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DOE OSTI2022

Learning two-phase microstructure evolution using neural operators and autoencoder architectures

Abstract Phase-field modeling is an effective but computationally expensive method for capturing the mesoscale morphological and microstructure evolution in materials. Hence, fast and generalizable surrogate models are needed to alleviate the cost of computationally taxing processes such as in optimization and design of materials. The intrinsic discontinuous nature of the physical phenomena incurred by the presence of sharp phase boundaries makes the training of the surrogate model cumbersome. We develop a framework that integrates a convolutional autoencoder architecture with a deep neural operator (DeepONet) to learn the dynamic evolution of a two-phase mixture and accelerate time-to-solution in predicting the microstructure evolution. We utilize the convolutional autoencoder to provide a compact representation of the microstructure data in a low-dimensional latent space. After DeepONet is trained in the latent space, it can be used to replace the high-fidelity phase-field numerical solver in interpolation tasks or to accelerate the numerical solver in extrapolation tasks.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Preliminary results addressing material qualification using combined ion irradiation and modeling data

Additively-manufactured (AM) materials have attracted increasing attention in recent years as a new method to make novel and customized components. While AM and conventionally produced materials are compositionally similar, they do possess different microstructures, necessitating assessment of materials produced via AM for their behavior in reactor environments. Some microstructures unique to AM materials, such as compositional micro-inhomogeneity and dislocation cell structures, are of particular importance since they may lead to different radiation performance. The performance of AM materials for advanced nuclear reactor applications is of interest to the Advanced Materials and Manufacturing Technologies (AMMT) program under the Department of Energy Office of Nuclear Energy. The AMMT program aims to demonstrate its new accelerated development and qualification methods via laser powder bed fusion (LPBF) 316 stainless steel (SS). Focusing on material bearing both 316L and 316H specifications, we integrate ion irradiation and modeling. This year, we focus on answering foundational questions related to process variability, alloy chemistry variation, and microchemical segregation. Experimental results provide information and motivate questions to the modeling effort, which aims to develop the ability to model radiation-driven microstructural evolution in additively-manufactured 316 stainless steel under a variety of advanced reactor conditions, including different temperatures, neutron spectra, and fluxes, in a sort of "virtual experiment". We perform in-situ and ex-situ ion irradiations and microstructural characterizations to support the development of AM materials for reactor applications, develop a phase field model of radiation-induced segregation in additively manufactured material with high angle grain boundaries and dislocation cells, and investigate the effect of carbon and chromium content on point defect behavior.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Three-dimensional microstructural characterization of FBR MOX fuel and the contribution of microstructural features to the thermal conductivity of the fuel

Combination of microstructural characterization, property measurements, and phase field modeling is used to investigate fast breeder reactor (FBR) mixed oxide (MOX) fuel irradiated to burnup of 13.7% fissions per initial metal atom (FIMA). Here, the fuel was characterized at different radial locations, which revealed that grey phase can be present in the central region if it nucleates on five metal precipitates (FMPs). In addition, in the mid-radial region FMPs do not diffuse out of the region once formed and the size of Pd–Te precipitates is dictated by the porosity present in the region. Thermal conductivity measurements were conducted as a function of radial location and the microstructure of the fuel was correlated with the observed trend. Reconstructions of the 3D solid and gaseous fission product structures in different regions of the fuel were used to simulate the effective thermal conductivity (ETC) of the respective regions and determine which microstructural feature has the strongest impact on thermal conductivity. Based on conducted assessment, FMPs and Pd-Te precipitates improve local conductivity of central and mid-radial regions even in the presence of grey phase, but defects are primary contributor to the degradation of thermal conductivity on the periphery of the fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2019

A New Efficient Quantitative Multi-component Phase Field: Lattice Boltzmann Model for Simulating Ti6Al4V Solidified Dendrite Under Forced Flow

Ti6Al4V is a widely used, multi-component alloy in additive manufacturing, during which the fluid flow in the molten pool significantly affects the solidified dendrites. To predict and further control the microstructure, modeling and simulating the microstructure evolution play a critical role. In this study, a newly developed, efficient, quantitative multi-component phase-field (PF) model is coupled with a lattice Boltzmann (LB) model to simulate Ti6Al4V solidified dendrite evolution under fluid flow. The accuracy and convergence behavior of the model is validated by the Gibbs–Thomson relation at the dendrite tip. Single and multiple two-dimensional (2D) equiaxed dendrite evolution cases under forced flow were simulated. Results show that the dendrite pattern is influenced remarkably by the fluid flow. Underlying mechanisms of the asymmetrical evolution are revealed by discussing the interaction among the flow, composition distribution and dendrite morphology, quantitatively. The dendrite kinetics are also derived, which ascertains the relationship between tip velocity and undercooling and inlet velocity and is the foundation for larger-scale simulation. We believe that the coupled quantitative multi-component PF–LB framework employed in this study helps in investigating the solidified dendrite morphology evolution in a deep and quantitate manner.

36 MATERIALS SCIENCE↗

DOE OSTI2019

A mechanism of defect-enhanced phase transformation kinetics in lithium iron phosphate olivine

Abstract Antisite defects are a type of point defect ubiquitously present in intercalation compounds for energy storage applications. While they are often considered a deleterious feature, here we elucidate a mechanism of antisite defects enhancing lithium intercalation kinetics in LiFePO 4 by accelerating the FePO 4 → LiFePO 4 phase transformation. Although Fe Li antisites block Li movement along the [010] migration channels in LiFePO 4 , phase-field modeling reveals that their ability to enhance Li diffusion in other directions significantly increases the active surface area for Li intercalation in the surface-reaction-limited kinetic regime, which results in order-of-magnitude improvement in the phase transformation rate compared to defect-free particles. Antisite defects also promote a more uniform reaction flux on (010) surface and prevent the formation of current hotspots under galvanostatic (dis)charging conditions. We analyze the scaling relation between the phase boundary speed, Li diffusivity and particle dimensions and derive the criteria for the co-optimization of defect content and particle geometry. A surprising prediction is that (100)-oriented LiFePO 4 plates could potentially deliver better performance than (010)-oriented plates when the Li intercalation process is surface-reaction-limited. Our work suggests tailoring antisite defects as a general strategy to improve the rate performance of phase-changing battery compounds with strong diffusion anisotropy.

36 MATERIALS SCIENCE↗

DOE OSTI2021

ORNL/Thermo4PFM

Library to compute equilibrium compositions and equal chemical potential compositions in binary and ternary alloys. This library supports thermodynamic data formulated according to CALPHAD (Computer Coupling of Phase Diagrams and Thermochemistry) models, as well as dilute binary alloys. One major aim is to solve the Kim-Kim-Suzuki (KKS) equations to obtain local compositions given a local mixture of two phases. These quantities are then used to evaluate the phase-field model driving force (right handside of time-evolution equation), as well as the energy density

Fattebert, Jean-Luc↗

DOE OSTI2024

Modeling Ni Coarsening and Migration in the Hydrogen Electrode of Solid oxide Cells under Operating Conditions

Ni coarsening and migration is the most important degradation in the hydrogen electrode of solid oxide cells. This presentation reviews our works on Ni coarsening and migration in NETL over the past years. We used simulation techniques including phase-field modeling and density function theory to investigate possible mechanisms of Ni coarsening and migration, including self-diffusion of Ni, diffusion of gaseous Ni(OH)2, surface diffusion of Ni(OH)x and Ni-YSZ wettability change, and examined the effect of operating conditions on these mechanisms. So far, none of the mechanisms can fully explain the experiments. Remaining questions and possible paths forward are summarized and discussed.

Lei, Yinkai↗

DOE OSTI2022

Electrochemically-Induced Phase Transformations in Battery Storage Compounds (Final Technical Report)

Compounds of interest for ion storage in advanced batteries frequently exhibit phase transformations as the working ion concentration varies. Under large electrochemical driving forces inherent to practical use, systems are often driven far from equilibrium. This program combines experiments and theory to understand the phase transition behavior of ion insertion compounds when electrochemically driven far from equilibrium. As model systems, we focus on alkaline metal phosphates AMPO4 (A = alkali; M = first row transition metal) of olivine structure, which are both technologically interesting and ideally suited for fundamental study due to the ability to systematically tune transformation strain, and along with it, the phase transformation pathway. Behavior in compositions having large transformation strains (~15 vol%) requiring plasticity for strain accommodation is emphasized. Experimental techniques include operando characterization of structure while simultaneously varying electrokinetic parameters, and high resolution microscopy of nanoscale and interfacial phenomena. Phase-field modeling is used to model the thermodynamics and kinetics of competing transformation pathways, extended to include the effects of plasticity, and integrated with porous electrode kinetic theory to treat multi-particle effects. Success in this project will lead to an ability to design ion storage compounds with predictable transformation pathways, electrochemical kinetics, capacity utilization, and durability. New technologically important compounds may also be discovered.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Chemomechanics in alloy phase stability

We describe a first-principles statistical mechanics method to calculate the free energies of crystalline alloys that depend on temperature, composition, and strain. The approach relies on an extension of the alloy cluster expansion to include an explicit dependence on homogeneous strain in addition to site occupation variables that track the degree of chemical ordering. The method is applied to the Si-Ge binary alloy and is used to calculate free energies that describe phase stability under arbitrary epitaxial constraints. We find that while the incoherent phase diagram (in which coexisting phases are not affected by coherency constraints) hosts a miscibility gap, coherent phase equilibrium predicts ordering and negative enthalpies of mixing. Instead of chemical instability, the chemomechanical free energy exhibits instabilities along directions that couple the composition of the alloy with a volumetric strain order parameter. Furthermore, this has fundamental implications for phase field models of spinodal decomposition as it indicates the importance of gradient energy coefficients that couple gradients in composition with gradients in strain.

Materials Science↗

DOE OSTI2022

Optimization of WAAM Process to Produce AUSC Components with Increased Service Life

Additive manufacturing has the potential to revolutionize industrial hardware and unlock efficiency gains through the fabrication of geometries and architectures not possible by conventional processing. Wire Arc Additive manufacturing (WAAM) process is a class of directed energy deposition process enabling higher build rate and allowing custom wire feedstock allowing spatial variation of microstructure. The larger spot size and lower speed creates a larger melt pool, reducing residual stress and often time creating directional/columnar microstructure for Ni-superalloy. The use of flexible platform provides freedom in deposition strategy, which can accommodate complex substrates, including feature addition onto existing structures, non-flat layers, and repair methods. However, the certification of the final component needs to match the strength requirement. Hence, the quality of the component produced is stringently monitored to avoid buildup of residual stress, cracks, porosity and to reduce detrimental segregated phases commonly observed during alloy solidification. Simulation plays a huge role in predicting the melt pool dimension and can be used to optimize the process parameter. Similar development is also required to perform physics-based modeling of microstructural development in WAAM that can predict the microstructural features during solidification and can be used to optimize the process more effectively. To move toward this goal, Raytheon Technologies Research Center together with Siemens worked to create a set of computational tools to control the process parameters, enable on-line measurements and acquisition with feedback to the optimized process parameters, and eventually track material evolution through each step of the additive process. Computational fluid dynamics is used for accurate prediction and calibration of the thermal field during WAAM process. and phase field models for microstructure evolution as a function of processing parameters to establish a connection between additive parameters and the final microstructure. Here we report cellular automata (CA) model development to predict the dendritic microstructure evolution with surface and bulk nuclei for single track and multiple layers. The CA model was developed to account for secondary element addition and predict segregation, local melting, and latent heat release as well as prediction of Euler angles from orientation information and validated against experiments. This framework was utilized to tailor spatially-varying composition in a part by appropriately controlling the microstructure evolution during the additive process. Functionally graded Haynes 282 alloy with high Cr content at the surface was tested for oxidation and mechanical properties. An advanced physics-based reaction-diffusion model predicting the simultaneous creation of chromium oxide and alumina is developed and validated to extend life expectancy of the WAAM manufactured high temperature part. A machine-learning data-driven framework establishing the process-structure relationship from a dataset of real microstructure images and corresponding process history data has been developed and implemented in the NX Siemens design system. The digital twin configuration along with the tool path generation enabled prediction of WAAM component buildup time and the techno-economic analysis provided a favorable option for all 4 cases with 15-40% cost reduction.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2024

Modeling Ni Coarsening under Humid Atmosphere in the Electrode of Solid Oxide Cells

Ni coarsening is an important degradation mechanism in solid oxide cells. It is reported that Ni coarsening is faster under a humid atmosphere experimentally, but the underline mechanism is not well understood. In this work, Ni coarsening through Ni(OH)x surface diffusion was investigated by a combination of density-functional theory (DFT) and phase-field modeling (PFM). DFT is used to evaluate the surface coverage and diffusivity of Ni(OH)x on Ni (111) surface and the results are used as an input to the PFM to simulate Ni coarsening under humid atmospheres on both reconstructed and synthetic microstructures. It is found that steam partial pressure and microstructure effect alone cannot explain the faster Ni coarsening under a humid atmosphere observed experimentally. Large local overpotential in fuel cell mode is needed to explain the fast Ni coarsening.

Lei, Yinkai↗

NASA NTRSDate not supplied

A General Model for the Electrochemical Double Layer in Solids

It has long been clear that electrochemical double layer / space charge zone in the vicinity of interfaces and other extended defects greatly influences transport and reactivity. Over the past several years, multiple microscopic measurements of defect concentrations in the vicinity of solid-solid interfaces made clear that dilute-case thermodynamic theories to describe the behavior of charged species in space charge zones are untenable. Inhomogeneous thermodynamics – i.e., phase field models – have delivered the most success in describing both microscopic and macroscopic experiments. We still need a generalized approach that quantitatively reproduces the microscopic and macroscopic evidence, while remaining accessible to a wide range of researchers and engineers. In my talk I will present such a framework, which builds on the previously introduced Poisson-Cahn theory but utilizes data science methods which come into the thermodynamic framework in a well-defined way. I will review recent applications to both microscopic and macroscopic datasets while previewing our plans for connecting the theory to atomistic / first principles calculations and experiment simultaneously. I will also review plans for releasing open source code that runs on desktop-level computational resources.

David Mebane↗

DOE OSTI2022

Simulating microgalvanic corrosion in alloys using the PRISMS phase-field framework

In this prospective paper, we first review the existing simulation tools to simulate microgalvanic corrosion during free immersion. Then, we describe a recently developed application that employs PRISMS-PF, an open-source, high-performance phase-field modeling framework. The model employed in the application accounts for the electrochemical reaction at the metal/electrolyte interface and ionic migration in the electrolyte to determine the evolution of the corrosion front. We present the implementation details for the application and discuss its features such as super-linear parallel scaling performance for a sufficiently large system. Finally, we demonstrate the capability of the application by simulating corrosion of the matrix phase of an alloy near a secondary phase particle in two and three dimensions.

36 MATERIALS SCIENCE↗

DOE OSTI2024

A variational phase-field framework for thermal softening and dynamic ductile fracture

A variational phase field model for dynamic ductile fracture is presented. Here, the model is designed for elasto-viscoplastic materials subjected to rapid deformations in which the effects of heat generation and material softening are dominant. The variational framework allows for the consistent inclusion of plastic dissipation in the heat equation as well as thermal softening. It employs a coalescence function to degrade fracture energy during regimes of high plastic flow. A variationally consistent form of the Johnson–Cook model is developed for use with the framework. Results from various benchmark problems in dynamic ductile fracture are presented to demonstrate capabilities. In particular, the ability of the model to regularize shear band formation and subsequent damage evolution in two- and three-dimensional problems is demonstrated. Importantly, these phenomena are naturally captured through the underlying physics without the need for phenomenological criteria such as stability thresholds for the onset of shear band formation.

42 ENGINEERING↗

DOE OSTI2023

Real-space imaging of periodic nanotextures in thin films via phasing of diffraction data

New properties and exotic quantum phenomena can form due to periodic nanotextures, including Moire patterns, ferroic domains, and topologically protected magnetization and polarization textures. Despite the availability of powerful tools to characterize the atomic crystal structure, the visualization of nanoscale strain-modulated structural motifs remains challenging. Here, we develop nondestructive real-space imaging of periodic lattice distortions in thin epitaxial films and report an emergent periodic nanotexture in a Mott insulator. Specifically, we combine iterative phase retrieval with unsupervised machine learning to invert the diffuse scattering pattern from conventional X-ray reciprocal-space maps into real-space images of crystalline displacements. Our imaging in PbTiO 3 /SrTiO 3 superlattices exhibiting checkerboard strain modulation substantiates published phase-field model calculations. Furthermore, the imaging of biaxially strained Mott insulator Ca 2 RuO 4 reveals a strain-induced nanotexture comprised of nanometer-thin metallic-structure wires separated by nanometer-thin Mott-insulating-structure walls, as confirmed by cryogenic scanning transmission electron microscopy (cryo-STEM). The nanotexture in Ca 2 RuO 4 film is induced by the metal-to-insulator transition and has not been reported in bulk crystals. We expect the phasing of diffuse X-ray scattering from thin crystalline films in combination with cryo-STEM to open a powerful avenue for discovering, visualizing, and quantifying the periodic strain-modulated structures in quantum materials.

Science & Technology - Other Topics↗

DOE OSTI2021

Development of High-Performance Ni-base Alloys for Gas Turbine Wheels Using a Coprecipitation Approach (Final Technical Report)

In this project, a synergistic approach involving experiments informed by modelling was used to develop γ'/γ'' coprecipitation-strengthened Ni-base superalloys for land-based gas turbine wheels. In thick sections of such turbine wheels, the slow cooling rate normally observed, as well as variations in cooling rate could potentially result in drastically inhomogeneous and coarsened microstructure. Thus, ten alloy compositions were selected based on coprecipitation and sluggish γ’ growth and coarsening during three iterations of alloy development, assisted by extensive CALPHAD modeling. Phase equilibrium calculations, informed by the characterization of early alloys, were successful in predicting suitable aging treatments to obtain bimodal coprecipitate distribution in several alloys. These aging treatments were applied to the subsequent round of alloys and the resulting microstructures were characterized in detail. Two different cooling rates were used during each of these heat treatments to simulate the range of cooling rates observed in a thick section forging. The microstructures were used to calibrate a multi-phase field model (MPF), which was used to study the formation mechanisms of various coprecipitate morphologies observed in the experiments. Following this, the most promising alloys in each round were selected and studied using high temperature tensile and creep tests. Considering that a slower cooling rate would lead to a strength debit, while a faster cooling rate might lead to a decline in creep rupture life of a full-scale wheel, tensile tests were carried out for slower cooled samples, while creep tests were carried out for faster cooled samples. The deformation microstructures were then characterized using advanced characterization techniques such as Diffraction Contrast-Scanning Transmission Electron Microscopy (DC-STEM) and Electron Channeling Contrast Imaging (ECCI). Further, a mean-field creep model was developed and calibrated using these experimental findings to predict long-term creep behavior of these coprecipitation-strengthened alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Development of a Gibbs Energy Minimiser for the MOOSE-based Corrosion Modelling App Yellowjacket and Validation of MSTDB

Nuclear materials are highly complex multiscale, multiphysics systems,and an effective prediction of nuclear reactor performance and safety requires simulation capabilities that tightly couple different physical phenomena. The Idaho National Laboratory’s Multiphysics Object Oriented Simulation Environment (MOOSE) provides the computational foundation for performing such simulations. With the move towards advanced reactors, such as the Molten Salt Reactor (MSR), that employ high temperature fluids compared to conventional reactors, corrosion has become a problem of great interest. A new application called Yellowjacket is currently under development to directly couple thermodynamic equilibrium and kinetics with phase field models in order to model corrosion in MSRs. As part of Yellowjacket, a Gibbs energy minimiser is being developed to perform thermochemical equilibrium calculations for a range of different materials, which is currently in its infancy. This report describes the further progress towards the development of Yellowjacket Gibbs energy minimiser. Ontario Tech University is developing a new Gibbs energy minimiser for Yellowjacket which is the primary contribution of this work. The aim to develop a thermochemistry solver for the MOOSE framework following the same development philosophy and using the same tools and libraries. A special focus is on performance, documentation and SQA. Furthermore through a scope extension partway through the fiscal year a thorough assessment of the MSTDB-TC v1.3 was performed at Ontario Tech University in the context of continuous improvement and quality assurance. The objective of the work was to have an arm’s length review of the database to give confidence that the database is performing as it was intended while assessing its current state to give recommendations to future developments. This assessment involved two parts: A) a quantitative assessment, and B) a qualitative assessment. Part A involved developing an automated test-suite that would compute values from the database using Thermochimica with comparisons to experimental measurements for validation purposes, which gives confidence to the database’s stakeholders that its functioning properly. Part B involved reviewing all binary systems in the database and making a qualitative assessment with two performance indicators: comprehensiveness and overall confidence. It is important to note that the models in the database are empirical, which is to say that the quality of any model is highly dependent on the experimental data used to inform its development.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

On-demand nanoengineering of in-plane ferroelectric topologies

Hierarchical assemblies of ferroelectric nanodomains, so-called super-domains, can exhibit exotic morphologies that lead to distinct behaviours. Controlling these super-domains reliably is critical for realizing states with desired functional properties. Here we reveal the super-switching mechanism by using a biased atomic force microscopy tip, that is, the switching of the in-plane super-domains, of a model ferroelectric Pb 0.6 Sr 0.4 TiO 3 . We demonstrate that the writing process is dominated by a super-domain nucleation and stabilization process. A complex scanning-probe trajectory enables on-demand formation of intricate centre-divergent, centre-convergent and flux-closure polar structures. Correlative piezoresponse force microscopy and optical spectroscopy confirm the topological nature and tunability of the emergent structures. The precise and versatile nanolithography in a ferroic material and the stability of the generated structures, also validated by phase-field modelling, suggests potential for reliable multi-state nanodevice architectures and, thereby, an alternative route for the creation of tunable topological structures for applications in neuromorphic circuits.

77 NANOSCIENCE AND NANOTECHNOLOGY↗