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All sources NASA NTRS DOE OSTI

DOE OSTI2024

Effective parameterization of phase-field models of fission gas bubble growth

Fission gas bubbles are one of the most important microstructural features of ceramic nuclear fuels. As gas bubbles grow and interconnect, they allow release of gases, with important consequences for fuel performance. Phase-field modeling has been increasingly used to simulate the evolution of fission gas bubble microstructural because of its capability to capture complex microstructural features. However, computational performance limitations have made it difficult to simulate all the defects present in fuels during operation. For this reason, phase-field models have often simulated only vacancies and used multiple approaches to include the effect of vacancy-interstitial recombination and sinks in a simplified way. Here, we compare some of the most prevalent approaches, including source-only and source/sink. The kinetics of bubble growth using these approaches are analyzed analytically, and simulations with these approaches are compared to a full vacancy-interstitial model.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Dynamical phase-field model of coupled electronic and structural processes

Abstract Many functional and quantum materials derive their functionality from the responses of both their electronic and lattice subsystems to thermal, electric, and mechanical stimuli or light. Here we propose a dynamical phase-field model for predicting and modeling the dynamics of simultaneous electronic and structural processes and the accompanying mesoscale pattern evolution under static or ultrafast external stimuli. As an illustrative example of application, we study the transient dynamic response of ferroelectric domain walls excited by an ultrafast above-bandgap light pulse. We discover a two-stage relaxational electronic carrier evolution and a structural evolution containing multiple oscillational and relaxational components across picosecond to nanosecond timescales. The phase-field model offers a general theoretical framework which can be applied to a wide range of functional and quantum materials with interactive electronic and lattice orders and phase transitions to understand, predict, and manipulate their ultrafast dynamics and rich mesoscale evolution dynamics of domains, domain walls, and charges.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Phase-field modeling of orientation-dependent crack growth in ductile single crystals with anisotropic elasticity

Crack growth in ductile single crystals (DuSCs) is orientation dependent due to the anisotropies of crystal plasticity and elastic tensor. This study develops a phase-field model incorporating both crystal plasticity and crack growth and proposes a general method to decompose the elastic energy into compressive and tensile parts to prevent crack growth under compression in the phase-field description. The phase-field model, in combination with three Euler angles, is employed to simulate orientation-dependent crack growth in DuSCs. The contributions from crystal plasticity and anisotropic elasticity are compared, and the former is found to dominate in the anisotropy of crack growth in copper single crystals. Furthermore, the simulation results demonstrate that crystal orientation strongly affects the heterogeneous distribution of plastic strain and the interaction between plastic strain and crack growth. High-throughput phase-field simulations are performed with exhaustive crystal orientations, and the results are explained based on the anisotropy of the Taylor factor.

Computational Solid Mechanics↗

DOE OSTI2014

A phase-field model coupled with lattice kinetics solver for modeling crystal growth in furnaces

In this study, we present a new numerical model for crystal growth in a vertical solidification system. This model takes into account the buoyancy induced convective flow and its effect on the crystal growth process. The evolution of the crystal growth interface is simulated using the phase-field method. Two novel phase-field models are developed to model the crystal growth interface in vertical gradient furnaces with two temperature profile setups: 1) fixed wall temperature profile setup and 2) time-dependent temperature profile setup. A semi-implicit lattice kinetics solver based on the Boltzmann equation is employed to model the unsteady incompressible flow. This model is used to investigate the effect of furnace operational conditions on crystal growth interface profiles and growth velocities. For a simple case of macroscopic radial growth, the phase-field model is validated against an analytical solution. Crystal growth in vertical gradient furnaces with two temperature profile setups have been also investigated using the developed model. The numerical simulations reveal that for a certain set of temperature boundary conditions, the heat transport in the melt near the phase interface is diffusion dominant and advection is suppressed.

Lin, Guang↗

DOE OSTI2025

Phase-field modeling and experiments of dynamic fracture in single crystal quartz

Predicting the onset and characteristics of brittle fracture is important for a wide range of engineering and geological material applications. In this paper, we study important aspects of brittle fracture in α-quartz by phase-field modeling and experiments using a top-down approach. In the modeling framework, the work term in the Griffith energy balance is replaced with internal energy contributions that represent surface energy, thermal energy, and elastic strain energy stored in defects. This allows parametrization of individual energy contributions in terms of internal state variables and keeps track of energy partitioning after the onset of fracture. The path and history dependence of fracture is included in evolution laws for internal state variables, e.g., entropy evolution, while the energy remains a true potential. In the experimental part, dynamic compression experiments coupled with X-ray phase contrast imaging are performed on cube-like samples with a hole. In the top-down analysis, dynamic compression and three point bending experiments from the literature are simulated with the developed phase-field damage model. In conclusion, the fitted model highlights the strain rate, size, and stress state dependence of damage nucleation and evolution in single crystal α-quartz.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Phase-field model of alloy solidification far from chemical equilibrium at the solid-liquid interface

We further develop a recently introduced phase-field model of far-from-equilibrium alloy solidification under additive manufacturing conditions [K. Ji et al., Phys. Rev. Lett. 130, 026203 (2023)]. This model utilizes enhanced solute diffusivity within the spatially diffuse interface region to quantitatively capture solute trapping with a larger interface width, thereby making simulations on experimentally relevant length and timescales computationally feasible. The main developments presented here include testing the robustness of different variational formulations, extending the model to concentrated alloys by incorporating solid and liquid free energies from thermodynamic databases, as illustrated for hypoeutectic Al-Ag alloys with CALPHAD, extending convergence tests as a function of interface width to 3D, and carrying out simulations in both 2D and 3D to examine existing theories of microstructure development. Our results indicate that the simplest variational formulation that interpolates the bulk free-energy density between its solid and liquid forms is the most robust. Remarkably, for hypoeutectic Al-Ag alloys, this formulation yields a high-velocity nonequilibrium phase diagram that is independent of interface width, thereby demonstrating that the framework of enhanced solute diffusivity can be nontrivially extended to concentrated alloys. Other variational formulations have restricted ranges of materials or processing parameters that can be reliably modeled. We use 2D simulations to construct high-velocity microstructure selection maps for dilute Al-Cu alloys. The results validate the important role of latent heat rejection at the interface and extend the limited predictions of linear stability analysis [A. Karma and A. Sarkissian, Phys. Rev. E 47, 513 (1993)] and sharp-interface 1D simulations to fully nonlinear regimes. Furthermore, 3D simulations, carried out using a computationally tractable axisymmetric cellular/dendritic interface shape, demonstrate a good convergence similar to that observed in 2D as a function of interface width. Full 3D simulations, in turn, reveal that the standard theory of absolute stability is a good predictor of the upper critical velocity beyond which steady-state growth becomes unstable, despite the different morphological manifestations of this instability in 2D and 3D.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Phase-field modeling of chemical control of polarization stability and switching dynamics in ferroelectric thin films

Phase-field simulation (PFS) has revolutionized the understanding of domain structure and switching behavior in ferroelectric thin films and ceramics. Generally, PFS is based on the solution of (a set of) Landau-Ginzburg-Devonshire equations for a defined order parameter field(s) under physical boundary conditions (BCs) of fixed potential or charge. While well matched to the interfaces in bulk materials and devices, these BCs are generally not applicable to free ferroelectric surfaces. Here, we developed a self-consistent phase-field model with BCs based on electrochemical equilibria. We chose Pb(Zr 0.2 Ti 0.8 )O 3 ultrathin film consisting of (001) oriented single tetragonal domain ( P z ) as a model system and systematically studied the effects of oxygen partial pressure, temperature, and surface ions on the ferroelectric state and compared it with the case of complete screening. We have further explored the polarization switching induced by the oxygen partial pressure and observed pronounced size effect induced by chemical screening. Finally, our paper thus helps to understand the emergent phenomena in ferroelectric thin films brought about by the electrochemical ionic surface compensations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Phase field modeling of discontinuous dynamic recrystallization in hot deformation of magnesium alloys

We have developed a quantitative phase field model of discontinuous dynamic recrystallization (PF-DDRX) for investigating grain structure evolution and its impact on mechanical response in magnesium alloy during hot deformation. A set of isothermal compression tests were conducted by Gleeble thermo-mechanical simulator and used to determine PF-DDRX model parameters such as critical stresses of recrystallization, activation energies of dislocation, grain boundaries and recrystallization grain nucleation. In the simulations, the experimentally measured average grain size and distribution were used to generate initial microstructures. The results show that the typical ‘necklace’ microstructures observed in DDRX forms at the earlier stage of recrystallization. The inhomogeneity of microstructures first increases rapidly and then decreases gradually and reaches a constant with the increase of dynamic recrystallization volume fraction. Both predicted grain structure and mechanical response are in good agreement with experimental results. This demonstrates that the model parameters determined by experimental data are reliable for the developed PF-DDRX model to predict the grain structure evolution and flow behavior of AZ80 magnesium alloy under hot deformation. This work presents a path to combine experiments and modeling to give quantitative prediction and minimize experimental cost.

magnesium alloy, Phase field method, dynamic recry↗

DOE OSTI2015

Mesoscale Phase Field Modeling of Glass Strengthening Under Triaxial Compression

Recent hydraulic bomb and confined sleeve tests on transparent armor glass materials such as borosilicate glass and soda-lime glass showed that the glass strength was a function of confinement pressure. The measured stress-strain relation is not a straight line as most brittle materials behave under little or no confinement. Moreover, borosilicate glass exhibited a stronger compressive strength when compared to soda-lime glass, even though soda-lime has higher bulk and shear moduli as well as apparent yield strength. To better understand these experimental findings, a mesoscale phase field model is developed to simulate the nonlinear stress versus strain behaviors under confinement by considering heterogeneity formation under triaxial compression and the energy barrier of a micro shear banding event (referred to as pseudo-slip hereafter) in the amorphous glass. With calibrated modeling parameters, the simulation results demonstrate that the developed phase field model can quantitatively predict the pressure-dependent strength, and it can also explain the difference between the two types of glasses from the perspective of energy barrier associated with a pseudo-slip event.

Confined Borosilicate↗

DOE OSTI2025

Phase-Field Modeling of Damage Evolution in Ceramic Matrix Composite (CMC) and Environmental Barrier Coating (EBC)

Ceramic matrix composites (CMCs) protected by environmental barrier coatings (EBCs) present a promising materials solution for next generation gas turbines. Developments of more robust and efficient EBCs and mechanically tougher CMCs are thus of significant technological importance. Here we develop a phase-field modeling framework that incorporates the thermally grown oxide (TGO), recognized as a critical factor for degradation and failure of EBCs. We simulate crack growth in the TGO and the potential extension into the bond coat / CMC substrate. The model efficiently takes account of the large inelastic deformation induced by the severe volume expansion of TGO, thanks to our recently developed, so-called incremental realization of inelastic deformation (IRID) algorithm. A phase-field model is built for damage evolution in CMCs including crack growth and interfacial sliding. The effects of fiber layout and interfacial sliding on the macroscopic toughness of CMCs are revealed by large-scale simulations and compared to experiments.

advanced energy systems and materials↗

NASA NTRS1999

Thin Interface Asymptotics for an Energy/Entropy Approach to Phase-Field Models with Unequal Conductivities

Karma and Rapped recently developed a new sharp interface asymptotic analysis of the phase-field equations that is especially appropriate for modeling dendritic growth at low undercoolings. Their approach relieves a stringent restriction on the interface thickness that applies in the conventional asymptotic analysis, and has the added advantage that interfacial kinetic effects can also be eliminated. However, their analysis focussed on the case of equal thermal conductivities in the solid and liquid phases; when applied to a standard phase-field model with unequal conductivities, anomalous terms arise in the limiting forms of the boundary conditions for the interfacial temperature that are not present in conventional sharp-interface solidification models, as discussed further by Almgren. In this paper we apply their asymptotic methodology to a generalized phase-field model which is derived using a thermodynamically consistent approach that is based on independent entropy and internal energy gradient functionals that include double wells in both the entropy and internal energy densities. The additional degrees of freedom associated with the generalized phased-field equations can be chosen to eliminate the anomalous terms that arise for unequal conductivities.

McFadden, G. B.↗

DOE OSTI2023

Phase-Field Modeling of Materials Interfaces and Nanostructures

Nanostructured materials offer unique properties for a wide range of energy applications. Among various known processing methods, liquid metal dealloying (LMD)—the selective dissolution of a base alloy element into a metallic melt—has emerged as a powerful technique to produce a new class of nano-/meso-scale open porous and bicontinuous composite structures with ultra-high interfacial area. LMD has recently been complemented by the advent of vapor phase dealloying (VPD), a novel technique that exploits the selective evaporation of one element from a parent alloy containing elements with very different vapor pressures, thereby enabling to fabricate open nanoporous structures of various elements from less-noble metals to inorganic elements regardless of their chemical activity without requiring high LMD temperatures and chemical etching. Together LMD and VPD have greatly expanded the scope of dealloying techniques, limited by traditional electrochemical means to noble metals, and boosted the design of new functional and structural materials that combine a wide variety of elements. Topologically-connected open porous structures with ultra-high surface area allow mass transport within the structure while preserving structural integrity, enabling them to serve as catalysts, fuel cells, supercapacitors, or high-capacity battery materials. Bicontinuous composite structures in turn can display high strength and high ductility or superior radiation-damage resistance due to the ultra-high interface area between interpenetrating solid phases. This research program makes use of state-of-the-art computational methods to understand at a basic level the self-organizing dealloying process with main focus on dealloying kinetics and interfacial pattern formation at the dealloying front controlling initial structure size, topology, and phase compositions. Phase-field simulation studies of LMD focus on solid solutions, line compounds, and intermetallic systems that can form ternary composites by nucleation and growth of a new phase. Studies of VPD employ phase-field modeling and a hybrid method combining a kinetic Monte Carlo (KMC) model of evaporation and surface diffusion with molecular dynamics for vapor-phase transport inside nanopores. Simulations explore mechanisms of interface- and diffusion-controlled dealloying kinetics, both observed in VPD but not fundamentally understood. In addition, our newly developed multi-physics phase-field approach of large-volume-change phase transformations is being used to model novel 3D anode geometries based on dealloyed nanoporous structures including novel sandwiched graphene/Si/silica for highrate Li ion battery. Those studies are aimed at elucidating geometric design principles that improve mechanical stability. We expect this research to enhance the capability to tailor nano-/mesoscale structures for a wide range of energy-related materials applications and to yield further advances in computational methodologies that benefit a broad materials research community.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2019

Phase field model of uranium carbide solidification through a combined KKS and orientation field approach

A Phase Field model is developed combining the Orientation Field approach to modeling solidification with the Kim, Kim, Suzuki (KKS) method of modeling binary alloys. These combined methods produce a model capable of simulating randomly oriented second phase dendrites with discrete control of the solid-liquid interface energy and thickness. The example system of carbon (C) in a liquid uranium (U) melt is used as a test for the model. The formation of uranium carbide (UC) within a liquid U melt is simulated for isothermal conditions and compares well with experiments.

Bair, Jacob L. (ORCID:0000000333273323)↗

DOE OSTI2019

A phase field model for dislocations in hexagonal close packed crystals

In this work, an application of a phase field formulation suitable for modeling the motion of individual partial and full dislocations in hexagonal close packed (HCP) crystals is presented. The formulation incorporates periodic potentials for glide on the distinct HCP slip systems, which are informed here by density functional theory (DFT). The model is applied to simulate the dissociation process starting from an unstable perfect dislocation and ending at its final equilibrium structure for different slip planes and in different HCP metals. The structural characteristics that are predicted for these dislocations include the partial Burgers vectors, dissociation distances, core widths of the partials, and any asymmetries in these quantities. Mg is selected as one of the model materials since its dislocations are the most well studied and it is nearly elastically isotropic. For Mg, it is shown that the predictions for dissociation distances agree with those reported previously by atomic-scale calculations, including density functional theory, for dislocations on the basal < a >, prismatic < a >, and pyramidal type II slip systems. Furthermore, phase field model results are also presented for dislocations in Ti and Zr, which we find develop distinctively different equilibrium structures than Mg.

36 MATERIALS SCIENCE↗

DOE OSTI2022

BattPhase—A Convergent, Non-Oscillatory, Efficient Algorithm and Code for Predicting Shape Changes in Lithium Metal Batteries Using Phase-Field Models: Part I. Secondary Current Distribution

Electrochemical models at different scales and varying levels of complexity have been used in the literature to study the evolution of the anode surface in lithium metal batteries. This includes continuum, mesoscale (phase-field approaches), and multiscale models. Thermodynamics-based equations have been used to study phase changes in lithium batteries using phase-field approaches. However, grid convergence studies and the effect of additional parameters needed to simulate these models are not well-documented in the literature. In this paper, using a motivating example of a moving boundary model in one- and two-dimensions, we show how one can formulate phase-field models, implement algorithms for the same and analyze the results. An open-access code with no restrictions is provided as well. This article concludes with some thoughts on the computational efficiency of phase-field models for simulating dendritic growth.

25 ENERGY STORAGE↗

DOE OSTI2024

Arbitrary Order Virtual Element Methods for High‐Order Phase‐Field Modeling of Dynamic Fracture

ABSTRACT Accurate modeling of fracture nucleation and propagation in brittle and ductile materials subjected to dynamic loading is important in predicting material damage and failure under extreme conditions. Phase‐field fracture models have garnered a lot of attention in recent years due to their success in representing damage and fracture processes in a wide class of materials and under a variety of loading conditions. Second‐order phase‐field fracture models are by far the most popular among researchers (and increasingly, among practitioners), but fourth‐order models have started to gain broader acceptance since their more recent introduction. The exact solution corresponding to these high‐order phase‐field fracture models has higher regularity. Thus, numerical solutions of the model equations can achieve improved accuracy and higher spatial convergence rates. In this work, we develop a virtual element framework for the high‐order phase‐field model of dynamic fracture. The virtual element method (VEM) can be regarded as a generalization of the classical finite element method. In addition to many other desirable characteristics, the VEM allows computing on polytopal meshes. Here, we use ‐conforming virtual elements and the generalized‐ time integration method for the momentum balance equation, and adopt ‐conforming virtual elements for the high‐order phase‐field equation. We verify our virtual element framework using classical quasi‐static benchmark problems and demonstrate its capabilities with the aid of numerical simulations of dynamic fracture in brittle materials.

42 ENGINEERING↗

DOE OSTI2025

Phase Field Modeling of Chemical Reaction Related Damage Evolution in Environmental Barrier Coatings

The advent of next-generation engines necessitates materials capable of withstanding temperatures beyond the reach of current superalloys. SiC-based ceramic matrix composites, augmented with environmental barrier coatings (EBCs), present a promising materials solution. Given the active search for effective and durable EBCs, there is a pressing need for modeling tools to understand and predict damage evolution in these materials to help accelerate their development. This study introduces a phase-field model (PFM) designed to simulate the thermally grown oxides (TGO) and phase transformation in the degradation and failure of EBCs. The model accounts for the severe volume expansion due to oxidation, alongside phase transformations and porosity evolution during thermal cycling, offering a comprehensive view of the damage processes. Simulation results are validated against experimental findings reported in the literature, establishing the model's potential as a significant tool for understanding and improving the resilience of EBCs in cyclic oxidative environments.

fast-diffusion path↗

DOE OSTI2016

Pore and grain boundary migration under a temperature gradient: A phase-field model study

In this study, the collective migration behavior of pores and grain boundaries under a temperature gradient is studied for simple single crystal, bi-crystal and polycrystal configurations with a phase-field model formulism. For simulation of the microstructure of solids, composed of pores and grain boundaries, the results indicate that not only the volume fraction of pores, but also its spatial partitioning between the grain boundary junctions and the grain boundary segments appears to be important. In addition to various physical properties, the evolution kinetics, under given temperature gradients, will be strongly influenced with the initial morphology of a poly-crystalline microstructure.

36 MATERIALS SCIENCE↗