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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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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

From irregular to regular eutectic growth in the Al-Al 3 Ni system: In situ observations during directional solidification

Here we investigate the irregular eutectic growth dynamics of the Al-Al 3 Ni alloy, in which one of the solid phases (Al 3 Ni) grows faceted from the liquid. Leveraging in situ optical microscopy and synchrotron transmission x-ray microscopy, we address the question of the degree of coupling between Al and Al 3 Ni at the growth front and that of the shape of the microstructures left behind in the bulk solid during directional solidification. Real-time optical observations bring evidence for a morphological transition from a eutectic-grain dependent, irregular eutectic growth at low solidification velocity V (typically 1 μm s -1 ), to a weakly anisotropic, regular growth at higher V ( reaching 10 μm s -1 ). Unprecedented x-ray nano-imaging of the solid–liquid interface, and 3D characterization of the growth patterns, were made possible by a new DS setup at Brookhaven National Laboratory’s NSLS-II. At low V, the leading tips of partly faceted Al 3 Ni crystals are observed to grow not far ahead of the Al growth front. Correlating in situ images and postmortem 3D tomographic reconstructions reveals that the presence of faceted and non-faceted regions of Al 3 Ni crystals in the solid is a direct consequence of coupling and decoupling during DS, respectively. Upon increasing V, the lead distance of Al 3 Ni vanishes, and the shape of Al 3 Ni ceases to be governed by faceted growth. These observations cast light onto the basic mechanisms (faceted growth, diffusive coupling, and the dynamics of trijunctions) governing a faceted to rod-like transition upon increasing V in the Al 3 Ni system, with broad implications to a large class of irregular eutectics.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Developing Robust Ceria-Supported Catalysts for Catalytic NO Reduction and CO/Hydrocarbon Oxidation

Synthesis of robust and hydrothermally stable PGM/ceria materials for NO, CO, and hydrocarbon abatement remains a formidable challenge, as ceria and PGMs are known to sinter severely >800 °C under hydrothermal conditions, leading to irreversible activity loss. In this work, we tackle this challenge by synthesizing well-defined catalysts with atomically dispersed rhodium supported on ceria with varying abundance of (100), (101), and (111) facets. Evaluation of these catalysts for NO reduction by CO as well as CO and propylene oxidation under model and industrially relevant conditions reveals pronounced reactivity and stability differences. Different modes of interaction of Rh ions with the ceria facets and their facile reducibility were shown to be the crucial parameters controlling reactivity, resulting in pronounced activity and stability variations. Facet-dependent poisoning of surfaces by nitrites was identified as the main reason for deactivation of the catalysts at low temperature, which is mitigated for (111) ceria facets. (111)-enriched ceria nanoparticles survive very harsh hydrothermal aging at 950 °C by maintaining and preserving (111) facets, unlike other ceria nanoparticles which sinter into poorly defined shapes. Thus, putting atomically dispersed PGM sites on (111) ceria facets lead to the catalytic material with the highest activity and stability for all studied reactions, providing the pathway to catalysts that can endure extremely harsh hydrothermal aging conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A Nonintrusive Optical Approach to Characterize Heliostats in Utility-Scale Power Tower Plants: Camera Position Sensitivity Analysis

Optics plays a major role in the effectiveness of concentrating solar power (CSP) technologies. The nonintrusive optical (NIO) approach developed by the National Renewable Energy Laboratory uses uncrewed aircraft system (UAS)-based imaging to survey heliostats in a commercial-scale power tower CSP plant and characterize their optical errors. The image processing algorithm uses photogrammetry to calculate the camera position for each image frame, and the accuracy of the estimated optical errors is highly sensitive to the calculated camera position accuracy. In this study, we simulate a series of case studies in python to examine the impact of different parameters of the sensitivity of the camera calculation, including the number of facet corners used as control points for the photogrammetric calculation, precision error in the detected pixel locations of the facet corners in the image, and precision error of the canting and mounting positions of the facets of the heliostat. The case studies consider heliostat geometry based on three commercial designs to serve as representative examples of different possible sizes of heliostats that the NIO method could be applied to. The results show that increasing the number of control points can improve accuracy for heliostats with many facets, pixel precision has a significantly larger impact on camera calculation accuracy than facet canting and mounting errors, and the camera distance and focal length must be chosen to ensure adequate pixel accuracy on the heliostat surface depending on the size of heliostat. In conclusion, based on the results, recommendations for the allowable values of each parameter are provided to achieve the required NIO optical error estimation accuracy depending on the size of heliostat.

14 SOLAR ENERGY↗
DOE OSTI2026

Emergence of complex-regular eutectic patterns in Al–Ge: Observations from correlative nano-imaging

Eutectic solidification exemplifies nonequilibrium pattern formation, making it a well-studied moving boundary problem. Yet the mechanisms behind the formation of complex-regular microstructures – particularly in highly anisotropic systems with a significant volume fraction of a faceted phase – remain poorly understood. Our understanding of such systems is made complicated by the nonlinear interface kinetics and unique growth dynamics characteristic of faceted phases. To address these challenges, we investigate a model Al–Ge eutectic system, where the faceted Ge phase constitutes a substantial volume fraction (~0.35) and where the two solid phases arrange into so-called “fishbone” or “feather” complex-regular patterns. Using synchrotron-based x-ray nano-imaging and nanotomography with high spatial resolution (22 nm per pixel), we capture in real-time the evolution of the solid–liquid interfaces and the resulting three-dimensional microstructures in this faceted/non-faceted eutectic system. By integrating these observations with electron backscattered diffraction, we elucidate the crystallographic biases on the solidification process and the mechanisms driving the formation of such complex-regular microstructures. These findings inform a new growth model for irregular eutectics in (near-)symmetrical phase diagrams, offering insight on advanced microstructural design and processing strategies. More broadly, we demonstrate how interfacial curvature is generated in irregular eutectic alloys and how it depends on the volume fraction of the faceted phase.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Insights into the Reactivity of Brookite TiO 2 Nanorods in Liquid Water from Ab Initio Molecular Dynamics Simulations

Brookite TiO 2 , a rare natural polymorph of TiO 2 , has been reported to be an excellent photocatalyst for the production of hydrogen from water and aqueous alcohol solutions, especially when it is reduced and synthesized in the form of nanorods. Here, we investigate the reactivity of stoichiometric and reduced brookite nanorods in liquid water using ab initio molecular dynamics and hybrid density functional theory calculations. Our simulations show a much higher water dissociation fraction on reduced nanorods than on stoichiometric ones, with an accumulation of the resulting bridging hydroxyls (O br H) and terminal hydroxyls (Ti –OH) on different facets of the nanorod. ObrH groups accumulate preferentially on low-energy (210) facets, where they are stabilized by adjacent reduced Ti (Ti 3+ ) sites, while Ti –OH groups prefer to form at the four-fold coordinated Ti atoms on high-energy (010) facets. This hydroxylation pattern also favors the spatial localization of excited holes on the (010) facets. This coupling between water-induced surface chemistry and charge separation underpins the enhanced photocatalytic activity of brookite nanorods, providing useful information for the design of more efficient TiO2-based nanostructures for solar-driven hydrogen evolution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Site-specific surface reactivity on SnO 2 : Evaluating selective atomic layer deposition processes

Area selective atomic layer deposition (AS-ALD) is a bottom-up synthesis approach with potential for deposition with molecular level precision. Here, the site-specific hydration of metal oxide substrates, combined with surface H 2 O-selective ALD processes, provides a potentially powerful path to targeted synthesis. Density functional theory (DFT) calculations are used to predict the thermodynamics of ALD precursor reactivity and hydration for (001), (101), (110), and (100) rutile SnO 2 facets as a function of temperature. Trimethylaluminum (TMA) and dimethyl aluminum isopropoxide (DMAI) dimers are predicted to react with both dehydrated and hydrated SnO 2 (001), (101), and (110) facets at ALD-relevant temperatures, while the SnO 2 (100) facet is predicted to be uniquely unreactive with TMA and DMAI monomers as well as dehydrate near 177 °C making this facet more amenable to targeted ALD. In situ ellipsometric studies of Al 2 O 3 ALD on polycrystalline SnO 2 at 150 °C are consistent with the computational predictions of rapid and unselective nucleation, in stark contrast to inhibited and selective ALD on isostructural rutile TiO 2 .

Atomic Layer Deposition↗
DOE OSTI2024

Selective atomic sieving across metal/oxide interface for super-oxidation resistance

Abstract Surface passivation, a desirable natural consequence during initial oxidation of alloys, is the foundation for functioning of corrosion and oxidation resistant alloys ranging from industrial stainless steel to kitchen utensils. This initial oxidation has been long perceived to vary with crystal facet, however, the underlying mechanism remains elusive. Here, using in situ environmental transmission electron microscopy, we gain atomic details on crystal facet dependent initial oxidation behavior in a model Ni-5Cr alloy. We find the (001) surface shows higher initial oxidation resistance as compared to the (111) surface. We reveal the crystal facet dependent oxidation is related to an interfacial atomic sieving effect, wherein the oxide/metal interface selectively promotes diffusion of certain atomic species. Density functional theory calculations rationalize the oxygen diffusion across Ni(111)/NiO(111) interface, as contrasted with Ni(001)/NiO(111), is enhanced. We unveil that crystal facet with initial fast oxidation rate could conversely switch to a slow steady state oxidation.

(S)TEM, oxidizing metals↗
DOE OSTI2025

Longitudinal position dependence of dark line defect growth rate in high-power diode lasers at 790 nm

Using a nondestructive, in situ near-infrared defect imaging technique, we obtained time-resolved images of dark line defect (DLD) growth in the cavities of several high-power 790-nm diode lasers and calculated individual DLD growth rates. A clear longitudinal spatial dependence in the DLD growth rate was observed, in which the DLD growth rate was faster near the anti-reflective (AR) facet. Longitudinal spatial hole burning simulation results indicate that the total photon density increases toward the AR facet, while the carrier density decreases toward the AR facet. Here, these results suggest that photon absorption plays a key role in enhancing DLD growth beyond the contribution of the traditional carrier capture mechanism. Asymmetric DLD growth that was preferentially directed toward the high-reflectivity facet was also observed, providing further support for the role of photon absorption in the growth process. To account for these findings, we propose a photon-accelerated mechanism for the enhancement of DLD growth in which the slower carrier capture process in the traditional recombination-enhanced dislocation glide mechanism is replaced by a faster photon absorption process.

Engineering - Electronic and electrical engineerin↗
DOE OSTI2025

Irreversible oxygen poisoning: Modeling the initial water dissociation kinetics on δ-Pu(111) and δ-Pu(100) through density functional theory

In this work, the initial kinetics of water dissociation on two facets of δ-plutonium, δ-Pu(111) and δ-Pu(100), are explored through density functional theory in order to understand how water dissociation occurs on these facets. We explored the dissociation of water via the formation of hydroxyls, atomic hydrogen, and atomic oxygen species on each facet. We calculate low energetic barriers for water to split to adsorbed hydrogen and hydroxyl species at 0.19 eV for δ-Pu(111) and 0.07 eV for δ-Pu(100). The hydroxyl has a barrier of 0.64 and 0.37 eV to cleave the hydrogen–oxygen bond on δ-Pu(111) and δ-Pu(100), respectively. Due to the highly exergonic adsorption free energy of atomic oxygen of −2.10 eV, the metallic surfaces are found to be fully covered in oxygen, even with the inclusion of oxygen lateral interactions. When combined with the reaction thermodynamics, this free energy of adsorption forms a molecular oxygen desorption barrier greater than 9.51 eV (918 kJ/mol). These results, combined with simulated temperature programed desorption spectra, indicate that oxygen formed via water dissociation on δ-Pu (111) and (100) facets induces an irreversible poison that prevents further reaction of water directly on metallic plutonium surfaces, most likely due to the strong hybridization of the Pu and O valence states. Therefore, these results imply that another mechanism is responsible for the continuously experimentally measured water dissociation, which is most likely due to the Pu oxide.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Impact of microkinetic modeling assumptions on predicted kinetics and mechanisms over undercoordinated sites

Accurate modeling of catalytic reactions on undercoordinated sites requires accounting for the structural and ensemble-specific nature of the active sites. This study examines how common microkinetic modeling (MKM) assumptions affect predicted kinetics and mechanisms on the stepped Pt(211) facet for the ethane dehydrogenation (EDH) and the ethane hydrogenolysis (EH). Six (211) MKMs were developed, differing in (i) the number of active sites represented, (ii) adsorbate site occupancy treatment, and (iii) inclusion of cross-facet interactions. These models are benchmarked against a particle-based microkinetic model (PB-MKM), which best represents step-edge behavior. MKM assumptions caused deviations in turnover frequencies exceeding ten orders of magnitude and led to contrasting mechanistic and selectivity predictions. Multi-site MKMs overestimate activity by inflating free site availability, single-site models underestimate activity, and uniform occupancy models overpredict coverage of multi-dentate intermediates, leading to reaction-specific artifacts. Overall, the Combined Site Edge Model (CSEM), a single-site MKM accounting for site occupancy and cross-facet interactions, most closely approximates PB-MKM predictions. All models predict similar kinetics when surfaces are clean or primarily occupied by monodentate species. This work provides practical guidance for selecting MKM frameworks for undercoordinated catalytic surfaces and highlights the critical role of modeling assumptions in catalytic predictions.

(211) facet↗
DOE OSTI2024

Morphology‐controlled synthesis of multi‐metal‐based spinel oxide nanocatalysts and their performance for oxygen reduction

Abstract We present a one‐pot colloidal synthesis method for producing monodisperse multi‐metal (Co, Mn, and Fe) spinel nanocrystals (NCs), including nanocubes, nano‐octahedra, and concave nanocubes. This study explores the mechanism of morphology control, showcasing the pivotal roles of metal precursors and capping ligands in determining the exposed crystal planes on the NC surface. The cubic spinel NCs, terminated with exclusive {100}‐facets, demonstrate superior electrocatalytic activity for the oxygen reduction reaction (ORR) in alkaline media compared to their octahedral and concave cubic counterparts. Specifically, at 0.85 V, (CoMn)Fe 2 O 4 spinel oxide nanocubes achieve a high mass activity of 23.9 A/g and exhibit excellent stability, highlighting the promising ORR performance associated with {100}‐facets of multi‐metal spinel oxides over other low‐index and high‐index facets. Motivated by exploring the correlation between ORR performance and surface atom arrangement (active sites), surface element composition, as well as other factors, this study introduces a prospective approach for shape‐controlled synthesis of advanced spinel oxide NCs. It underscores the significance of catalyst shape control and suggests potential applications as nonprecious metal ORR electrocatalysts.

Li, Can↗
DOE OSTI2025

Cosmohedra

It has been a long-standing challenge to find a geometric object underlying the cosmological wavefunction for Tr(ϕ 3 ) theory, generalizing associahedra and surfacehedra for scattering amplitudes. In this note, we describe a new class of polytopes — “cosmohedra” — that provide a natural solution to this problem. The faces of associahedra capture the combinatorics of non-overlapping chords of the momentum polygon, reflecting all partial factorizations of amplitudes. Cosmohedra are far richer — instead of non-overlapping chords, their faces capture the “russian doll” structure of non-overlapping subpolygons that determine the wavefunction. We show that cosmohedra are intimately related to associahedra, obtained by “blowing up” faces of the associahedron in a simple way. We give a full combinatorial description of cosmohedron faces and their factorization properties, and provide an explicit realization in terms of facet inequalities that further “shave” the facet inequalities of the associahedron. We also discuss a novel way for computing the wavefunction from cosmohedron geometry that extends the usual connection with polytope canonical forms. We illustrate cosmohedra with examples at tree-level and one loop; the close connection to surfacehedra suggests the generalization to all loop orders. Moving beyond the wavefunction, we briefly describe “cosmological correlahedra” for full correlators, which are one higher-dimensional polytopes, interpolating between associahedra and cosmohedra on opposite facets in an extra direction associated with the total energy. We speculate on how the existence of cosmohedra might suggest a “stringy” formulation for the cosmological wavefunction/correlators, generalizing the way in which the Minkowski sum decomposition of associahedra naturally extend particle to string amplitudes.

Scattering Amplitudes↗
DOE OSTI2024

Crystal structure and shape selection in the growth of 3D metallic crystallites on layered materials: Fe on MoS 2

Nucleation and growth of supported 3D metal clusters or crystallites during deposition on MoS 2 , or on other weakly-adhering layered materials, can potentially produce diverse growth shapes, and even crystal structures differing from the bulk metal. For Fe deposition on MoS 2 , SEM and AFM observations reveal three distinct crystallite shapes. By comparison with atomistic structure models incorporating realistic Fe-MoS 2 interface structures, here we conclude that these are: triangular fcc(111) pyramids with sloped {100} side facets; bcc(110) A-frame tents with sloped {100} side facets; and bcc(110) mesas with vertical {100} and {110} side facets. The following picture is proposed for the competitive formation of clusters and crystallites with different structures: (i) small nanoclusters formed at the onset of deposition exhibit facile fluxional dynamics allowing sampling of different crystal structures and shapes; (ii) sufficient fluxionality implies a Boltzmann distribution of sampled structures, and thus coexistence of different structures follows from the demonstrated similar energies for those structures; (iii) growing clusters reach a threshold size above which the characteristic time scale for restructuring exceeds that for cluster growth. Thereafter, clusters are locked-in to a specific crystal structure and shape as revealed by imaging of larger crystallites. Despite a penalty for fcc(111) over bcc(111) pyramids based on bulk energetics, favorable surface and interface energies makes them preferable for smaller sizes.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Variable Surface Termination and Ligand Passivation of Lead Sulfide Nanocrystals Synthesized with Excess Lead Chloride

The surface termination and ligand passivation of semiconducting nanocrystals (NCs) impact the stability, optical properties, and self-assembly of NCs. In this work, we definitively characterize the surface of lead sulfide (PbS) NCs synthesized from excess PbCl 2 . With a combination of small-angle neutron scattering (SANS), photoluminescence, and 1D and 2D NMR experiments, we show that the surface termination of PbS NCs depends on the presence of PbCl 2 during ligand exchange. When excess PbCl 2 is removed prior to ligand exchange, PbS[RNH 3 + Cl – ] NCs are obtained, which are terminated by a monolayer of PbCl x on the {100} PbS facet and passivated by oleylammonium chloride ligands. On the other hand, when excess PbCl 2 remains in solution during ligand exchange, lead oleate forms and attaches to the {111} PbS facets of PbS[RNH 3 + Cl – ] NCs, creating PbS@PbCl x NCs. PbS@PbCl x NCs are coated in an epitaxial layer of PbCl x on both the {100} PbS and {111} PbS facets, making them 0.3–0.4 nm larger on average than PbS[RNH 3 + Cl – ] NCs with identical absorption wavelengths. Additionally, PbS@PbCl x NCs have a consistently higher photoluminescence quantum yield and longer photoluminescence lifetimes than PbS[RNH 3 + Cl – ] NCs. This study clarifies the surface structure of PbS NCs synthesized from excess PbCl 2 , highlighting ligand exchange strategies and reconciling observations from across the literature.

Anions↗
DOE OSTI2024

Hybrid Quantum Mechanical, Molecular Mechanical, and Machine Learning Potential for Computing Aqueous-Phase Adsorption Free Energies on Metal Surfaces

Performing reliable computer simulations of elementary processes occurring at metal–water interfaces is pivotal for novel catalyst design in sustainable energy applications. Computational catalyst design hinges on the ability to reliably and efficiently compute the potential energy surface (PES) of the system. Here, due to the large system sizes needed for studying processes at liquid water–metal interfaces, these systems can currently not be described using density functional theory (DFT). In this work, we used a hybrid quantum mechanical, molecular mechanical, and machine learning potential for studying the adsorption behavior of phenol, atomic hydrogen, 2-butanol, and 2-butanone on the (0001) facet of Ru under reducing conditions when Ru is not oxidized. Specifically, we describe the adsorbate and the surrounding metal atoms at the DFT level of theory. Here, we also considered the electrostatic field effect of the water molecules on adsorbate–metal interactions. Next, for the water–water and water–adsorbate interactions, we used established classical force fields. Finally, for the water–Ru surface interaction, for which no reliable force fields have been published, we used Behler–Parrinello high-dimensional neural network potentials (HDNNPs). Employing this setup, we used our explicit solvation for metal surface (eSMS) approach to compute the aqueous-phase effect on the low-coverage adsorption of selected molecules and atoms on the (0001) facet of Ru. In agreement with previous experimental and computational studies of oxygenated molecules over transition metal facets, we found that liquid water destabilizes the tested adsorbates on Ru(0001). Interestingly, our findings indicate that adsorbates on Ru are less affected by the presence of an aqueous phase than on other transition metals (e.g., Pt), highlighting the necessity of experimental investigations of Ru-based catalytic systems in liquid water.

Adsorption↗
DOE OSTI2025

Anisotropic surface potentials induced by competitive ion adsorption enable the synthesis of branched cubic Pt mesocrystals

Creation of complex nanostructured materials through oriented attachment (OA) requires the manipulation of interparticle forces, including electrostatic repulsion, which depends strongly on surface potentials and can be modified through the effect of solution environment on interfacial chemistry. Here we show that time-dependent anisotropies in surface potential driven by competitive ion adsorption can alter facet-selectivity during OA. This phenomenon enables the synthesis of branched cubic Pt mesocrystals. Initially, Pt nanoparticles attach preferentially at their {100} facets to form a well-defined cubic core. Over time, changes in ion adsorption shift the attachment preference to the {111} facets, promoting branch formation. In both stages, anisotropic surface potentials generate electrostatic torques that align the particles prior to attachment. These findings demonstrate a generalizable strategy for directing the architecture of nanomaterials through time-resolved control of interfacial chemistry during OA, offering new pathways for the design of complex mesoscale structures.

Bae, Yuna [Pacific Northwest National Laboratory (↗
DOE OSTI2025

Formation of open ruthenium branched structures with highly exposed active sites for oxygen evolution reaction electrocatalysis

The formation of exposed active sites that have high activity and stability for oxygen evolution reaction (OER) catalysis is a significant opportunity for improving water electrolysers. Low-index facets surface Ru can achieve both high activity and stability for OER. Here, we present a new catalyst design where low-index faceted Ru branches are grown off the corners of Pt nanocubes, forming open Ru branched nanoparticles. This open branched structure, exposing low-index facets on its length-tunable branch, enables a high electrochemically active surface area (ECSA), achieving high activity and stability for OER. This design strategy and synthetic control provide a principle for achieving high-performance OER nanocatalysts.

Xiao, Sa [The University of New South Wales, Sydne↗
DOE OSTI2026

Phase-field model of freeze casting

Directional solidification of water-based solutions has emerged as a versatile technique for templating hierarchical porous materials. However, the underlying mechanisms of pattern formation remain incompletely understood. In this work, we present a detailed derivation and analysis of a quantitative phase-field model for simulating this nonequilibrium process. The phase-field model extends the thin-interface formulation of dilute binary alloy solidification with antitrapping to incorporate the highly anisotropic energetic and kinetic properties of the partially faceted ice-water interface. This interface is faceted in the basal plane normal to the ⟨0001⟩ directions and atomically rough in other directions within the basal plane. On the basal plane, the model reproduces a linear or nonlinear relationship between the interface growth rate and the kinetic undercooling that can be linked to experimental measurements. In both cases, spontaneous parity breaking of the solidification front is observed when the preferred growth direction is aligned with the temperature gradient. This phenomenon leads to the formation of partially faceted ice lamellae that drift laterally in one of the ⟨0001⟩ directions. Here, we demonstrate that the drifting velocity of the ice lamellae is controlled by the kinetics on the basal plane and converges as the thickness of the diffuse solid-liquid interface decreases. Furthermore, we examine the effect of the form of the kinetic anisotropy, which is chosen here such that the inverse of the kinetic coefficient varies linearly from a finite value in the ⟨0001⟩ directions to zero in all other directions within the basal plane, consistent with the assumption that the interface grows in local thermodynamic equilibrium in this plane. Our results indicate that the drifting velocity of ice lamellae is not affected by the slope of this linear relation, and the radius and undercooling at the tip of an ice lamella converge at relatively small slope values. Consequently, the phase-field simulations remain quantitative with computationally tractable choices of both the interface thickness and the slope assumed in the form of the kinetic anisotropy.

Materials science↗