quadrupolar mode in rotating SN models. Our findings highlight the power of using neutrinos as probes of SN hydrodynamics.

Electroplating of 3D Sn-rich solder for MEMS packaging applications

Electroplating is a popular method to produce solders in microelectromechanical systems (MEMS) encapsulation and interconnection applications. In this work, a fabrication process is introduced for the generation of three-dimensional (3D) Sn solder microstructures. An aluminum membrane was employed as the conducting layer while electroplating. Based on the proposed method, Sn solders with different heights can be easily obtained after reflow. Taking advantage of these 3D structures, MEMS packaging, electrical interconnections, hermetic seals and metal-armoring can be formed simultaneously in one step. Metal-armoring provided by the solder–solder contact can be used at the extremes of the suspension travel, greatly increasing the capability of shock resistance. The helium leak rates of the packaged samples are lower than the reject limit (5 × 10−8 atm cc s−1 based on MIL-STD-883E standard). The bonding strength of samples is measured by a die shear strength tests with an average value of 7.4 MPa. In addition, the ohmic behavior of the Sn solder bonding is verified as well. These excellent results show an outstanding packaging quality in MEMS encapsulation applications.

Dendrite fragmentation: an experiment-driven simulation.

The processes leading to the fragmentation of secondary dendrite arms are studied using a three-dimensional Sn dendritic structure that was measured experimentally as an initial condition in a phase-field simulation. The phase-field model replicates the kinetics of the coarsening process seen experimentally. Consistent with the experiment, the simulations of the Sn-rich dendrite show that secondary dendrite arm coalescence is prevalent and that fragmentation is not. The lack of fragmentation is due to the non-axisymmetric morphology and comparatively small spacing of the dendrite arms. A model for the coalescence process is proposed, and, consistent with the model, the radius of the contact region following coalescence increases as t1/3 We find that small changes in the width and spacing of the dendrite arms can lead to a very different fragmentation-dominated coarsening process. Thus, the alloy system and growth conditions of the dendrite can have a major impact on the fragmentation process.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.

Li-insertion/extraction properties of three-dimensional Sn electrode prepared by facile electrodeposition method

Toward the realization of reliable Li-ion batteries with high performance and safety, component materials such as those of the current collector and negative electrode require further innovation. Sn, one of the most promising negative-electrode materials, can be electrochemically fixed on a substrate without any binder or conductive additive. However, the pulverization of Sn-plated films on substrates caused by large volume changes during Li–Sn reactions is the main reason hindering the practical application of Sn-plated electrodes. In the present study, we developed an electrodeposited three-dimensional (3D) Cu substrate applied to underlayer of the electrode. The effect of substrate geometry on the charge–discharge performance of the Sn electrode was investigated. The 3D-Cu/Sn electrode exhibited superior cycling performance with a reversible capacity of 470 mA h g−1 even at the 300th cycle, whereas the Sn-plated electrode prepared on a typical flat Cu substrate showed a capacity of only 20 mA h g−1. The results demonstrated that the 3D structure played a key role in accommodating volumetric changes in the Sn to suppress electrode disintegration. The developed 3D-Cu substrate will be significantly useful as a current collector for alloy-based active materials.

Three-dimensional Sn rich Cu6Sn5 negative electrodes for Li ion batteries

Three-dimensional Sn rich Cu6Sn5 electrodes were fabricated by the pulse electrodeposition process on a porous nickel foam substrate to improve discharge capacity and cycleability of the SnCu alloy negative electrodes for Li-ion batteries. It was aimed to investigate the effect of peak current density on the structure and electrochemical performance of the Sn rich Cu6Sn5 electrodes. The morphology and the structures of the SnCu alloy electrodes were characterized by scanning electron microscopy (SEM). X-ray diffraction (XRD) analyses was also performed to investigate the structure of electrodeposited SnCu based electrodes. The electrochemical features of the electrodes were investigated by charge/discharge tests, cyclic voltammetry experiments and the ac impedance technique. Results showed that morphology of the electrodes exhibited a strong effect on the electrochemical performances and the best electrochemical performances were achieved in the alloy electrodes, which has dendritic like structure obtained using high peak current density.

Facile synthesis of three-dimensional reinforced Sn@polyaniline/sodium alginate nanofiber hydrogel network for high performance lithium-ion battery

An innovative three-dimensional (3D) Sn@ polyaniline (PANI)/sodium alginate (SA) nanofiber hydrogel is designed as high performance anode for lithium-ion batteries. The nanofiber conductive hydrogel was successfully synthesized via in situ polymerization of aniline in an aqueous solution of Sn nanoparticles (NPs) and SA. Scanning electron microscopy and transmission electron microscopy were used to characterize the morphology of Sn@PANI/SA. It was found that the 3D porous nanofiber hydrogel network was generated by the entanglement of PANI and SA chains and Sn NPs were embedded homogeneously inside. Because there are strong hydrogen bonding interactions between PANI and SA, SA has a remarkable reinforcement effect on PANI. And Sn@PANI/SA electrode exhibits more stable structure and better electrochemical performance than the Sn@PANI electrode. The galvanostatic charge/discharge profiles exhibit better reversible capacity (616 mAh g−1 after 100 cycles), more excellent rate capability and higher coulomb efficiency than those of the Sn@PANI electrodes indicating that such a reinforced hydrogel network has great application values on the anode materials of lithium-ion battery.

Lagrange Discrete Ordinates: A New Angular Discretization for the Three-Dimensional Linear Boltzmann Equation

The classical Sn equations of Carlson and Lee have been a mainstay in multidimensional radiation transport calculations. In this paper, an alternative to the Sn equations, the “Lagrange Discrete Ordinates” (LDO) equations, are derived. These equations are based on an interpolatory framework for functions on the unit sphere in three dimensions. While the LDO equations retain the formal structure of the classical Sn equations, they have a number of important differences. The LDO equations naturally allow the angular flux to be evaluated in directions other than those found in the quadrature set. To calculate the scattering source in the LDO equations, no spherical harmonic moments are needed—only values of the angular flux. Moreover, the LDO scattering source preserves the eigenstructure of the continuous scattering operator. The formal similarity of the LDO equations with the Sn equations should allow easy modification of mature three-dimensional Sn codes such as PARTISN or PENTRAN to solve the LDO equations. Numerical results are shown that demonstrate the spectral convergence (in angle) of the LDO equations for smooth solutions and the ability to mitigate ray effects by increasing the angular resolution of the LDO equations.

Comparison of Spatial Discretization Methods for Solving the SN Equations Using a Three-Dimensional Method of Manufactured Solutions Benchmark Suite with Escalating Order of Nonsmoothness

A comparison of the accuracy and computational efficiency of spatial discretization methods of the three-dimensional SN equations is conducted, including discontinuous Galerkin finite element methods, the arbitrarily high-order transport method of nodal type (AHOTN), the linear-linear method, the linear-nodal (LN) method, and the higher-order diamond difference method. For this purpose, we have developed a suite of method of manufactured solutions benchmarks that provides an exact solution of the SN equations even in the presence of scattering. Most importantly, our benchmark suite permits the user to set an arbitrary level of smoothness of the exact solution across the singular characteristics. Our study focuses on the computational efficiency of the considered spatial discretization methods.Numerical results indicate that the best-performing method depends on the norm used to measure the discretization error. We employ discrete Lp norms and integral error norms in this work. For configurations with continuous exact angular flux, high-order AHOTNs perform best under Lp error norms, while the LN method performs best when measured by integral error norms. When the angular flux is discontinuous, a new singular-characteristic tracking method for three-dimensional geometries performs best among the considered methods.

One-step electrochemical growth of a three-dimensional Sn-Ni@PEO nanotube array as a high performance lithium-ion battery anode.

Various well-designed nanostructures have been proposed to optimize the electrode systems of lithium-ion batteries for problems like Li(+) diffusion, electron transport, and large volume changes so as to fulfill effective capacity utilization and increase electrode stability. Here, a novel three-dimensional (3D) hybrid Sn-Ni@PEO nanotube array is synthesized as a high performance anode for a lithium-ion battery through a simple one-step electrodeposition for the first time. Superior to the traditional stepwise synthesis processes of heterostructured nanomaterials, this one-step method is more suitable for practical applications. The electrode morphology is well preserved after repeated Li(+) insertion and extraction, indicating that the positive synergistic effect of the alloy nanotube array and 3D ultrathin PEO coating could authentically optimize the current volume-expansion electrode system. The electrochemistry results further confirm that the superiority of the Sn-Ni@PEO nanotube array electrode could largely boost durable high reversible capacities and superior rate performances compared to a Sn-Ni nanowire array. This proposed ternary hybrid structure is proven to be an ideal candidate for the development of high performance anodes for lithium-ion batteries.

LAVENDER: A steady-state core analysis code for design studies of accelerator driven subcritical reactors

Abstract Accelerator driven subcritical reactors (ADSRs) have been proposed and widely investigated for the transmutation of transuranics (TRUs). ADSRs have several special characteristics, such as the subcritical core driven by spallation neutrons, anisotropic neutron flux distribution and complex geometry etc. These bring up requirements for development or extension of analysis codes to perform design studies. A code system named LAVENDER has been developed in this paper. It couples the modules for spallation target simulation and subcritical core analysis. The neutron transport-depletion calculation scheme is used based on the homogenized cross section from assembly calculations. A three-dimensional S N nodal transport code based on triangular-z meshes is employed and a multi-channel thermal-hydraulics analysis model is integrated. In the depletion calculation, the evolution of isotopic composition in the core is evaluated using the transmutation trajectory analysis algorithm (TTA) and fine depletion chains. The new code is verified by several benchmarks and code-to-code comparisons. Numerical results indicate that LAVENDER is reliable and efficient to be applied for the steady-state analysis and reactor core design of ADSRs.

Fabrication of Three-Dimensional Porous Sn Films as Anode for Li-Ion Batteries

A polystyrene spheres (PS) coated copper foil was adopted as a template to prepare three-dimensional (3D) porous Sn film electrode. The PS colloidal spheres were synthesized through emulsion polymerization and spin-coated on copper foil. Then Tin was electrodeposited on the template foil, following by etching in tetrahydrofuran to remove PS template. The obtained Sn film has a honeycomb-like porous structure and showed improved electrochemical performance.

Electrochemical synthesis and lithium storage properties of three-dimensional porous Sn–Co alloy/CNT composite

Three-dimensional (3-D) porous copper with stable pore structure is prepared by electroless plating. 3-D porous Sn–Co alloy/carbon nanotube (CNT) composite is synthesized by electrodeposition using 3-D porous copper as the substrate. The scanning electron microscope results indicate that 3-D porous Sn–Co alloy/CNT composite contains a large amount of interconnected pores with the diameter size of ~3 μm. Upon cycling, the pore structure gradually disappears, but no serious exfoliation appears due to porous structure and reinforcement by CNT. The charge/discharge results demonstrate that the 3-D porous Sn–Co alloy/CNT composite electrode delivers high first reversible specific capacity of 490 mAh g−1, and remains 441 mAh g−1 after 60 cycles tested at different current densities. Even at the current density of 3,200 mA g−1, the reversible specific capacity remains 319 mAh g−1, which is 65 % of the first specific capacity cycled at the current density of 100 mA g−1.

Three-dimensional Sn–graphene anode for high-performance lithium-ion batteries

Tin (Sn) has been considered as one of the most promising anode materials for high-capacity lithium-ion batteries (LIBs) due to its high energy density, abundance, and environmentally benign nature. However, the problems of fast capacity fading at prolonged cycling and poor rate capacity hinder its practical use. Herein, we report the development of a novel architecture of Sn nanoparticle-decorated three-dimensional (3D) foothill-like graphene as an anode in LIBs. Electrochemical measurements demonstrated that the 3D Sn-graphene anode delivered a reversible capacity of 466 mA h g(-1) at a current density of 879 mA g(-1) (1 C) after over 4000 cycles and 794 mA h g(-1) at 293 mA g(-1) (1/3 C) after 400 cycles. The capacity at 1/3 C is over 200% that of conventional graphite anodes, suggesting that the 3D Sn-graphene structure enables a significant improvement in the overall performance of a LIB in aspects of capacity, cycle life, and rate capacity.

Three-dimensional delayed-detonation models with nucleosynthesis for Type Ia supernovae

We present results for a suite of fourteen three-dimensional, high resolution hydrodynamical simulations of delayed-detonation modelsof Type Ia supernova (SN Ia) explosions. This model suite comprises the first set of three-dimensional SN Ia simulations with detailed isotopic yield information. As such, it may serve as a database for Chandrasekhar-mass delayed-detonation model nucleosynthetic yields and for deriving synthetic observables such as spectra and light curves. We employ a physically motivated, stochastic model based on turbulent velocity fluctuations and fuel density to calculate in situ the deflagration to detonation transition (DDT) probabilities. To obtain different strengths of the deflagration phase and thereby different degrees of pre-expansion, we have chosen a sequence of initial models with 1, 3, 5, 10, 20, 40, 100, 150, 200, 300, and 1600 (two different realizations) ignition kernels in a hydrostatic white dwarf with central density of 2.9 x 10^9 gcc, plus in addition one high central density (5.5 x 10^9 gcc), and one low central density (1.0 x 10^9 gcc) rendition of the 100 ignition kernel configuration. For each simulation we determined detailed nucleosynthetic yields by post-processing 10^6 tracer particles with a 384 nuclide reaction network. All delayed detonation models result in explosions unbinding the white dwarf, producing a range of 56Ni masses from 0.32 to 1.11 solar masses. As a general trend, the models predict that the stable neutron-rich iron group isotopes are not found at the lowest velocities, but rather at intermediate velocities (~3,000 - 10,000 km/s) in a shell surrounding a 56Ni-rich core. The models further predict relatively low velocity oxygen and carbon, with typical minimum velocities around 4,000 and 10,000 km/s, respectively.

Chemical bath deposition of three-dimensional ternary Sn–Zn–Ni film and its application as anode for Li ion battery

A three-dimensional ternary Sn–Zn–Ni film was prepared by a modified chemical bath deposition method, which involved the alkaline disproportionating reaction and other redox reactions happening simultaneously. Sn was obtained by the disproportionating reaction of Sn(OH)2−4, while Zn and Ni were produced by the aid of two different kinds of reducing agents: NaBH4 and NaHPO2.H2O together. X-ray diffraction, SEM and energy dispersive X-ray spectrometry (EDS) were used to characterise the phases, morphology and composition of the films respectively. The EDS results showed that the elements of Sn, Zn and Ni could all be found in both films by optimising the deposition conditions. Ternary Sn–Zn–Ni film was deposited on copper foam for use as anode in a lithium ion battery. The electrode showed a high level capacity of ∼500 mAh g−1 with good cycle stability for 35 cycles.

Three-dimensional macroporous Sn–Ag thin film anode prepared by electro-less reduction method: effect of micro-structure

A three-dimensional Sn–Ag thin film with open interconnected walls consisting of active small grains of Sn and Ag was fabricated by electro-less reduction method as anode for lithium-ion batteries application. The morphologies and electrochemical performance of the macroporous Sn–Ag thin films were investigated by using scanning electron microscopy, energy dispersive X-ray spectroscopy, X-ray diffraction, cyclic voltammetry, and galvanostatical charge–discharge measurement. The results demonstrated that through controlling the plating time, the electrode with optimized microstructure exhibited the largest reversible capacities, maintaining a capacity of 583 mAh g−1 after 100 cycles, due to the well-preserved micro-porous structure after extended cycling.

Electrochemical performances of Sn anode electrodeposited on porous Cu foam for Li-ion batteries

Abstract A three-dimensional Sn electrode is fabricated by the electrodeposition of Sn on a porous Cu foam substrate that consists of grape-like Cu nanodeposits. It is revealed from the XRD results that a small amount of Cu 6 Sn 5 is formed at the interface of Sn deposits and the Cu foam, thereby forming Sn–Cu 6 Sn 5 /Cu foam electrode. The electrode shows better cyclic performance and higher charge capacity than the Sn electrode electrodeposited on a smooth Cu foil does. The improved electrochemical performances of the Sn–Cu 6 Sn 5 /Cu foam electrode is due to the fact that the porous Cu foam accommodates the volumetric expansion of Sn–Cu 6 Sn 5 , and hence inhibits the pulverization or delamination of the active materials from the substrate. Furthermore, ex situ XRD analysis and SEM observation demonstrate that Sn deposits electrodeposited on the Cu foam are gradually blended with the Cu deposits, causing the transformation of Sn into Cu 6 Sn 5 . The phase transformation of Sn into Cu 6 Sn 5 enhances the bonding force between the Sn and the Cu foam, and reducing the volume changes of active materials during cycling.

Attila Validation with Fusion Benchmark Experiments at JAEA/FNS

The three-dimensional Sn code Attila of Transpire, Inc., can use computer-aided-design data as direct geometrical input and can deal with assemblies of complicated geometry without much effort. The International Thermonuclear Experimental Reactor (ITER) organization plans to adopt this code as one of the standard codes for nuclear analyses. However, validation of calculations with this code has not been carried out in detail so far. Thus, we validate this code through analyses of some bulk experiments and streaming experiments with deuterium-tritium neutrons at the Japan Atomic Energy Agency Fusion Neutronics Source. Analyses with the Sn code system DOORS and Monte Carlo code MCNP4C were also carried out for comparison. The agreement between the Attila and DOORS calculations is very good for the bulk experiments. For the streaming experiments Attila requires special treatment (biased angular quadrature sets or last collided source calculation) as well as DOORS in order to obtain similar results as those with MCNP, though Attila consumes much more time than DOORS.