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At least 163 records · Page 9

The effects of microstructure on deformation twinning in Mg WE43

The interplay between microstructure and deformation twinning in a WE43-T6 Mg alloy under uniaxial compression was investigated using a combination of scanning electron microscopy with digital image correlation (SEM-DIC) and crystal plasticity finite element (CPFE) simulation. To improve understanding of the statistical characteristics of deformation twin formation, microstructural effects were characterized in over 1000 grains through metrics including the nominal Schmid Factor, grain size, geometric compatibility factor (m'), residual Burgers vector, and the strain accommodated by neighboring grains. There was a strong correlation between the nominal Schmid Factor and both twin activation and variant selection, but this was not fully deterministic. Deformation twinning also exhibited a strong dependence on existing slip and twinning in the neighboring grain and on the m' value. Within the range of grain sizes present in this condition, grain size was determined to have minimal effect on deformation twinning. Finally, statistical analysis of CPFE simulations was used to further investigate microstructural effects on twinning, and qualitatively captured the effect of the nominal Schmid Factor.

36 MATERIALS SCIENCE↗

A long short-term memory embedding for hybrid uplifted reduced order models

In this paper, we introduce an uplifted reduced order modeling (UROM) approach through the integration of standard projection based methods with long short-term memory (LSTM) embedding. Our approach has three modeling layers or components. In the first layer, we utilize an intrusive projection approach to model dynamics represented by the largest modes. The second layer consists of an LSTM model to account for residuals beyond this truncation. This closure layer refers to the process of including the residual effect of the discarded modes into the dynamics of the largest scales. However, the feasibility of generating a low rank approximation tails off for higher Kolmogorov n -width systems due to the underlying nonlinear processes. The third uplifting layer, called super-resolution, addresses this limited representation issue by expanding the span into a larger number of modes utilizing the versatility of LSTM. Therefore, our model integrates a physics-based projection model with a memory embedded LSTM closure and an LSTM based super-resolution model. In several applications, we exploit the use of Grassmann manifold to construct UROM for unseen conditions. We performed numerical experiments by using the Burgers and Navier-Stokes equations with quadratic nonlinearity. Finally, our results show robustness of the proposed approach in building reduced order models for parameterized systems and confirm the improved trade-off between accuracy and efficiency.

42 ENGINEERING↗

Characterizing defect structures in AM steel using direct electron detection EBSD

The mechanical properties of additive and traditionally manufactured alloys are largely dependent on the characteristics and distribution of dislocation cell networks that develop during the fabrication process. This work demonstrates the ability to quantitatively characterize these dislocation structures by high angular resolution electron backscatter diffraction analysis using a direct electron detector. The defect structures are characterized in terms of the geometrically necessary dislocation density and the associated Burgers vector and line direction. Furthermore, the results are discussed in terms of potential defect formation mechanisms.

36 MATERIALS SCIENCE↗

Extended defects in GaAs/GaAs 1-x Sb x /GaAs (001) heterostructures

The atomic-scale structure of extended defects in GaAs/GaAs 1-x Sb x /GaAs (001) heterostructures has been characterized using aberration-corrected scanning transmission electron microscopy. The defect located at the tensile-strained GaAs(cap)/GaAs 0.34 Sb 0.66 interface had no edge component in the projection plane and is identified as either a dissociated screw dislocation or a partial dislocation dipole. The associated intrinsic stacking fault is bounded by two 30° Shockley partial dislocations of opposite sign. Another defect, located at the compressively-strained GaAs 0.91 Sb 0.09 /GaAs(substrate) interface, is identified as a dissociated 90° dislocation. The associated intrinsic stacking fault is bounded by a 30° Shockley partial dislocation and a partial dislocation with a Burgers vector of either or , where a is the lattice constant. Unpaired atomic columns observed at the cores of the 30° Shockley partial dislocations indicate that both defects belong primarily to the glide set.

36 MATERIALS SCIENCE↗

Correlating results from high resolution EBSD with TEM- and ECCI-based dislocation microscopy: Approaching single dislocation sensitivity via noise reduction

High resolution electron backscatter diffraction (HREBSD), an SEM-based diffraction technique, may be used to measure the lattice distortion of a crystalline material and to infer the geometrically necessary dislocation content. Uncertainty in the image correlation process used to compare diffraction patterns leads to an uneven distribution of measurement noise in terms of the lattice distortion, which results in erroneous identification of dislocation type and density. This work presents a method of reducing noise in HREBSD dislocation measurements by removing the effect of the most problematic components of the measured distortion. The method is then validated by comparing with TEM analysis of dislocation pile-ups near a twin boundary in austenitic stainless steel and with ECCI analysis near a nano-indentation on a tantalum oligocrystal. Finally, the HREBSD dislocation microscopy technique is able to resolve individual dislocations visible in TEM and ECCI and correctly identify their Burgers vectors.

36 MATERIALS SCIENCE↗

Application of Dislocation Theory to Minimize Defects in Artificial Solids Built with Nanocrystal Building Blocks

Conspectus. Oriented atomic attachment of colloidal inorganic nanocrystals represents a powerful synthetic method for preparing complex inorganic superstructures. Examples include fusion of nanocrystals into dimer and superlattice structures. If the attachment were perfect throughout, then the resulting materials would have single crystal-like alignment of the individual nanocrystals' atomic lattices. While individual colloidal nanocrystals typically are free of many defects, there are a multitude of pathways that can generate defects upon nanocrystal attachment. These attachment generated defects are typically undesirable, and thus developing strategies to favor defect-free attachment or heal defective interfaces are essential. There may also be some cases where attachment-derived defects are desirable. In this Account, we summarize our current understanding of how these defects arise, in order to offer guidance to those who are designing nanocrystal derived solids. The small size of inorganic nanocrystals means short diffusion lengths to the surface, which favor the formation of nanocrystal building blocks with pristine atomic structures. Upon attachment, however, there are numerous pathways that can lead to atomic scale defects, and bulk crystal dislocation theory provides an invaluable guide to understanding these phenomena. As an example, an atomic step edge can be incorporated into the interface leading to an extra half-plane of atoms, known as an edge dislocation. These dislocations can be well described by the Burgers vector description of dislocations, which geometrically identifies planes in which a dislocation can move. Our in situ measurements have verified that bulk dislocation theory predictions for 1D defects hold true at few-nanometer length scales in PbTe and CdSe nanocrystal interfaces. Ultimately, the applicability of dislocation theory to nanocrystal attachment enables the predictive design of attachment to prevent or facilitate healing of defects upon nanocrystal attachment. We applied similar logic to understand formation of planar (2D) defects such as stacking faults upon nanocrystal attachment. Again concepts from bulk crystal defect crystallography can identify attachment pathways that can prevent or deterministically form planar defects upon nanocrystal attachment. The concepts we discuss work well for identifying favorable attachment geometries for nanocrystal pairs ; however it is currently unclear how to translate these ideas to near-simultaneous multiparticle attachment. Geometric frustration, which prevents nanocrystal rotation, and yet-to-be considered defect generation pathways unique to multiparticle attachment complicate defect-free superlattice attachment. New imaging methods now allow for the direct observation of local attachment trajectories and may enable improved understanding of such multiparticle phenomena. With further refinement, a unified framework for understanding and ultimately eliminating structural defects in fused nanocrystal superstructures may well be achievable in coming years.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Insights into Prismatic Loop Formation in Irradiated Fe–Cr Alloys from Hypothesis-Driven Active Learning and Causal Analysis

Neutron and electron irradiation experimental studies conducted on body-centered cubic Fe and Fe–Cr alloys have established two prismatic dislocation loop populations, which have Burgers vectors of either a/2$\langle$111$\rangle$ or a$\langle$100$\rangle$. Here, the loop formation depends on factors such as dose (D), dose rate (D rt ), temperature (T), chromium content (Cr%), and other alloying elements. Hence, it is important to understand how irradiation-induced dislocation loops evolve conditional upon the loop characteristics, such as loop density (DD), average loop size d̅, and irradiation parameters (D, D rt , T, and irradiation type), which is still an active area of research. To understand these complex structure–property relationships, machine learning (ML) is employed in a three-step approach. This includes imputing missing data with a k-nearest neighbor, generating functionalized features, and assessing feature importance with random forest classification and regression. Physics-based features are incorporated in a hypothesis-driven active learning scheme to overcome data unavailability challenges. Insights obtained from ML models (i) to categorize dislocation loop types, show the highest correlation with d̅; (ii) Log(DD), obtained through mathematical formulations involving D, Cr%, d̅, and T (e.g., Log(DD) ~ D + exp(-Cr%) + 1/d̅ and log(DD) ~ D + exp(-Cr%) + 1/T). Hypothesis-driven active learning is able to predict Log(DD) in which the experimental date is not known. Causal models verify cause–effect relationships for dislocation loop classification and irradiation factors in FeCr alloys.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Generation of low–latitude seamount–trapped waves: a case study of the Seychelles Plateau

Baroclinic seamount-trapped waves are thought to influence their surrounding ecosystem; however, trapped waves are not well-studied in near-equatorial settings, where stratification is strong and Burger numbers are large. Motivated by observations, we use daily output (2005-2009) from the global 0.1-degree Parallel Ocean Program Model (POP) to examine topographically trapped baroclinic waves around the Seychelles Plateau (S > 400) in the tropical Indian Ocean. These trapped waves are associated with velocity and temperature oscillations at periods of 15–16 days, similar to the dominant period of some equatorial Yanai waves. Energy flux maps using POP output suggest that quasi-biweekly equatorial Yanai waves excite trapped waves on the western and south-western flanks of the Seychelles Plateau, near the surface. Here, the anticyclonic energy flux associated with the trapped wave extends vertically throughout the water column and around most of the plateau circumference, diminishing on the eastern flank of the plateau. This work highlights the role that equatorial planetary waves and trapped waves play in facilitating energy redistribution, dissipation, and mixing in the tropical ocean.

58 GEOSCIENCES↗

Mild-to-wild plastic transition is governed by athermal screw dislocation slip in bcc Nb

Plastic deformation in crystals is mediated by the motion of line defects known as dislocations. For decades, dislocation activity has been treated as a homogeneous, smooth continuous process. However, it is now recognized that plasticity can be determined by long-range correlated and intermittent collective dislocation processes, known as avalanches. Here we demonstrate in body-centered cubic Nb how the long-range and scale-free dynamics at room temperature are progressively quenched out with decreasing temperature, eventually revealing intermittency with a characteristic length scale that approaches the Burgers vector itself. Plasticity is shown to be bimodal across the studied temperature regime, with conventional thermally-activated smooth plastic flow (‘mild’) coexisting with sporadic bursts (‘wild’) controlled by athermal screw dislocation activity, thereby violating the classical notion of temperature-dependent screw dislocation motion at low temperatures. An abrupt increase of the athermal avalanche component is identified at the critical temperature of the material. Our results indicate that plasticity at any scale can be understood in terms of the coexistence of these mild and wild modes of deformation, which could help design better alloys by suppressing one of the two modes in desired temperature windows.

36 MATERIALS SCIENCE↗

Variational multiscale reinforcement learning for discovering reduced order closure models of nonlinear spatiotemporal transport systems

Abstract A central challenge in the computational modeling and simulation of a multitude of science applications is to achieve robust and accurate closures for their coarse-grained representations due to underlying highly nonlinear multiscale interactions. These closure models are common in many nonlinear spatiotemporal systems to account for losses due to reduced order representations, including many transport phenomena in fluids. Previous data-driven closure modeling efforts have mostly focused on supervised learning approaches using high fidelity simulation data. On the other hand, reinforcement learning (RL) is a powerful yet relatively uncharted method in spatiotemporally extended systems. In this study, we put forth a modular dynamic closure modeling and discovery framework to stabilize the Galerkin projection based reduced order models that may arise in many nonlinear spatiotemporal dynamical systems with quadratic nonlinearity. However, a key element in creating a robust RL agent is to introduce a feasible reward function, which can be constituted of any difference metrics between the RL model and high fidelity simulation data. First, we introduce a multi-modal RL to discover mode-dependant closure policies that utilize the high fidelity data in rewarding our RL agent. We then formulate a variational multiscale RL (VMRL) approach to discover closure models without requiring access to the high fidelity data in designing the reward function. Specifically, our chief innovation is to leverage variational multiscale formalism to quantify the difference between modal interactions in Galerkin systems. Our results in simulating the viscous Burgers equation indicate that the proposed VMRL method leads to robust and accurate closure parameterizations, and it may potentially be used to discover scale-aware closure models for complex dynamical systems.

97 MATHEMATICS AND COMPUTING↗

Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by incorporating physical principles into the model. Most PiDL approaches regularize training by embedding governing equations into the loss function, yet this depends heavily on extensive hyperparameter tuning to weigh each loss term. To this end, we propose to leverage physics prior knowledge by “baking” the discretized governing equations into the neural network architecture via the connection between the partial differential equations (PDE) operators and network structures, resulting in a PDE-preserved neural network (PPNN). This method, embedding discretized PDEs through convolutional residual networks in a multi-resolution setting, largely improves the generalizability and long-term prediction accuracy, outperforming conventional black-box models. The effectiveness and merit of the proposed methods have been demonstrated across various spatiotemporal dynamical systems governed by spatiotemporal PDEs, including reaction-diffusion, Burgers’, and Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗

Multiscale analysis of large twist ferroelectricity and swirling dislocations in bilayer hexagonal boron nitride

With its atomically thin structure and intrinsic ferroelectric properties, heterodeformed bilayer hexagonal boron nitride (hBN) has gained prominence in next-generation non-volatile memory applications. However, studies to date have focused almost exclusively on small-twist bilayer hBN, leaving the question of whether ferroelectricity can persist under small heterostrain and large heterodeformation entirely unexplored. In this work, we establish the crystallographic origin of ferroelectricity in bilayer hBN configurations heterodeformed relative to high-symmetry configurations such as AA-stacking and 21.786789° twisted configurations (Σ7), using Smith normal form bicrystallography. We then demonstrate out-of-plane ferroelectricity in bilayer hBN across configurations vicinal to both the AA and Σ7 stackings. Atomistic simulations reveal that AA-vicinal systems support ferroelectricity under both small twist and small strain, with polarization switching in the latter governed by the deformation of swirling dislocations rather than the straight interface dislocations seen in the former. For Σ7-vicinal systems, where existing interatomic potentials underperform particularly under extreme out-of-plane compression, we develop a density-functional-theory-informed continuum framework—the bicrystallography-informed frame-invariant multiscale (BFIM) model, which captures out-of-plane ferroelectricity in heterodeformed configurations vicinal to Σ7 stacking. Interface dislocations in these large heterodeformed bilayer configurations exhibit markedly smaller Burgers vectors compared to interface dislocations in small-twist and small-strain bilayer hBN. The BFIM model reproduces experimental results and provides a powerful, computationally efficient framework for predicting ferroelectricity in large-unit-cell heterostructures where atomistic simulations are prohibitively expensive.

Ahmed, Md Tusher [Univ. of Illinois at Urbana-Cham↗

Stability analysis of the Eulerian–Lagrangian finite volume methods for nonlinear hyperbolic equations in one space dimension

In this paper, we construct a novel Eulerian–Lagrangian finite volume (ELFV) method for nonlinear scalar hyperbolic equations in one space dimension. It is well known that the exact solutions to such problems may contain shocks though the initial conditions are smooth, and direct numerical methods may suffer from restricted time step sizes. To relieve the restriction, we propose an ELFV method, where the space-time domain was separated by the partition lines originated from the cell interfaces whose slopes are obtained following the Rakine–Hugoniot junmp condition. Unfortunately, to avoid the intersection of the partition lines, the time step sizes are still limited. To fix this gap, we detect effective troubled cells (ETCs) and carefully design the influence region of each ETC, within which the partitioned space-time regions are merged together to form a new one. Then with the new partition of the space-time domain, we theoretically prove that the proposed first-order scheme with Euler forward time discretization is total-variation-diminishing and maximum-principle-preserving with at least twice larger time step constraints than the classical first order Eulerian method for Burgers’ equation. Numerical experiments verify the optimality of the designed time step sizes.

97 MATHEMATICS AND COMPUTING↗

Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

A common strategy for the dimensionality reduction of nonlinear partial differential equations (PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics in this reduced space. However, advection-dominated PDEs are represented poorly by this methodology since the process of truncation discards important interactions between higher-order modes during time evolution. In this study, we demonstrate that encoding using convolutional autoencoders (CAEs) followed by a reduced-space time evolution by recurrent neural networks overcomes this limitation effectively. We demonstrate that a truncated system of only two latent space dimensions can reproduce a sharp advecting shock profile for the viscous Burgers equation with very low viscosities, and a six-dimensional latent space can recreate the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Furthermore, our results show that these advection-dominated systems are more amenable to low-dimensional encoding and time evolution by a CAE and recurrent neural network combination than the POD-Galerkin technique.

97 MATHEMATICS AND COMPUTING↗

Probing the lattice structure of dynamically compressed and released single crystal iron through the alpha to epsilon phase transition

In this work, experiments using broadband Laue x-ray diffraction (XRD) were used to examine the lattice structure of dynamically compressed [100]-oriented single crystal iron samples at the Dynamic Compression Sector at the Advanced Photon Source. These experiments used 1 μm thick iron single crystal samples sandwiched between a polyimide ablator and a polycarbonate window. A 100 J, 10 ns duration laser pulse incident on the polyimide ablator was used to shock compress the iron samples to initial stresses greater than 25 GPa, exceeding the ~13 GPa alpha (body-centered-cubic or bcc structure) to epsilon (hexagonal-close-packed or hcp structure) phase transition stress. XRD measurements were performed at various times relative to the shock wave entering the iron sample: early times, <~150 ps while the initial shock waves propagated through the iron; intermediate times, after the iron equilibrated with the ablator and window reaching a plateau stress state (12 or 17 GPa) lasting several nanoseconds; and late times, during uniaxial strain release. The early time measurements show that in <~150 ps, the high-pressure hcp phase is relaxed with a c/a ratio of 1.61, contrary to previous laser shock experiments where a c/a ratio of 1.7 was inferred. In the plateau stress state and partially released states, XRD measurements showed that the hcp structure retained a c/a ratio of 1.61 with no observable changes in the microstructure. Upon stress release at ~1 GPa/ns release rate, the reverse phase transition (hcp to bcc) to the original single crystal orientation (implying a transformation memory effect) was observed to reach completion somewhere between 13 and 11 GPa, indicating little stress hysteresis under rapid uniaxial strain release. A similar memory effect for the reverse hcp to bcc transformation has been previously observed under hydrostatic compression. However, the bcc/hcp orientation relationships differ somewhat between dynamic and static compression experiments, implying that the transformation pathway under uniaxial dynamic strain differs from the Burgers mechanism.

36 MATERIALS SCIENCE↗

Structure of V-defects in long wavelength GaN-based light emitting diodes

The V-defect is a naturally occurring inverted hexagonal pyramid structure that has been studied in GaN and InGaN growth since the 1990s. Strategic use of V-defects in pre-quantum well superlattices or equivalent preparation layers has enabled record breaking efficiencies for green, yellow, and red InGaN light emitting diodes (LEDs) utilizing lateral injection of holes through the semi-polar sidewalls of the V-defects. In this article, we use advanced characterization techniques such as scattering contrast transmission electron microscopy, high angle annular dark field scanning transmission electron microscopy, x-ray fluorescence maps, and atom probe tomography to study the active region compositions, V-defect formation, and V-defect structure in green and red LEDs grown on (0001) patterned sapphire and (111) Si substrates. We identify two distinct types of V-defects. The “large” V-defects are those that form in the pre-well superlattice and promote hole injection, usually nucleating on mixed (Burgers vector b = ±a±c⁠) character threading dislocations. In addition, “small” V-defects often form in the multi-quantum well region and are believed to be deleterious to high-efficiency LEDs by providing non-radiative pathways. The small V-defects are often associated with basal plane stacking faults or stacking fault boxes. Furthermore, we show through scattering contrast transmission electron microscopy that during V-defect filling, the threading dislocation, which runs up the center of the V-defect, will “bend” onto one of the six {10$\overline{1}$1} semi-polar planes. In conclusion, this result is essential to understanding non-radiative recombination in V-defect engineered LEDs.

42 ENGINEERING↗

Polarization near dislocation cores in SrTiO 3 single crystals: The role of flexoelectricity

Spontaneous polarization as large as ~28 μC/cm 2 was recently observed around the dislocation cores in non-polar SrTiO 3 bulk crystals, and its origin was attributed to the flexoelectric effect, i.e., polarization induced by strain gradients. However, the roles of flexoelectricity, relative to other electromechanical contributions, and the nature of dislocations, i.e., edge vs screw dislocations in the induced polarization, are not well understood. In this work, we study the role of flexoelectricity in inducing polarization around three types of dislocation cores in SrTiO 3 : b= a(100) edge dislocation, b= a(110) edge dislocation, and b= a(010) screw dislocation, where b is the Burgers vector. For the edge dislocations, polarization can be induced by electrostriction alone, while flexoelectricity is essential for stabilizing the symmetric polarization pattern. The shear component of the flexoelectric tensor has a dominant effect on the magnitude and spatial distribution of the flexoelectric polarization. In contrast, no polarization is induced around the b= a(010) screw dislocation through either electrostriction or flexoelectricity. Finally, our findings provide an in-depth understanding of the role of flexoelectricity in inducing polarization around dislocation cores and offer insights into the defect engineering of dielectric/ferroelectric materials.

36 MATERIALS SCIENCE↗

Probabilistic flux limiters

The stable numerical integration of shocks in compressible flow simulations relies on the reduction or elimination of Gibbs phenomena (unstable, spurious oscillations). A popular method to virtually eliminate Gibbs oscillations caused by numerical discretization in under-resolved simulations is to use a flux limiter. A wide range of flux limiters have been studied in the literature, with recent interest in their optimization via machine learning methods trained on high-resolution datasets. The common use of flux limiters in numerical codes as plug-and-play blackbox components makes them key targets for design improvement. Even for deterministic dynamical models, numerical uncertainty is introduced via coarse-graining required by insufficient computational power to solve all scales of motion. Conventional flux limiters are deterministic and lack the capacity to address uncertainties, both aleatoric (inherent randomness) and epistemic (modeling uncertainty due to limited knowledge), which arise in coarse-grained numerical simulations. Here, we introduce a conceptually distinct type of flux limiter that is designed to handle the effects of randomness in the model and uncertainty in model parameters. Unlike traditional single-function flux limiters, these new probabilistic flux limiters incorporate multiple flux limiting functions, each applied with a learned probability drawn from high-resolution data to mitigate the effects of uncertainty in numerical simulations. This approach departs from traditional single-function limiters by explicitly modeling and incorporating uncertainty into the shock capturing process. Using the example of Burgers' equation as a testbed, we show that a machine learned, probabilistic flux limiter may be used in a shock capturing code to more accurately capture shock profiles. In particular, we show that our probabilistic flux limiter outperforms standard limiters and can be successively improved upon (up to a point) by expanding the set of probabilistically chosen flux limiting functions.

97 MATHEMATICS AND COMPUTING↗