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At least 523 records · Page 29

Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion

Reproducing kernel (RK) approximations are meshfree methods that construct shape functions from sets of scattered data. We present an asymptotically compatible (AC) RK collocation method for nonlocal diffusion models with Dirichlet boundary condition. The numerical scheme is shown to be convergent to both nonlocal diffusion and its corresponding local limit as nonlocal interaction vanishes. The analysis is carried out on a special family of rectilinear Cartesian grids for a linear RK method with designed kernel support. The key idea for the stability of the RK collocation scheme is to compare the collocation scheme with the standard Galerkin scheme, which is stable. In addition, assembling the stiffness matrix of the nonlocal problem requires costly computational resources because high-order Gaussian quadrature is necessary to evaluate the integral. We thus provide a remedy to the problem by introducing a quasi-discrete nonlocal diffusion operator for which no numerical quadrature is further needed after applying the RK collocation scheme. The quasi-discrete nonlocal diffusion operator combined with RK collocation is shown to be convergent to the correct local diffusion problem by taking the limits of nonlocal interaction and spatial resolution simultaneously. The theoretical results are then validated with numerical experiments. We additionally illustrate a connection between the proposed technique and an existing optimization based approach based on generalized moving least squares.

97 MATHEMATICS AND COMPUTING↗

Development of Multilayer Sinter Cladding of Cold Work Tool Steel on Hadfield Steel Plates for Wear-Resistant Applications

Machinery components used for mining and mineral processing activities are often subjected to high impact loads and wear which have placed demands for the development of materials with high resistance to dynamic loads and aggressive wear conditions. In this study, a multilayered cladding of high alloyed cold work tool steel (X245VCrMo9-4), interlayered with Hadfield steel (X120Mn12) plates, which was also used as substrate using super-solidus liquid-phase sintering technique was investigated. A stack of the cold work tool steel powder was prepared with interlayered X120Mn12 steel plates in an alumina crucible at tap density with the substrate placed on it and was sintered in a vacuum furnace at 1250 °C at a heating rate of 10 K/min, held for 30 min under a nitrogen atmosphere at 0.08 MPa and furnace-cooled. Sample from the as-sintered cladding was subjected to austenization at 1000 °C, quenched in oil and tempered at 150 °C for 2 h. Samples were subjected to microstructural examination using optical and scanning electron microscopy. The microstructural investigations were supplemented by hardness and impact wear tests. Computational thermodynamics was used to support experimental findings. The results revealed that a near-net densification of the sintered X245 was achieved with 99.93 ± 0.01% density. The sintered X245 was characterized by a dispersion of vanadium carbonitride precipitates, especially at the grain boundaries. The heat-treated X245 sample had the highest hardness of 680 ± 7 HV30 due to the matrix of tempered martensitic microstructure when compared to as-sintered with hardness of 554 ± 2 HV30. The X245/X120 interface was characterized by diffusion of Cr, Mo, Mn and C, which resulted in metallurgical bonding between the cladded materials. The impact wear resistance of the sintered X245 was eight times that of the X120; hence, a tough and wear-resistant tool is anticipated when the X120 work hardened in service.

36 MATERIALS SCIENCE↗

Homogeneous hydride formation path in α-Zr: Molecular dynamics simulations with the charge-optimized many-body potential

A formation path for homogeneous γ hydride formation in hcp α-Zr, from solid solution to the ζ and then the γ hydride, was demonstrated using molecular static calculations and molecular dynamic simulations with the charge-optimized many-body (COMB) potential. Hydrogen has limited solubility in α-Zr. Once the solubility limit is exceeded, the stability of solid solution gives way to that of coherent hydride phases such as the ζ hydride by planar precipitation of hydrogen. At finite temperatures, the ζ hydride goes through a partial hcp-fcc transformation via 1/3 <1¯100> slip on the basal plane, and transforms into a mixture of γ hydride and α-Zr. In the ζ hydride, slip on the basal plane is favored thermodynamically with negligible barrier, and is therefore feasible at finite temperatures without mechanical loading. The transformation process involves slips of three equivalent shear partials, in contrast to that proposed in the literature where only a single shear partial was involved. The adoption of multiple slip partials minimizes the macroscopic shape change of embedded hydride clusters and the shear strain accumulation in the matrix, and thus reduces the overall barrier needed for homogeneous γ hydride formation. In conclusion, this formation path requires finite temperatures for hydrogen diffusion without mechanical loading. Therefore, it should be effective at the cladding operating conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Algebraic Multigrid with Optimal Interpolation and Adaptive Smoothers (Final Report)

The project team continued with work on developing new bootstrap AMG techniques for solving symmetric and non-symmetric PDE systems. The focus of this work is to derive more reliable measures of the quality of the coarse space set than the convergence rate of the standard F-relaxation form of CR and a more robust form of interpolation than the so-called ideal form. We have successfully derived a sharp variant of CR that gives the precise convergence rate of the two-grid method using this optimal interpolation and, in addition, we derived a new Generalized Bootstrap AMG setup algorithm that uses as its main tool a multilevel eigensolver for the generalized eigenvalue problem involving the system matrix and the symmetrized smoother. In addition, the approach allows for general block smoothers with overlap. We have applied the method to scalar diffusion problems, linear elasticity, and Maxwell’s and the method shows marked improvements over existing AMG methods for these problems. In addition, the team worked with CASC members on new forms of ideal AMG interpolation.

97 MATHEMATICS AND COMPUTING↗

Reaction of cobalt in SO2 atmospheric at elevated temperatures

The reaction rate of cobalt in SO2 argon environments was measured at 650 C, 700 C, 750 C and 800 C. Product scales consist primarily of an interconnected sulfide phase in an oxide matrix. At 700 C to 800 C a thin sulfide layer adjacent to the metal is also observed. At all temperatures, the rapid diffusion of cobalt outward through the interconnected sulfide appears to be important. At 650 C, the reaction rate slows dramatically after five minutes due to a change in the distribution of these sulfides. At 700 C and 750 C the reaction is primarily diffusion controlled values of diffusivity of cobalt (CoS) calculated from this work show favorable agreement with values of diffusivity of cobalt (CoS) calculated from previous sulfidation work. At 800 C, a surface step becomes rate limiting.

Jacobson, N. S.↗

Reaction of cobalt in SO2 atmospheres at elevated temperatures

The reaction rate of cobalt in SO2 argon environments was measured at 650 C, 700 C, 750 C and 800 C. Product scales consist primarily of an interconnected sulfide phase in an oxide matrix. At 700 C to 800 C, a thin sulfide layer adjacent to the metal is also observed. At all temperatures, the rapid diffusion of cobalt outward through the interconnected sulfide appears to be important. At 650 C, the reaction rate slows dramatically after five minutes due to a change in the distribution of these sulfides. At 700 C and 750 C, the reaction is primarily diffusion controlled; values of diffusivity of cobalt (CoS) calculated from this work show favorable agreement with values of diffusivity of cobalt (CoS) calculated from previous sulfidation work. At 800 C, a surface step becomes rate limiting. Previously announced in STAR as N83-35104

Jacobson, N. S.↗

Distribution of species and Ga–N bonds in silicon co-implanted with gallium and nitrogen ions

The concentration profiles of species in silicon subjected to gallium and nitrogen co-implantation and subsequent annealing have been investigated by the method of X-ray photoelectron spectroscopy combined with the layer-by-layer ion etching of the implanted layer. It is shown that practically entire implanted gallium undergoes out-diffusion, but the preliminary implantation of nitrogen for the synthesis of a barrier SiN{sub x} layer makes it possible to avoid the essential loss of gallium. In this case, about 14 % of implanted gallium bond to nitrogen. The obtained data are discussed from the viewpoint of the possibility of ion synthesis of GaN inclusions in silicon matrix.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Structural and chemical disorder enhance point defect diffusion and atomic transport in Ni 3 Al-based γ' phase

The ordered L1 2 γ' Ni 3 Al intermetallic inclusions are routinely used as strengthening constituents in Ni-based superalloys and recent high-entropy alloys. As there are different metallic elements relative to the alloy matrix, the composition of γ' phase inclusions usually suffers some variations. In this work, we studied the elemental partition and its influence on atomic transport properties in a model (NiCo) 3 Al γ' phase with chemical and structural disorder. Combining the Monte Carlo and molecular static techniques, we first determined the elemental distribution in such compositionally-complexed γ' phase. The results suggest that Co tends to segregate, which profoundly influences defect energetics and diffusion properties. By modeling thermally activated diffusion by molecular dynamics, we found that chemical disorder induced by Co can enhance vacancy diffusion while significantly suppress diffusion via interstitial atom migration, as compared to the stoichiometric γ' Ni 3 Al. We further reveal that these observations are closely related to the defect energetics in these systems. Furthermore, our results explain the effects of disorder, long- and short-range orders on the diffusion properties in multicomponent intermetallic alloys, which helps to understand the stability and, thus, γ'-phase-assisted strengthening at different conditions including annealing and irradiation.

36 MATERIALS SCIENCE↗

Finite-element solution for a combined radiative-conductive analysis with mixed diffuse-specular surface characteristics

The finite-element method has been applied to solve a combined radiative-conductive heat transfer problem for a large space telescope similar to those used in orbiting satellites. The derivation of the underlying matrices and associated solution algorithm for a 2-D triangular element is presented in detail. The resulting expressions for this triangular element typify such an analysis, which yields constitutive matrices when the heat equation is cast in the matrix form. The relevant matrices include those pertaining to thermal conductance, internal heat generation, radiative exchanges, and all possible external thermal loadings. Emphasis is placed on the treatment of non-linear radiative interchange between surfaces in an enclosure having mixed diffuse-specular surface characteristics. Essential differences in governing equations describing these distinctive surface characteristics are identified. Concluding remarks are drawn from an example simulating a Cassegrainian space telescope.

Lee, H.-P.↗

Time-dependent variational principle for mixed matrix product states in the thermodynamic limit

Here, we describe a time evolution algorithm for quantum spin chains whose Hamiltonians are composed of an infinite uniform left and right bulk part, and an arbitrary finite region in between. The left and right bulk parts are allowed to be different from each other. The algorithm is based on the time-dependent variational principle (TDVP) of matrix product states. It is inversion-free and very simple to adapt from an existing TDVP code for finite systems. The importance of working in the projective Hilbert space is highlighted. We study the quantum Ising model as a benchmark and an illustrative example. The spread of information after a local quench is studied in both the ballistic and the diffusive case. We also offer a derivation of TDVP directly from symplectic geometry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolution in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Advanced Moderation Module for High-Temperature Micro-Reactor Applications

Development and deployment of micro-reactors that provide competitive efficiency, prevailing compactness, and inherent safety is an immediate focus of the U.S. nuclear industry. For thermal neutron micro-reactors operating at elevated temperature for optimized efficiency, such as micro molten-salt reactors (MSRs), heat-pipe reactors, and very-high temperature reactors (VHTRs), high-performance moderator based on metal hydride can enhance the neutron economy and therefore achieve reduced weight and enhanced portability. As unclad metal hydride inevitably decomposes at elevated temperature, an enclosure is required for hydride moderator to deliver desired performance at elevated temperatures. Conventional moderator enclosure solutions based on high-temperature alloys introduce extraneous neutron penalty into the micro-reactor, affecting the neutronic benefits provided by the hydride moderator. Additionally, the compatibility between the high-temperature alloy enclosure and the micro-reactor matrix is also a potential issue. In this report, we disclose an Advanced Moderator Module (AMM) concept enabled by an innovative enclosure solution combining the advantages of refractory metals, ceramic matrix composites (CMCs), and advanced coating technology to serve as hydrogen permeation barrier up to very-high temperatures. A schematic description of the AMM structure is illustrated in Figure A1. The AMM contains a moderating material core made of metal hydride with high thermal stability, such as YH 2-x . The hydride core is enclosed by an H 2 barrier layer coated on a ductile refractory metal liner to minimize hydrogen loss during high-temperature operation. A ceramic matrix composite (CMC) cladding is adopted to provide further structural strength, especially during power transients. Between the CMC cladding and metal liner, an extra diffusion barrier coating is inserted to suppress the chemical interaction at elevated temperatures. Hence, based on a series of innovative material solutions, the AMM is capable of containing the metal hydride core at elevated temperature (>900oC) inside coated and lined CMC envelop with negligible hydrogen loss throughout the microreactor lifetime. The benefit of the AMM technology was assessed based on a comprehensive multi-stage reactor-physics analysis. Advanced moderation based on hydride metals (such as YH2-x) enables reaching optimum moderation with higher fuel content than traditional VHTR technology, which is required to design compact micro-reactor cores targeting long-life operation. The AMM enclosure technology provides lower thermal neutron absorption rates than traditional solutions (based on stainless steel or Mo-based alloy such as TZM), which reduces the fissile enrichment requirements by 6-8% on a TRISO-fueled design based on the EMPIRE core. Finally, combining the hydride moderator with neutron transparent enclosure solutions provides significant potential to boost neutronics performance of micro-reactors in terms of increased core lifetime or reduced size and weight by 30-50% on a micro-reactor based on the Holos Quad technology. The progress and plans for on-going development and demonstration efforts are also discussed in this report. The current demonstration of AMM is focused on the hydrogen diffusion barrier demonstration under thermal cycling, while radiation tolerance demonstration is planned. The next step of the demonstration plan will be the assembly of miniature AMM for high-temperature testing, which can be used as a prototype for future pilot scale demonstration.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Bernstein dual-Petrov–Galerkin method: application to 2D time fractional diffusion equation

In this paper, we develop a Bernstein dual-Petrov–Galerkin method for the numerical simulation of a two-dimensional fractional diffusion equation. A spectral discretization is applied by introducing suitable combinations of dual Bernstein polynomials as the test functions and the Bernstein polynomials as the trial ones. We derive the exact sparse operational matrix of differentiation for the dual Bernstein basis which provides a matrix-based approach for the spatial discretization. It is shown that the method leads to banded linear systems that can be solved efficiently. The stability and convergence of the proposed method is discussed. Finally, some numerical examples are provided to support the theoretical claims and to show the accuracy and efficiency of the method.

97 MATHEMATICS AND COMPUTING↗

Analytic error analysis of cross section interpolation methods in nodal diffusion codes - I : Theory

This paper discusses two cross section interpolation methods commonly found in popular nodal codes; the partial derivatives and multiple tables models. The motivation for choosing a model, and thus a case matrix structure, is a trade off between accuracy and computational cost. Due to decades of experience, there are default structures that are sufficient for current light water reactor analysis. However, this is not necessarily the case for advanced reactor designs. Therefore, it is advantageous to understand the sources of error in cross section interpolation models so that the quality of a case matrix may be improved. A mathematical framework for these models is presented in this work that provides a more rigorous connection between the nuclear engineering field's cross section interpolation methods and the broader mathematical field of function approximation. The two cross section models examined in this paper were found to utilize Lagrange interpolation and are a subset of Lagrange tensor products. Classical results of Lagrange polynomial error analysis were then applied to the partial derivative and multiple tables models to derive expressions for the total point-wise error. The analytical results classify the total error into two parts: the model form error and interpolation error. Finally, based on our observations, a better foundation for improving the quality of a case matrix is proposed. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The role of tungsten phases formation during tungsten metal powder consolidation by FAST: Implications for high-temperature applications

Highlights: • Lowering the sintering temperature of W to 2173 K by using FAST. • Application of electron microscopy for microstructure characterisation. • W{sub 2}C shell formation due to C difussion from graphite tooling. • Identification of co-formed secondary phase, WO{sub 2}. • Influence of WO{sub 2} on high-thermal applications. - Abstract: Tungsten is a candidate material for the demonstration fusion power plant DEMO. To ensure high density and structural stability, Field-Assisted Sintering Technique (FAST) is proposed as a consolidation method. This study discusses the formation of phases during sintering of tungsten by the FAST. Scanning electron microscopy, X-ray diffraction and transmission electron microscopy were used to evaluate the microstructure in tungsten-based materials. The results of microscopic examinations revealed the in-situ formation of tungsten oxide and a formation of tungsten carbide shell around tungsten core. Tungsten carbide-rich shell is formed due to the carbon diffusion from the graphite die used in the FAST into tungsten at high temperatures. In contrast to easy removal of tungsten carbide shell by mechanical grinding, the formation of tungsten oxide in the W-matrix can influence the performance of such material when used as plasma-facing material in the fusion reactor. High-temperature experiments at 1873 K showed that tungsten-oxide phase starts to decompose, which results in material degradation and formation of voids and surface blisters.

36 MATERIALS SCIENCE↗

Computational Design of Cost-Effective High-Entropy Thermal/Environmental Barrier Coatings

Developing cost-effective thermal/environmental barrier coatings (TEBC) requires balance among various properties including low thermal conductivity, matching coefficient of thermal expansion (CTE), high thermal stability, high fracture toughness, and high recession resistance while being affordable. Low oxygen diffusivity is desirable as it can slow down oxygen transport to reach the underlying bond coating and hence delay oxidation of the bond coating. This project aims to design low-cost high-performance TEBC based on high entropy rare earth disilicates to protect SiC-based ceramic matrix composites from chemical and thermal attack for better performance of components in the hot section of gas turbine engines. To accelerate the TEBC design, we utilize first-principles density functional theory to predict key properties including phase stability, CTE, lattice thermal conductivity, temperature-dependent elastic constants, and oxygen diffusivity. Alloying elements including Yb, Y, Er, Eu, Gd, Lu, La, and Ce are considered, and modeling prediction are compared with available experimental results.

coefficient of thermal expansion↗

Grain Boundary Segregation Suppresses Local Short‐Range Ordering in Nanocrystalline High‐Entropy Alloys

Multi-principal-element alloys like high-entropy alloys (HEAs) have potential applications in many engineering fields due to their unique mechanical/functional properties. While HEAs are generally considered random solid solutions, recent studies revealed that they are prone to short-range-ordering (SRO) due to the complex multi-pair-wise interactions among the constituent elements. Meanwhile, SROs' evolution can sometimes be deleterious, and it is necessary to have control over their evolution. Examining the AlCoCrFe-Zr model alloy, long-range ordering occurs following the expectation of enthalpic predictions. Advanced characterization techniques—transmission electron microscopy, high-energy synchrotron X-ray diffraction/pair distribution function, and atom probe tomography, reveal that SRO is suppressed in as-milled and GB-decorated NC-(AlCoCrFe)100-xZrx (x = 0–1.5 atomic %). Warren-Cowley coefficient calculations are further used to validate the suppression of SRO. Besides the low segregation enthalpies of Cr, Fe, and Zr, and the high-mixing enthalpy of Cr and Fe, the short diffusion path to GBs due to high-GB density in the NC-HEAs and the higher energy state of the GBs than the matrix promotes GB-segregation that further alters the matrix chemistry and consequently disfavors SRO formation within the matrix. Despite the GB-segregation of Cr, Fe, and Zr, the matrices and GBs remain in a random solid solution.

36 MATERIALS SCIENCE↗

Application of BISON to UO 2 MiniFuel fission gas release analysis

There has been a recent push to accelerate fuel qualification by developing revolutionary capabilities to reduce irradiation periods, and thereby, reduce the time required to qualify a new fuel system. One such capability is the MiniFuel irradiation capsule designed to miniaturize fuel samples and irradiate “mini” fuel samples under isothermal temperature conditions. MiniFuel allows steady-state irradiations to decouple the traditionally coupled fission rate (i.e., power) and temperature parameters to understand and generate microstructures observed in fuel operated in a commercial reactor. Furthermore, this process offers the possibility to gather in situ data as well as postirradiation or transient data such as thermal conductivity, specific heat, fission gas diffusion and release, etc. However, accelerating fuel qualification is not solely reliant on generating large amounts of data but also on developing an informed test matrix designed to rapidly generate impactful data. Additionally, this process is reliant on fuel performance codes, such as BISON, to evaluate MiniFuel irradiations using existing material models. This process pinpoints model/data gaps, identifies desired irradiation conditions, and subsequently supports model validation and development. This work describes the use of BISON to perform a number of sensitivity studies designed to understand conditions that lead to fission gas release (FGR) under steady-state isothermal irradiation conditions and temperature transient conditions. The model is applied to a UO 2 MiniFuel example and shows an overall good qualitative agreement with experimental FGR annealing tests under different temperature conditions. It also accounts well for microstructural effects on FGR. When quantitatively compared with FGR data from previously irradiated 103 MWd/kgU UO 2 discs under thermal annealing, the model shows a less satisfactory agreement with the experimental data. Finally, a UO 2 MiniFuel test matrix is proposed to help to extend the model's operational range and validate the new FGR model capabilities to higher burnups and transient conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗