arXiv subjects

Katsuyo Thornton

Publications and source records attributed to Katsuyo Thornton.

12 recordsLinked to original sources

arXiv2026

Origin of the reaction temperature in solid-state materials synthesis

Temperature plays a crucial role in solid-state materials synthesis, but there is currently no mechanistic theory to explain or predict which temperature is best to conduct a solid-state reaction. Reactions between powder precursors are conventionally assumed to be slow diffusion-limited processes; however, recent in situ experiments show that solid-state reactions can complete in minutes above a critical onset temperature. Here, we present evidence that a transient liquid phase forms above the metastable eutectic temperature, and that this non-equilibrium liquid serves as a fast diffusion medium to intermix precursors and initiate a solid-state reaction. This thermodynamic principle is agnostic to the structure or chemistry of the reactants, and can be applied towards the synthesis and manufacturing of a wide range of complex materials.

cond-mat.mtrl-sci↗

arXiv2026

Benchmarking of Massively Parallel Phase-Field Codes for Directional Solidification

We present a detailed benchmark comparing two state-of-the-art phase-field implementations for simulating alloy solidification under experimentally relevant conditions. The study investigates the directional solidification of Al-3wt%Cu under high-velocity solidification conditions and SCN-0.46wt% camphor under microgravity conditions from National Aeronautics and Space Administration (NASA) DECLIC-DSI-R experiments. Both codes, one employing finite-difference discretization with uniform mesh and GPU-acceleration (GPU-PF) and the other one employing finite-element discretization with adaptive-mesh and CPU-parallelization (PRISMS-PF), solve the same quantitative phase-field formulation that incorporates an anti-trapping current for the solidification of dilute alloys. We evaluate the predictions of each code for dendritic morphology, primary spacing, and tip dynamics in both 2D and 3D, as well as their numerical convergence and computational performance. While existing benchmark problems have primarily focused on simplified or small-scale simulations, they do not reflect the computational and modeling challenges posed by employing experimentally relevant time and length scales. Our results provide a practical framework for assessing phase-field code performance as well as validating and facilitating their application in integrated computational materials engineering (ICME) workflows that require integration with realistic experimental data.

cond-mat.mtrl-sci↗

arXiv2026

Phase-field simulations of nucleation, growth, and coarsening of $β_1$ precipitates in Mg-Nd alloys

The spatial distribution and morphology of precipitates formed during aging are key factors that determine the precipitation hardening response of various magnesium-rare earth alloys. In recent years, the use of high-performance computing clusters and massively parallel frameworks has enabled quantitative simulations of the evolution of individual and multiple precipitates at relevant length and time scales. However, predictive modeling of precipitate evolution remains challenging, in part because many key thermodynamic and kinetic parameters governing the underlying physics are either unknown or have a high degree of uncertainty. In this work, we developed a workflow in which experimental data were used to parameterize a phase-field model to perform two-dimensional (2D) simulations of concurrent nucleation and evolution of $β_1$ precipitates in magnesium-neodymium alloy during aging. Matrix composition and precipitate number density at different aging times were obtained from atom probe tomography and transmission electron microscopy measurements, respectively. We applied a stereological method to estimate the three-dimensional (3D) number densities from experimental cross-sectional transmission electron micrographs. The estimated 3D number density data were then converted to effective 2D number densities. The effective 2D number density and composition data were used to determine the required model parameters by minimizing the discrepancy between simulation and experimental results. The parameterized model allows for quantitative phase-field simulations of nucleation and growth of $β_1$ precipitates, which can be employed to optimize aging time to achieve a target number density of precipitates. This work highlights an approach to overcome the challenges associated with parameterizing a coupled phase-field and nucleation model.

cond-mat.mtrl-sci↗

arXiv2026

Understanding the kinetics of static recrystallization in Mg-Zn-Ca alloys using an integrated PRISMS simulation framework

Recrystallization is a phenomenon in which a plastically deformed polycrystalline microstructure with a high dislocation density transforms into another that has low dislocation density. This evolution is driven by the stored energy in dislocations, rather than grain growth driven by grain boundary energy alone. One difficulty in quantitative modeling of recrystallization is the uncertainty in material parameters, which can be addressed by integration of experimental data into simulations. In this work, we compare simulated static recrystallization dynamics of a Mg-3Zn-0.1Ca wt.% alloy to experiments involving thermomechanical processing followed by measurements of the recrystallization fraction over time. The simulations are performed by combining PRISMS software for crystal plasticity and phase-field models (PRISMS-Plasticity and PRISMS-PF, respectively) in an integrated computational materials engineering framework. At 20% strain and annealing at 350 °C, the model accurately describes recrystallization dynamics up to a mobility-dependent time scale factor. While the average grain boundary mobility and the fraction of plastic work converted into stored energy are not precisely known, by fitting simulations to experimental data, we show that the average grain boundary mobility can be determined if the fraction of plastic work converted to stored energy is known, or vice versa. For low annealing temperatures, we observe a discrepancy between the model and experiments in the late stages of recrystallization, where a slowdown in recrystallization kinetics occurs in the experiments. We discuss possible sources of this slowdown and propose additional physical mechanisms that need to be accounted for in the model to improve its predictions.

cond-mat.mtrl-sci↗

arXiv2022

Simulation of coarsening in two-phase systems with dissimilar mobilities

In this work, we apply phase field simulations to examine the coarsening behavior of morphologically complex two-phase microstructures in which the phases have highly dissimilar mobilities, a condition approaching that found in experimental solid-liquid systems. Specifically, we consider a two-phase system at the critical composition ($50\%$ volume fraction) in which the mobilities of the two phases differ by a factor of 100. This system is simulated in two and three dimensions using the Cahn-Hilliard model with a concentration-dependent mobility, and results are compared to simulations with a constant mobility. A morphological transition occurs during coarsening of the two-dimensional system (corresponding to a thin film geometry) with dissimilar mobilities, resulting in a system of nearly-circular particles of high-mobility phase embedded in a low-mobility matrix. This morphological transition causes the coarsening rate constant to decrease over time, which explains why a previous study found lack of agreement with the theoretical $t^{1/3}$ power law. Three-dimensional systems with dissimilar mobilities resulted in bicontinuous microstructures that evolve self-similarly, as determined by quantitative analysis of the interfacial shape distribution. Coarsening kinetics in three dimensions agreed closely with the $t^{1/3}$ power law after the initial transient stage. A model is derived to explain a nearly-linear relationship between the coarsening rate constant and the variance of scaled mean curvature that is observed during this transient stage.

cond-mat.mtrl-sci↗

arXiv2020

Effect of Transport Mechanism on the Coarsening of Bicontinuous Structures: A Comparison between Bulk and Surface Diffusion

Coarsening of bicontinuous microstructures is observed in a variety of systems, such as nanoporous metals and mixtures that have undergone spinodal decomposition. To better understand the morphological evolution of these structures during coarsening, we compare the morphologies resulting from two different coarsening mechanisms, surface and bulk diffusion. We perform phase-field simulations of coarsening via each mechanism in a two-phase mixture at nominal volume fractions of 50%-50% and 36%-64%, and the simulated structures are characterized in terms of topology (genus density), the interfacial shape distribution, structure factor, and autocorrelations of phase and mean curvature. We observe self-similar evolution of morphology and topology and agreement with the expected power laws for dynamic scaling, in which the characteristic length scale increases over time proportionally to $t^{1/4}$ for surface diffusion and $t^{1/3}$ for bulk diffusion. While we observe the expected difference in the coarsening kinetics, we find that differences in self-similar morphology due to coarsening mechanism are relatively small, although typically they are larger at 36% volume fraction than at 50% volume fraction. In particular, we find that bicontinuous structures coarsened via surface diffusion have lower scaled genus densities than structures coarsened via bulk diffusion. We also compare the self-similar morphologies to those in literature and to two model bicontinuous structures, namely, constant-mean-curvature surfaces based on the Schoen G minimal surface and random leveled-wave structures. The average scaled mean curvatures of these model structures agree reasonably with those of the coarsened structures at both 36% and 50%, but we find substantial disagreements in the scaled genus densities and the standard deviations of mean curvature.

cond-mat.soft↗

arXiv2017

Simulating complex crystal structures using the phase-field crystal model

We introduce a phase-field crystal model that creates an array of complex three- and two-dimensional crystal structures via a numerically tractable three-point correlation function. The three-point correlation function is designed in order to energetically favor the principal interplanar angles of a target crystal structure. This is achieved via an analysis performed by examining the crystal's structure factor. This approach successfully yields energetically stable simple cubic, diamond cubic, simple hexagonal, graphene layers, and CaF$_2$ crystals. To illustrate the ability of the method to yield a particularly complex and technologically important crystal structure, we show how this three-point correlation function method can be used to generate perovskite crystals.

cond-mat.mtrl-sci↗

arXiv2015

Thermodynamic Relationships for Bulk Crystalline and Liquid Phases in the Phase-Field Crystal Model

We present thermodynamic relationships between the free energy of the phase-field crystal (PFC) model and thermodynamic state variables for bulk phases under hydrostatic pressure. This relationship is derived based on the thermodynamic formalism for crystalline solids of Larché and Cahn [Larché and Cahn, Acta Metallurgica, Vol. 21, 1051 (1973)]. We apply the relationship to examine the thermodynamic processes associated with varying the input parameters of the PFC model: temperature, lattice spacing, and the average value of the PFC order parameter, $\bar{n}$. The equilibrium conditions between bulk crystalline solid and liquid phases are imposed on the thermodynamic relationships for the PFC model to obtain a procedure for determining solid-liquid phase coexistence. The resulting procedure is found to be in agreement with the method commonly used in the PFC community, justifying the use of the common-tangent construction to determine solid-liquid phase coexistence in the PFC model. Finally, we apply the procedure to an eighth-order-fit (EOF) PFC model that has been parameterized to body-centered-cubic ($bcc$) Fe [Jaatinen et al., Physical Review E 80, 031602 (2009)] to demonstrate the procedure as well as to develop physical intuition about the PFC input parameters. We demonstrate that the EOF-PFC model parameterization does not predict stable $bcc$ structures with positive vacancy densities. This result suggests an alternative parameterization of the PFC model, which requires the primary peak position of the two-body direct correlation function to shift as a function of $\bar{n}$.

cond-mat.mtrl-sci↗

arXiv2013

Particle-Level Modeling of the Charge-Discharge Behavior of Nanoparticulate Phase-Separating Li-Ion Battery Electrodes

In nanoparticulate phase-separating electrodes, phase separation inside the particles can be hindered during their charge/discharge cycles even when a thermodynamic driving force for phase separation exists. In such cases, particles may (de)lithiate discretely in a process referred to as mosaic instability. This instability could be the key to elucidating the complex charge/discharge dynamics in nanoparticulate phase-separating electrodes. In this paper, the dynamics of the mosaic instability is studied using Smoothed Boundary Method simulations at the particle level, where the concentration and electrostatic potential fields are spatially resolved around individual particles. Two sets of configurations consisting of spherical particles with an identical radius are employed to study the instability in detail. The effect of an activity-dependent exchange current density on the mosaic instability, which leads to asymmetric charge/discharge, is also studied. While we show that our model reproduces the results of a porous-electrode model for the simple setup studied here, it is a powerful framework with the capability to predict the detailed dynamics in three-dimensional complex electrodes and provides further insights into the complex dynamics that result from the coupling of electrochemistry, thermodynamics, and transport kinetics.

cond-mat.mtrl-sci↗

arXiv2012

Ni coarsening in the three-phase solid oxide fuel cell anode - a phase-field simulation study

Ni coarsening in Ni-yttria stabilized zirconia (YSZ) solid oxide fuel cell anodes is considered a major reason for anode degradation. We present a predictive, quantative modeling framework based on the phase-field approach to systematically examine coarsening kinetics in such anodes. The initial structures for simulations are experimentally acquired functional layers of anodes. Sample size effects and error analysis of contact angles are examined. Three phase boundary (TPB) lengths and Ni surface areas are quantatively identified on the basis of the active, dead-end, and isolated phase clusters throughout coarsening. Tortuosity evolution of the pores is also investigated. We find that phase clusters with larger characteristic length evolve slower than those with smaller length scales. As a result, coarsening has small positive effects on transport, and impacts less on the active Ni surface area than the total counter part. TPBs, however, are found to be sensitive to local morphological features and are only indirectly correlated to the evolution kinetics of the Ni phase.

physics.comp-ph↗

arXiv2004

Diffuse-Charge Dynamics in Electrochemical Systems

The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate, blocking electrodes which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The ``weakly nonlinear'' limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter $ε= λ_D/L$, where $λ_D$ is the screening length and $L$ the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of $λ_D L / D$ (not $λ_D^2/D$), where $D$ is the ionic diffusivity, but nonlinearity violates this common picture and introduce multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, $L^2/D$. In the ``strongly nonlinear'' regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multi-component electrolytes, and Faradaic processes.

cond-mat.soft↗

arXiv1997

Energy Input and Mass Redistribution by Supernovae in the Interstellar Medium

We present the results of numerical studies of supernova remnant evolution and their effects on galactic and globular cluster evolution. We show that parameters such as the density and the metallicity of the environment significantly influence the evolution of the remnant, and thus change its effects on the global environment (e.g., globular clusters, galaxies) as a source of thermal and kinetic energy. We conducted our studies using a one-dimensional hydrodynamics code, in which we implemented a metallicity dependent cooling function. Global time-dependent quantities such as the total kinetic and thermal energies and the radial extent are calculated for a grid of parameter sets. The quantities calculated are the total energy, the kinetic energy, the thermal energy, the radial extent, and the mass. We distinguished between the hot, rarefied bubble and the cold, dense shell, as those two phases are distinct in their roles in a gas-stellar system. We also present power-law fits to those quantities as a function of environmental parameters after the extensive cooling has ceased. The power-law fits enable simple incorporation of improved supernova energy input and matter redistribution (including the effect of the local conditions) in galactic/globular cluster models. Our results for the energetics of supernova remnants in the late stages of their expansion give total energies ranging from 9e49 to 3e50 ergs, with a typical case being 1e50 erg, depending on the surrounding environment. About 8.5e49 erg of this energy can be found in the form of kinetic energy. Supernovae play an important role in the evolution of the interstellar medium

astro-ph↗