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At least 685 records · Page 38

A machine learning approach to predict thermal expansion of complex oxides

Although it is of scientific and practical importance, the state-of-the-art of predicting the thermal expansion of oxides over broad temperature and composition ranges by physics-based atomistic simulations is currently limited to qualitative agreements. We present an emerging machine learning (ML) approach to accurately predict the thermal expansion of cubic oxides with a dataset consisting of experimentally measured lattice parameters while using the metal cation polyhedron and temperature as descriptors. High-fidelity ML models that can accurately predict temperature- and composition-dependent lattice parameters of cubic oxides with isotropic thermal expansions have been successfully trained. The ML-predicted thermal expansions of oxides not included in the training dataset have shown good agreement with available experiments. The limitations of the current approach and challenges to go beyond cubic oxides with isotropic thermal expansion are also briefly discussed.

36 MATERIALS SCIENCE↗

Molecular tail chemistry controls thermal transport in fullerene films

Herein we report on the thermal conductivities of alkyl- and indene-group functionalized fullerene derivative thin films as measured via time domain thermoreflectance and steady state thermoreflectance. The thermal conductivities vary from 0.064 ± 0.007 W m – 1 K – 1 for [6,6]-phenyl C 61 -butyric acid methyl ester (PCBM) to 0.15 ± 0.017 W m – 1 K – 1 for indene- C 60 bisadduct at room temperature and do not exhibit significant temperature dependence from 300 to 375 K. In comparison to the thermal conductivity of PCBM, increasing the length of the alkyl chain, as in the case of [6,6]-phenyl C 61 -butyric acid butyl ester, and [6,6]-phenyl C 61 -butyric acid octyl ester leads to higher thermal conductivities. Likewise, increasing the number of alkyl chains attached to the fullerenes as in the case of bisadduct PCBM leads to a higher thermal conductivity compared to that of PCBM. We present atomistic insights into the role of chemical functionalization on the overall heat transfer in these fullerene derivatives by conducting molecular dynamics simulations and lattice dynamics calculations. The thermal conductivities predicted via our atomistic simulations qualitatively agree with the experimental trends for our fullerene derivatives. Lattice dynamics calculations reveal that one of the main factors dictating the ultralow thermal conductivities in fullerene derivatives is the large reduction in modal diffusivities in the molecular crystals as calculated from the Allen-Feldman model, thus providing an explanation for their largely reduced thermal conductivities as compared to that of C 60 crystals. The low diffusivities result from high degrees of localization of Einstein-like vibrations in fullerene derivatives due to the molecular side chains, providing the ability to dial-in the properties of these low thermal conductivity solids via molecular engineering.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Sulfonated polybenzimidazole membrane with graphene oxide additive for 2,3-butanediol/water separation: A molecular simulation

Membrane separation for 2,3-butanediol (2,3-BDO) recovery from fermentation broth is highly valued for sustainable and renewable processes, but it requires efficient membrane materials. Here, this work evaluates the sulfonated polybenzimidazole (sPBI) and its graphene oxide (GO) doped composite membrane for separating 2,3-BDO and water via atomistic simulations. Density functional theory calculations are applied to identify various forms of sPBI structures and quantify their binding interactions with 2,3-BDO and water. Classical molecular dynamic simulations are used to evaluate the structural changes, diffusivity, and selectivity of 2,3-BDO and water in different sPBI models, GO surfaces, and GO-doped sPBI composite models. Our results suggest that sPBI slightly increases the crystallinity of the membrane structures, enhances the adsorption strength for both 2,3-BDO and water, and improves the water/2,3-BDO selectivity by 2–3 times. The GO surfaces display a maximum selectivity at a surface coverage of 0.1–0.15 for both hydroxyl and epoxy surface groups. The addition of GO flakes to sPBI creates new interaction sites for 2,3-BDO and water at the interface of sPBI and GO, and the water/2,3-BDO selectivity of GO-doped sPBI models is further increased up to 3 times. This work illustrates how the integrated addition of sPBI and GO flakes offers a promising approach to selective separation of 2,3-BDO and water, providing theoretical guidance for polybenzimidazole-based membranes in the potential application of 2,3-BDO recovery.

2,3-butanediol↗

Interlayer Interactions in 1D Van der Waals Moiré Superlattices.

Studying two-dimensional (2D) van der Waals (vdW) moiré superlattices and their interlayer interactions have received surging attention after recent discoveries of many new phases of matter that are highly tunable. Different atomistic registry between layers forming the inner and outer nanotubes can also form one-dimensional (1D) vdW moiré superlattices. In this review, experimental observations and theoretical perspectives related to interlayer interactions in 1D vdW moiré superlattices are summarized. The discussion focuses on double-walled carbon nanotubes (DWNTs), a model 1D vdW moiré system, and the authors highlight the new optical features emerging from the non-trivial strong interlayer coupling effect and the unique physics in 1D DWNTs. Future directions and questions in probing the intriguing physical phenomena in 1D vdW moiré superlattices such as, correlated physics in different 1D moiré systems beyond DWNTs are proposed and discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Plasticity of irradiated materials at the nano and micro-scales

Here, we review here our recent work on plastic deformation in irradiated materials at the nano- and micro-scales, as revealed by Discrete Dislocation Dynamics (DDD) simulations. Two methods of including irradiation effects in the DDD framework are presented. The first directly captures the atomistic interaction mechanisms, while the second can effectively study high-dose irradiation. Computer simulations lead to new understanding of the dynamics of collective dislocation-irradiation defect interactions, as well as the quantitative analysis of the temporal and spatial characteristics associated with plastic instabilities. Based on these insights, theoretical models are developed to predict the critical conditions for dislocation channel formation. A simple probability model is proposed and demonstrated to predict the width of dislocation channels in bulk irradiated materials with good agreement with experimental data. The fundamental understanding of the origins of plastic flow localization in irradiated materials sheds light on the design of future generations of radiation-resistant materials.

36 MATERIALS SCIENCE↗

Computing chemical potentials with machine-learning-accelerated simulations to accurately predict thermodynamic properties of molten salts

The successful design and deployment of next-generation nuclear technologies heavily rely on thermodynamic data for relevant molten salt systems. However, the lack of accurate force fields and efficient methods has limited the quality of thermodynamic predictions from atomistic simulations. Here we propose an efficient free energy framework for computing chemical potentials, which is the central free energy quantity behind many thermodynamic properties. We accelerate our simulations without sacrificing accuracy by using machine learning interatomic potentials trained on density functional theory (DFT) data. Using lithium chloride as our model system, we compute chemical potentials with DFT-accuracy for solid and liquid phases by transmuting ions into noninteracting particles. Notably, in the liquid phase, we demonstrate consistency whether we transmute one ion pair or the entire system into ideal gas particles. By locating the temperature where the chemical potential of solid and liquid phases cross, we predict a melting point of 880 ± 18 K for lithium chloride, which is remarkably close to the experimental value of 883 K. With this successful demonstration, we lay the foundation for high-throughput thermodynamic predictions of many properties that can be derived from the chemical potentials of the minority and majority components in molten salts.

Gibson, Luke D. [Oak Ridge National Laboratory (OR↗

Defect-Driven Redox Interplay on Anatase TiO 2 : Surface-Structure Dependent Activation for CO 2 Hydrogenation Catalysis

Titanium dioxide (TiO 2 ) is one of the most extensively studied oxides as an active catalyst or catalyst support, particularly in energy and environmental applications, but the atomistic mechanisms governing its dynamic response to reactive environments and their correlation to reactivity remain largely elusive. Using in situ environmental transmission electron microscopy (ETEM), synchrotron X-ray diffraction (XRD), ambient-pressure X-ray photoelectron spectroscopy (AP-XPS), temperature-programmed reduction (TPR), reactivity measurements, and theoretical modeling, we reveal the dynamic interplay between oxygen loss and replenishment of anatase TiO 2 under varying reactive conditions. Under H 2 exposure, anatase TiO 2 undergoes surface reduction via lattice oxygen loss, forming Ti 3 O 5 . In contrast, CO 2 exposure induces oxygen replenishment, reversing stoichiometry. In mixed H2/CO 2 environments, the reverse water–gas shift (RWGS) reaction proceeds selectively on stepped and high-indexed TiO 2 surfaces, whereas the thermodynamically stable TiO 2 (101) surface remains inactive and intact. Critically, H 2 pretreatment generates oxygen vacancies on TiO 2 (101), transforming it into an active Ti 3 O 5 or defect-rich surface that catalyzes RWGS. By correlating surface structure, defect dynamics, and gas-phase interactions, this work deciphers the competition between H 2 -driven reduction and CO 2 -driven oxidation pathways at the atomic scale. Furthermore, these insights establish defect engineering as a strategic lever to activate inert TiO 2 facets, advancing the design of adaptive catalysts for sustainable fuel synthesis technologies.

36 MATERIALS SCIENCE↗

Salts in Hot Water: Developing a Scientific Basis for Supercritical Desalination and Strategic Metal Recovery

The w21_superdesal project is part of an LDRD-DR on supercritical desalination (20190057DR). The goal of the simulation work is to use atomistic simulations to understand at a molecular level the changes in hydrogen bonding and ion solvation that occur as we increase the temperature and/or pressure and change the density and ion concentration. Our simulation results will also aid in the interpretation of experimental data and guide the development of applied thermodynamic models for engineering design calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Virtual diffraction simulations using the quasi-coarse-grained dynamics method to understand and interpret plasticity contributions during in situ shock experiments

The dynamic deformation response of metallic materials has contributions from dislocations, deformation twinning, and plastic deformation. The current state-of-art techniques can detail the complex mechanistic history of deformation modes under shock loading in real-time using in situ X-ray diffraction (XRD). However, the capability of these experiments to unravel plasticity contributions is challenging due to limitations in interpreting results and the lack of validation from atomistic simulations. Molecular dynamics (MD) simulations can successfully capture various deformation modes in metals and complement experiments using simulated diffractograms at various stages of evolution. However, the difference in length and time scales of MD simulations and experiments is a substantial obstacle in completing and interpreting in situ diffractograms. Therefore, the existing modeling methods require various approximations to model defect evolution and interaction at the mesoscales. However, while using approximations to correlate the peak broadening behavior to the density of dislocations or the shifts/splitting due to the presence of twins, the interpretations of the plasticity contributions from diffractograms are non-trivial, especially when multiple modes of deformation may be operating. This viewpoint discusses combining a mesoscale modeling method called quasi-coarse-grained dynamics and virtual XRD to characterize the plasticity contributions in BCC metals from slip, twinning, and phase transformation behavior. Furthermore, the combined approach shows promise in bridging the mesoscale gap between the capabilities of atomic-scale simulations and in situ experiments to characterize the dynamic deformation of materials.

36 MATERIALS SCIENCE↗

Applications of Nickelate perovskites for neuromorphic computing from electronic structure and Machine Learning

While the limit of Moore's law is presently being reached with current microelectronic technologies, we need to develop new paradigms that overcome this limitation. In that respect, neuromorphic computing is a concept that emulates the neural behavior and response of the human brain, and it has been recognized as a promising alternative approach. In this research project, we will perform multi-fidelity scale bridging to explore the potential use of materials with metal to insulator transition for neuromorphic applications. In particular, rare earth nickelates are promising for such purposes, as the transition in these materials is quite sensitive to a broad set of different external stimuli. Our multi-fidelity approach will bridge the high-fidelity electronic structure calculations with classical potentials. We will bridge dynamical mean field theory with a classical atomistic representation via a deep learning force field. The neural network is trained with energies, charges, and forces obtained by accurate electronic structure theories based on Dynamical Mean Field Theory. The configurational space is generated from known crystal phases, ab initio molecular dynamics with exchange-correlation functionals corrected with the Hubbard model, disordered phases with different concentrations of oxygen vacancies, and nonsymmetrical positions and induced strain by grain interfaces or contact with a substrate. Strategies to train the model with a reduced number of training examples are obtained from active learning methods, and new structures for improving the learning process are generated by using machine learning autoencoders. This classical potential will be validated through a diversity of electronic structure methods and represents an important step to combine the flexibility and accuracy of first-principles with the speed of classical potentials. The generated multi-fidelity surrogate model will be used to understand the role of strain, oxygen vacancies, proton doping, the variation of the crystal phase, substrate effects, vibrational effects as the octahedral rotation, grain boundaries and defect effects on the response of a Metal to Insulator Transition (MIT) in correlated materials. Long time and large-scale simulations will help understand the role of different stimuli to control the hysteresis of the MIT, as it has been experimentally suggested. Selected configurations will be analyzed with higher-level theories to provide an accurate electronic description and to study how the orbitals and charges are rearranged under different conditions.

36 MATERIALS SCIENCE↗

Triple junction solute segregation in Al-based polycrystals

Solute segregation is a crucial means of stabilizing nanostructured alloys, and at very small grain sizes, this requires consideration of triple junctions (TJs), which attain a meaningful volume fraction and thus become relevant for bulk material behavior. Here, in this study, the solute segregation spectra for grain boundary (GB) and TJ sites are calculated for a large number of dilute Al-based binary systems with available interatomic potentials. A defect-identifying algorithm is applied to quantify the average GB thickness and classify the intergranular site spectra into GB and junction subspectra. The algorithm is also applied to a hybrid electronic-level database for GB segregation of various solutes in Al, yielding polycrystalline TJ solute segregation spectra from first principles. The results suggest that TJ segregation is alloy or interatomic potential dependent and can exhibit either boundary or junction preference. With these spectra as inputs, the spectral GB segregation model gives quantitative predictions of segregation as a function of grain size, temperature, and total solute concentration, suitable for alloy screening and design.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Investigation of the Effect of Framework Flexibility on Adsorption in SIFSIX-3-Cu using a Machine-Learned Force Field

Metal-organic frameworks (MOFs) are a promising class of adsorbents. The performance of MOF sorbents relies on high selectivity and low regeneration energy. This work focuses on the use of machine learned force fields (MLFFs) to model adsorption in a flexible MOF, SIFSIX-3-Cu. A DeePMD-based MLFF was trained to reproduce DFT (PBE+D3) energies, forces, and stresses, using an iterative sampling scheme combining sampling based on molecular dynamics, Monte Carlo, and geometry optimization to capture both attractive and repulsive regions of the potential energy surface. Flexibility of the MOF was explicitly included in this model. Hybrid Monte Carlo/molecular dynamics (MC/MD) simulations using the MLFF predicted adsorption isotherms in good agreement with experimental data for a range of pressures (40 Pa – 104 Pa) in contrast to rigid models, which overpredict CO2 adsorption at low pressures. The improvement was the result of a description of the variability of fluorine-fluorine diagonal distances at adsorption sites. This detailed description of flexibility afforded by the MLFF resulted in more accurate predictions adsorption isotherms when compared to the experimentally measured values. These results underscore the importance of including framework flexibility when modeling adsorption phenomena in MOFs, particularly for low pressure applications and provide a robust procedure for training MLFF models for MOFs.

Atomistic Simulation↗

Extended Rice–Thomson analysis and atomistic simulations revealing grain boundary effects on fracture in refractory high-entropy alloys

Significance This work serves to extend the fundamental ductile vs. brittle fracture theory, specifically the Rice–Thomson criterion, by introducing a grain boundary ahead of an initiating crack which propagates at an oblique angle to impinge the boundary. Atomistic fracture simulations on two refractory complex concentrated alloys, the brittle NbMoTaW and the ductile Nb 45 Ta 25 Ti 15 Hf 15 , demonstrate qualitative correspondence with the extended Rice–Thomson criterion and experimental observations. Abstract Understanding how grain boundaries mediate fracture remains a critical challenge in designing ductile, high-performance refractory alloys. Here, we extend the Rice–Thomson criterion to account for the angle between cracks and the impinging grain boundaries (GBs), capturing the competition between intergranular fracture and dislocation-mediated plasticity. Using machine learning interatomic potentials, we performed molecular statics simulations to probe fracture mechanisms in nanocrystalline NbMoTaW and Nb 45 Ta 25 Ti 15 Hf 15 , each with two different grain sizes, revealing trends consistent with experimental observations and the extended Rice model. Comparison with averaged R-curves for bulk samples demonstrates that GBs enhance ductility in Nb 45 Ta 25 Ti 15 Hf 15 in both grain sizes investigated. In contrast, GBs only locally improve fracture resistance in NbMoTaW when cracks are temporarily pinned at GBs inclined at high angles from the crack, but generally promote brittle intergranular fracture. These contrasting behaviors are attributed to differences in GB cohesion, reflecting clear alloying trends that align with ab-initio calculations and trends observed experimentally. Our results bridge classical fracture theory, atomistic simulations, and experimental observations, providing a comprehensive understanding of the fracture mechanisms in nanocrystalline refractory complex concentrated alloys.

36 MATERIALS SCIENCE↗

Effect of a micro-scale dislocation pileup on the atomic-scale multi-variant phase transformation and twinning

In this paper, we perform concurrent atomistic–continuum (CAC) simulations to assess the contribution of the internal stress induced by the microscale dislocation pileup at an atomically structured interface to the atomic-scale phase transformations (PTs), reverse PTs, and twinning. The main novelty of this work is to unify the atomistic description of the interface and the coarse-grained (CG) description of the lagging dislocations away from the interface within one single framework. Our major findings are: (a) the interface dynamically responds to a pileup by forming steps/ledges, the height of which is proportional to the number of dislocations arriving at the interface; (b) the pileup-induced internal stress concentration profile follows neither the classical Eshelby model nor the super-dislocation model alone, but a combination of them; (c) when the pre-sheared sample is compressed, a direct square-to-hexagonal PT occurs ahead of the pileup tip and eventually grows into a wedge shape. The two variants of the hexagonal phases form a twin with respect to each other; (d) upon a further increase of the loading, part of the newly formed hexagonal phase transforms back to the square phase. The square product phase resulting from this reverse PT forms a twin with respect to the initial square phase. All phase boundaries (PBs) and twin boundaries (TBs) are stationary and correspond to zero thermodynamic Eshelby driving forces; and (e) the microscale dislocation pileup-induced internal shear stress and the structural change at the atomic-scale interface reduces the stress required for initiating a PT by a factor of 5.5, comparing with that in the sample containing no dislocations. This work is the first characterization of the behavior of PTs/twinning resulting from the reaction between a microscale dislocation slip and an atomically structured interface. In conclusion, the gained knowledge will advance our understanding of how the multi-phase material behaves in many complex physical processes, such as the synthesis of multi-phase high-entropy alloys or superhard ceramics under high-pressure torsion, deep mantle earthquakes in geophysics, and so on, which all involve dislocation slip, PTs, twinning, and their interactions across from the atomistic to the microscale and beyond.

36 MATERIALS SCIENCE↗

Bridging the time scale in exascale computing of chemical systems (Final Technical Report)

This report summarizes the work carried out with support of the United States Department of Energy under Award DE-SC0019441. The theme of this project was to develop and apply methods that allowed for the acceleration of atomistic calculations, particularly in challenging areas such as multiphase systems, electrified interfaces, uncertainty estimation, and applications requiring chemical accuracy, which tend to be applications where simulation time is severely bottlenecked by the computational time requirements. Much of the focus was on the application of emerging machine-learning methodologies, although a wide range of methodologies were employed. This report has two major sections. The first focuses on the methodological advances themselves. Within this part, we report a number of major advances, a few examples of which are described here. We report the first machine-learning scheme for the acceleration of electronically grand-canonical calculations (that is, those applicable to electrochemistry). We report new methods of performing transfer learning, in which physics-based priors can be used to provide predictions, often with uncertainty estimates, of images well outside of training sets; we also offer ways to fine-tune these transfer-learning models. We provide a new systematic means to generate and apply minimal training data sets to very large (10,000’s of atoms) systems, with only small training sets appropriate for electronic structure. We developed new methodologies to integrate surface vibrations into surface adsorption calculations. We made advances to the applicability of diffusion Monte Carlo methods to allow (learned) force prediction, finite-size error correction, and force-free means of searching for transition states. We integrated machine-learned atomistic predictions into mechanism generation codes. Additionally, we released new software including AmpTorch, a modernized version of our original atomistic machine-learning code Amp. The second part of this report focuses on the scientific applications that accompanied, and were often enabled by, the methodological advances described earlier. A few examples follow, but full details are in the individual chapters of the report. For example, we developed a general theory of phonon-induced friction on molecular adsorbates. We showed fundamentally how solvent influences the adsorption and desorption process and how it differs from the processes typically involved at the solid–gas interface, making aqueous-phase and electrocatalysis different from traditional thermocatalysis. We examined how metal–insulator and magnetic transitions can be probed, and accelerated exciton dynamics via Frenkel Hamiltonian parameters. We showed that the nearsighted force-training approach, developed within this project, can predict both the stability and reactivity of large nanoparticles, and can also lead to insights on catalyst coverage on binding energies and entropies. These applied studies, which generally integrated with our method development, allowed us to push forward the theoretical understanding of several reaction classes.

08 HYDROGEN↗

The role of SAXS and molecular simulations in 3D structure elucidation of a DNA aptamer against lung cancer

Aptamers are short, single-stranded DNA or RNA oligonucleotide molecules that function as synthetic analogs of antibodies and bind to a target molecule with high specificity. Aptamer affinity entirely depends on its tertiary structure and charge distribution. Therefore, length and structure optimization are essential for increasing aptamer specificity and affinity. Here, we present a general optimization procedure for finding the most populated atomistic structures of DNA aptamers. Based on the existed aptamer LC-18 for lung adenocarcinoma, a new truncated LC-18 (LC-18t) aptamer LC-18t was developed. A three-dimensional (3D) shape of LC-18t was reported based on small-angle X-ray scattering (SAXS) experiments and molecular modeling by fragment molecular orbital or molecular dynamic methods. Molecular simulations revealed an ensemble of possible aptamer conformations in solution that were in close agreement with measured SAXS data. The aptamer LC-18t had stronger binding to cancerous cells in lung tumor tissues and shared the binding site with the original larger aptamer. The suggested approach reveals 3D shapes of aptamers and helps in designing better affinity probes.

59 BASIC BIOLOGICAL SCIENCES↗

Salts in Hot Water: Developing a Scientific Basis for Supercritical Desalination and Strategic Metal Recovery

Given the steady growth in world population and the ever-increasing fresh water demand, the only sustainable water supply option is desalination. Conceptually, desalination is very simple - just separate dissolved salts from water. While desalination research programs have existed since the 1960s and have resulted in a multitude of approaches, realizing affordable desalination has proven to be a challenge. Our goal is to meet this challenge using low cost heat sources to drive a liquid-discharge-free desalination process that can be co-mingled with the extraction of economically valuable co-products. High temperatures and pressures will be used to manipulate water’s properties, such as the dielectric constant, and hence its ability to solvate ions. Selective precipitation/recovery of valuable metal co-products creates new revenue streams (i.e., cost offsets). We will develop the scientific understanding necessary to control salt precipitation from supercritical seawater, inland brines, and water commonly co-produced with oil and gas. Atomistic simulations will be used to understand at a molecular level the changes in hydrogen bonding and ion solvation that occur as we increase the temperature and/or pressure and change the density and ion concentration. Our simulation results will also aid in the interpretation of experimental data and guide the development of applied thermodynamic models for engineering design calculations.

58 GEOSCIENCES↗

Migration energy barriers and diffusion anisotropy of point defects on tungsten surfaces

We report tungsten is one of the most promising candidates for plasma-facing materials in future fusion devices, owing to its high performance under extreme irradiation conditions. However, irradiation-induced surface morphology varies significantly, depending on the irradiation type, fluence, and flux. Therefore, it is critical to examine the dynamics of point defects on tungsten (W) surfaces to understand how irradiation affects surface morphology. In this study, we employ the Self-Evolving Atomistic Kinetic Monte Carlo (SEAKMC) method to search for potential migration paths of point defects on W (1 0 0), (1 1 0) and (1 1 1) surfaces. The first-principles calculations are then used to accurately determine the migration energy barriers. The obtained paths and barriers are incorporated into a kinetic Monte Carlo (KMC) model to determine trajectories and diffusivities, which are described by diffusion tensors to demonstrate their anisotropic features. Multiple diffusion mechanisms have been identified on different surfaces, with various anisotropy factors. Particularly, point defects on the W (1 1 0) surface have the highest diffusivities, with anisotropy factors independent of temperatures. In comparison, the anisotropy of the W (1 0 0) surface decreases as temperature increases, while the W (1 1 1) surface is isotropic for point defects. This study provides insights into defect transport properties on different surfaces, which are essential for understanding the early stages of irradiation-induced microstructural evolutions and surface morphology of tungsten.

36 MATERIALS SCIENCE↗