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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

11-th order of accuracy for numerical solution of 3-D Poisson equation with irregular interfaces on unfitted Cartesian meshes

For the first time the optimal local truncation error method (OLTEM) with 125-point stencils and unfitted Cartesian meshes has been developed in the general 3-D case for the Poisson equation for heterogeneous materials with smooth irregular interfaces. The 125-point stencils equations that are similar to those for quadratic finite elements are used for OLTEM. The interface conditions for OLTEM are imposed as constraints at a small number of interface points and do not require the introduction of additional unknowns, i.e., the sparse structure of global discrete equations of OLTEM is the same for homogeneous and heterogeneous materials. The stencils coefficients of OLTEM are calculated by the minimization of the local truncation error of the stencil equations. These derivations include the use of the Poisson equation for the relationship between the different spatial derivatives. Such a procedure provides the maximum possible accuracy of the discrete equations of OLTEM. In contrast to known numerical techniques with quadratic elements and third order of accuracy on conforming and unfitted meshes, OLTEM with the 125-point stencils provides 11-th order of accuracy, i.e., an extremely large increase in accuracy by 8 orders for similar stencils. The numerical results show that OLTEM yields much more accurate results than high-order finite elements with much wider stencils. The increased numerical accuracy of OLTEM leads to an extremely large increase in computational efficiency. Additionally, a new post-processing procedure with the 125-point stencil has been developed for the calculation of the spatial derivatives of the primary function. The post-processing procedure includes the minimization of the local truncation error and the use of the Poisson equation. It is demonstrated that the use of the partial differential equation (PDE) for the 125-point stencils improves the accuracy of the spatial derivatives by 6 orders compared to post-processing without the use of PDE as in existing numerical techniques. At an accuracy of 0.1% for the spatial derivatives, OLTEM reduces the number of degrees of freedom by 900 - 4∙10 6 times compared to quadratic finite elements. The developed post-processing procedure can be easily extended to unstructured meshes and can be independently used with existing post-processing techniques (e.g., with finite elements).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

2D materials-assisted heterogeneous integration of semiconductor membranes toward functional devices

Heterogeneous integration techniques allow the coupling of highly lattice-mismatched solid-state membranes, including semiconductors, oxides, and two-dimensional materials, to synergistically fuse the functionalities. The formation of heterostructures generally requires two processes: the combination of crystalline growth and a non-destructive lift-off/transfer process enables the formation of high-quality heterostructures. Although direct atomic interaction between the substrate and the target membrane ensures high-quality growth, the strong atomic bonds at the substrate/epitaxial film interface hinder the non-destructive separation of the target membrane from the substrate. Alternatively, a 2D material-coated compound semiconductor substrate can transfer the weakened (but still effective) surface potential field of the surface through the 2D material, allowing both high-quality epitaxial growth and non-destructive lift-off of the grown film. This Perspective reviews 2D/3D heterogeneous integration techniques, along with applications of III–V compound semiconductors and oxides. Here, the advanced heterogeneous integration methods offer an effective method to produce various freestanding membranes for stackable heterostructures with unique functionalities that can be applied to novel electrical, optoelectronic, neuromorphic, and bioelectronic systems.

2D materials↗
DOE OSTI2022

Understanding Heterogeneities in Quantum Materials

Quantum materials are usually heterogeneous, with structural defects, impurities, surfaces, edges, interfaces, and disorder. These heterogeneities are sometimes viewed as liabilities within conventional systems; however, their electronic and magnetic structures often define and affect the quantum phenomena such as coherence, interaction, entanglement, and topological effects in the host system. Therefore, a critical need is to understand the roles of heterogeneities in order to endow materials with new quantum functions for energy and quantum information science applications. In this article, several representative examples are reviewed on the recent progress in connecting the heterogeneities to the quantum behaviors of real materials. Specifically, three intertwined topic areas are assessed: i) Reveal the structural, electronic, magnetic, vibrational, and optical degrees of freedom of heterogeneities. ii) Understand the effect of heterogeneities on the behaviors of quantum states in host material systems. iii) Control heterogeneities for new quantum functions. This progress is achieved by establishing the atomistic-level structure-property relationships associated with heterogeneities in quantum materials. Finally, the understanding of the interactions between electronic, magnetic, photonic, and vibrational states of heterogeneities enables the design of new quantum materials, including topological matter and quantum light emitters based on heterogenous 2D materials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Computational prediction of dielectric breakdown strength of a transformer paper in oil with uncertainty quantification

The determination of the dielectric breakdown strengths of microstructurally heterogeneous materials has been a primarily experimental endeavor. We report the development of a microstructure-level model for computationally predicting the breakdown strength and analyzing the interactions between electromagnetic pulses (EMP) and the constituents in a composite of cellulose-based paper and mineral oil found in electrical transformers. The model allows explicit simulation of the material breakdown process by tracking the transition of dielectric constituents from non-conductive to conductive states. The focus is on the electric fields induced in the materials and the overall conditions for dielectric breakdown (defined as the onset of avalanche) caused by the electric field induced in the composite. Responses to three distinct pulse shapes, i.e., Steep Front (SF), Lightning (L), and AC with spectra spanning 60–9 × 105 Hz are considered. It is found that the breakdown strength of the material is significantly affected by microstructure heterogeneities, the spatial variations of the constituent properties, and the pulse shapes. A probabilistic characterization of the breakdown strength is computationally obtained and compared with experimental measurements. Although one particular material is analyzed, the model and approach are applicable to other heterogeneous materials as well.

breakdowns↗
DOE OSTI2024

Subsurface Spectroscopy of Thermal Degradation Inside an Inert Plastic Bonded Explosive (PBX) Simulant Using Feedback-Assisted Wavefront Shaping

We characterize the subsurface thermal degradation of an inert analog of high-explosive molecular crystals (Eu:Y(acac) 3 (DPEPO)) (EYAD) embedded inside of a plastic bonded explosive simulant using feedback-assisted wavefront shaping-based fluorescence and Raman spectroscopies. This technique utilizes wavefront shaping to focus pump light inside a heterogeneous material onto a target particle, which significantly improves its spectroscopic signature. We find that embedding the EYAD crystals in the heterogeneous polymer results in improved thermal stability, relative to bare crystal measurements, with the crystal remaining fluorescent to >612 K inside of the heterogeneous material, while the bare crystal’s fluorescence is fully quenched by 500 K. We hypothesize that this improvement is due to the polymer restricting the effects of EYAD melting, which occurs at 400 K and is the primary mechanism for spectroscopic changes in the temperature range explored.

Anderson, Benjamin R.↗
DOE OSTI2025

Adaptive Interface-PINNs (AdaI-PINNs) for inverse problems: Determining material properties for heterogeneous systems

Here, we determine spatially varying discontinuous material properties using a domain-decomposition based physics-informed neural networks (PINNs) framework named the Adaptive Interface-PINNs or AdaI-PINNs (Roy et al., 2024). We propose the use of distinct neural networks for the field variables and material properties within each material, utilizing adaptive activation functions. While the neural networks across different materials share the same weights and biases, their activation functions are uniquely tailored using a hyperparameter that influences the slope of the activation function. The proposed framework is tested on several one-dimensional and two-dimensional benchmark examples, and its performance is compared with conventional PINNs and existing domain-decomposition PINNs frameworks, namely, the Multi-domain physics-informed neural network (M-PINN), and the eXtended physics-informed neural networks (XPINNs). The results demonstrate that the proposed approach can determine randomly distributed discontinuous material properties with an L 2 error of $\mathscr{O}$ (10 -3 ) for the material property and the root-mean-square error of $\mathscr{O}$ (10 -3 ) for the primary variable while the other approaches yield errors that are approximately two orders of magnitude larger (that is, $\mathscr{O}$ (10 -1 )). Moreover, the spatial distribution of material properties obtained using the proposed framework is in close agreement with the true distribution, whereas the other approaches fare much worse. Additionally, the proposed approach is approximately 40% faster than its competitors, indicating its potential as a robust alternative for solving inverse problems in heterogeneous materials.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Pressure Heterogeneity and Material Utilization in Thin-Film Solid-State Cathodes

Intimate interfacial contact between the solid electrolyte and the cathode active material is critical for maximizing cathode utilization in solid-state batteries. However, volume changes during electrochemical cycling induce internal stresses that drive interfacial degradation, particularly under nonuniform stack pressure. In this study, we employ in situ energy-dispersive X-ray diffraction tomography to visualize and quantify reaction heterogeneities across a 3 mm-diameter solid-state cathode with a well-defined interface. Our results reveal that regions under a lower stack pressure exhibit reduced material utilization and reversibility, which negatively affect the high-pressure regions. Interfacial degradation further impedes lithium-ion transport and amplifies microscale reaction heterogeneity. These findings highlight the critical role of stack pressure distribution in governing interfacial stability and electrochemical performance, offering important design insights into practical solid-state battery systems.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Three-dimensional microstructure-explicit and void-explicit mesoscale simulations of detonation of HMX at millimeter sample size scale

Fully three-dimensional (3D) microstructure-explicit and void-explicit mesoscale simulations of the shock-to-detonation (SDT) process of pressed granular HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) are performed. The overall size scale of the models is up to 3 × 3 × 15 mm3, with ∼30 000 grains and 206 265 voids. The models account for the heterogeneous material microstructure, constituent distribution, constituent morphology, and voids. Loading conditions considered involve piston velocities in the range of 600–1200 m/s or pressures in the range of 4–8 GPa. The focus is on analyzing the SDT process and the effects of microstructure and voids on the run-to-detonation distance (RDD). Companion two-dimensional (2D) simulations are also carried out to assess the differences between 2D and 3D. Statistically equivalent microstructure sample sets (SEMSSs) are generated and used for both 2D and 3D, allowing the prediction of the statistical and probabilistic Pop plots (PPs). The predictions are in general agreement with trends in available experimental data in the literature. It is found that both the microstructure (heterogeneous grain size, morphology, and size distribution) and voids significantly affect the RDD and the PPs. These effects are systematically delineated and quantified via the use of SEMSSs with different combinations of attributes. A recently developed probabilistic formulation for the PPs is used to characterize the results, allowing uncertainties in the relations between the shock pressure and RDD arising from material heterogeneities to be quantified. The probabilistic formulation is further used to quantify the confidence levels in the ranked order of influences of different combinations of microstructure and voids on the PPs.

Miller, Christopher (ORCID:0000000206844381)↗
DOE OSTI2022

High-Throughput Nanoindentation Mapping of Additively Manufactured T91 Steel

Here, this work aims to adapt nanoindentation mapping combined with a k-means algorithm as a high-throughput technique to study the nano-scale spatial changes in mechanical properties for a heterogeneous material. This technique can also classify the individual data points based on their properties. Hundreds to thousands of indents were performed on additively manufactured T91 at room temperature, 300°C, 400°C, and 500°C across a square area with a side length of 120 μm to 400 μm. From this data, the hardness and reduced modulus at each point could be calculated and mapped. Using k-means clustering, we were able to arrange the data into three or four clusters corresponding roughly to the ferritic and martensitic phases as well as one or two intermediate clusters sampling both the phases. The hardness of these two phases appears to be quite stable as a function of temperature. Nanoindentation mapping and the k-means algorithm can therefore be used to rapidly assess the feasibility of heterogeneous materials under extreme conditions, such as nuclear reactor steels.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Heterostructure engineering in electrode materials for sodium-ion batteries: Recent progress and perspectives

Sodium-ion batteries (SIBs) have stepped into the spotlight as a promising alternative to lithium-ion batteries for large-scale energy storage systems. However, SIB electrode materials, in general, have inferior performance than their lithium counterparts because Na + is larger and heavier than Li + . Heterostructure engineering is a promising strategy to overcome this intrinsic limitation and achieve practical SIBs. We provide a brief review of recent progress in heterostructure engineering of electrode materials and research on how the phase interface influences Na + storage and transport properties. Efficient strategies for the design and fabrication of heterostructures (in situ methods) are discussed, with a focus on the heterostructure formation mechanism. The heterostructure's influence on Na + storage and transport properties arises primarily from local distortions of the structure and chemomechanical coupling at the phase interface, which may accelerate ion/electron diffusion, create additional active sites, and bolster structural stability. Finally, we offer our perspectives on the existing challenges, knowledge gaps, and opportunities for the advancement of heterostructure engineering as a means to develop practical, high-performance sodium-ion batteries.

25 ENERGY STORAGE↗
DOE OSTI2023

Novel X-Ray Probes of Electronically Heterogeneous Quantum Materials

The goal of this research was to advance the use of resonant soft x-ray scattering (RSXS) by deepening our theoretical understanding of the technique and expanding its use to a wide range of materials. Under this award, we showed how RSXS techniques can be applied to oxide heterostructures, studied commensuration effects in Wigner crystals, discovered a charge density wave in nickel-arsenide superconductors, and measured time-resolved dynamics of charge order in copper-oxide superconductors, among many other achievements. This award contributed to adoption of RSXS techniques by researchers around the nation and the world.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Metal oxide-organic hybrid materials for heterogeneous catalysis and methods of making and using thereof

Catalysts prepared from abundant, cost effective metals, such as cobalt, nickel, chromium, manganese, iron, and copper, and containing one or more neutrally charged ligands (e.g., monodentate, bidentate, and/or polydentate ligands) and methods of making and using thereof are described herein. Exemplary ligands include, but are not limited to, phosphine ligands, nitrogen-based ligands, sulfur-based ligands, and/or arsenic-based ligands. In some embodiments, the catalyst is a cobalt-based catalyst or a nickel-based catalyst. The catalysts described herein are stable and active at neutral pH and in a wide range of buffers that are both weak and strong proton acceptors. While its activity is slightly lower than state of the art cobalt-based water oxidation catalysts under some conditions, it is capable of sustaining electrolysis at high applied potentials without a significant degradation in catalytic current. This enhanced robustness gives it an advantage in industrial and large-scale water electrolysis schemes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Results of the Micromorphic Upscaling Workflow for the PSAAP III Year 3 Report

Predicting the mechanical response and failure of heterogeneous materials has proven difficult. Multiscale numerical methods based in higher order continuum theories attempt to bridge the gap between microscale and macroscale structural behavior. Micromorphic continuum theories have shown promise. The Tardigrade software package is an implementation of Eringen’s micromorphic continuum theory with capabilities to support multiscale material modeling workflows. These include homogenization through the Micromorphic Filter, calibration of micromorphic material models, and macroscale simulation in Tardigrade-MOOSE. This work discusses micromorphic upscaling efforts of the University of Colorado Boulder PSAAP III multidisciplinary simulation center (MSC). Verification studies are presented that compare the accuracy of the upscaling workflow with analytical solutions for a trivial stress state and homogeneous material using direct numerical simulations (DNS) conducted in the Ratel finite element method (FEM) and GEOS material point method (MPM) codes. These verification studies consider upscaling using the Micromorphic Filter for a “single filter domain”. Finally, DNS of a heterogeneous composite material is upscaled using a “multiple filter domain” method.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Unequal {110} Facets: The Potential Role of Intraparticle Heterogeneity and Facet Termination in Photoelectrochemical Activity of Single BiVO 4 Particles

BiVO 4 photoanodes are promising for solar water splitting, with photogenerated electrons and holes preferentially reacting at top {010} and lateral {110} facets, respectively. However, the mechanisms driving this facet-dependent reactivity remain unclear. Here, in this study, we investigate facet-dependent photocurrent and material heterogeneity using correlative scanning photoelectrochemical microscopy (SPCM), electron beam induced current (EBIC) mapping, and mid-IR scattering scanning near-field optical microscopy (s-SNOM). SPCM measurements of 62 BiVO 4 particles confirmed higher photocurrents at lateral {110} facets compared to top {010} facets, but unexpectedly revealed variations in photocurrent among lateral facets within the same particle. Variations in lateral facet surface termination could explain the intraparticle-level reactivity heterogeneity, consistent with theoretical predictions. Nano-FTIR spectroscopy and Raman microspectroscopy indicated significant materials chemistry heterogeneity within individual particles and facets that could be attributed to variations in lattice vibration distortions that enhance the overlap between Bi 6s and O 2p orbitals. The increased orbital overlap is significant as it potentially increases hole mobility in the valence band and potentially explains the lateral facet-dependent charge separation efficiency observed in photocurrent maps. Facet-dependent electrical and EBIC measurements showed no space charge regions at interfacet junctions or metal-BiVO 4 contacts under vacuum, suggesting that photogenerated holes beneath top {010} facets are unlikely to transport to lateral {110} facets to drive water/sulfite oxidation. These findings indicate the potential influence of distinct bulk properties and surface termination chemistries across different particles and facets, highlighting the importance of carefully controlling defects and surface chemistry during sample growth to optimize photocatalytic performance.

BiVO4↗
DOE OSTI2023

A state-of-the-art review of experimental and computational studies of granular materials: Properties, advances, challenges, and future directions

Modeling of heterogeneous materials and media is a problem of fundamental importance to a wide class of phenomena and systems, ranging from condensed matter physics, soft materials, and composite media to porous media, biological systems, geosystems, ceramic engineering, pharmaceutical science and even in space discoveries. Among the most important materials are granular systems, which have received intense interest from the engineering, physics, and mathematics communities. In this review paper, the recent developments and new advances in experimental, and computational methods on a variety of scales and physics that extend understanding to a wide range of materials and phenomena are reviewed. Experimental advances include computed neutron and nanometer-scale tomography, magnetic resonance imaging, refractive index matching, digital image correlation, acoustic emission analysis, and the most recent 4D techniques. Furthermore, a tremendous shift has occurred from the continuum scale to micro-scale and developing multiscale approaches. As such, various computational methods, including, constitutive modeling, discrete modeling, and multiscale approaches, have been developed. In conclusion, aside from all these evolutions, more complicated modeling called coupled, or multiphysics, systems representing a simultaneous presence of heat, fluid, chemical variation, and mechanical effect are also explored.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Learning macroscopic internal variables and history dependence from microscopic models

This paper concerns the study of history dependent phenomena in heterogeneous materials in a two-scale setting where the material is specified at a fine microscopic scale of heterogeneities that is much smaller than the coarse macroscopic scale of application. Here, we specifically study a polycrystalline medium where each grain is governed by crystal plasticity while the solid is subjected to macroscopic dynamic loads. The theory of homogenization allows us to solve the macroscale problem directly with a constitutive relation that is defined implicitly by the solution of the microscale problem. However, the homogenization leads to a highly complex history dependence at the macroscale, one that can be quite different from that at the microscale. In this paper, we examine the use of machine-learning, and especially deep neural networks, to harness data generated by repeatedly solving the finer scale model to: (i) gain insights into the history dependence and the macroscopic internal variables that govern the overall response; and (ii) to create a computationally efficient surrogate of its solution operator, that can directly be used at the coarser scale with no further modeling. We do so by introducing a recurrent neural operator (RNO), and show that: (i) the architecture and the learned internal variables can provide insight into the physics of the macroscopic problem; and (ii) that the RNO can provide multiscale, specifically FE 2 , accuracy at a cost comparable to a conventional empirical constitutive relation.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Stabilization of Ultrasmall Platinum Nanoparticles by Nitrogen-Doped Carbon: Implications for Catalysis and Electrocatalysis

Heterogeneous materials comprising platinum nanoparticles on carbon supports have numerous applications including fuel cell electrodes and heterogeneous catalysts. The effective application of these materials for fuel cells and catalysis will be greatly advanced by the ability to control the oxidation and sintering of the nanoparticles by modifications of the carbon support. One attempt of such control has been doping carbon supports with nitrogen. Here, in this work, a cutting-edge, high-sensitivity, in situ XRD instrument, which allows observation of ultrasmall Pt nanoparticles, has been combined with in situ XPS to provide unprecedented clarity in the characterization of supported Pt nanoparticles in oxidizing and high-temperature environments. On a nitrogen-doped carbon support derived from poly-phenylporphyrin, Pt nanoparticles show increased stability to oxidation and thermal sintering. The enhanced Pt–support interaction arising from the N dopant versus the N-free carbon is manifested by (1) decreased initial Pt particle sizes, (2) small particle size at higher surface densities, (3) increased resistance of Pt nanoparticles to oxidation, (4) increased electron binding energy of Pt0, and (5) increased resistance of Pt nanoparticles to sintering. It is expected that the higher stability of Pt on NC will be manifested in higher activity in fuel cells and high-temperature catalytic reactions.

catalytic reactions↗
DOE OSTI2020

Understanding Microstructure Variability in Vapor-Deposited Energetic Materials by Using Phase-Field Methods

Critical components, such as detonators, in Sandia's stockpile contain heterogeneous materials whose performance and reliability depend on accurate, predictive models of coupled, complex phenomena to predict their synthesis, processing, and operation. Ongoing research in energetic materials has shown that microstructural properties, such as density, pore-size, morphology, and specific surface area are correlated to their initiation threshold and detonation behavior. However, experiments to study these specific characteristics of energetic materials are challenging and time consuming. Therefore, in this work, we turn to mesoscale modeling methods that may be capable of reproducing some observed phenomena to refine and predict outcomes beforehand. Even so, we have no physics-based modeling capability to predict how the microstructure of an energetic material will evolve over near- and long-term time scales. Thus, the goal of this work is to (i) identify any knowledge gaps in how the underlying microstructure forms and evolves during the synthesis process, and (ii) develop and test a mesoscale phase-field model for vapor deposition to capture critical mechanisms of microstructure formation, evolution, and variability in vapor-deposited energetic materials, such as processing conditions, material properties, and substrate interactions. Based on this work, the phase-field method is shown to be a valuable tool for developing the necessary models containing coupled, complex phenomena to investigate and understand the synthesis and processing of energetic materials.

36 MATERIALS SCIENCE↗