arXiv subjects

Peter W. Voorhees

Publications and source records attributed to Peter W. Voorhees.

17 recordsLinked to original sources

arXiv2026

Crystallizing Substrates Drag Supported Nanoparticles

When a solid support undergoes crystallization, the advancing amorphous-to-crystalline transformation front separates regions of distinct surface energy, creating a moving interfacial energy boundary. A supported nanoparticle straddling such a boundary experiences an asymmetric particle-substrate interfacial energy environment that constitutes a lateral thermodynamic driving force for migration. Here, using in situ transmission electron microscopy to track Pt nanoparticle motion statistically, paired with time-resolved diffraction and 4D-STEM analysis to characterize support crystallization, we demonstrate that propagating crystallization fronts in amorphous AlO$_x$ thin films actively drag supported Pt nanoparticles over long distances. Temporal correlation between the onsets of support crystallization and rapid particle migration, together with 4D-STEM virtual crystallinity maps, establishes that the front drives particle motion. Phase-field simulations confirm that particle-substrate interfacial energy contrast alone sustains particle drag, and identify curvature gradients along the particle surface as the mechanism by which the advancing front redistributes mass and displaces the particle. These results establish a general mechanism by which any propagating surface-energy boundary on a substrate can act as a deterministic driver of supported nanoparticle transport.

cond-mat.mtrl-sci↗

arXiv2026

A phase field model with arbitrary misorientation dependence of grain boundary energy

Grain growth in polycrystals is often simulated using orientation-field models, which employ a field to represent the local orientation of the crystal lattice. These models can be challenging to represent a realistic misorientation dependence of grain boundary free energy. We prove that existing orientation-field models, in general, cannot reproduce a decrease in the grain boundary free energy with a increasing misorientation angle, demonstrating a significant limitation of previous models in applications to polycrystalline materials. To overcome this limitation, we propose a modification to the Kobayashi-Warren-Carter model for grain growth wherein the coefficients of the free-energy functional become functions of the misorientation between the grains, which is a non-local quantity. Due to this modification, an arbitrary dependence of the grain boundary free energy on the misorientation can be embedded in the model. We propose calculating the non-local misorientation by interpolating the orientation field at a fixed distance in both directions along the local grain boundary normal vector. The capabilities of the model are demonstrated by introduction of a sharp cusp to the misorientation dependent grain boundary free energy. Finally, we propose an extension of the model to three dimensions.

cond-mat.mtrl-sci↗

arXiv2026

Morphological Stability of Metal Anodes: Roles of Solid Electrolyte Interphases (SEIs) and Desolvation Kinetics

Achieving stable lithium metal anodes requires control over the solid-electrolyte interphase (SEI) and desolvation kinetics. Here, we develop a unified theoretical framework integrating ion transport, desolvation, charge transfer, and SEI breakdown to predict morphological instabilities during electrodeposition. Using linear stability analysis, we identify six dimensionless parameters that govern the onset and evolution of instabilities. We show that SEI transport and desolvation rate effectively modulate apparent reaction kinetics, shifting the system toward a stable, reaction-limited regime. Extending the classical limiting current concept, we demonstrate that a thick, poorly conductive SEI and sluggish desolvation significantly reduce the limiting current. We introduce an apparent Damköhler number to quantify the critical balance: suppressing diffusion-limited instabilities by reaction rate reduction, while maintaining a high limiting current. Our theory enables predictive mapping of electrodeposition morphologies across diverse materials and operating conditions, guiding the rational design of stable lithium metal anodes.

cond-mat.mtrl-sci↗

arXiv2025

Interfacial Energy Gradients Drive Coalescence of Supported Nanoparticles

Understanding and controlling nanoparticle coalescence is crucial for applications ranging from catalysis to nanodevice fabrication, yet the behavior of nanoparticles on dynamically evolving, heterogeneous substrates remains poorly understood. Here, we employ in situ transmission electron microscopy to investigate platinum (Pt) nanoparticle dynamics on silicon nitride (SiN$_x$) substrates where localized crystalline silicon (Si) nanodomains are deliberately formed via electron beam irradiation at $800^\circ$C. We observe that Pt nanoparticles in contact with these Si pads transform into a more mobile platinum silicide (Pt$_3$Si) phase. Strikingly, these Pt$_3$Si nanoparticles exhibit pronounced directional migration away from the Si pads, driven by interfacial energy gradients, rather than undergoing stochastic Brownian motion. This directed movement fundamentally dictates coalescence pathways, leading to either enhanced sintering when particles are channeled together or inhibited coalescence when Si pads act as repulsive barriers. Our findings reveal that local substrate chemistry and the resulting interfacial energy landscapes can dominate over initial particle size or proximity in controlling solid-state nanoparticle migration and assembly. This work provides insights into how substrate heterogeneity can be used to direct nanoparticle behavior, challenging conventional coalescence models and offering pathways for the rational design of supported nanomaterials.

cond-mat.mtrl-sci↗

arXiv2025

Nonequilibrium thermodynamic foundation of the grand-potential phase field model

Choosing the correct free energy functional is critical when developing thermodynamically consistent phase field models. We show that the grand-potential phase field model minimizes the Helmholtz free energy when mass conservation is imposed. While both functionals are at a minimum at equilibrium, the Helmholtz free energy decreases monotonically with time in the grand-potential phase field model, whereas the grand potential does not. Minimizing the grand potential implies a different problem where a system can exchange mass with its surroundings at every point, leading to a condition of isochemical potential and invalidating mass conservation of the system.

cond-mat.stat-mech↗

arXiv2024

Morphological stability of electrostrictive thin films

A large electric field is typically present in anodic or passive oxide films. Stresses induced by such a large electric field are critical in understanding the breakdown mechanism of thin oxide films and improving their corrosion resistance. In this work, we consider electromechanical coupling through the electrostrictive effect. A continuum model incorporating lattice misfit and electric field-induced stresses is developed. We perform a linear stability analysis of the full coupled model and show that, for typical oxides, neglecting electrostriction underestimates the film's instability, especially in systems with a large electric field. Moreover, a region where electrostriction can potentially provide a stabilizing effect is identified, allowing electrostriction to enhance corrosion resistance. We identified an equilibrium electric field intrinsic to the system and the corresponding equilibrium film thickness. The film's stability is very sensitive to the electric field: a 40 percent deviation from the equilibrium electric field can change the maximum growth rate by nearly an order of magnitude. Moreover, our model reduces to classical morphological instability models in the limit of misfit-only, electrostatic-only, and no-electrostriction cases. Finally, the effect of various parameters on the film's stability is studied.

cond-mat.mtrl-sci↗

arXiv2023

Quantitative Phase Field Model for Electrochemical Systems

Modeling microstructure evolution in electrochemical systems is vital for understanding the mechanism of various electrochemical processes. In this work, we propose a general phase field framework that is fully variational and thus guarantees that the energy decreases upon evolution in an isothermal system. The bulk and interface free energies are decoupled using a grand potential formulation to enhance numerical efficiency. The variational definition of the overpotential is used, and the reaction kinetics is incorporated into the evolution equation for the phase field to correctly capture capillary effects and eliminate additional model parameter calibrations. A higher-order kinetic correction is derived to accurately reproduce general reaction models such as the Butler-Volmer, Marcus, and Marcus-Hush-Chidsey models. Electrostatic potentials in the electrode and the electrolyte are considered separately as independent variables, providing additional freedom to capture the interfacial potential jump. To handle realistic materials and processing parameters for practical applications, a driving force extension method is used to enhance the grid size by three orders of magnitude. Finally, we comprehensively verify our phase field model using classical electrochemical theory.

cond-mat.mtrl-sci↗

arXiv2023

A quantitative variational phase field framework

The finite solid-liquid interface width in phase field models results in non-equilibrium effects, including solute trapping. Prior phase field modeling has shown that this extra degree of freedom, when compared to sharp-interface models, results in solute trapping that is well captured when realistic parameters, such as interface width, are employed. However, increasing the interface width, which is desirable for computational reasons, leads to artificially enhanced trapping thus making it difficult to model departure from equilibrium quantitatively. In the present work, we develop a variational phase field model with independent kinetic equations for the solid and liquid phases. Separate kinetic equations for the phase concentrations obviate the assumption of point wise equality of diffusion potentials, as is done in previous works. Non-equilibrium effects such as solute trapping, drag and interface kinetics can be introduced in a controlled manner in the present model. In addition, the model parameters can be tuned to obtain ``experimentally-relevant" trapping while using significantly larger interface widths than prior efforts. A comparison with these other phase field models suggests that interface width of about three to twenty-five times larger than current best-in-class models can be employed depending upon the material system at hand leading to a speed-up by a factor of $W^{(d+2)}$, where $W$ and $d$ denote the interface width and spatial dimension, respectively. Finally the capacity to model non-equilibrium phenomena is demonstrated by simulating oscillatory instability leading to the formation of solute bands.

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↗

arXiv2019

Phase Field Benchmark Problems for Dendritic Growth and Linear Elasticity

We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from other members in the phase field community. As the integrated computational materials engineering (ICME) approach to materials design has gained traction, there is an increasing need for quantitative phase field results. New algorithms and numerical implementations increase computational capabilities, necessitating standard problems to evaluate their impact on simulated microstructure evolution as well as their computational performance. We propose one benchmark problem for solidification and dendritic growth in a single-component system, and one problem for linear elasticity via the shape evolution of an elastically constrained precipitate. We demonstrate the utility and sensitivity of the benchmark problems by comparing the results of 1) dendritic growth simulations performed with different time integrators and 2) elastically constrained precipitate simulations with different precipitate sizes, initial conditions, and elastic moduli. These numerical benchmark problems will provide a consistent basis for evaluating different algorithms, both existing and those to be developed in the future, for accuracy and computational efficiency when applied to simulate physics often incorporated in phase field models.

cond-mat.mtrl-sci↗

arXiv2018

Self-consistent modeling of anisotropic interfaces and missing orientations: Derivation from phase-field crystal

Highly anisotropic interfaces play an important role in the development of material microstructure. Using the diffusive atomistic phase-field crystal (PFC) formalism, we determine the capability of the model to quantitatively describe these interfaces. Specifically, we coarse grain the PFC model to attain both its complex amplitude formulation and its corresponding phase-field limit. Using this latter formulation, in one-dimensional calculations, we determine the surface energy and the properties of the Wulff shape. We find that the model can yield Wulff shapes with missing orientations, the transition to missing orientations, and facet formation. We show that the corresponding phase-field limit of the complex amplitude model yields a self-consistent description of highly anisotropic surface properties that are a function of the surface orientation with respect to the underlying crystal lattice. The phase-field model is also capable of describing missing orientations on equilibrium shapes of crystals and naturally includes a regularizing contribution. We demonstrate, in two dimensions, how the resultant model can be used to study growth of crystals with varying degrees of anisotropy in the phase-field limit.

cond-mat.mtrl-sci↗

arXiv2018

Non-equilibrium Solute Capture in Passivating Oxide Films

If all humans vanished tomorrow, almost every metal structure would collapse within a century or less, the metal converting to an oxide. In applications ranging from the mature technology of nuts and bolts to high technology batteries, nuclear fuels and turbine engines, protective oxide films are critical to limiting oxidation. To date models of these oxide films have assumed that they form thermodynamic equilibrium stable or metastable phases doped within thermodynamic solubility limits. Here we demonstrate experimentally and theoretically the formation of unusual non-equilibrium oxide phases, that can be predicted using a scientific framework for solute capture at a moving oxide/substrate interface. The theory shows that solute capture is likely a generic process for many electrochemical processes, and suggests that similar phenomena yielding non-equilibrium phases can occur and be predicted for a wide range of other processes involving solid-fluid and solid-solid chemical reactions.

cond-mat.mtrl-sci↗

arXiv2017

Predicting the morphologies of γ' precipitates in cobalt-based superalloys

Cobalt-based alloys with γ/γ' microstructures have the potential to become the next generation of superalloys, but alloy compositions and processing steps must be optimized to improve coarsening, creep, and rafting behavior. While these behaviors are different than in nickel-based superalloys, alloy development can be accelerated by understanding the thermodynamic factors influencing microstructure evolution. In this work, we develop a phase field model informed by first-principles density functional theory and experimental data to predict the equilibrium shapes of Co-Al-W γ' precipitates. Three-dimensional simulations of single and multiple precipitates are performed to understand the effect of elastic and interfacial energy on coarsened and rafted microstructures; the elastic energy is dependent on the elastic stiffnesses, misfit strain, precipitate size, applied stress, and precipitate spatial distribution. We observe characteristic microstructures dependent on the type of applied stress that have the same γ' morphology and orientation seen in experiments, indicating that the elastic stresses arising from coherent γ/γ' interfaces are important for morphological evolution during creep. The results also indicate that the narrow γ channels between γ' precipitates are energetically favored, and provide an explanation for the experimentally observed directional coarsening that occurs without any applied stress.

cond-mat.mtrl-sci↗

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↗

arXiv2016

Phase-field crystal model for ordered crystals

We describe a general method to model multicomponent ordered crystals using the phase-field crystal (PFC) formalism. As a test case, a generic B2 compound is investigated. We are able to produce a line of either first-order or second-order order-disorder phase transitions, features that have not been incorporated in existing PFC approaches. Further, it is found that the only elastic constant for B2 that depends on ordering is $C_{11}$. This B2 model was then used to study antiphase boundaries (APBs). The APBs were shown to reproduce classical mean field results. Dynamical simulations of ordering across small-angle grain boundaries predict that dislocation cores pin the evolution of APBs.

cond-mat.mtrl-sci↗

arXiv2013

Phase-Field Crystal Model with a Vapor Phase

Phase-Field Crystal (PFC) models are able to resolve atomic length scale features of materials during temporal evolution over diffusive time scales. Traditional PFC models contain solid and liquid phases, however many important materials processing phenomena involve a vapor phase as well. In this work, we add a vapor phase to an existing PFC model and show realistic interfacial phenomena near the triple point temperature. For example, the PFC model exhibits density oscillations at liquid-vapor interfaces that compare favorably to data available for interfaces in metallic systems from both experiment and molecular dynamics simulations. We also quantify the anisotropic solid-vapor surface energy for a 2D PFC hexagonal crystal and find well defined step energies from measurements on the faceted interfaces. Additionally, the strain field beneath a stepped interface is characterized and shown to qualitatively reproduce predictions from continuum models, simulations, and experimental data. Finally, we examine the dynamic case of step-flow growth of a crystal into a supersaturated vapor phase. The ability to model such a wide range of surface and bulk defects makes this PFC model a useful tool to study processing techniques such as Chemical Vapor Deposition or Vapor-Liquid-Solid growth of nanowires.

cond-mat.mtrl-sci↗