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At least 1,279 records · Page 71

Aleph Field Solver Challenge Problem Results Summary

Aleph models continuum electrostatic and steady and transient thermal fields using a finite-element method. Much work has gone into expanding the core solver capability to support enriched modeling consisting of multiple interacting fields, special boundary conditions and two-way interfacial coupling with particles modeled using Aleph's complementary particle-in-cell capability. This report provides quantitative evidence for correct implementation of Aleph's field solver via order- of-convergence assessments on a collection of problems of increasing complexity. It is intended to provide Aleph with a pedigree and to establish a basis for confidence in results for more challenging problems important to Sandia's mission that Aleph was specifically designed to address.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Mathematical and Numerical Analyses of Peridynamics for Multiscale Materials Modeling

We have treated the modeling, analysis, numerical analysis, and algorithmic development for nonlocal models of diffusion and mechanics. Variational formulations were developed and finite element methods were developed based on those formulations for both steady state and time dependent problems. Obstacle problems and optimization problems for the nonlocal models were also treated and connections made with fractional derivative models.

97 MATHEMATICS AND COMPUTING↗

A new efficient approach for 3D hydrodynamics simulation

LANL’s CHICOMA code solves the compressible hydrodynamic equations on moving tetrahedral grids. Hydrodynamic equations can be solved in Lagrangian, Eulerian, and Arbitrary Lagrangian-Eulerian reference frames. The equations are solved using a finite element method coupled to approximate Riemann solvers. The methods have been extensively verified against relevant analytical solutions. CHICOMA is 10 3 -10 4 times faster than current production codes for the same level of accuracy!

42 ENGINEERING↗

Development of Seismic Isolation Systems Using Periodic Materials

Advanced fast nuclear power plants and small modular fast reactors are composed of thin-walled structures such as pipes; as a result, they do not have sufficient inherent strength to resist seismic loads. Seismic isolation, therefore, is an effective solution for mitigating earthquake hazards for these types of structures. Base isolation, on which numerous studies have been conducted, is a well-defined structure protection system against earthquakes. In conventional isolators, such as high-damping rubber bearings, lead-rubber bearings, and friction pendulum bearings, large relative displacements occur between upper structures and foundations. Only isolation in a horizontal direction is provided; these features are not desirable for the piping systems. The concept of periodic materials, based on the theory of solid-state physics, can be applied to earthquake engineering. The periodic material is a material that possesses distinct characteristics that prevent waves with certain frequencies from being transmitted through it; therefore, this material can be used in structural foundations to block unwanted seismic waves with certain frequencies. The frequency band of periodic material that can filter out waves is called the band gap, and the structural foundation made of periodic material is referred to as the periodic foundation. The design of a nuclear power plant, therefore, can be unified around the desirable feature of a periodic foundation, while the continuous maintenance of the structure is not needed. In this research project, three different types of periodic foundations were studied: one-dimensional, two-dimensional, and three-dimensional. The basic theories of periodic foundations are introduced first to find the band gaps; then the finite element methods are used, to perform parametric analysis, and obtain attenuation zones; finally, experimental programs are conducted, and the test data are analyzed to verify the theory. This procedure shows that the periodic foundation is a promising and effective way to mitigate structural damage caused by earthquake excitation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The Density of Uranium Hydride Formed Under Mechanical Load

The conversion of uranium metal (ρ = 19 g/cc) to uranium hydride (theoretical ρ = 11 g/cc) results in a large volumetric expansion due to both the density decrease and the substantial porosity of the hydride if not volumetrically constrained. This transformation from a monolithic solid to a particulate material can generate substantial forces when the growing hydride impacts a nearby target. The resulting displacement of the target is dependent upon both its resistance to motion and the strength of the growing hydride. We have observed columns of growing uranium hydride apply forces of hundreds to thousands of pounds to flex high-strength cantilever beams, and have measured applied forces of over 5000 pounds when growing hydride columns impacted rigid targets. The force/displacement behavior of growing uranium hydride was originally modeled by finite element methods to develop an elastic, perfectly plastic constitutive model of UH 3 . The UH 3 constitutive model was then applied to simulate the response of components impacted by growing uranium hydride. More recently we have used an experimental apparatus that simultaneously and independently provides measurement of applied force and target displacement during uranium hydride formation. These efforts confirm previous work and allow for increased confidence in modeling results. The design, testing, and experimental results using such an apparatus over a variety of system stiffnesses and with a variety of sample sizes has been completed. This work extended our understanding of UH 3 growth dynamics and mechanics and enabled the development of a higher fidelity constitutive Drucker-Prager model for UH 3 , and greater confidence in predictions of component behavior in systems impacted by uranium hydride formation.

36 MATERIALS SCIENCE↗

Proteus-SN user manual

This user manual describes how to set up a neutron transport simulation with the PROTEUS-SN code. A companion methodology manual describes the theory and algorithms within PROTEUS-SN.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A Kinetic Approach to Modeling the Manufacture of High Density Polyurethane Structural Foam: Foaming and Polymerization

This report details the study of PMDI structural foam and the development of a computational model to represent it. This polyurethane has a fast catalyst, such that foaming and polymerization occur simultaneously. The foam is over-packed to twice or more of its free rise density to reach the density of interest. Our approach is to combine model development closely with experiments to discover underlying physical phenomena, to parameterize models, and to validate the models once they have been developed. The model must be able to represent the expansion, filling of molds, curing, and final foam properties. PMDI is a chemically blown foam, where carbon dioxide is produced via the reaction of water and isocyanate. The isocyanate also reacts with polyol in a competing reaction, which produces the polymer. A new kinetic model is developed and implemented, which follows a simplified mathematical formalism that decouples these two reactions. The model predicts the polymerization reaction via condensation chemistry, where vitrification and glass transition temperature evolution must be included to correctly predict the temperature dependence of the kinetics. The foam gas generation kinetics are determined by tracking the molar concentration of both water and carbon dioxide. Understanding the thermal history and loads on the foam due to exothermicity and oven curing is very important to the results, since the kinetics and material properties are all sensitive to temperature. The conservation equations, including the equations of motion, an energy balance, and three rate equations are solved via a stabilized finite element method. We assume generalized-Newtonian rheology that is dependent on the extent of cure, gas fraction, and temperature. The conservation equations are combined with a level set method to determine the location of the free surface over time. Results from the model are compared to experimental flow visualization data and post-test X-ray computed tomography (CT) data for the density. Several geometries are investigated including a mock encapsulation part, two configurations of a mock structural part, and a bar geometry to specifically test the density model. We have found that the model predicts both average density and filling profiles well. However, it under predicts density gradients, especially in the gravity direction. Further model improvements are also discussed.

36 MATERIALS SCIENCE↗

Multi-scale Modeling of Plasticity in Tantalum.

In this report, we present a multi-scale computational model to simulate plastic deformation of tantalum and validating experiments. In atomistic/ dislocation level, dislocation kink- pair theory is used to formulate temperature and strain rate dependent constitutive equations. The kink-pair theory is calibrated to available data from single crystal experiments to produce accurate and convenient constitutive laws. The model is then implemented into a BCC crystal plasticity finite element method (CP-FEM) model to predict temperature and strain rate dependent yield stresses of single and polycrystalline tantalum and compared with existing experimental data from the literature. Furthermore, classical continuum constitutive models describing temperature and strain rate dependent flow behaviors are fit to the yield stresses obtained from the CP-FEM polycrystal predictions. The model is then used to conduct hydro- dynamic simulations of Taylor cylinder impact test and compared with experiments. In order to validate the proposed tantalum CP-FEM model with experiments, we introduce a method for quantitative comparison of CP-FEM models with various experimental techniques. To mitigate the effects of unknown subsurface microstructure, tantalum tensile specimens with a pseudo-two-dimensional grain structure and grain sizes on the order of millimeters are used. A technique combining an electron back scatter diffraction (EBSD) and high resolution digital image correlation (HR-DIC) is used to measure the texture and sub-grain strain fields upon uniaxial tensile loading at various applied strains. Deformed specimens are also analyzed with optical profilometry measurements to obtain out-of- plane strain fields. These high resolution measurements are directly compared with large-scale CP-FEM predictions. This computational method directly links fundamental dislocation physics to plastic deformations in the grain-scale and to the engineering-scale applications. Furthermore, direct and quantitative comparisons between experimental measurements and simulation show that the proposed model accurately captures plasticity in deformation of polycrystalline tantalum.

36 MATERIALS SCIENCE↗

PROTEUS-SN User Manual

PROTEUS-SN is a three-dimensional, highly scalable, high-fidelity neutron transport code developed at Argonne National Laboratory. The code is applicable to all spectrum reactor transport calculations, particularly those in which a high degree of fidelity is needed either to represent spatial detail or to resolve solution gradients. PROTEUS-SN solves the second order formulation of the transport equation using the continuous Galerkin finite element method in space, the discrete ordinates approximation in angle, and the multigroup approximation in energy. PROTEUS-SN’s parallel methodology permits the efficient decomposition of the problem by both space and angle, permitting large problems to run efficiently on hundreds of thousands of cores. PROTEUS-SN can also be used in serial or on smaller compute clusters (10’s to 100’s of cores) for smaller homogenized problems, although it is generally more computationally expensive than traditional homogenized methodology codes. PROTEUS-SN has been used to model partially homogenized systems, where regions of interest are represented explicitly and other regions are homogenized to reduce the problem size and required computational resources. PROTEUS-SN solves forward and adjoint eigenvalue problems and permits both neutron upscattering and downscattering. An adiabatic kinetics option has recently been included for performing simple time-dependent calculations in addition to standard steady state calculations. PROTEUS-SN handles void and reflective boundary conditions. Multigroup cross sections can be generated externally using the MC2-3 fast reactor multigroup cross section generation code or internally using the cross section application programming interface (API) which can treat the subgroup or resonance table libraries. PROTEUS-SN is written in Fortran 90 and also includes C preprocessor definitions. The code links against the PETSc, METIS, HDF5, and MPICH libraries. It optionally links against the MOAB library and is a part of the SHARP multi-physics suite for coupled multi-physics analysis of nuclear reactors. This user manual describes how to set up a neutron transport simulation with the PROTEUS-SN code. A companion methodology manual describes the theory and algorithms within PROTEUS-SN.

97 MATHEMATICS AND COMPUTING↗

Modeling and Validation of the Thermal Response of TDI Encapsulating Foam as a function of Initial Density

TDI foams of nominal density from 10 to 45 pound per cubic foot were decomposed within a heated stainless steel container. The pressure in the container and temperatures measured by thermocouples were recorded with each test proceeding to an allowed maximum pressure before venting. Two replicate tests for each of four densities and two orientations in gravity produced very consistent pressure histories. Some thermal responses demonstrate random sudden temperature increases due to decomposition product movement. The pressurization of the container due to the generation of gaseous products is more rapid for denser foams. When heating in the inverted orientation, where gravity is in the opposite direction of the applied heat flux, the liquefied decomposition products move towards the heated plate and the pressure rises more rapidly than in the upright configuration. This effect is present at all the densities tested but becomes more pronounced as density of the foam is decreased. A thermochemical material model implemented in a transient conduction model solved with the finite element method was compared to the test data. The expected uncertainty of the model was estimated using the mean value method and importance factors for the uncertain parameters were estimated. The model that was assessed does not consider the effect of liquefaction or movement of gases. The result of the comparison is that the model uncertainty estimates do not account for the variation in orientation (no gravitational affects are in the model) and therefore the pressure predictions are not distinguishable due to orientation. Temperature predictions were generally in good agreement with the experimental data. Predictions for response locations on the outside of the can benefit from reliable estimates associated with conduction in the metal. For the lighter foams, temperatures measured on the embedded component fall well with the estimated uncertainty intervals indicating the energy transport rate through the decomposed region appears to be accurately estimated. The denser foam tests were terminated at maximum allowed pressure earlier resulting in only small responses at the component. For all densities the following statements are valid: The temperature response of the embedded component in the container depends on the effective conductivity of the foam which attempts to model energy transport through the decomposed foam and on the stainless steel specific heat. The pressure response depends on the activation energy of the reactions and the density of the foam and the foam specific heat and effective conductivity. The temperature responses of other container locations depend heavily on the boundary conditions and the stainless steel conductivity and specific heat.

36 MATERIALS SCIENCE↗

HPC Institutional Computing Project: W15_lesreactiveflow KIVA-hpFE Development: A Robust and Accurate Engine Modeling Software

KIVA-hpFE is a high performance computer software for solving the physics of multi-species and multiphase turbulent reactive flow in complex geometries having immersed moving parts. The code is written in Fortran 90/95 and can be used on any computer platform with any popular complier. The code is in two versions, a serial version and a parallel version utilizing MPICH2 type Message Passing Interface (MPI or Intel MPI) for solving distributed domains. The parallel version is at least 30x faster than the serial version and much faster than our previous generation of parallel engine modeling software, by many factors. The 5th generation algorithm construction is a Galerkin type Finite Element Method (FEM) solving conservative momentum, species, and energy transport equations along with two-equation turbulent model k-ω Reynolds Averaged Navier-Stokes (RANS) model and a Vreman type dynamic Large Eddy Simulation (LES) method. The LES method is capable modeling transitional flow from laminar to fully turbulent; therefore, this LES method does not require special hybrid or blending to walls. The FEM projection method also uses a Petrov-Galerkin (P-G) stabilization along with pressure stabilization. We employ hierarchical basis sets, constructed on the fly with enrichment in areas associated with relatively larger error as determined by error estimation methods. In addition, when not using the hp-adaptive module, the code employs Lagrangian basis or shape functions. The shape functions are constructed for hexahedral, prismatic and tetrahedral elements. The software is designed to solve many types of reactive flow problems, from burners to internal combustion engines and turbines. In addition, the formulation allows for direct integration of solid bodies (conjugate heat transfer), as in heat transfer through housings, parts, cylinders. It can also easily be extended to stress modeling of solids, used in fluid structure interactions problems, solidification, porous media modeling and magneto hydrodynamics.

97 MATHEMATICS AND COMPUTING↗

The Effect of Rolling As-Cast and Homogenized U-10Mo Samples on the Microstructure Development and Recovery Curves

Over the past several years Pacific Northwest National Laboratory (PNNL) has been actively involved in supporting the U.S. Department of Energy National Nuclear Security Administration Office of Material Management and Minimization (formerly Global Threat Reduction Initiative). The U.S. High- Power Research Reactor (USHPRR) project is developing alternatives to existing highly enriched uranium alloy fuel to reduce the proliferation threat. One option for a high-density metal fuel is uranium alloyed with 10 wt% molybdenum (U-10Mo). Forming the U-10Mo fuel plates/foils via rolling is an effective technique and is actively being pursued as part of the baseline manufacturing process. The processing of these fuel plates requires systematic investigation/understanding of the pre- and post-rolling microstructure, end-state mechanical properties, residual stresses, and defects, their effect on the mill during processing, and eventually, their in-reactor performance. In the work documented herein, studies were conducted to determine the effect of cold and hot rolling the as-cast and homogenized U-10Mo on its microstructure and hardness. The samples were homogenized at 900°C for 48 h, then later annealed for several durations and temperatures to investigate the effect on the material’s microstructure and hardness. The rolling of the as-cast plate, both hot and cold, was observed to form a molybdenum-rich and -lean banded structure. The cold rolling was ineffective, and in some cases exacerbated the as-cast defects. The grains elongated along the rolling direction and formed a pancake shape, while the carbides fractured perpendicularly to the rolling direction and left porosity between fractured particles of UC. The subsequent annealing of these samples at sub-eutectoid temperatures led to rapid precipitation of the ' lamellar phase, mainly in the molybdenum-lean regions. Annealing the samples above the eutectoid temperature did not refine the grain size or the banded microstructure. However, annealing the samples led to quick recovery in hardness as evidenced by a drop in Vickers hardness of 20%. Hot rolling was performed at 650 and 800°C. The hot-rolling mill loads (load separation force) were approximately 40 to 50% less than the cold-rolling for the same reduction and thickness. It was observed that hot rolling the samples with 50% or more reduction in thickness were responsible for dynamic recrystallization in the hot-rolled samples and led to grain refinement. Unlike the cold-rolled samples, the hot-rolled samples did not fracture the carbides and appeared to heal the casting defects. The recovery phenomenon was similar to the cold-rolled samples above the eutectoid temperatures, but owing to the refined grain size, the precipitation of the lamellar phase was far more rapid in these samples and the hardness increased more rapidly than in the cold rolled sample when heated below the eutectoid temperature. The data generated from these rolling efforts has been used to make the process modeling efforts more robust and applicable to all USHPRR partner rolling mills. The flow stress for cold rolling the samples was determined to be between 170-190 ksi, with frictional forces between 0.2 and 0.4 for the PNNL mill. The measured roll separation forces and those simulated using finite element methods for hot and cold rolling for the PNNL rolling mill were in good agreement.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

File-Based One-Way BISON Coupling Through VERA: User's Manual

Activities to incorporate fuel performance capabilities into the Virtual Environment for Reactor Applications (VERA) are receiving increasing attention [1–6]. The multiphysics emphasis is expanding as the neutronics (MPACT) and thermal-hydraulics (CTF) packages are becoming more mature. Capturing the finer details of fuel phenomena (swelling, densification, relocation, gap closure, etc.) is the natural next step in the VERA development process since these phenomena are currently not directly taken into account. While several codes could be used to accomplish this, the BISON fuel performance code [8,9] being developed by the Idaho National Laboratory (INL) is the focus of ongoing work in the Consortium for Advanced Simulation of Light Water Reactors (CASL). Built on INL’s MOOSE framework [10], BISON uses the finite element method for geometric representation and a Jacobian-free Newton-Krylov (JFNK) scheme to solve systems of partial differential equations for various fuel characteristic relationships. There are several modes of operation in BISON, but, this work uses a 2D azimuthally symmetric (R-Z) smeared-pellet model. This manual is intended to cover (1) the procedure pertaining to the standalone BISON one-way coupling from VERA and (2) the procedure to generate BISON fuel temperature tables that VERA can use.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Statistical Analysis of CO 2 Exposed Wells to Predict Long Term Leakage through the Development of an Integrated Neural-Genetic Algorithm

The objective of this project is to develop a computerized statistical model with the Integrated Neural-Genetic Algorithm (INGA) for predicting the probability of long-term leak of wells in CO 2 sequestration operations. This object has been accomplished by conducting research in three phases: 1) data mining of CO 2 -explosed wells, 2) INGA computer model development, and 3) evaluation of the predictive performance of the computer model with data from field tests. Data mining was conducted for 510 wells in two CO 2 sequestration projects in the Texas Gulf Coast region. They are the Hasting West field and Oyster Bayou field in the Southern Texas. Missing wellbore integrity data were estimated using an analytical and Finite Element Method (FEM) model. The INGA was first tested for performances of convergence and computing efficiency with the obtained data set of high dimension. It was concluded that the INGA can handle the gathered data set with good accuracy and reasonable computing time after a reduction of dimension with a grouping mechanism. A computerized statistical model with the INGA was then developed based on data pre-processing and grouping. Comprehensive training and testing of the model were carried out to ensure that the model is accurate and efficient enough for predicting the probability of long-term leak of wells in CO 2 sequestration operations. The Cranfield in the southern Mississippi was select as the test site. Observation wells CFU31F2 and CFU31F3 were used for pressure-testing, formation-logging, and cement-sampling. Tools run in the wells include Isolation Scanner, Slim Cement Mapping Tool (SCMT), Cased Hole Formation Dynamics Tester (CHDT), and Mechanical Sidewall Coring Tool (MSCT). Analyses of the obtained data indicate no leak of CO 2 cross the cap zone while it is evident that the well cement sheath was invaded by the CO 2 from the storage zone. This observation is consistent with the result predicted by the INGA model which indicates the well has a CO 2 leak-safe probability of 72%. This comparison implies that the developed INGA model is valid for future use in predicting well leak probability.

97 MATHEMATICS AND COMPUTING↗

Performance and Reliability of Bonded Interfaces for High-temperature Packaging: Annual Progress Report

As maximum device temperatures approach 200 °Celsius, continuous operation, sintered silver materials promise to maintain bonds at these high temperatures without excessive degradation rates. A detailed characterization of the thermal performance and reliability of sintered silver materials and processes has been initiated for the next year. Future steps in crack modeling include efforts to simulate crack propagation directly using the extended finite element method (X-FEM), a numerical technique that uses the partition of unity method for modeling discontinuities such as cracks in a system.

30 DIRECT ENERGY CONVERSION↗

Final Report for Project 13-4791: New Mechanistic Models of Creep-Fatigue Crack Growth Interactions for Advanced High Temperature Reactor Components

This project developed and validated a novel, multi-scale, mechanism-based model to quantitatively predict creep-fatigue crack growth and failure for Ni-based Alloy 617 at 800°C. Alloy 617 is a target material for intermediate heat exchangers in Generation IV very high temperature reactor designs, and it is envisioned that this model will aid in the design of safe, long lasting nuclear power plants. The technical effectiveness of the model was shown by demonstrating that experimentally observed crack growth rates can be predicted under both steady state and overload crack growth conditions. Feasibility was considered by incorporating our model into a commercially available finite element method code, ABAQUS, that is commonly used by design engineers. While the focus of the project was specifically on an alloy targeted for Generation IV nuclear reactors, the benefits to the public are expected to be wide reaching. Indeed, creep-fatigue failure is a design consideration for a wide range of high temperature mechanical systems that rely on Ni-based alloys, including industrial gas power turbines, advanced ultra-super critical steam turbines, and aerospace turbine engines. It is envisioned that this new model can be adapted to a wide range of engineering applications.

36 MATERIALS SCIENCE↗

Improved Fracture Models for Relocation Modeling

The BISON fuel performance code is being developed to provide a modern tool that has the flexibility to analyze a wide variety of fuel forms and to model conditions and phenomena that could not be represented in legacy tools. There are a number of motivations for this, including providing support for development of advanced fuel with improved accident tolerance for existing light water (LWR) reactors, improved understanding of mechanisms in fuel designs in current use in a wider variety of conditions, and facilitating the development of fuel for advanced reactor designs. To accomplish these goals, it is clear that BISON must rely on models of fuel behavior that are based on fundamental physical behavior, rather than on empirical correlations that represent that behavior in a simplified fashion. BISON still does employ many empirical models that were originally developed for other fuel performance codes, but efforts are underway to replace these with models that are more physically based. Radial relocation in LWR fuel is an example of a phenomenon that is currently represented by an empirical model, but which is ripe for replacement by physically based models. During normal operation, ceramic LWR fuel experiences significant fracturing that is driven by spatially nonuniform volumetric expansion. This occurs due to the significant thermal gradients within the fuel that occur in fresh and irradiated fuel, as well as nonuniform swelling due to fission products that occurs over longer-term irradiation. Fracture and fragmentation of fuel allows the outer radius of the fuel pellet to expand due to the loss of mechanical constraint and outward radial migration of fragments. This radial expansion has a significant effect on the fuel system response because it decreases the size of the gap between the fuel and cladding. This decreases the thermal resistance across that gap, which leads to decreased fuel centerline temperatures. This report documents recent work to improve the ability of BISON to model radial relocation using the extended finite element method (XFEM). These enhancements include the ability to include cohesive zone models, improved code architecture for propagating cracks based on fracture integrals, and improved handling of fuel and cladding interfaces with XFEM. These capabilities are demonstrated on a simulation of radial relocation including a surface interaction model that enforces residual opening.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

FY17 CAES LDRD Annual Report

Metallic alloys are widely used or planned for use as structural and cladding materials in current and future reactors. Under irradiation, grain boundary (GB) cohesion strength decreases due to interaction with defects and impurities, leading to intergranular fracture and embrittlement of alloys. The objective of this project is to develop a technique for quantifying GB cohesion and its impact on fracture behavior in irradiated alloys, by utilizing transmission electron microscopic (TEM) in situ cantilever testing in concert with multi-scale modeling. The TEM in situ cantilever testing is a novel approach for studying the real-time mechanical response of materials. It will be used in this work for studying intergranular fracture behavior in several irradiated iron-based ferritic alloys and providing key information to link atomistic level events with mesoscale/macroscopic mechanical properties. The Multi-Physics Object-Oriented Simulation Environment (MOOSE)-based cohesive zone model (CZM) and extended finite element method (XFEM) for intergranular fracture of irradiated ferritic alloys will be developed in this work by utilizing atomistic results as inputs and experimental results for validation.

36 MATERIALS SCIENCE↗