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At least 73 records · Page 4

Modeling The Nucleosynthetic Imprint of Stellar Merger Phenomena - Final Technical Report

This DOE CAREER project developed a comprehensive, multi-physics framework for modeling stellar mergers and their observable consequences. The work successfully integrated analytical models, three-dimensional hydrodynamic simulations, stellar evolution calculations, nucleosynthesis, and radiation transport into a unified pipeline. Key scientific advances include demonstrating stellar mergers as a unifying explanation for systems such as Betelgeuse and R Coronae Borealis stars, quantifying merger-driven chemical signatures, and establishing the connection between merger physics and circumstellar environments. A major outcome of the project is the development of SuperLite, an open-source Monte Carlo radiation transport code that enables the generation of synthetic spectra for astrophysical transients. This work bridges dynamical, thermal, and radiative timescales and provides a powerful, DOE-relevant computational framework for interpreting observations of supernovae and related transient phenomena, while also contributing to workforce development through the training of postdoctoral researchers and graduate students.

Chatzopoulos, Emmanouil [Louisiana State Universit

Statistical Uncertainty of Inhalation Dose Coefficients in Consequence Management: Propagated Dose Uncertainty in ICRP 66 Human Respiratory Tract Model

Reference inhalation dose models rely on deterministic biokinetics and reference computational phantoms, limiting their applicability to the variability present in population-specific exposures encountered in emergency response scenarios. Here, this study introduces REDCAL, a Python-based computational framework developed to propagate uncertainty in inhalation dose coefficients using the International Commission on Radiological Protection (ICRP) Publication 66 Human Respiratory Tract Model. REDCAL integrates ICRP deposition and clearance models, systemic biokinetics, and governing physics principles, and leverages Sandia National Laboratories’ Dakota toolkit for uncertainty quantification via Latin Hypercube Sampling. REDCAL was validated against DCAL, with biokinetic retention results differing by less than 1% and effective dose coefficients by less than 2% across all tested radionuclides. Stochastic sampling introduced variability in dose coefficients, with geometric standard deviations (GSD) in committed effective dose coefficients (CEDC) ranging from 1.0 to 1.5, based on lognormal distribution fits. Analysis demonstrated that variations in the activity median aerodynamic diameter (AMAD) notably influenced the computed CEDC values. Smaller particles (<1 µm) increased doses by 20–30% due to deeper lung deposition and prolonged retention for alpha emitting radionuclides, such as 241 Am and 239 Pu. Radionuclides with fast clearance, such as 133 I, demonstrated a dose reduction exceeding 50%, as AMAD increased beyond 5 µm due to upper airway deposition and rapid mucociliary clearance. The greatest GSD among the radionuclides reported in this study was for 241 Am. In most cases, the largest GSDs in the CEDC were associated with larger particle sizes, an expected outcome, as ICRP Publication 66 defines GSD in particle size as a function of AMAD, resulting in an extended tail of the lognormal distribution. The findings support improved inhalation dose assessments and enhance consequence management strategies for the U.S. Federal Radiological Monitoring and Assessment Center by quantifying uncertainty in dose coefficients and strengthening decision-making for emergency response scenarios.

Biokinetic Modeling

Toward engineering lattice structures with the material point method (MPM)

This study examines the potential of two variants of the material point method—the generalized interpolation material point (GIMP) and dual domain material point (DDMP) methods—in developing a robust computational framework for engineering lattice structures under different loading conditions. The study begins with assessing the ability of the two methods in predicting elastic buckling phenomena using column geometries with and without initial geometric imperfections. The results indicate that both methods effectively capture buckling phenomena when initial geometric imperfections are introduced. After this verification step, we create several models of tetrahedral lattice structures with varying strut diameter and orientation and subject them to quasi-static loading. We then validate the numerical results using laboratory test results. The results show that, while both methods accurately predict load–displacement curves in the pre-buckling regime, their predictive capabilities diminish in the post-buckling regime. Through visual comparison between the numerical and experimental deformed shapes, it appears that the discrepancies between model and experimental results are attributed to initial geometric imperfections in the lattices that occurred during 3D printing. We then establish a second set of lattice models where different types of initial geometric imperfections are considered. The results from these models show that imperfections have a negligible influence in the pre-buckling regime but affect the behavior considerably in the post-buckling regime. As a final step in this work, we subject the lattice models to impact loading and employ hypothetical soft and stiff materials. These results show that the lattice stiffness, which depends on material stiffness, strut diameter, and orientation, significantly influences the ability of a lattice structure to resist impact. In particular, we find that a stiffer lattice (i.e., one made with a stiff material and thicker struts) is capable of absorbing more energy than a softer one during impact. Although material nonlinearities, inelasticity, and detailed contact formulations are not considered in this study, the findings obtained herein lay the groundwork for engineering lattice structures under extreme loading conditions through a simulation-driven framework based on particle-based methods.

97 MATHEMATICS AND COMPUTING

A Multiphysics Multiscale Simulation Platform for Damage, Environmental Degradation, and Life Prediction of CMCs in Extreme Environments

This project successfully developed a multiphysics, multiscale computational framework to enhance the design and development of CMCs, with a focus on modeling highly nonlinear, time-dependent damage mechanisms and material degradation under extreme conditions, such as those experienced in turbine service environments. The project made significant advances in improving our understanding of progressive damage, oxidative degradation, and time-dependent inelastic deformation in CMCs, with particular attention to the role of uncertainties in predictions. Key outcomes include the integration of advanced material characterization, uncertainty quantification, and multiphysics constitutive models to predict the behavior of CMCs over their service life. A novel multiscale methodology was employed, which integrated microscale constituent behaviors with structural-scale responses, enabling the manufacturing defects in the microstructure that are prone to damage nucleation. Through the development of DL algorithms, the project advanced the prediction of damage initiation and crack propagation, taking into account the defect morphology and statistical variations across multiple scales. The framework was rigorously validated using thermomechanical experiments, which tested CMCs under various mechanical loadings at elevated temperatures, further enhancing the model's predictive capability. Overall, the research outcomes have provided a more accurate, reliable method for predicting CMC component life, significantly advancing material design, and improving component reliability in extreme environments. This work has strong implications for the optimization of turbine components and other high-performance applications where CMCs are used.

03 NATURAL GAS

First-Principles Statistical Mechanics Study of Magnetic Fluctuations and Order–Disorder in the Spinel LiNi 0.5 Mn 1.5 O 4 Cathode

While significant magnetic interactions exist in lithium transition metal oxides, commonly used as Li-ion cathodes, the interplay between magnetic couplings, disorder, and redox processes remains poorly understood. In this work, we focus on the high-voltage spinel LiNi 0.5 Mn 1.5 O 4 (LNMO) cathode as a model system on which to apply a computational framework that uses first principles-based statistical mechanics methods to predict the finite temperature magnetic properties of materials and provide insights into the complex interplay between magnetic and chemical degrees of freedom. Density functional theory calculations on multiple distinct Ni–Mn orderings within the LNMO system, including the ordered ground-state structure (space group P4332), reveal a preference for a ferrimagnetic arrangement of the Ni and Mn sublattices due to strong antiferromagnetic superexchange interactions between neighboring Mn 4+ and Ni 2+ ions and ferromagnetic Mn–Mn and Ni–Ni couplings, as revealed by magnetic cluster expansions. These results are consistent with qualitative predictions using the Goodenough-Kanamori-Anderson rules. Simulations of the finite temperature magnetic properties of LNMO are conducted using Metropolis Monte Carlo. We find that a “semiclassical” Monte Carlo sampling method based on the Heisenberg Hamiltonian accurately predicts experimental magnetic transition temperatures observed in magnetometry measurements. This study highlights the importance of a robust computational toolkit that accurately captures the complex chemomagnetic interactions and predicts finite temperature magnetic behavior to help analyze experimental magnetic and magnetic resonance spectroscopy data acquired ex situ and operando.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Software For Advanced Large-scale Analysis Of Magnetic Confinement For Numerical Design, Engineering & Research (salamander)

As magnetic confinement fusion energy gains traction internationally to enable abundant energy production, designing components for fusion systems is a pressing challenge. During the planned lifetime of a fusion device, components evolve in extreme environments and must withstand large, repeated thermal loads and bombardment by 14 MeV neutrons, plasma ions, and neutral particles (deuterium, tritium, and helium), corrosive conditions, etc. All these physical processes take place simultaneously, interact in intricate ways, and impose important constraints that can affect performance. Experimental data is rare and costly to obtain, making design particularly challenging. Predictive computational frameworks must be an integral part of an accelerated and cost-effective design process by modeling fusion system performance in simulated environments. To better understand component degradation and operational impacts on their performance, the Software for Advanced Large-scale Analysis of MAgnetic confinement for Numerical Design, Engineering & Research (SALAMANDER) is designed as an open-source, fully integrated, multiphysics, multiscale, NQA-1 compliant framework facilitating 3D, high-fidelity fusion system modeling. To that end, SALAMANDER is a MOOSE-based framework, and therefore leverages MOOSE upstream libraries such as PETSc and libMesh to deliver sophisticated finite element, finite volume, and nonlinear solver technology for fusion energy simulations. SALAMANDER couples MOOSE physics module capabilities—such as thermal hydraulics, heat conduction, Navier-Stokes, and thermomechanics—with tritium transport via TMAP8, neutronics via Cardinal, and nascent particle-in-cell capabilities. Direct simulation Monte Carlo methods will be used to address neutral transport near the walls. By coupling all these physics in an integrated application, SALAMANDER will enable high-fidelity modeling of irradiation levels and plasma exposure conditions of plasma facing components and their impact on heat and tritium distributions, as well as the resulting mechanical constraints experienced by the plasma facing components and performance of blanket systems. Furthermore, SALAMANDER will be particularly suited for engineering studies thanks to the stochastic tool module readily available in MOOSE, allowing for extended uncertainty quantification and risk analysis studies. It is also able to use computer-aided design (CAD) meshes to model complex geometries, which is indispensable for fusion systems. SALAMANDER therefore supports design, safety, engineering, and research projects for magnetic confinement fusion systems

Simon, Pierre-Clement [Idaho National Laboratory (

Tailoring composition and deformation modes at the microstructural level for next generation low-cost high-strength austenitic stainless steels

The objective of this project is to enable deliberate development of cost-effective, hydrogen resistant alloys by establishing detailed relationships specific to the effects of alloy composition, short-range order (SRO), and microsegregation in the presence of hydrogen on the transition between homogeneous deformation and localized plasticity in shear bands. In collaboration with the International Institute for Carbon-Neutral Energy Research, I2CNER, at Kyushu University in Japan, we conceptualized, designed, and manufactured four austenitic alloys that maintain corrosion resistance and ensure lower cost relative to baseline commercial alloys. The mechanical properties and deformation modes of the novel alloys (KU alloys) were assessed in the presence of hydrogen (H). Correlations between composition and performance revealed that two of the KU alloys are suitable replacements for 316 steel, while another is a viable replacement for 304 steel at room temperature. We found that, in the presence of other austenite stabilizing elements namely Mn and N, replacing Ni with Cu does not lead to martensite formation as has been previously reported.1–3 Furthermore, we found that the addition of Cu leads to an earlier onset of multiple slip resulting in an relative earlier onset of a higher work hardening rate (WHR). Greater understanding of the relationships between alloy composition and SRO required the development of a novel advanced electron diffraction methodology to characterize SRO in complex FCC alloys. This innovative approach, which combines fluctuation and correlation analyses of diffuse-scattering signals, successfully differentiated between SRO and long-range ordering (LRO). Further investigations into annealed austenitic stainless steels could provide insights into manipulating SRO and its effects on material properties. Atomistic simulations provided understanding of SRO behavior that was difficult to capture experimentally. This project created the first spin cluster expansion model that is able to capture and describe SRO effects in Fe-Ni-Cr FCC alloys, accounting for the non-negligible effects of magnetism. An automated computational workflow was established to provide reliable predictions of SRO in Fe-Ni-Cr austenitic alloys, both with and without the presence of H atoms. Analysis of the propensity for SRO in Fe-Ni-Cr alloys revealed that H tends to cluster with specific, well-defined SRO domains. The computational framework is general purpose and can be extended to realistic stainless steels across diverse composition ranges. With confidence that SRO is possible in austenitic stainless steels, we developed a discrete dislocation finite element code to understand the interaction of dislocations with SRO in the presence of H. By incorporating H effects on the dislocation emission and SRO stress field we show that the critical stress for the dislocation pileup to breakthrough the SRO domain decreases in the presence of H, which directly contributes localized deformation at the macroscale. Through the simulation of a uniaxial tension test, we demonstrated that H-induced weakening of SRO stress field and H-enhanced dislocation emission can lead to the onset of shear localization at lower macroscopic strains. As a whole, this project identified three novel alloys that show improvements in performance and cost efficiency for H-facing applications by studying correlations between alloy chemistry and deformation behavior. We also made significant advancements to experimental and computational methodologies necessary to study the chemistry and distribution of SRO across a range of alloys, which in turn allowed us to demonstrate how deformation mechanisms change due to the contributions of SRO in austenitic alloys in the presence of H. The combined advancements in fundamental understanding with novel alloy development in this project has increased the viability of next generation H-technologies for the broader public through accessible low-cost alloys and accelerated development towards future H-infrastructure.

08 HYDROGEN

Scalable Control Co-design for Resilient-by-Design Cyber Physical Systems

Critical infrastructure networks, such as power and transportation networks, are often modelled as cyber-physical systems. With ever increasing complexity of these systems, there is a need for newer and more relevant metrics and design tools that will co-optimize the physical system components and control policies to guarantee resilience against cyber and natural threats. To this end, a simulation-based control co-design computational framework that will concurrently determine the system and control parameters of a cyber-physical system to meet pre-specified resilience, operational and economic objectives has been developed. The capabilities of the developed co-design engine are demonstrated by designing the physical components and control parameters of a microgrid system that will meet its resiliency objectives when subjected to various cyber and physical threats.

42 ENGINEERING

Vibrational Signatures of Electronic Properties in Renewable-Energy Catalysis

The objective of this research program is to discover and develop new approaches for ab initio computational simulations of molecular motion. Specifically, this program aims to decipher the connection between the underlying electronic structure and the accordant molecular vibrations in reactive ions and radicals for renewable-energy purposes. Recent experimental progress in ion sources and optical spectroscopies has unearthed considerable new inner-sphere detail for these complexes, but the connection between these spectral signatures and mechanistic information often remains elusive, to the continued frustration of experimentalists. For this purpose, new anharmonic vibrational frequency methods, along with a publicly deployed software package, will be developed. Working closely with committed experimental collaborators, this conceptual and computational framework will be used to explain the results of new spectroscopy experiments, focusing specifically on the inner-shell mechanisms of renewable-energy catalysis. The oxidation half of catalytic water-splitting chemistry will be a central focus, along with fundamental studies of the manner in which strong ions and radicals activate solvent as a chemical species. The resulting products of the research program will include openly available software and algorithms for the ab initio simulation of challenging vibrational spectra, as well as critical mechanistic insight into energy-focused catalytic processes that are opaque to other existing analytical techniques.

42 ENGINEERING

A cross-platform execution engine for the quantum intermediate representation

Hybrid languages like the quantum intermediate representation (QIR) are essential for programming systems that mix quantum and conventional computing models, while execution of these programs is often deferred to a system-specific implementation. Here, we develop the QIR Execution Engine (QIR-EE) for parsing, interpreting, and executing QIR across multiple hardware platforms. QIR-EE uses LLVM to execute hybrid instructions specifying quantum programs and, by design, presents extension points that support customized runtime and hardware environments. We demonstrate an implementation that uses the XACC quantum hardware-accelerator library to dispatch prototypical quantum programs on different commercial quantum platforms and numerical simulators, and we validate execution of QIR-EE on IonQ, Quantinuum, and IBM hardware. Our results highlight the efficiency of hybrid executable architectures for handling mixed instructions, managing mixed data, and integrating with quantum computing frameworks to realize cross-platform execution.

LLVM

HPC-Driven Modeling with ML-Based Surrogates for Magnon-Photon Dynamics in Hybrid Quantum System

Here, we introduce a hybrid computational framework that merges HPC-based numerical solvers with physics-informed ML surrogates for efficient modeling of magnon-photon interactions. By running short-duration, high-fidelity Maxwell-LLG simulations and feeding their results into an ML model, we substantially cut simulation time while achieving accurate predictions across larger spatiotemporal domains.

Accuracy

Semi-Analytical Hierarchical Bayesian Inference of Nonlinear Model Structure in Stochastic Dynamics: Applied to Compartmental Models of Infectious Diseases

A Bayesian computational framework for parsimonious inference in stochastic nonlinear dynamical systems is presented. This framework enables the concurrent estimation of system states, time-varying parameters, time-invariant parameters, and the optimal sparsity structure of the model parameters. Because differential equation-based models are often simplified mechanistic or phenomenological representations, robust inference from noisy measurement data requires explicit treatment of model error and uncertainty. Model error and time-varying parameters can be represented as random processes, enabling inference while making minimal assumptions about the underlying sources of discrepancy and variability. Adopting stochastic differential equation representations affords the model significant flexibility, but can also render it susceptible to overfitting during statistical inversion, where the inferred model may track noise rather than the underlying signal. To alleviate the effects of overfitting and to enable the discovery of the optimal sparse representation of the time-invariant parameters, a Bayesian sparse learning algorithm is embedded within the framework. This sparse learning framework adopts an approximate hierarchical Bayesian setting defined by a series of semi-analytical expressions. The model structure inference framework is validated using a stochastic compartmental model for tracking and forecasting active cases of an infectious disease. Compartmental models describe population-level infectious disease dynamics through interactions among population fractions grouped by disease state. Mathematically, such models consist of a system of coupled ordinary differential equations. This example adopts an expressive compartmental model that includes multiple possible interactions between disease states, motivated by early uncertainty surrounding COVID-19 reinfection dynamics and their implications for long-term epidemic forecasting. The sparse learning exercise permits the inference of a priori unknown epidemiological dynamics from simulated public health data, discovering the nested compartmental model that optimizes the trade-off between average data-fit and model complexity. It is shown that inducing sparsity among the model parameters eliminates redundant interactions between compartments, equivalently revealing the optimal coupling structure between differential equations.

97 MATHEMATICS AND COMPUTING

SAM Theory Manual

The System Analysis Module (SAM) is an advanced and modern system analysis tool under development at Argonne National Laboratory for advanced non-LWR reactor safety analysis. It aims to provide fast-running, modest-fidelity, whole-plant transient analyses capabilities, which are essential for fast turnaround design scoping and engineering analyses of advanced reactor concepts. While SAM is being developed as a system-level modeling and simulation tool, advanced modeling techniques being implemented include a reduced-order three-dimensional module, pseudo 3-D conjugate heat transfer modeling in reactor core, flexible and multi-scale modeling of heat transfer between fluid and structures, in addition to the advances in software environments and design, and numerical methods. SAM aims to be a generic system-level safety analysis tool for advanced non-LWRs, including Liquid-Metal-cooled fast Reactors (LMR), Molten Salt Reactors (MSR), Fluoride-salt-cooled High-temperature Reactors (FHR), and High-Temperature Gas-cooled Reactors (HTGR). SAM takes advantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented computational framework (MOOSE), and its underlying meshing and finite-element library and linear and non-linear solvers, to leverage the modern advanced software environments and numerical methods. This document provides the theoretical and technical basis of the code to help users understand the underlying physical models (such as governing equations, closure models, and component models), system modeling approaches, numerical discretization and solution methods, and the overall capabilities in SAM. As new code capabilities and features are added, the SAM Theory Manual will be updated periodically to keep it consistent with the state of the development.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Quantum Simulations of Radiation Damage in a Molecular Polyethylene Analog

Abstract An atomic‐level understanding of radiation‐induced damage in simple polymers like polyethylene is essential for determining how these chemical changes can alter the physical and mechanical properties of important technological materials such as plastics. Ensembles of quantum simulations of radiation damage in a polyethylene analog are performed using the Density Functional Tight Binding method to help bind its radiolysis and subsequent degradation as a function of radiation dose. Chemical degradation products are categorized with a graph theory approach, and occurrence rates of unsaturated carbon bond formation, crosslinking, cycle formation, chain scission reactions, and out‐gassing products are computed. Statistical correlations between product pairs show significant correlations between chain scission reactions, unsaturated carbon bond formation, and out‐gassing products, though these correlations decrease with increasing atom recoil energy. The results present relatively simple chemical descriptors as possible indications of network rearrangements in the middle range of excitation energies. Ultimately, the work provides a computational framework for determining the coupling between nonequilibrium chemistry in polymers and potential changes to macro‐scale properties that can aid in the interpretation of future radiation damage experiments on plastic materials.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA

Lessons Learned and Scalability Achieved When Porting Uintah to DOE Exascale Systems

A key challenge faced when preparing codes for Department of Energy (DOE) exascale systems was designing scalable applications for systems featuring hardware and software not yet available at leadership-class scale. With such systems now available, it is important to evaluate scalability of the resulting software solutions on these target systems. One such code designed with the exascale DOE Aurora and DOE Frontier systems in mind is the Uintah Computational Framework, an open-source asynchronous many-task (AMT) runtime system. To prepare for exascale, Uintah adopted a portable MPI+X hybrid parallelism approach using the Kokkos performance portability library (i.e., MPI+Kokkos). This paper complements recent work with additional details and an evaluation of the resulting approach on Aurora and Frontier. Results are shown for a challenging benchmark demonstrating interoperability of 3 portable codes essential to Uintah-related combustion research. These results demonstrate single-source portability across Aurora and Frontier with scaling characteristics shown to 3,072 Aurora nodes and 9,216 Frontier nodes. In addition to showing results run to new scales on new systems, this paper also discusses lessons learned through efforts preparing Uintah for exascale systems.

Holmen, John [ORNL] (ORCID:0000000259342641)

Real-time chiral dynamics at finite temperature from quantum simulation

In this study, we explore the real-time dynamics of the chiral magnetic effect (CME) at a finite temperature in the (1+1)-dimensional QED, the massive Schwinger model. By introducing a chiral chemical potential μ 5 through a quench process, we drive the system out of equilibrium and analyze the induced vector currents and their evolution over time. The Hamiltonian is modified to include the time-dependent chiral chemical potential, thus allowing the investigation of the CME within a quantum computing framework. We employ the quantum imaginary time evolution (QITE) algorithm to study the thermal states, and utilize the Suzuki-Trotter decomposition for the real-time evolution. This study provides insights into the quantum simulation capabilities for modeling the CME and offers a pathway for studying chiral dynamics in low-dimensional quantum field theories.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

From PINNs to PIKANs: recent advances in physics-informed machine learning

Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements. Over the past few years, significant advancements have been made in the training and optimization of PINNs, covering aspects such as network architectures, adaptive refinement, domain decomposition, and the use of adaptive weights and activation functions. A notable recent development is the Physics-Informed Kolmogorov-Arnold Networks (PIKANS), which leverage a representation model originally proposed by Kolmogorov in 1957, offering a promising alternative to traditional PINNs. In this review, we provide a comprehensive overview of the latest advancements in PINNs, focusing on improvements in network design, feature expansion, optimization techniques, uncertainty quantification, and theoretical insights. We also survey key applications across a range of fields, including biomedicine, fluid and solid mechanics, geophysics, dynamical systems, heat transfer, chemical engineering, and beyond. Lastly, we review computational frameworks and software tools developed by both academia and industry to support PINN research and applications.

Kolmogorov-Arnold networks

Assessment of critical flaw sizes and crack driving forces during additive manufacturing of metallic materials

Additive manufacturing (AM) of complex engineering components is often plagued by a high susceptibility to cracking, particularly in high-strength metallic materials. While alloy design efforts have made progress in mitigating solidification defects, there remains a need for mechanistic guidelines to predict susceptibility to solid-state cracking. To address this gap, driving forces for the growth of melt pool cracks are calculated across a wide range of alloys using an efficient computational framework. Calculations are coupled with rapid single track laser experiments to elucidate trends in cracking from laser melting. The analyses conducted here highlight the important role of material properties in susceptibility to cracking, notably fracture toughness and elastic modulus. An important finding is that residual stresses that are limited in magnitude to the yield stress of the material are likely insufficient to drive cracking during cooling. Furthermore, the implications of these results are discussed in the context of alloy design for AM and residual stress accumulation during AM.

36 MATERIALS SCIENCE