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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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402 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Chemo‐Mechanical Coupling in Hydrogels: Dynamics in the Diffusion‐Limited Regime

Hydrogels are characterized by substantial volume changes in response to external stimuli, making them promising candidates for developing smart materials with enhanced adaptability and responsiveness. By integrating chemical reactions, hydrogels acquire dynamic and tunable responsiveness to external stimuli through chemo‐mechanical coupling, expanding their potential in emerging applications. However, capturing their transient behavior remains challenging due to the complex interplay of chemical reactions, solvent transport, and polymer network deformation. Classical theories capture equilibrium swelling but fail to describe time‐dependent phenomena. To address this, a time‐dependent continuum model is developed that explicitly couples these processes. Volume phase transition in hydrogels with homogeneous chemical reactions is investigated, then the effects of reaction kinetics on these transitions are analyzed. The coupling of these mechanisms is further explored through a study of transient mechanical instabilities. To illustrate the impact of distinct reaction and diffusion timescales, a photo‐active gripper is studied for robotic applications. Finally, a photo‐active microswimmer that exhibits non‐reciprocal motion is proposed to highlight the solvent diffusion for locomotion at the micro‐ and nano‐ scales. The work establishes that transient dynamics of chemo‐mechanical hydrogels generate functions not accessible by steady state models and provides a predictive platform for designing adaptive materials in emerging applications.

chemo-mechanical coupling↗
DOE OSTI2026

Challenges and Opportunities for HVAC + Phase Change Material Thermal Energy Storage in Buildings

Phase-change material (PCM) thermal-energy storage (TES) integrated with HVAC and domestic hot water (DHW) can shift a large share of building thermal loads. By flattening and shifting loads, PCM TES reduces peak electricity use, eases stress on local and grid infrastructure, and lowers costs. It can also defer costly upgrades to service panels, distribution, and transmission. Higher energy density relative to chilled or hot water storage makes PCM TES practical for small, space limited, and retrofit projects, while packaged HVAC-integrated systems expand cost-effective load shifting to commercial buildings that previously lacked options. Despite this promise, deployment faces barriers. This paper presents challenges, opportunities, and lessons learned from lab and field integrations of PCM TES with packaged HVAC systems. Key challenges include misalignment between default heat pump controls tuned for direct-to-load operation and TES charge/discharge objectives, PCM properties that diverge from manufacturer claims and evolve with cycling, and high integration and deployment costs with off-the-shelf products. These studies underscore the need for factory built, integrated systems that arrive as prepackaged modules with proven controls, reducing design and installation effort and delivering predictable performance across projects. The paper outlines steps to enable viable and scalable PCM TES HVAC and DHW systems, including 1) validated methods that can be used to characterize PCM properties and TES system performance, 2) supervisory controls that optimize charge/discharge scheduling, and 3) factory integrated packaging that eliminates bespoke field engineering.

Dutton, Spencer↗
DOE OSTI2026

Robust Heat-Flux Sensors for Coal-Fired Boiler Extreme Environments

In this project, robust heat-flux measurement systems were developed. The heat-flux sensors utilize thermoelectric effects to directly transduce the heat-flux inputs to analog electrical voltage signals. They were constructed from dedicated materials that can withstand temperatures of at least 1000°C and maintain adequate performance at these conditions for prolonged periods of time. The proposed approaches took into account numerous considerations, including system cost, sensor head resilience, sensor footprint, data accuracy, response time, and maintenance requirements. Through modern thermoelectric materials design, methodical materials selection and rigorous testing in materials characterization labs and medium-scale fire research facilities, we have demonstrated functioning laboratory prototypes, upon which one could base industrial heat-flux sensing platforms capable of operating in the challenging high-temperature, corrosive environments of the boilers of coal-fired power plants. A distributed sensor array for heat-flux measurements throughout the furnace water-wall, the superheater area and the economizer coils can provide critical data for the power plant control systems to increase efficiency, improve safety and reduce down times. For example, the combined heat-flux sensor/control systems can contribute to the optimization of burner and boiler operations under flexible loads, the optimization of heat-exchange conditions and overall reduction of heat rate and emissions, the prediction of imminent overheating conditions, and the optimization of the soot-blowing protocols.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2026

Dirac Fermions and Flat Bands in Phosphorus Carbide Nanotubes: Structural and Quantum Phase Transitions in a Quasi-One-Dimensional Material

Chemically realistic quasi-one-dimensional (1D) materials in which Dirac Fermions and highly degenerate flat bands coexist intrinsically at the Fermi level are exceedingly rare, while representing a highly desirable platform for correlated and topological quantum phenomena. Here, in this work, using specialized symmetry-adapted first-principles calculations we predict a new class of nanomaterials─phosphorus carbide nanotubes (P 2 C 3 NTs)─obtained by rolling monolayer P 2 C 3 , a two-dimensional material shown in a previous letter to host “double Kagome bands”. Both armchair and zigzag P 2 C 3 NTs are stable at room temperature and feature the rare coexistence of Dirac crossings and multiple flat bands at the Fermi level inherited from the underlying honeycomb–Kagome lattice, with the flat bands resilient to elastic deformations. Under large strain, the structure transforms from honeycomb–Kagome to “brick-wall”, accompanied by multiple coupled structural and quantum phase transitions. We also uncover localized edge states, spin splitting from vacancies and dopants, and strain-tunable magnetism. Together, these results establish P 2 C 3 NTs as a chemically specific and mechanically tunable 1D material platform with potential applications in quantum hardware and spintronics.

carbon nanotubes↗
DOE OSTI2025

Robust and tunable oxide nanoscrolls for solar-driven H 2 generation and storage

Hydrogen gas is a promising alternative to fossil fuels due to its high energy output and environmentally safe byproducts. Various morphologies of photocatalytic materials have been explored for high-efficiency H 2 production, for instance, quasi-1D nanoscroll structures that provide a larger surface-to-volume ratio. Recently, we predicted layer-by-layer formation of stable oxide nanoscrolls directly from dichalcogenide precursors, eliminating the need for costly formation of two-dimensional oxides for a roll-up synthesis of nanoscrolls. Here, in this study, we evaluate the suitability of those oxide nanoscroll materials—MoO 3 , WO 3 , PdO 2 , HfO 2 , and GeO 2 —for solar-driven photocatalytic H 2 production and storage. Using excited state theory coupled with Bethe–Salpeter equation simulations, we discern their electronic and optical properties as a function of interlayer scroll spacing and find them to be highly conducive for solar-driven photocatalysis. Additionally, using ab initio molecular dynamics simulations, we show that they are also suitable for H 2 storage as the nanoscrolls exhibit an effective trapping of hydrogen, even in the presence of defects and vacancies in the oxides. This work thus demonstrates the discovery of robust and tunable oxide nanoscrolls as materials for advancing solar-driven hydrogen technologies.

Chemical compounds↗
NASA NTRS2019

Rewet Temperature Correlations for Liquid-Nitrogen Boiling Pipe Flows Across Varying Flow Conditions and Orientations

In many convective liquid-vapor phase change heat transfer engineering applications, cryogenic fluids are widely used in industrial processes, spacecraft and cryosurgery systems, and so on. For example, cryogens are usually used as liquid fuels such as liquid hydrogen and oxygen in the rocket industry, liquid nitrogen (LN2) and helium are frequently used to cool superconducting magnetic device for medical applications. In these systems, proper transport, handling, and storage of cryogenic fluids are of extreme importance. Among all the cryogenic transport processes performed in room temperatures, quenching, also termed chilldown, is a unavoidable initial, transient phase-change heat transfer process that brings the system down to the cryogenic condition. The Leidenfrost temperature or rewet temperature that signals the end of film boiling is practically considered the completion point of a quenching process. Therefore, rewet temperature has been considered the most important parameter for the engineering design of cryogenic thermal management systems. As most of the previous correlations for predicting the Leidenfrost temperature and the rewet temperature have been basically developed for water, they are shown to disagree with recent liquid nitrogen pipe chilldown experiments in upward and downward flow directions over a wide range of flow rates, pressures, and degrees of inlet subcooling. In addition to a complete review of the literature, two new correlations are presented in this work, one based on bubble growth and another based on the theoretical maximum limit of superheat. Each correlation performs well over the entire data set.

liquid nitrogen↗
DOE OSTI2026

Fracture Analysis of Cohesive Zone Models for Modeling Residual Stress Induced Delamination in Composite Structures

A fracture study of coupon-scale composite cylinders with embedded defects was conducted with an objective to assess and validate a modeling approach using two available cohesive material models. The study included experimental and simulation evaluations of initiation of crack growth and progression. Interrupted thermal experiments used acoustic emissions monitoring to identify the onset of crack progression during each cooling interval and ultrasonic scanning provided images of defect growth. Verification, validation, and uncertainty quantification (VVUQ) processes were performed in the assessment of the simulation predicted temperature at which crack propagation begins (quantity of interest). The Sobol sensitivity analysis identified the hoop direction elastic modulus in the carbon fiber reinforced polymer (CFRP) plies as the most influential parameter for simulations using both cohesive models, accounting for at least 70% of the variation in the temperature at crack propagation. The UQ temperature range for the Tvergaard-Hutchinson model was higher (more conservative) than the experimental acoustic measurement indicators of crack progression, while the temperature range for the Thouless-Parmigiani model enveloped the experimental data points for the primary defect size of 0.75 x 1 in. The simulations could not capture the stable crack growth indicated in the experiments. This is likely due to the models’ inability to represent anisotropic fracture toughness attributed to the structure of the orthotropic fiber weave in a woven composite laminate.

42 ENGINEERING↗
DOE OSTI2026

Preliminary Assessment for the Electric Load Shifting Potential of Integrating Thermal Energy Storage with Heat Pumps in Residential Buildings in Texas of United States

The widespread adoption of electric-driven heat pumps for heating and cooling is expected to significantly increase electric demand. Cooling electric demand will result in an increase in peak hours electric loads, placing additional strain on the grid during peak hours. This challenge, combined with the current rapidly increasing demand from data centers, exacerbates the electric demand duck curve problem. Integrating thermal energy storage (TES) with heat pump can shift electric use for heating and cooling from peak to off-peak hours of the electric grid, which can help flatten the daily electric demand profile of a building. This paper presents a novel design that integrates heat pump with TES (HP-TES), which uses phase change materials (PCM). Heat pump charges TES by melting or freezing PCM during off-peak hours when there is no thermal demand from the building. TES is then discharged (i.e., by freezing or melting PCM) during peak hours to provide a more favorable heat source or heat sink for the heat pump to meet the thermal demand of the building with lower electricity use than conventional air-source heat pumps. Computer simulations were developed to predict the performance of HP-TES applied to a typical single-family house in the US. The building-level simulation results were scaled up to preliminarily assess the aggregated impacts of deploying HP-TES across all single-family houses in Texas of the United States, including reduction of peak demand of the electric grid.

Anees, Fady [ORNL]↗
DOE OSTI2026

Machine learning approach for vibronically renormalized electronic band structures

Here, we present a machine learning (ML) method for efficient computation of vibrational thermal expectation values of physical properties from first principles. Our approach is based on the nonperturbative frozen phonon formulation in which stochastic Monte Carlo algorithm is employed to sample configurations of nuclei in a supercell at finite temperatures based on a first-principles phonon model. A deep-learning neural network is trained to accurately predict physical properties associated with sampled phonon configurations, thus bypassing the time-consuming ab initio calculations. To incorporate the point-group symmetry of the electronic system into the ML model, group-theoretical methods are used to develop a symmetry-invariant descriptor for phonon configurations in the supercell. We apply our ML approach to compute the temperature dependent electronic energy gap of silicon based on density functional theory (DFT). We show that, with less than a hundred DFT calculations for training the neural network model, an order of magnitude larger number of sampling can be achieved for the computation of the vibrational thermal expectation values. Our work highlights the promising potential of ML techniques for finite temperature first-principles electronic structure methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Computational discovery of a tetragonal MBene phase: diamond-shaped boron lattices, viable MAB precursors, and selective CO 2 reduction

MBenes are a class of two-dimensional transition-metal borides derived from layered MAB phases. Here, we use first-principles calculations to predict a new tetragonal MB (1 : 1) MBene phase featuring a diamond-shaped B–B lattice and systematically assess its phase stability, synthetic accessibility, and catalytic performance towards the CO 2 reduction reaction (CO 2 RR). Four tetragonal configurations are benchmarked against known hexagonal and orthorhombic phases, and a multi-tier screening identifies six robust members (CrB, FeB, MoB, WB, IrB, and PtB). Exploration of the I4/mmm MAB space reveals 11 viable precursors, including the experimentally synthesized Ir 2 ZnB 2 , which validates our screening approach. CO 2 RR free-energy diagrams show that CrB favors CH 3 OH while FeB, MoB, WB, IrB, and PtB preferentially yield HCOOH. The corresponding limiting potentials are competitive with, and in some cases superior to, those reported for state-of-the-art orthorhombic and hexagonal MBenes. These findings expand the MBene landscape by establishing a tetragonal phase with structural, synthetic, and catalytic promise.

Lu, Linguo [University of Puerto Rico, San Juan, P↗
NASA NTRSDate not supplied

The NASA Turbulent Heat Flux (THX) Experiments: Summary and Lessons Learned

The Turbulent Heat Flux (THX) experiments were conducted at NASA Glenn Research Center (GRC) in order to collect measurements of velocities and temperatures for computational fluid dynamics (CFD) validation of heated flows, with a focus on propulsion system components. The experiments spanned 5 phases; four of which were conducted in the GRC AeroAcoustic Propulsion Laboratory (AAPL) using the Small Hot Jet Flow Rig (SHJAR). In addition to making velocity measurements with Particle Image Velocimetry (PIV), the THX experiments introduced a new Raman-scattering based capability to measure temperatures. Computational studies were also conducted for each of the experimental configurations, in order to provide a baseline of expected CFD results and conduct an assessment of the capability of various CFD approaches for calculating flows where the turbulent transport of heat was important. Two of the collected sets of data were used for American Institute of Aeronautics and Astronautics (AIAA) Propulsion Aerodynamic Workshops (PAWs). The data set from the 5th phase, collected for heated supersonic jets, was also used to construct new validation cases for the NASA Turbulence Model Resource (TMR). This paper provides an overview of the experiments and associated computations for each of the 5 test phases. Key experimental findings are presented. Lessons learned are provided concerning the effect of computational modeling choice on accuracy of predicting turbulent flows where thermal transport is important. Emphasis is placed on comparing Reynolds-averaged Navier-Stokes approaches with large-eddy simulation approaches. The benefits of utilizing a conjugate heat transfer method in conjunction with CFD solver for film cooling is demonstrated.

RANS↗
DOE OSTI2024

Osmotic and phoretic competition explains chemotaxic assembly and sorting

Microscale objects responding to chemical gradients by migrating toward or away from a preferred species is a simple yet constitutive mechanism by which transport occurs in biological organisms. Synthetic chemotaxis provides key physical descriptions of simplified systems that can be used in biological models, or in the creation of advanced responsive material systems. In this article, we provide a quantitative framework for understanding synthetic chemotaxis of microparticles which involves a competition between phoresis and osmosis. We present separate quantitative measurements of phoresis and osmosis acting on individual taxing particles, finding that phoresis follows the long-predicted v ∼ 1 / r 2 scaling while the osmotic contribution depends on the geometry and details of the system, and must be solved on a case-by-case basis. Through this, we are able to develop a more accurate picture of particle transport at the single particle level. Equipped with this approach, we go on to describe how high concentrations of particles in a symmetric chemical gradient grow close-packed hives that reach a steady-state size tunable through light intensity or particle size. Last, we demonstrate that mixed particles experiencing the same chemical gradient will selectively migrate toward or away depending on the nature of the particle surface, thereby locally sorting out a particular species. We anticipate these results will be important in describing both biological and synthetic chemotaxis in phoretic systems and should bring a wealth of studies that take advantage of competing osmotic flows to illicit unexpected dynamic active behavior.

Science & Technology - Other Topics↗
DOE OSTI2026

Sensitivity Analysis of Numerical Modeling Input Parameters on Wind Turbine Loads in Deterministic Transient Load Cases

Aero-hydro-elastic-servo numerical models used to design and analyze wind turbines are based on thousands of variable input parameters that dictate the inflow, aerodynamic, structural, and control characteristics of the system as well as sea state, hydrodynamic, and mooring characteristics for fixed-bottom and floating offshore wind turbines. Each of these parameters has some level of uncertainty, which can significantly impact the predicted loads. Understanding the uncertainty in the inputs is critical to understanding the uncertainty in the outputs. This work demonstrates a screening technique to identify which parameters ultimate loads are most sensitive to so that more focus can be given to quantifying the possible range of those parameters. This technique has been demonstrated previously for different turbine and load case types and is extended here for a floating offshore wind turbine in design load cases with transient events both in the inflow and operations. Each load case features a deterministic gust, including variations in wind speed, direction, and shear. Load cases are considered with an operating turbine as well as with prescribed fault, startup, and shutdown procedures. The study found that key input parameters with a large impact on loads include the length of the gust, the magnitude of direction change and speed in the gust, the initial wind speed, and the shape of the gust profile.

17 WIND ENERGY↗
DOE OSTI2026

A Full-Induction Magnetohydrodynamics Solver for Liquid Metal Fusion Blankets in Vertex-CFD

Multiphysics modeling of liquid metal fusion blankets, which produce tritium and convert energy of neutrons created via fusion reactions into heat, is crucial for predicting performance, ensuring structural integrity, and optimizing energy production. While traditional blanket modeling of liquid metal flows during normal steady operating conditions commonly employs the inductionless approximation of the magnetohydrodynamics (MHD) equations, transient scenarios, when the plasma-confining magnetic field varies on millisecond time scales, require a full-induction MHD approach that dynamically evolves the magnetic field via the time-dependent induction equation. This paper presents the formulation, implementation, and initial verification of a full-induction MHD solver integrated within the open-source Vertex-CFD framework, which aims to achieve tight multiphysics coupling, a flexible software design enabling easy extension and addition of physics models, and performance portability across computing platforms. The solver utilizes finite element spatial discretization, implicit Runge–Kutta time integration, and an inexact Newton method to solve the resulting discrete nonlinear system, leveraging Trilinos packages for efficient computation. Verification against selected benchmark problems demonstrates accuracy and robustness of the solver. Furthermore, when the solver is applied to an idealized blanket model in 2.5D and full 3D, results obtained with Vertex-CFD are in good agreement with recently published quasi-2D simulations. These findings establish a computational foundation for future simulations of transient MHD phenomena in liquid metal blankets with Vertex-CFD, and open avenues for future extensions and performance optimizations.

Endeve, Eirik [ORNL] (ORCID:0000000312519507)↗
NASA NTRSDate not supplied

Time-History Statistics of Soot Formation in A Model Gas Turbine Combustor

Soot formation is a complex dynamic and intermittent process determined by properties of the fuel, combustor design, and combustor operation. Although the major steps in soot formation (i.e., formation of precursors, inception, growth and evolution) are similar for a variety of carbonaceous fuels, applications, and operating conditions, it remains unclear when the temporal transition between these steps occurs. An engineering prediction tool coupled with computational fluid physics (CFD), therefore needs to accurately model all these complex steps. To develop such a model, we propose the time-history concept for understanding the time dependency of soot formation as a function of local properties (i.e., temperature, velocity, local fuel air ratio, etc.). We continue our previous work with modeling the DLR aero-combustor [1] with our updated in-house CFD code, Open National Combustion Code (OpenNCC), that now includes a Multiple Time-Scale Flamelet Progress Variable approach and a the semi-empirical two-equation soot model. We injected massless tracer particles upstream of the injector region of the combustor to collect time-history statistics of the solution variables. The correlations between the collected statistics with respect to the experimental soot volume fraction data showed that time-history effect of certain flow variables, including turbulent kinetic energy (TKE), and multiple species is indeed important for soot formation. We then conducted a time-history based correlation analysis to determine the key species and the concentration ranges critical for soot formation (C6H5-based nucleation, acetylene-based surface growth, and oxidation with OH and O2). Based on the time-history correlation coefficient (THCC) analysis, we propose possible modifications to improve the current two-equation model.

LES↗
NASA NTRSDate not supplied

The NASA Turbulent Heat Flux Experiments: Summary and Lessons Learned

The Turbulent Heat Flux (THX) experiments were conducted at NASA Glenn Research Center (GRC) in order to collect measurements of velocities and temperatures for computational fluid dynamics (CFD) validation of heated flows, with a focus on propulsion system components. The experiments spanned 5 phases; four of which were conducted in the GRC AeroAcoustic Propulsion Laboratory (AAPL) using the Small Hot Jet Flow Rig (SHJAR). In addition to making velocity measurements with Particle Image Velocimetry (PIV), the THX experiments introduced a new Raman-scattering based capability to measure temperatures. Computational studies were also conducted for each of the experimental configurations, in order to provide a baseline of expected CFD results and conduct an assessment of the capability of various CFD approaches for calculating flows where the turbulent transport of heat was important. Two of the collected sets of data were used for American Institute of Aeronautics and Astronautics (AIAA) Propulsion Aerodynamic Workshops (PAWs). The data set from the 5th phase, collected for heated supersonic jets, was also used to construct new validation cases for the NASA Turbulence Model Resource (TMR). This paper provides an overview of the experiments and associated computations for each of the 5 test phases. Key experimental findings are presented. Lessons learned are provided concerning the effect of computational modeling choice on accuracy of predicting turbulent flows where thermal transport is important. Emphasis is placed on comparing Reynolds- averaged Navier-Stokes approaches with large-eddy simulation approaches. The benefits of utilizing a conjugate heat transfer method in conjunction with CFD solver for film cooling is demonstrated.

RANS↗
DOE OSTI2026

Thermodynamics of Tritium Trapping by Point Defects at Interfacial Cr-based Phases of the Al Coating

Density functional theory (DFT) simulations have been carried out to evaluate the potential for tritium trapping by metal vacancies in four phases Cr-containing phases (i.e., Cr3Si, Al0.3Cr0.7, Al8Cr5-HT, and Al8Cr5) identified near the interface between the Al coating and 316 stainless steel (316 SS) cladding. In addition, an ab initio thermodynamics approach has been employed to predict the temperature and T2-partial pressure dependence on the thermodynamics of singly tritiated defects. Key results in this work suggest that metal vacancies in the four phases have the potential to favorably trap tritium species, especially Si vacancies in Cr3Si phase. This overall thermodynamic trend can be correlated to the energy cost of having an interstitial tritium in the lattice, which has been calculated to range from 0.17 eV in Al8Cr5-HT to 0.89 eV in Cr3Si. A comparison of the results from this study with previous theoretical works investigating tritium behavior in other Fe-Al phases identified in the aluminide coating, suggests that metal vacancies are generally able to trap tritium in various Fe-Al aluminide phases. Especially, it was found that Si and Al vacancies would be the most efficient to trap for tritium, followed by Cr vacancies, then Fe and Ni vacancies. In the four Cr-based material phases investigated in this work, it is interesting to note that, in the absences of Fe or Ni species, strong interactions between tritium and the metal vacancies are always occurring by the formation of preferential Cr—T bonds (i.e., no Si—T or Al—T bonds were formed).

Sassi, Michel J.↗
DOE OSTI2026

In situ studies on heavy ion irradiation and partial oxidation induced stacking faults and nanograins in tungsten nanolaminates

Understanding the microstructural evolution of tungsten (W) under extreme irradiation environments is critical for its application as a plasma-facing material in future fusion reactors. Heavy ion irradiation study offers expedited damage accumulation and thus allows irradiation tolerance property prediction in a short period of time. In this study we explore in situ Kr ion irradiation of W nanolaminates at 800 °C and uncover a complex interplay of irradiation-induced transformations, including the emergence of stacking faults, nanograin formation, and generation of thickened grain boundaries defined as GB regions with the thickness of up to 15 nm. High-resolution transmission electron microscopy studies reveal the formation of extended planar faults and a metastable hexagonal close-packed (hcp) phase within the body-centered cubic (bcc) matrix. These structural transitions are facilitated by irradiation-induced shear. They are further stabilized by the presence of oxygen, which promotes stacking fault formation and vacancy trapping. Elevated temperatures enhance defect mobility, enabling dynamic recrystallization into ultrafine grains and the thickening of GBs due to defect absorption and impurity segregation. These findings unravel non-equilibrium phase transformation pathways in heavy ion irradiated W and highlight the critical role of impurity-mediated defect dynamics in governing its radiation tolerance properties.

Wazeer, Adil [Purdue University]↗