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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 343 records · Page 19

Predicting Open Quantum Dynamics with Data-Informed Quantum-Classical Dynamics

We introduce a data-informed quantum-classical dynamics (DIQCD) approach for predicting the evolution of an open quantum system. The equation of motion in DIQCD is a Lindblad equation with a flexible, time-dependent Hamiltonian that can be optimized to fit sparse and noisy data from local observations of an extensive open quantum system. We demonstrate the accuracy and efficiency of DIQCD for both experimental and simulated quantum devices. We show that DIQCD can predict entanglement dynamics of ultracold molecules (calcium fluoride) in optical tweezer arrays. DIQCD also successfully predicts carrier mobility in organic semiconductors (rubrene) with accuracy comparable to nearly exact numerical methods.

Lindblad equation↗

Stability and Mobility of Disconnections in Solute Atmospheres: Insights from Interfacial Defect Diagrams

This Letter explores the stability of disconnections (step-dislocation defects) at grain boundaries in binary alloys. We introduce interfacial defect diagrams, derived from atomistic simulations and segregation theory, to predict the stability of disconnections in the temperature-solute concentration phase space and relate it to governing segregation mechanisms. These diagrams reveal multiple stability regimes influenced by solute-induced clustering and pinning effects impacting the thermal migration of disconnections and offering insights into their thermodynamics and kinetic properties.

Crystal structure↗

Mobilization of trace metals from caprock and formation rocks at the Illinois Basin – Decatur Project demonstration site under geological carbon dioxide sequestration conditions

One concern for geologic CO 2 sequestration is the potential leakage of CO 2 or CO 2 -saturated brine containing trace metals into overlying aquifers, which poses the risk of adversely affecting underground sources of drinking water. In this work, rock and brine samples collected in the Illinois Basin – Decatur Project (IBDP), a large-scale geological CO 2 sequestration demonstration project in Decatur, Illinois, USA, as well as synthetic brine samples were used to understand the mobilization of trace metals as a result of CO 2 –rock–brine interactions under IBDP-specific conditions (50 °C and 20.6 MPa). Rock sample characterization indicated that, at the IBDP site, trace metal concentrations were greatest in cap rock samples from the Eau Claire Formation, compared with those from formations above and below this Formation. The natural brine samples collected from the Mt. Simon Sandstone reservoir were highly reducing and saline, with trace metal concentrations up to 680 times greater than the U.S. Environmental Protection Agency-prescribed drinking water standards. Batch leaching experiments indicated that both trace metal mobilization from rock and immobilization from the brine occurred when high-pressure CO 2 was introduced into the rock-brine system. The amounts of metals mobilized from the rock generally accounted for <5% of the total metals in the rock, but for some metals, including Ni, Pb, and Tl, up to 63% of the metals in the rock were mobilized to the brine. Leaching of trace metals into synthetic brines was different from that into the natural brine. The results of this study provided current information on the trace element sources and will help in risk simulations and experimental design to further evaluate potential impact of leakage on groundwater quality, which is important for future GCS projects to consider for monitoring and containment assurance purposes.

58 GEOSCIENCES↗

Simulation of dislocation evolution in microparticle impacts over a wide range of impact velocities

We report the dynamic loading environment created by high velocity microparticle impacts is very difficult to model. The extremely high strain rates, large deformations, and high temperatures affect the flow stress of the material in ways that standard flow stress models cannot capture. Plastic deformation and strain hardening in metals is controlled by the motion of dislocations. Dislocations can be nucleated, stored as forest dislocations, or be annihilated as loading progresses. A comprehensive accounting of dislocation density change is needed to accurately describe rate and temperature dependent dislocation glide and evolution across the wide rage of loading conditions present in microparticle impact problems. Therefore, we implement and apply a newly proposed flow stress model (Hunter and Preston, 2015, 2022) that is then coupled with mobile and immobile dislocation density evolution equations. This model is implemented in Los Alamos National Laboratory’s hydrodynamics code, FLAG, to model copper-on-copper microparticle impacts. This new strength model allows for accurate simulation of particle rebound and flattening across a wide range of impact velocities.

36 MATERIALS SCIENCE↗

Non-dilute helium-related defect interactions in the near-surface region of plasma-exposed tungsten

We report a systematic energetic analysis of helium-related defect interactions that mediate helium (He) segregation on surfaces of plasma-exposed tungsten at different levels of He ion implantation. We focus on high He fluences that increase the He content in the plasma-exposed material well beyond the dilute limit of He concentration and employ atomic configurations generated by large-scale molecular dynamics simulations of He-implanted tungsten. We perform systematic molecular statics computations of cluster– defect interaction energetics in the highly defect-rich near-surface region of plasma-exposed tungsten for small mobile helium clusters as a function of the cluster distance from the surface. In this region, mobile clusters are also subjected to the stress fields generated by defects such as helium bubbles and other clusters, which govern cluster–defect interactions in addition to the cluster–surface interaction. Based on systematic investigation of individual cluster–defect interactions, we develop a mathematical framework to describe the interaction energy landscapes consisting of elastic interaction potential perturbations to finite-width square-well potentials, where the potential well accounts for cluster trapping by the defect at close range and subsequent coalescence and the perturbation potential is parameterized according to elastic inclusion theory. Superposition of all the relevant interaction potentials provides a comprehensive description of the interaction energy landscape that would be experienced by a small mobile cluster along its migration path toward the plasma-exposed surface at high He fluence. Such descriptions are particularly important for developing atomistically-informed, hierarchical multi-scale models of helium cluster dynamics in plasma-facing materials.

36 MATERIALS SCIENCE↗

In-Situ Atomic-Scale Revelation of Amorphous Metallic Iron Formation during Hydrogen-Driven Reduction of Iron Oxides

The transition to hydrogen as a green reductant in metal production is critical for decarbonizing the metallurgical industry, yet atomic-scale mechanisms governing reduction pathways and phase evolution remain unresolved. Using in-situ environmental transmission electron microscopy, we identify a hidden pathway that reveals dynamic formation of amorphous metallic iron (Fe) during the hydrogen-driven reduction of ferrous oxides of Fe 3 O 4 and FeO. Real-time imaging uncovers three coexisting transformation routes: (i) Fe 3 O 4 → FeO, (ii) Fe 3 O 4 → amorphous Fe, and (iii) FeO → amorphous Fe. The resulting amorphous Fe exhibits fluid-like mobility, enabling its rapid aggregation and crystallization into core-shell nanostructures, with a crystalline core enveloped by an amorphous shell. Complementary ab initio molecular dynamics simulations trace the amorphous Fe formation to interfacial strain at the metal/oxide interfaces, where large lattice mismatches destabilize the metal lattice during initial metallization. This interplay between thermodynamics and kinetics governs phase evolution: thermodynamics favors a self-limiting amorphous Fe overlayer, while rapid oxide reduction kinetics drives amorphous overgrowth. Our findings demonstrate that amorphous intermediates bypass rate-limiting crystalline steps, providing mechanistic insights to optimize H 2 -based processes for sustainable steelmaking. In conclusion, these insights bridge the gap between macroscopic process engineering and atomic-scale dynamics, with broader implications for catalysis and nanostructured material synthesis, where oxide reduction pathways critically shape functional phases and microstructures.

36 MATERIALS SCIENCE↗

Diversifying Composition Leads to Hierarchical Composites with Design Flexibility and Structural Fidelity

Although significant progress has been made in the self-assembly of nanostructures, present successes heavily rely on precision in building block design, composition, and pair interactions. These requirements fundamentally limit our ability to synthesize macroscopic materials where the likelihood of impurity inclusion escalates and, more importantly, to access molecular-to-nanoscopic-to-microscopic-to-macroscopic hierarchies, since the types and compositions of building blocks vary at each stage. Inspired by biological blends and high-entropy alloys, we hypothesize that diversifying the blend’s composition can overcome these limitations. Increasing the number of components increases mixing entropy, leading to the dispersion of different components and, as a result, enhances interphase miscibility, weakens the dependence on specific pair interactions, and enables long-range cooperativity. This hypothesis is validated in complex blends containing small molecules, block copolymer-based supramolecules, and nanoparticles/colloidal particles. Hierarchically structured composites can be obtained with formulation flexibility in the filler selection and blend composition. It is worth noting that, by adding small molecules, we can solve the size constraint that plagues traditional block copolymer/nanoparticle blends. Detailed characterization and simulation further confirm that each component is distributed to locally mediate unfavorable interactions, cooperatively mitigate composition fluctuations, and retain structural fidelity. Furthermore, the blends have sufficient mobility to access tunable microstructures without compromising the order of the nanostructure. Besides establishing a kinetically viable pathway to release current constraints in the composite design and to navigate uncertainties during structure formation over multiple length scales, the present study demonstrates that entropy-driven behaviors can be realized in systems beyond high-entropy alloys despite inherent differences between metal alloys and organic/inorganic hybrids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

THz cyclotron resonance of a 2D hole gas in a GaN/AlN heterostructure

The recent discovery of highly conducting two-dimensional hole gases (2DHGs) in GaN/AlN heterojunctions has opened the door to efficient complementary GaN electronics, a long-standing challenge in wide-bandgap semiconductor device physics. Electrical transport studies and simulations indicate that both heavy- and light-hole valence bands are occupied in these 2DHGs, but direct experimental characterization of the fundamental parameters of the mobile holes remains at an early stage. Here, we use time-domain terahertz spectroscopy and pulsed magnetic fields up to 31 T to directly measure cyclotron resonance of the mobile 2D holes in these GaN-based 2DHGs at low temperature (8 K), revealing key material properties including effective masses, densities, scattering times, and mobilities.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Real-Twin

Real-Twin is a unified, model-agnostic scenario generation tool designed to streamline and standardize the evaluation of emerging mobility technologies. It provides an end-to-end framework that includes robust workflows, integrated tools, and comprehensive metrics to generate, calibrate, and benchmark microscopic traffic simulation scenarios across multiple platforms. Key Features of Real-Twin include: - Unified Scenario Generation: generate transferable, simulation-ready scenarios from heterogeneous data sources using a consistent workflow. - Automated Calibration Workflow: bridges simulation and real-world data, minimizing manual effort and making traffic simulation more accessible to researchers and engineers. - Model-Agnostic Compatibility: supports SUMO, VISSIM, and AIMSUN for cross-platform scenario generation and benchmarking. Enables reliable comparisons and reproducibility across different simulation tools. - Consistent Scenarios across Different Simulators: generate comparable simulation scenarios across different microscopic traffic simulators, providing users the ability to conduct benchmarking and cross-validation that are crucial for ensuring the reliability and reproducibility of simulation results. - Emerging Technology Support: includes a scenario database and pipeline for studying autonomous vehicles (AVs), with planned extensions to CAVs, EVs, and other advanced technologies.

Wang, Chieh (Ross) [Oak Ridge National Laboratory ↗

Intercomparison of Aerosol Instrumental Responses Using AEROTRAK, SMPS, and APS in a Simulated Building

In this work, three aerosol instruments were intercompared by using data collected from field campaigns in a simulated building environment during the last quarter of 2020 from October to December at Oak Ridge National Laboratory. The three aerosol instruments—AeroTrak Model 9110, Scanning Mobility Particle Spectrometer (SMPS) 3080L + 3025A, and Aerodynamic Particle Sizer (APS) 3320—were manufactured by TSI Inc. to perform in situ measurements of particle number concentration in the air. These instruments were co-located in one room in which an aerosol generator was used to produce a defined aerosol population for the instruments to sample and detect in each campaign. The SMPS measured aerosol particles with diameters from 0.01 to 0.7 µm, APS measured aerosol particles with diameters from 0.5 to 20 µm, and AeroTrak measured aerosol particles with diameters from 0.1 to 10 µm. The results suggest that although AeroTrak is fast and easy to use, it does not provide measurements comparable with those obtained by SMPS and APS. The differences in particle counts were orders of magnitude in size (i.e., the AeroTrak data were unreasonably small in the tested scenarios). The results clearly indicate that AeroTrak should not be used in ambient applications in which the level of particle concentration is expected to be high. This would cause difficulty to a campaign in which the dilution factor is unknow a priori. The high particle concentration could also lead to an erroneous aerosol size distribution (e.g., a bimodal size distribution was measured as opposed to a single-mode one). The number concentration limit that AeroTrak is expected to run reliably (i.e., with a counting coincidence error less than ±10%) is approximately three to four per cubic centimeter. This suggests that the instrument is best used in a clean room environment, not in an ambient or indoor application, such as the Flexible Research Platform campaigns.

47 OTHER INSTRUMENTATION↗

Benchmarking the PCMCI Causal Discovery Algorithm for Spatiotemporal Systems

Causal discovery algorithms construct hypothesized causal graphs that depict causal dependencies among variables in observational data. While powerful, the accuracy of these algorithms is highly sensitive to the underlying dynamics of the system in ways that have not been fully characterized in the literature. In this report, we benchmark the PCMCI causal discovery algorithm in its application to gridded spatiotemporal systems. Effectively computing grid-level causal graphs on large grids will enable analysis of the causal impacts of transient and mobile spatial phenomena in large systems, such as the Earth’s climate. We evaluate the performance of PCMCI with a set of structural causal models, using simulated spatial vector autoregressive processes in one- and two-dimensions. We develop computational and analytical tools for characterizing these processes and their associated causal graphs. Our findings suggest that direct application of PCMCI is not suitable for the analysis of dynamical spatiotemporal gridded systems, such as climatological data, without significant preprocessing and downscaling of the data. PCMCI requires unrealistic sample sizes to achieve acceptable performance on even modestly sized problems and suffers from a notable curse of dimensionality. This work suggests that, even under generous structural assumptions, significant additional algorithmic improvements are needed before causal discovery algorithms can be reliably applied to grid-level outputs of earth system models.

54 ENVIRONMENTAL SCIENCES↗

The mobility of small, over-pressurized helium bubbles in tungsten at 2000 K

Fusion reactor environments inevitably lead to the formation of high-pressure helium bubbles whose nucleation, growth, and diffusion strongly impact the performance of plasma-facing components. Here this research describes a diffusion mechanism of over-pressurized bubbles via a sequence of Frenkel pair nucleation, self-interstitial migration, and Frenkel pair annihilation. Molecular dynamics was used to simulate the diffusion of small bubbles in tungsten at 2000 K with helium-per-vacancy ratios in the range of 4.5 to 7. The diffusion coefficients are calculated and their dependence on helium content, number of vacancies, and number of attached self-interstitials is characterized. It is found that bubbles are most mobile when the nucleation/annihilation rates of Frenkel pairs are nearly equal and when the bubbles nucleate and annihilate a single self-interstitial. All bubbles experience a peak diffusivity, which can be as high as 10 -11 m 2 /s decreasing with bubble size. The calculated diffusion coefficients provide valuable insight into the mobility of small, high-pressure bubbles, and can be used as input parameters in mesoscale models to improve predictions of plasma-surface interactions. (LA-UR-21-21881)

36 MATERIALS SCIENCE↗

Initial Mobility Analysis for ORNL VA-EDH Synthetic Populations

Travel burdens are a major barrier to healthcare access among US Veteran patient populations, particularly those residing in rural areas. Spatial accessibility to points of care for US Veteran populations is commonly assessed in two ways. The first approach uses open data from the US Census to represent collective travel burdens, for example the distance between population-weighted census tract centroids and VHA points of care. The second approach uses restricted-access VHA patient data to measure travel costs (e.g., distance, time) for accessing points of care with respect to geolocated patient addresses and real or approximated transportation networks. While the advantage of the open data approach lies in its reproducibility, it has notable limitations in its tendency to infer individual travel behavior from aggregate population characteristics, a problem known as ecological fallacy. Conversely, while the patient data approach is able to account for individual travel behavior, its ability to account for localized access disparities (e.g., a neighborhood with exceptionally high transportation costs) and patient demographics is limited as protecting individual patient data requires their storage in closed systems with limited capacity for adequately modeling real-world travel patterns or for supplementing patient attributes. Additionally, the patient data approach cannot account for veterans who are not enrolled in the VHA system but who may be eligible for care. These challenges limit the ability to perform “what if” analyses on the effects of place-specific interventions on veteran populations with high access barriers to healthcare. To address these challenges, we explore the application of realistic synthetic populations to examine travel burdens and spatial accessibility issues among veteran patient populations. Synthetic populations provide a virtual, individually-resolved and cross-sectional representation of the veteran patient population that enables investigation of spatial access to points of care in ways in which aggregate data and patient data do not. First, synthetic populations allow one to directly assess how individuals access points of care, from synthesized residential locations to outpatient facilities on real-world transportation networks. Modeling access to points of care at the individual scale addresses the ecological fallacy problem associated with using aggregated census data to represent veteran populations and patterns of movement. Second, synthetic populations provide a means of completely representing an area’s veteran population using only publicly available, anonymized census microdata from the American Community Survey (ACS) to ensure the privacy of real-world individuals. Generating synthetic populations from the ACS also expands descriptive characteristics beyond what patient data typically offers to include socio-demographic, economic, housing, and mobility attributes. More detailed profiles of both VHA patient populations and veterans not enrolled in the VA system will provide a comprehensive picture of groups that may benefit from interventions or outreach. As an initial exercise for using synthetic populations to measure veteran travel burdens to VA care, we apply Oak Ridge National Laboratory’s (ORNL) UrbanPop capability to generate a series of synthetic VHA patient populations for 9 Veterans Integrated Services Networks (VISN) market areas in 9 Census Divisions across the continental United States, which are listed in Table 1. We use UrbanPop to produce synthetic populations for the VISN markets selected for each US Census Division, then assign VA outpatient clinic destinations to synthetic VHA patients based on travel about each VISN market’s road network. To demonstrate using the synthetic populations to evaluate healthcare travel burdens, we compare the time-based impedance between simulated home locations and VA outpatient clinics in each VISN market. We then perform validation exercises on the synthetic populations with respect to neighborhood (block group) demographic composition as well as patient mobility, comparing aggregate origin-destination statistics for the synthetic population to outpatient visits available in restricted patient data from the VA’s Corporate Data Warehouse (CDW) database.

97 MATHEMATICS AND COMPUTING↗

Zooming in on virtual commutes: Telecommuting impacts on mobility and sustainability

Motivated by a societal shift towards remote work and rapid advancement in information and communication technologies, this study examines the impact of telecommuting on urban mobility across the nine counties of the San Francisco Bay Area, California. Utilizing a behaviorally realistic integrated agent-based transportation model and recent data on telecommuting patterns, we simulate the impact of multiple telecommuting scenarios on transportation system outcomes. This provides a comprehensive picture of the impact of remote work on travel costs and accessibility of all travelers, factoring in changes in mode use and congestion. We analyze how telecommuting influences broader societal factors such as transportation energy consumption. Our findings indicate that increased telecommuting reduces overall person miles traveled and transportation energy consumption. Furthermore, telecommuting results in externality benefits by improving accessibility and reducing commute times for non-telecommuters.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Large-volume CdZnTe bar detectors characterized by laser-induced transient currents

In this work, we studied the free-carrier transport properties and space-charge formation/polarization in a CdZnTe bar-shaped radiation detector using the Laser-Induced Transient Current technique. We found out that a steady-state space charge ranging from 8 x 10 8 to 2.1 x 10 9 cm -3 is formed throughout the detector at about 0.5 s following biasing. The measured current waveforms were modeled by Monte Carlo simulations after taking into account the electric and weighting fields inside the detector and shielding box. Modeling of the unpolarized waveforms revealed an exceptionally high electron mobility-lifetime product μ e τ e ≥0.095cm 2 V -1 . The observed formation of positive space charge in the biased detector and linear scaling of the current waveform shapes on applied bias revealed that the detector polarization is attributed to carrier injection at the anode. In conclusion, measurements in pulsed and DC bias in modified electrode geometry proved the surface-charge formation.

47 OTHER INSTRUMENTATION↗

Combined Machine Learning and Molecular Dynamics Reveal Two States of Hydration of a Single Functional Group of Cationic Polymeric Brushes

The state of hydration of a macromolecular system regulates a plethora of different properties of such a system. In this article, we develop a novel machine learning (ML) approach, based on the unsupervised clustering algorithm, for probing the hydration behavior of the {N(CH 3 ) 3 } + functional group of the PMETAC [Poly(2-(methacryloyloxy)ethyl trimethylammonium chloride] polyelectrolyte (PE) brush system. The PE brushes and the brush-supported water molecules and counterions (chloride ions) are first described using all-atom molecular dynamics (MD) simulations. The simulation data is subsequently used in our ML framework to identify that (1) the {N(CH 3 ) 3 } + functional groups of the PMETAC brushes have two distinct hydration states with one state (state 1) being characterized by less structured water molecules and the other state (state 2) being characterized by more structured water molecules and (2) an enhancement in the brush grafting density leads to the progressive dissapparenace of state 2. An increase in the grafting density increases the number of chloride counterions in a given volume around the {N(CH 3 ) 3 } + functional group and increases the number of shared water molecules between the {N(CH 3 ) 3 } + and Cl - . The chloride counterions are associated with a hydration layer with much less structured water molecules. Therefore, with an increase in the grafting density, an increase in the percentage of shared water molecules leads to the prevalence of the hydration state [of the {N(CH 3 ) 3 } + moiety] with less structured water molecules. Finally, we explain how the present findings are commensurate with two key previous related results, namely a significantly large chloride ion mobility inside the PMETAC brush layer and the {N(CH 3 ) 3 } + -Cl - average distance remaining independent of the PMETAC brush grafting density. Furthermore, we anticipate that the combined ML-MD-simulation approach proposed in this study can be adapted to probe other soft matter systems to reveal new insights of the underlying mechanisms of emergent phenomenon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Addition of Chloroform in a Solvent-in-Salt Electrolyte: Outcomes in the Microscopic Dynamics in Bulk and Confinement

Solvent-in-salt electrolytes (SISEs) are a promising alternative to the electrolytes currently used in commercial devices. Despite the SISEs’ advantages, their utilization is not yet realized due to the poor mobility of their chemical species. Here, we explore this problem by adding chloroform to a SISE formed by acetonitrile and a Li-salt. First, we performed illustrative cycling experiments to highlight the potential of this approach. Then, we focused on the description of the microscopic dynamics of the electrolytes and exposed the relevant aspects to be considered for their optimal performance. While the conductivity at low temperatures may be enhanced by the addition of chloroform, only subtle changes occur at room temperature. As revealed by molecular dynamics simulations and quasielastic neutron scattering (QENS) experiments, this effect is related to the preservation of the structure expected for a highly concentrated solution and promotion of the formation of ionic aggregates. These outcomes occur despite the increase in the overall mobility of the chemical species. The dynamics of the electrolytes in porous carbon was also investigated using QENS. In these circumstances, low concentrations of chloroform lead to diffusivities of the molecular species higher than those observed for the bulk electrolytes. As chloroform’s concentration increases, no further changes in the diffusivities are observed. Nonetheless, chloroform is mostly immobilized on the carbon surfaces and this behavior may be intensified at compositions closer to the eutectic mixture.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Kinetics of solid–liquid interface motion in molecular dynamics and phase-field models: crystallization of chromium and silicon

The results of molecular dynamics (MD) simulations of the crystallization process in one-component materials and solid solution alloys reveal a complex temperature dependence of the velocity of the crystal–liquid interface featuring an increase up to a maximum at 10–30% undercooling below the equilibrium melting temperature followed by a gradual decrease of the velocity at deeper levels of undercooling. At the qualitative level, such non-monotonous behaviour of the crystallization front velocity is consistent with the diffusion-controlled crystallization process described by the Wilson–Frenkel model, where the almost linear increase of the interface velocity in the vicinity of melting temperature is defined by the growth of the thermodynamic driving force for the phase transformation, while the decrease in atomic mobility with further increase of the undercooling drives the velocity through the maximum and into a gradual decrease at lower temperatures. At the quantitative level, however, the diffusional model fails to describe the results of MD simulations in the whole range of temperatures with a single set of parameters for some of the model materials. The limited ability of the existing theoretical models to adequately describe the MD results is illustrated in the present work for two materials, chromium and silicon. It is also demonstrated that the MD results can be well described by the solution following from the hodograph equation, previously found from the kinetic phase-field model (kinetic PFM) in the sharp interface limit. The ability of the hodograph equation to describe the predictions of MD simulation in the whole range of temperatures is related to the introduction of slow (phase field) and fast (gradient flow) variables into the original kinetic PFM from which the hodograph equation is obtained. The slow phase-field variable is responsible for the description of data at small undercoolings and the fast gradient flow variable accounts for local non-equilibrium effects at high undercoolings. The introduction of these two types of variables makes the solution of the hodograph equation sufficiently flexible for a reliable description of all nonlinearities of the kinetic curves predicted in MD simulations of Cr and Si. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

Science & Technology - Other Topics↗