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James A. Warren

Publications and source records attributed to James A. Warren.

At least 19 recordsLinked to original sources
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↗
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↗
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↗
arXiv2019

Phase-field modeling of crystal nucleation in undercooled liquids -- A review

We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the conventional phase-field approaches that rely on spatially averaged (coarse grained) order parameters in capturing freezing, and by the recently developed phase-field crystal models that work on the molecular scale, while employing time averaged particle densities, and are regarded as simple dynamical density functional theories of classical particles. Besides simpler cases of homogeneous and heterogeneous nucleation, phenomena addressed by these techniques include precursor assisted nucleation, nucleation in eutectic and phase separating systems, phase selection via competing nucleation processes, growth front nucleation (a process, in which grains of new orientations form at the solidification front) yielding crystal sheaves and spherulites, and transition between the growth controlled cellular and the nucleation dominated equiaxial solidification morphologies.

cond-mat.mtrl-sci↗
arXiv2019

On topological defects in two-dimensional orientation-field models for grain growth

Standard two-dimensional orientation-field based phase-field models rely on a continuous scalar field to represent crystallographic orientation. The corresponding order parameter space is the unit circle, which is not simply-connected. This topological property has important consequences for the resulting multi-grain structures: (i) trijunctions may be singular; (ii) for each pair of grains, there exist two different grain boundary solutions that cannot continuously transform to one another; (iii) if both solutions appear along a grain boundary, a topologically stable, singular point defect must exist between them. While (i) can, (ii) and therefore (iii) cannot be interpreted in the classical picture of grain boundaries. In addition, singularities cause difficulties, such as lattice pinning in numerical simulations. To overcome these problems, we propose two new formulations of the model. The first is based on a 3-component unit vector field, while in the second we utilise a 2-component vector field with an additional potential. In both cases, the additional degree of freedom introduced make the order parameter space simply-connected, which removes the topological stability of these defects.

cond-mat.mtrl-sci↗
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↗
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↗
arXiv2010

Modeling Reactive Wetting when Inertial Effects are Dominant

Recent experimental studies of molten metal droplets wetting high temperature reactive substrates have established that the majority of triple-line motion occurs when inertial effects are dominant. In light of these studies, this paper investigates wetting and spreading on reactive substrates when inertial effects are dominant using a thermodynamically derived, diffuse interface model of a binary, three-phase material. The liquid-vapor transition is modeled using a van der Waals diffuse interface approach, while the solid-fluid transition is modeled using a phase field approach. The results from the simulations demonstrate an $O \left( t^{-\nicefrac{1}{2}} \right)$ spreading rate during the inertial regime and oscillations in the triple-line position when the metal droplet transitions from inertial to diffusive spreading. It is found that the spreading extent is reduced by enhancing dissolution by manipulating the initial liquid composition. The results from the model exhibit good qualitative and quantitative agreement with a number of recent experimental studies of high-temperature droplet spreading, particularly experiments of copper droplets spreading on silicon substrates. Analysis of the numerical data from the model suggests that the extent and rate of spreading is regulated by the spreading coefficient calculated from a force balance based on a plausible definition of the instantaneous interface energies. A number of contemporary publications have discussed the likely dissipation mechanism in spreading droplets. Thus, we examine the dissipation mechanism using the entropy-production field and determine that dissipation primarily occurs in the locality of the triple-line region during the inertial stage, but extends along the solid-liquid interface region during the diffusive stage.

cond-mat.mtrl-sci↗
arXiv2008

Grain Boundary Motion Exhibits the Dynamics of Glass-Forming Liquids

Polycrystalline materials can be viewed as composites of crystalline particles or grains separated from one another by thin amorphous grain boundary (GB) regions. While GB have been exhaustively investigated at low temperatures, where these regions resolve into complex ordered structures accessible to measurement, much less is known about them at higher temperatures where the GB can exhibit significant mobility, structural disorder, and where experimental characterization methods are limited. The time and spatial scales accessible to molecular dynamics (MD) simulation make this method appropriate for investigating both the dynamical and structural properties of grain boundaries at elevated temperatures. In the present study, we use MD simulations to determine how the GB dynamics changes with temperature and applied stress. It has long been hypothesized that GB have features in common with glass-forming liquids based on the processing characteristics of polycrystalline materials. We find remarkable support for this suggestion, as evidenced by string-like collective motion, transient caging of atom motion, and non-Arrhenius (Vogel-Fulcher) temperature dependence of GB mobility. Evidently, the frustration caused by the inability of atoms in GB region to simultaneously order with respect to competing grains is responsible for this striking similarity. The paradigm that grains in a polycrystalline material are encapsulated by a frustrated fluid provides a powerful conceptual model of polycrystalline materials, pointing the way to improved control over their material properties.

cond-mat.mtrl-sci↗
arXiv2006

An Efficient Algorithm for Solving the Phase Field Crystal Model

We present and discuss the development of an unconditionally stable algorithm used to solve the evolution equations of the Phase Field Crystal (PFC) model. This algorithm allows for an arbitrarily large algorithmic time step. As the basis for our analysis of the accuracy of this algorithm, we determine an effective time step in Fourier space. We then compare our calculations with a set of representative numerical results, and demonstrate that this algorithm is an effective approach for the study of the PFC models, yielding a time step effectively 180 times larger than the Euler algorithm for a representative set of material parameters. As the PFC model is just a simple example of a wide class of density functional theories, we expect this method will have wide applicability to modeling systems of considerable interest to the materials modeling communities.

physics.comp-ph↗
arXiv2006

Controlling the accuracy of unconditionally stable algorithms in Cahn-Hilliard Equation

Given an unconditionally stable algorithm for solving the Cahn-Hilliard equation, we present a general calculation for an analytic time step $\d τ$ in terms of an algorithmic time step $\dt$. By studying the accumulative multi-step error in Fourier space and controlling the error with arbitrary accuracy, we determine an improved driving scheme $\dt=At^{2/3}$ and confirm the numerical results observed in a previous study \cite{Cheng1}.

cond-mat.mtrl-sci↗
arXiv2006

Phase Field Theory of Heterogeneous Crystal Nucleation

A phase eld approach is developed to model wetting and heterogeneous crystal nucleation of an undercooled pure liquid in contact with a sharp wall. We discuss various choices for the boundary condition at the wall and determine the properties of critical nuclei, including their free energy of formation and the contact angle as a function of undercooling. We nd for particular choices of boundary conditions, we may realize either an analog of the classical spherical cap model or decidedly non-classical behavior, where the contact angle decreases from its value taken at the melting point towards complete wetting at a critical undercooling.

cond-mat.mtrl-sci↗
arXiv2005

Exact Solution of a Field Theory Model of Frontal Photopolymerization

Frontal photopolymerization (FPP) provides a versatile method for the rapid fabrication of solid polymer network materials by exposing photosensitive molecules to light. Dimensional control of structures created by this process is crucial in applications ranging from microfluidics and coatings to dentistry, and the availability of a predictive mathematical model of FPP is needed to achieve this control. Previous work has relied on numerical solutions of the governing kinetic equations in validating the model against experiments because of the intractability of the governing nonlinear equations. The present paper provides exact solutions to these equations in the general case in which the optical attenuation decreases (photobleaching) or increases (photodarkening) with photopolymerization. These exact solutions are of mathematical and physical interest because they support traveling waves of polymerization that propagate logarithmically or linearly in time, depending on the evolution of optical attenuation of the photopolymerized material.

cond-mat.mtrl-sci↗
arXiv2004

On the growth and form of spherulites

Many structural materials (metal alloys, polymers, minerals, etc.) are formed by quenching liquids into crystalline solids. This highly non-equilibrium process often leads to polycrystalline growth patterns that are broadly termed "spherulites" because of their large-scale average spherical shape. Despite the prevalence and practical importance of spherulite formation, only rather qualitative concepts of this phenomenon exist. The present work explains the growth and form of these fundamental condensed matter structures on the basis of a unified field theoretic approach. Our phase field model is the first to incorporate the essential ingredients for this type crystal growth: anisotropies in both the surface energy and interface mobilities that are responsible for needle-like growth, trapping of local orientational order due to either static heterogeneities (impurities) or dynamic heterogeneities in highly supercooled liquids, and a preferred relative grain orientation induced by a misorientation-dependent grain boundary energy. Our calculations indicate that the diversity of spherulite growth forms arises from a competition between the ordering effect of discrete local crystallographic symmetries and the randomization of the local crystallographic orientation that accompanies crystal grain nucleation at the growth front (growth front nucleation or GFN). The large-scale isotropy of spherulitic growth arises from the predominance of GFN.

cond-mat.mtrl-sci↗
arXiv2001

Phase field model of premelting of grain boundaries

We present a phase field model of solidification which includes the effects of the crystalline orientation in the solid phase. This model describes grain boundaries as well as solid-liquid boundaries within a unified framework. With an appropriate choice of coupling of the phase field variable to the gradient of the crystalline orientation variable in the free energy, we find that high angle boundaries undergo a premelting transition. As the melting temperature is approached from below, low angle grain boundaries remain narrow. The width of the liquid layer at high angle grain boundaries diverges logarithmically. In addition, for some choices of model coupling, there may be a discontinuous jump in the width of the fluid layer as function of temperature.

cond-mat.mtrl-sci↗
arXiv2000

Sharp interface limit of a phase-field model of crystal grains

We analyze a two-dimensional phase field model designed to describe the dynamics of crystalline grains. The phenomenological free energy is a functional of two order parameters. The first one reflects the orientational order while the second reflects the predominant local orientation of the crystal. We consider the gradient flow of this free energy. Solutions can be interpreted as ensembles of grains (in which the phase of the order parameter is approximately constant in space) separated by grain boundaries. We study the dynamics of the boundaries as well as the rotation of the grains. In the limit of the infinitely sharp interface, the normal velocity of the boundary is proportional to both its curvature and its energy. We obtain explicit formulas for the interfacial energy and mobility and study their behavior in the limit of a small misorientation. We calculate the rate of rotation of a grain in the sharp interface limit and find that it depends sensitively on the choice of the model.

cond-mat.mtrl-sci↗