We introduce physics-informed multimodal autoencoders (PIMA)-a variational inference framework for discovering shared information in multimodal datasets. Individual modalities are embedded into a shared latent space and fused through a product-of-experts formulation, enabling a Gaussian mixture prior to identify shared features. Sampling from clusters allows cross-modal generative modeling, with a mixture-of-experts decoder that imposes inductive biases from prior scientific knowledge and thereby imparts structured disentanglement of the latent space. This approach enables cross-modal inference and the discovery of features in high-dimensional heterogeneous datasets. Consequently, this approach provides a means to discover fingerprints in multimodal scientific datasets and to avoid traditional bottlenecks related to high-fidelity measurement and characterization of scientific datasets.
Finding alloys with specific design properties is challenging due to the large number of possible compositions and the complex interactions between elements. This study introduces a multi-objective Bayesian optimization approach guiding molecular dynamics simulations for discovering high-performance refractory alloys with both targeted intrinsic static thermomechanical properties and also deformation mechanisms occurring during dynamic loading. The objective functions are aiming for excellent thermomechanical stability via a high bulk modulus, a low thermal expansion, a high heat capacity, and for a resilient deformation mechanism maximizing the retention of the BCC phase after shock loading. Contrasting two optimization procedures, we show that the Pareto-optimal solutions are confined to a small performance space when the property objectives display a cooperative relationship. Conversely, the Pareto front is much broader in the performance space when these properties have antagonistic relationships. Density functional theory simulations validate these findings and unveil underlying atomic-bond changes driving property improvements.
We present a comprehensive benchmarking framework for evaluating machine-learning approaches applied to phase-field problems. This framework focuses on four key analysis areas crucial for assessing the performance of such approaches in a systematic and structured way. Firstly, interpolation tasks are examined to identify trends in prediction accuracy and accumulation of error over simulation time. Secondly, extrapolation tasks are also evaluated according to the same metrics. Thirdly, the relationship between model performance and data requirements is investigated to understand the impact on predictions and robustness of these approaches. Finally, systematic errors are analyzed to identify specific events or inadvertent rare events triggering high errors. Quantitative metrics evaluating the local and global description of the microstructure evolution, along with other scalar metrics representative of phase-field problems, are used across these four analysis areas. This benchmarking framework provides a path to evaluate the effectiveness and limitations of machine-learning strategies applied to phase-field problems, ultimately facilitating their practical application.
Materials simulations based on direct numerical solvers are accurate but computationally expensive for predicting materials evolution across length- and time-scales, due to the complexity of the underlying evolution equations, the nature of multiscale spatiotemporal interactions, and the need to reach long-time integration. We develop a method that blends direct numerical solvers with neural operators to accelerate such simulations. This methodology is based on the integration of a community numerical solver with a U-Net neural operator, enhanced by a temporal-conditioning mechanism to enable accurate extrapolation and efficient time-to-solution predictions of the dynamics. We demonstrate the effectiveness of this hybrid framework on simulations of microstructure evolution via the phase-field method. Such simulations exhibit high spatial gradients and the co-evolution of different material phases with simultaneous slow and fast materials dynamics. We establish accurate extrapolation of the coupled solver with large speed-up compared to DNS depending on the hybrid strategy utilized. This methodology is generalizable to a broad range of materials simulations, from solid mechanics to fluid dynamics, geophysics, climate, and more.
This dataset is comprised of a library of atomistic structure files and corresponding X-ray diffraction (XRD) profiles and vibrational density of states (VDoS) profiles for bulk single crystal silicon (Si), gold (Au), magnesium (Mg), and iron (Fe) with and without disorder introduced into the atomic structure and with and without mechanical loading. Included with the atomistic structure files are descriptor files that measure the stress state, phase fractions, and dislocation content of the microstructures. All data was generated via molecular dynamics or molecular statics simulations using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code. This dataset can inform the understanding of how local or global changes to a materials microstructure can alter their spectroscopic and diffraction behavior across a variety of initial structure types (cubic diamond, face-centered cubic (FCC), hexagonal close-packed (HCP), and body-centered cubic (BCC) for Si, Au, Mg, and Fe, respectively) and overlapping changes to the microstructure (i.e., both disorder insertion and mechanical loading).
As the field of low-dimensional materials (1D or 2D) grows and more complex and intriguing structures are continuing to be found, there is an emerging need for techniques to characterize the nanoscale mechanical properties of all kinds of 1D/2D materials, in particular in their most practical state: sitting on an underlying substrate. While traditional nanoindentation techniques cannot accurately determine the transverse Young's modulus at the necessary scale without large indentations depths and effects to and from the substrate, herein an atomic-force-microscopy-based modulated nanomechanical measurement technique with Angstrom-level resolution (MoNI/ÅI) is presented. This technique enables non-destructive measurements of the out-of-plane elasticity of ultra-thin materials with resolution sufficient to eliminate any contributions from the substrate. This method is used to elucidate the multi-layer stiffness dependence of graphene deposited via chemical vapor deposition and discover a peak transverse modulus in two-layer graphene. While MoNI/ÅI has been used toward great findings in the recent past, here all aspects of the implementation of the technique as well as the unique challenges in performing measurements at such small resolutions are encompassed.
Junctions are discontinuities in flat grain boundaries that arise in all polycrystalline materials and are thought to play important roles in the response of a grain boundary network to thermal and mechanical loads. A key open question concerns the mechanisms by which solute segregation to junctions impacts properties of the grain boundary. Here, in this work, we investigate the influence of grain boundary facet junctions on solute embrittlement, and we present an analytical model that uses the hydrostatic stress field contributed by dislocations at multiple junctions to describe these effects. Specifically, we study junctions between {112} facets of various lengths in Au $\langle111\rangle$ Σ3 tilt grain boundaries. Copper and silver solutes are employed to determine if the effect of junctions on solute segregation and embrittlement is dependent on size relative to the host. Combined, atomistic simulation data and the analytical model show that Cu and Ag have opposite segregation responses to junctions due to the sign of the hydrostatic stress field induced by junctions. However, a positive shift in the embrittling potency is computed near junctions regardless of solute type or the stress state of the segregation site. Hence, for the conditions studied, junctions consistently shift the energetic landscape towards embrittlement.
We present a high-level architecture for how artificial intelligences might advance and accumulate scientific and technological knowledge, inspired by emerging perspectives on how human intelligences advance and accumulate such knowledge. Agents advance knowledge by exercising a technoscientific method—an interacting combination of scientific and engineering methods. The technoscientific method maximizes a quantity we call “useful learning” via more-creative implausible utility (including the “aha!” moments of discovery), as well as via less-creative plausible utility. Society accumulates the knowledge advanced by agents so that other agents can incorporate and build on to make further advances. The proposed architecture is challenging but potentially complete: its execution might in principle enable artificial intelligences to advance and accumulate an equivalent of the full range of human scientific and technological knowledge.
Recent developments integrating micromechanics and neural networks offer promising paths for rapid predictions of the response of heterogeneous materials with similar accuracy as direct numerical simulations. The deep material network is one such approaches, featuring a multi-layer network and micromechanics building blocks trained on anisotropic linear elastic properties. Once trained, the network acts as a reduced-order model, which can extrapolate the material’s behavior to more general constitutive laws, including nonlinear behaviors, without the need to be retrained. However, current training methods initialize network parameters randomly, incurring inevitable training and calibration errors. Here, we introduce a way to visualize the network parameters as an analogous unit cell and use this visualization to “quilt” patches of shallower networks to initialize deeper networks for a recursive training strategy. The result is an improvement in the accuracy and calibration performance of the network and an intuitive visual representation of the network for better explainability.
Characterizing and quantifying microstructure evolution is critical to forming quantitative relationships between material processing conditions, resulting microstructure, and observed properties. Machine-learning methods are increasingly accelerating the development of these relationships by treating microstructure evolution as a pattern recognition problem, discovering relationships explicitly or implicitly. These methods often rely on identifying low-dimensional microstructural fingerprints as latent variables. However, using inappropriate latent variables can lead to challenges in learning meaningful relationships. In this work, we survey and discuss the ability of various linear and nonlinear dimensionality reduction methods including principal component analysis, autoencoders, and diffusion maps to quantify and characterize the learned latent space microstructural representations and their time evolution. We characterize latent spaces by their ability to represent high-dimensional microstructural data in terms of compression achieved as a function of the number of latent dimensions required to represent the data accurately, their accuracy based on their reconstruction performance, and the smoothness of the microstructural trajectories in latent dimension. We quantify these metrics for common microstructure evolution problems in material science including spinodal decomposition of a binary metallic alloy, thin film deposition of a binary metallic alloy, dendritic growth, and grain growth in a polycrystal. This study provides considerations and guidelines for choosing dimensionality reduction methods when considering materials problems that involve high dimensional data and a variety of features over a range of lengths and time scales.
Nearly all metals, alloys, ceramics, and their associated composites are polycrystalline in nature, with grain boundaries that separate well-defined crystalline regions that influence materials properties. In all but the most pure elemental systems, intentional solutes or impurities are present and can segregate to, or less commonly away from, the grain boundaries, in turn influencing boundary behavior, their stability, and associated materials properties. In some cases, grain-boundary segregation can also trigger “phase-like” structural transitions that dramatically alter the essential nature of the boundary. With the development of advanced electron microscopy techniques, researchers can directly observe grain-boundary structures and segregation with atomic precision. Despite such spatial resolution, the underlying mechanisms governing grain-boundary segregation remain difficult to characterize. As a result, computational modeling techniques such as density functional theory, molecular dynamics, mesoscale phase-field, continuum defect theory, and others are important complementary tools to experimental observations for studying grain-boundary segregation behavior. In conclusion, these computational methods offer the ability to explore the underlying formation mechanisms of grain-boundary segregation, elucidate complex segregation behavior, and provide insights into solutions to effectively controlling microstructure.
Computer Methods in Applied Mechanics and Engineering
Dingreville, Remi; Francis, Noah M.; Pourahmadian, Fatemeh; Lebensohn, Ricardo A.
This work presents a spectral micromechanical formulation for obtaining the full-field and homogenized response of elastic micropolar composites. The algorithm relies on a coupled set of convolution integral equations for the micropolar strains, where periodic Green’s operators associated with a linear homogeneous reference medium are convolved with functions of the Cauchy and couple stress fields that encode the material’s heterogeneity, as well as any potential material nonlinearity. Such convolution integral equations take an algebraic form in the reciprocal Fourier space that can be solved iteratively. In this vein, the fast Fourier transform (FFT) algorithm is leveraged to accelerate the numerical solution, resulting in a mesh-free formulation in which the periodic unit cell representing the heterogeneous material can be discretized by a regular grid of pixels in two dimensions (or voxels in three dimensions). For verification, the numerical solutions obtained with the micropolar FFT solver are compared with analytical solutions for a matrix with a dilute circular inclusion subjected to plane strain loading. The developed computational framework is then used to study length-scale effects and effective (micropolar) moduli of composites with various topological configurations.
Dingreville, Remi; Startt, Jacob K.; Elmslie, Timothy A.; Yang, Yang; Soto-Medina, Sujeily; Zappala, Emma; Meisel, Mark W.; Manuel, Michele V.; Frandsen, Benjamin A.; Hamlin, James J.
Magnetic properties of more than 20 Cantor alloy samples of varying composition were investigated over a temperature range of 5 K to 300 K and in fields of up to 70 kOe using magnetometry and muon spin relaxation. Two transitions are identified: a spin-glass-like transition that appears between 55K and 190K, depending on composition, and a ferrimagnetic transition that occurs at approximately 43K in multiple samples with widely varying compositions. The magnetic signatures at 43K are remarkably insensitive to chemical composition. A modified Curie-Weiss model was used to fit the susceptibility data and to extract the net effective magnetic moment for each sample. The resulting values for the net effective moment were either diminished with increasing Cr or Mn concentrations or enhanced with decreasing Fe, Co, or Ni concentrations. Beyond a sufficiently large effective moment, the magnetic ground state transitions from ferrimagnetism to ferromagnetism. The effective magnetic moments, together with the corresponding compositions, are used in a global linear regression analysis to extract element-specific effective magnetic moments, which are compared to the values obtained by ab initio based density functional theory calculations. Finally, these moments provide the information necessary to controllably tune the magnetic properties of Cantor alloy variants.
Machine learning is on a bit of a tear right now, with advances that are infiltrating nearly every aspect of our lives. In the domain of materials science, this wave seems to be growing into a tsunami. Yet, there are still real hurdles that we face to maximize its benefit. This Matter of Opinion, crafted as a result of a workshop hosted by researchers at Sandia National Laboratories and attended by a cadre of luminaries, briefly summarizes our perspective on these barriers. By recognizing these problems in a community forum, we can share the burden of their resolution together with a common purpose and coordinated effort.
Multimodal datasets of materials are rich sources of information which can be leveraged for expedited discovery of process–structure–property relationships and for designing materials with targeted structures and/or properties. For this data descriptor article, we provide a multimodal dataset of magnetron sputter-deposited molybdenum (Mo) thin films, which are used in a variety of industries including high temperature coatings, photovoltaics, and microelectronics. In this dataset we explored a process space consisting of 27 unique combinations of sputter power and Ar deposition pressure. Here, the phase, structure, surface morphology, and composition of the Mo thin films were characterized by x-ray diffraction, scanning electron microscopy, atomic force microscopy, and Rutherford backscattering spectrometry. Physical properties—namely, thickness, film stress and sheet resistance—were also measured to provide additional film characteristics and behaviors. Additionally, nanoindentation was utilized to obtain mechanical load-displacement data. The entire dataset consists of 2072 measurements including scalar values (e.g., film stress values), 2D linescans (e.g., x-ray diffractograms), and 3D imagery (e.g., atomic force microscopy images). An additional 1889 quantities, including film hardness, modulus, electrical resistivity, density, and surface roughness, were derived from the experimental datasets using traditional methods. Minimal analysis and discussion of the results are provided in this data descriptor article to limit the authors’ preconceived interpretations of the data. Overall, the data modalities are consistent with previous reports of refractory metal thin films, ensuring that a high-quality dataset was generated. The entirety of this data is committed to a public repository in the Materials Data Facility.
Nanocrystalline metals are inherently unstable against thermal and mechanical stimuli, commonly resulting in significant grain growth. Also, while these metals exhibit substantial Hall-Petch strengthening, they tend to suffer from low ductility and fracture toughness. With regard to the grain growth problem, alloying elements have been employed to stabilize the microstructure through kinetic and/or thermodynamic mechanisms. And to address the ductility challenge, spatially-graded grain size distributions have been developed to facilitate heterogeneous deformation modes: high-strength at the surface and plastic deformation in the bulk. In the present work, we combine these two strategies and present a new methodology for the fabrication of gradient nanostructured metals via compositional means. We have demonstrated that annealing a compositionally stepwise Pt-Au film with a homogenous microstructure results in a film with a spatial microstructural gradient, exhibiting grains which can be twice as wide in the bulk compared to the outer surfaces. Additionally, phase-field modeling was employed for the comparison with experimental results and for further investigation of the competing mechanisms of Au diffusion and thermally induced grain growth. This fabrication method offers an alternative approach for developing the next generation of microstructurally stable gradient nanostructured films.
Twinning is a frequent deformation mechanism in nanocrystalline metals, and segregation of solute atoms at twin boundaries is a thermodynamic process that plays an important role in the stability and strengthening of these materials. In pristine, defect-free twin boundaries, solute segregation generally follows a single- or multilayer patterned coverage of solutes that is uniformly and symmetrically distributed at segregation sites across the boundary. However, when a disconnection, a type of interfacial line defect, is present at the twin boundary, we report a possible discontinuity of the segregation patterns across this defect for a broad range of binary alloys. The change of segregation pattern is explained by a break of the local symmetry across the disconnection terraces. The characteristics of this change are dictated by the orientation of the dislocation content sitting at the step region of the disconnection and its synergistic/antagonistic interactions with the step character. These findings not only advance our understanding of the origin of the interface segregation phenomena and the key contribution from interfacial defects, but they also shed light on applications for tailoring atomically precise interfacial structures to design alloys with emerging properties.
Vibrational spectroscopy is a nondestructive technique commonly used in chemical and physical analyses to determine atomic structures and associated properties. However, the evaluation and interpretation of spectroscopic profiles based on human-identifiable peaks can be difficult and convoluted. To address this challenge, we present a reliable protocol based on supervised manifold learning techniques meant to connect vibrational spectra to a variety of complex and diverse atomic structure configurations. As an illustration, we examined a large database of virtual vibrational spectroscopy profiles generated from atomistic simulations for silicon structures subjected to different stress, amorphization, and disordering states. We evaluated representative features in those spectra via various linear and nonlinear dimensionality reduction techniques and used the reduced representation of those features with decision trees to correlate them with structural information unavailable through classical human-identifiable peak analysis. We show that our trained model accurately (over 97% accuracy) and robustly (insensitive to noise) disentangles the contribution from the different material states, hence demonstrating a comprehensive decoding of spectroscopic profiles beyond classical (human-identifiable) peak analysis.
Fracture and short circuit in the Li7La3Zr2O12 (LLZO) solid electrolyte are two key issues that prevent its adoption in battery cells. In this paper, we utilize phase-field simulations that couple electrochemistry and fracture to evaluate the maximum electric potential that LLZO electrolytes can support as a function of crack density. In the case of a single crack, we find that the applied potential at the onset of crack propagation exhibits inverse square root scaling with respect to crack length, analogous to classical fracture mechanics. Here, we further find that the short-circuit potential scales linearly with crack length. In the realistic case where the solid electrolyte contains multiple cracks, we reveal that failure fits the Weibull model. The failure distributions shift to favor failure at lower overpotentials as areal crack density increases. Furthermore, when flawless interfacial buffers are placed between the applied potential and the bulk of the electrolyte, failure is mitigated. When constant currents are applied, current focuses in near-surface flaws, leading to crack propagation and short circuit. We find that buffered samples sustain larger currents without reaching unstable overpotentials and without failing. Our findings suggest several mitigation strategies for improving the ability of LLZO to support larger currents and improve operability.
Through atomistic simulations, we uncover the dynamic properties of the Cantor alloy under shock-loading conditions and characterize its equation-of-state over a wide range of densities and pressures along with spall strength at ultra-high strain rates. Simulation results reveal the role of local phase transformations during the development of the shock wave on the alloy's high spall strength. The simulated shock Hugoniot results are in remarkable agreement with experimental data, validating the predictability of the model. These mechanistic insights along with the quantification of dynamical properties can drive further advancements in various applications of this class of alloys under extreme environments.
Radiation-induced segregation is a phenomenon commonly observed in many alloys which consists of the redistribution of elements (solute or interstitial impurities) under irradiation. The onset and development of radiation-induced segregation can only occur when a sufficient flux of defects is sustained and defect sinks are present. Irradiation dose, dose rate, and particle types all affect defect flux. In this work, we employ a phase-field model to examine the effects of dose, dose rate, and type of incident particles on radiation-induced segregation behavior in a model binary alloy. The phase-field model takes into account the formation and evolution of point defects as well as defect clusters, the diffusion and clustering of alloy species, the presence of additional extrinsic defect sinks in the form of dislocations, and two different methods of radiation-damage insertion, which are intended to simulate either light-ion/electron irradiation via Frenkel pairs or heavy-ion irradiation in the form of cascades. Our results show a dose-rate and particle-type dependence on the amount of solute segregation. We show that the material systems exposed to higher dose rates are less subjected to solute segregation at equivalent doses. We also show that such dose-rate-dependence behavior is due to a delay of the incubation dose at which radiation-induced segregation effectively starts. Particle type and the presence of dislocations can accentuate this behavior. Our model predictions correlate with many experimental observations made over the years on radiation-induced segregation providing credence to the simulation results. The methodology presented in this study allows for a first-order prediction of the dose rate at which proxy irradiation experiments could be performed to approximate radiation-induced segregation behaviors seen in targeted irradiation conditions.
In this study, we experimentally investigate the high stain rate and spall behavior of Cantor high-entropy alloy (HEA), CoCrFeMnNi. First, the Hugoniot equations of state (EOS) for the samples are determined using laser-driven CoCrFeMnNi flyers launched into known Lithium Fluoride (LiF) windows. Photon Doppler Velocimetry (PDV) recordings of the velocity profiles find the EOS coefficients using an impedance mismatch technique. Following this set of measurements, laser-driven aluminum flyer plates are accelerated to velocities of 0.5–1.0 km/s using a high-energy pulse laser. Upon impact with CoCrFeMnNi samples, the shock response is found through PDV measurements of the free surface velocities. From this second set of measurements, the spall strength of the alloy is found for pressures up to 5 GPa and strain rates in excess of 106 s−1. Further analysis of the failure mechanisms behind the spallation is conducted using fractography revealing the occurrence of ductile fracture at voids presumed to be caused by chromium oxide deposits created during the manufacturing process.
Embrittling potency is a thermodynamic metric that assesses the influence of solute segregation to a grain boundary (GB) on intergranular fracture. Historically, authors of studies have reported embrittling potency as a single scalar value, assuming a single segregation site of importance at a GB and a particular cleavage plane. However, the topography of intergranular fracture surfaces is not generally known a priori. Accordingly, in this paper, we present a statistical ensemble approach to compute embrittling potency, where many free surface (FS) permutations are systematically considered to model fracture of a GB. The result is a statistical description of the thermodynamics of GB embrittlement. As a specific example, embrittling potency distributions are presented for Cr segregation to sites at two Ni (111) symmetric tilt GBs using atomistic simulations. We show that the average embrittling potency for a particular GB site, considering an ensemble of FS permutations, is not equal to the embrittling potency computed using the lowest energy pair of FSs. A mean GB embrittlement is proposed, considering both the likelihood of formation of a particular FS and the probability of solute occupancy at each GB site, to compare the relative embrittling behavior of two distinct GBs.
The phase-field method is a popular modeling technique used to describe the dynamics of microstructures and their physical properties at the mesoscale. However, because in these simulations the microstructure is described by a system of continuous variables evolving both in space and time, phase-field models are computationally expensive. They require refined spatio-temporal discretization and a parallel computing approach to achieve a useful degree of accuracy. As an alternative, we present and discuss an accelerated phase-field approach which uses a recurrent neural network (RNN) to learn the microstructure evolution in latent space. We perform a comprehensive analysis of different dimensionality-reduction methods and types of recurrent units in RNNs. Specifically, we compare statistical functions combined with linear and nonlinear embedding techniques to represent the microstructure evolution in latent space. We also evaluate several RNN models that implement a gating mechanism, including the long short-term memory (LSTM) unit and the gated recurrent unit (GRU) as the microstructure-learning engine. We analyze the different combinations of these methods on the spinodal decomposition of a two-phase system. Our comparison reveals that describing the microstructure evolution in latent space using an autocorrelation-based principal component analysis (PCA) method is the most efficient. We find that the LSTM and GRU RNN implementations provide comparable accuracy with respect to the high-fidelity phase-field predictions, but with a considerable computational speedup relative to the full simulation. This study not only enhances our understanding of the performance of dimensionality reduction on the microstructure evolution, but it also provides insights on strategies for accelerating phase-field modeling via machine learning techniques.
Elmslie, Timothy A.; Startt, Jacob K.; Soto-Medina, Sujeily; Feng, Keke; Zappala, Emma; Frandsen, Benjamin A.; Meisel, Mark W.; Dingreville, Remi; Hamlin, James J.
Magnetic, specific heat, and structural properties of the equiatomic Cantor alloy system are reported for temperatures between 5 and 300 K, and up to fields of 70 kOe. Magnetization measurements performed on as-cast, annealed, and cold-worked samples reveal a strong processing history dependence and that high-temperature annealing after cold working does not restore the alloy to a "pristine"state. Measurements on known precipitates show that the two transitions, detected at 43 and 85 K, are intrinsic to the Cantor alloy and not the result of an impurity phase. Experimental and ab initio density functional theory computational results suggest that these transitions are a weak ferrimagnetic transition and a spin-glass-like transition, respectively, and magnetic and specific heat measurements provide evidence of significant Stoner enhancement and electron-electron interactions within the material.
We present a combination of machine-learned models that predicts the surface elastic properties of general free surfaces in face-centered cubic (FCC) metals. These models are built by combining a semi-analytical method based on atomistic simulations to calculate surface properties with the artificial neural network (ANN) method or the boosted regression tree (BRT) method. The latter is also used to link bulk properties and surface orientation to surface properties. The surface elastic properties are represented by their invariants considering plane elasticity within a polar method. The resulting models are shown to accurately predict the surface elastic properties of seven pure FCC metals (Cu, Ni, Ag, Au, Al, Pd, Pt). The BRT model reveals the correlations between bulk and corresponding surface properties in terms of invariants, which can be used to guide the design of complex nano-sized particles, wires and films. Finally, by expressing the surface excess energy density as a function of surface elastic invariants, fast predictions of surface energy as a function of in-plane deformations can be made from these model constructs.
Metals subjected to irradiation environments undergo microstructural evolution and concomitant degradation, yet the nanoscale mechanisms for such evolution remain elusive. Here, we combine in situ heavy ion irradiation, atomic resolution microscopy, and atomistic simulation to elucidate how radiation damage and interfacial defects interplay to control grain boundary (GB) motion. While classical notions of boundary evolution under irradiation rest on simple ideas of curvature-driven motion, the reality is far more complex. Focusing on an ion-irradiated Pt Σ3 GB, we show how this boundary evolves by the motion of 120° facet junctions separating nanoscale {112} facets. Our analysis considers the short- and mid-range ion interactions, which roughen the facets and induce local motion, and longer-range interactions associated with interfacial disconnections, which accommodate the intergranular misorientation. We suggest how climb of these disconnections could drive coordinated facet junction motion. These findings emphasize that both local and longer-range, collective interactions are important to understanding irradiation-induced interfacial evolution.
Digital twins are emerging as powerful tools for supporting innovation as well as optimizing the in-service performance of a broad range of complex physical machines, devices, and components. A digital twin is generally designed to provide accurate in-silico representation of the form (i.e., appearance) and the functional response of a specified (unique) physical twin. This paper offers a new perspective on how the emerging concept of digital twins could be applied to accelerate materials innovation efforts. Specifically, it is argued that the material itself can be considered as a highly complex multiscale physical system whose form (i.e., details of the material structure over a hierarchy of material length) and function (i.e., response to external stimuli typically characterized through suitably defined material properties) can be captured suitably in a digital twin. Accordingly, the digital twin can represent the evolution of structure, process, and performance of the material over time, with regard to both process history and in-service environment. This paper establishes the foundational concepts and frameworks needed to formulate and continuously update both the form and function of the digital twin of a selected material physical twin. The form of the proposed material digital twin can be captured effectively using the broadly applicable framework of n-point spatial correlations, while its function at the different length scales can be captured using homogenization and localization process-structure-property surrogate models calibrated to collections of available experimental and physics-based simulation data.
This review discusses atomistic modeling techniques used to simulate radiation damage in crystalline materials. Radiation damage due to energetic particles results in the formation of defects. The subsequent evolution of these defects over multiple length and time scales requiring numerous simulations techniques to model the gamut of behaviors. This work focuses attention on current and new methodologies at the atomistic scale regarding the mechanisms of defect formation at the primary damage state.
Garnet-type, solid electrolytes, such as Li7La3Zr2O12 (LLZO), are a promising alternative to liquid electrolytes for lithium-metal batteries. However, such solid-electrolyte materials frequently exhibit undesirable lithium (Li) metal plating and fracture along grain boundaries. In this study, we employ atomistic simulations to investigate the mechanisms and key fracture properties associated with intergranular fracture along one such boundary. Our results show that, in the case of a Σ5(310) grain boundary, this boundary exhibits brittle fracture behavior, i.e. the absence of dislocation activity ahead of the propagating crack tip, accompanied with a decrease in work of separation, peak stress, and maximum stress intensity factor as the temperature increases from 300 K to 1500 K. As the crack propagates, we predict two temperature-dependent Li clustering regimes. For temperatures at or below 900 K, Li tends to cluster in the bulk region away from the crack plane driven by a void-coalescence mechanism concomitant a simultaneous cubic-to-tetragonal phase transition. The tetragonalization of LLZO in this temperature regime acts as an emerging toughening mechanism. At higher temperatures, this phase transition mechanism is suppressed leading to a more uniform distribution of Li throughout the grain-boundary system and lower fracture properties as compared to lower temperatures.
Alloying is often employed to stabilize nanocrystalline materials against microstructural coarsening. The stabilization process results from the combined effects of thermodynamically reducing the curvature-dominated driving force of grain-boundary motion via solute segregation and kinetically pinning these same grain boundaries by solute drag and Zener pinning. The competition between these stabilization mechanisms depends not only on the grain-boundary character but can also be affected by imposed compositional and thermal fields that further promote or inhibit grain growth. In this work, we study the origin of the stability of immiscible nanocrystalline alloys in both homogeneous and heterogeneous compositional and thermal fields by using a multi-phase-field formulation for anisotropic grain growth with grain-boundary character-dependent segregation properties. This generalized formulation allows us to model the distribution of mobilities of segregated grain boundaries and the role of grain-boundary heterogeneity on solute-induced stabilization. As an illustration, we compare our model predictions to experimental results of microstructures in platinum-gold nanocrystalline alloys. Our results reveal that increasing the initial concentration of available solute progressively slows the rate of grain growth via both heterogeneous grain-boundary segregation and Zener pinning, while increasing the temperature generally weakens thermodynamic stabilization effects due to entropic contributions. Finally, we demonstrate as a proof-of-concept that spatially-varying compositional and thermal fields can be used to construct dynamically-stable, graded, nanostructured materials. We discuss the implications of using such concepts as alternatives to conventional plastic deformation methods.
Refractory complex concentrated alloys are an emerging class of materials that attracts attention due to their stability and performance at high temperatures. In this study, we investigate the variations in the mechanical and thermal properties across a broad compositional space for the refractory MoNbTaTi quaternary using high-throughput ab-initio calculations and experimental characterization. For all the properties surveyed, we note a good agreement between our modeling predictions and the experimentally measured values. We reveal the particular role of molybdenum (Mo) to achieve high strength when in high concentration. We trace the origin of this phenomenon to a shift from metallic to covalent bonding when the Mo content is increased. Additionally, a mechanistic, dislocation-based description of the yield strength further explains such high strength due to a combination of high bulk and shear moduli, accompanied by the relatively small size of the Mo atom compared to the other atoms in the alloy. Our analysis of the thermodynamics properties shows that regardless of the composition, this class of quaternary alloys shows good stability and low sensitivity to temperature. Taken together, these results pave the way for the design of new high-performance refractory alloys beyond the equimolar composition found in high-entropy alloys.
Silicon-based layered nanocomposites, comprised of covalent-metal interfaces, have demonstrated elevated resistance to radiation. The amorphization of the crystalline silicon sublayer during irradiation and/or heating can provide an additional mechanism for accommodating irradiation-induced defects. In this study, we investigated the mechanical strength of irradiated Si-based nanocomposites using atomistic modeling. We first examined dose effects on the defect evolution mechanisms near silicon-gold crystalline and amorphous interfaces. Our simulations reveal the growth of an emergent amorphous interfacial layer with increasing dose, a dominant factor mitigating radiation damage. We then examined the effect of radiation on the mechanical strength of silicon-gold multilayers by constructing yield surfaces. These results demonstrate a rapid onset strength loss with dose. Nearly identical behavior is observed in bulk gold, a phenomenon that can be rooted to the formation of radiation-induced stacking fault tetrahedra which dominate the dislocation emission mechanism during mechanical loading. Taken together, these results advance our understanding of the interaction between radiation-induced point defects and metal-covalent interfaces.
Diffraction techniques can powerfully and nondestructively probe materials while maintaining high resolution in both space and time. Unfortunately, these characterizations have been limited and sometimes even erroneous due to the difficulty of decoding the desired material information from features of the diffractograms. Currently, these features are identified non-comprehensively via human intuition, so the resulting models can only predict a subset of the available structural information. In the present work we show (i) how to compute machine-identified features that fully summarize a diffractogram and (ii) how to employ machine learning to reliably connect these features to an expanded set of structural statistics. To exemplify this framework, we assessed virtual electron diffractograms generated from atomistic simulations of irradiated copper. When based on machine-identified features rather than human-identified features, our machine-learning model not only predicted one-point statistics (i.e. density) but also a two-point statistic (i.e. spatial distribution) of the defect population. Hence, this work demonstrates that machine-learning models that input machine-identified features significantly advance the state of the art for accurately and robustly decoding diffractograms.
During the various stages of shock loading, many transient modes of deformation can activate and deactivate to affect the final state of a material. In order to fundamentally understand and optimize a shock response, researchers seek the ability to probe these modes in real-time and measure the microstructural evolutions with nanoscale resolution. Neither post-mortem analysis on recovered samples nor continuum-based methods during shock testing meet both requirements. High-speed diffraction offers a solution, but the interpretation of diffractograms suffers numerous debates and uncertainties. By atomistically simulating the shock, X-ray diffraction, and electron diffraction of three representative BCC and FCC metallic systems, we systematically isolated the characteristic fingerprints of salient deformation modes, such as dislocation slip (stacking faults), deformation twinning, and phase transformation as observed in experimental diffractograms. This study demonstrates how to use simulated diffractograms to connect the contributions from concurrent deformation modes to the evolutions of both 1D line profiles and 2D patterns for diffractograms from single crystals. Harnessing these fingerprints alongside information on local pressures and plasticity contributions facilitate the interpretation of shock experiments with cutting-edge resolution in both space and time.
Structural alloys may experience corrosion when exposed to molten chloride salts due to selective dissolution of active alloying elements. One way to prevent this is to make the molten salt reducing. For the KCl + MgCl2 eutectic salt mixture, pure Mg can be added to achieve this. However, Mg can form intermetallic compounds with nickel at high temperatures, which may cause alloy embrittlement. This work shows that an optimum level of excess Mg could be added to the molten salt which will prevent corrosion of alloys like 316 H, while not forming any detectable Ni-Mg intermetallic phases on Ni-rich alloy surfaces.
The dissolution and depletion of chromium (Cr) in salt facing nickel (Ni) alloy surfaces is one of the predominant degradation mechanisms of structural components in molten salt technology. In this work, we use density functional theory to investigate the role of electronic level interactions that may underlie the depletion phenomenon of Cr in a Ni 100 surface exposed to various adsorbed salt species. Our results show that, under vacuum, Ni preferentially segregates to the surface layer. Conversely, in the presence of adsorbed anionic salt species (e.g., chlorine (Cl), fluorine (F) or the impurity oxygen (O)) Cr segregation becomes more favorable. In these cases, Cl has the weakest effect on segregation, while O has the strongest effect. Our analysis reveals the strong correlation between Cr segregation and the amount of valence charge transferred between the Cr atom and surface adsorbate: the greater the charge transfer, the lower the segregation energy. We also show that, when considered, secondary cations screen Cr-anion interactions, which in turn reduce the magnitude of the anions effect on segregation. These results shed light on the role of salt impurities likely play in the overall corrosion phenomena in molten salt environments. This work provides insights into the atomic level interactions fundamental to molten salt corrosion and on the importance of maintaining salt purity.
Echeverria, Marco J.; Galitskiy, Sergey; Mishra, Avanish; Dingreville, Remi; Dongare, Avinash M.
A hybrid atomic-scale and continuum-modeling framework is used to study the microstructural evolution during the laser-induced shock deformation and failure (spallation) of copper microstructures. A continuum two-temperature model (TTM) is used to account for the interaction of Cu atoms with a laser in molecular dynamics (MD) simulations. The MD-TTM simulations study the effect of laser-loading conditions (laser fluence) on the microstructure (defects) evolution during various stages of shock wave propagation, reflection, and interaction in single-crystal (sc) Cu systems. In addition, the role of the microstructure is investigated by comparing the defect evolution and spall response of sc-Cu and nanocrystalline Cu systems. The defect (stacking faults and twin faults) evolution behavior in the metal at various times is further characterized using virtual in situ selected area electron diffraction and x-ray diffraction during various stages of evolution of microstructure. The simulations elucidate the uncertain relation between spall strength and strain-rate and the much stronger relation between the spall strength and the temperatures generated due to laser shock loading for the small Cu sample dimensions considered here.
Metamaterials are artificial structures that can manipulate and control sound waves in ways not possible with conventional materials. While much effort has been undertaken to widen the bandgaps produced by these materials through design of heterogeneities within unit cells, comparatively little work has considered the effect of engineering heterogeneities at the structural scale by combining different types of unit cells. In this paper, we use the relaxed micromorphic model to study wave propagation in heterogeneous metastructures composed of different unit cells. We first establish the efficacy of the relaxed micromorphic model for capturing the salient characteristics of dispersive wave propagation through comparisons with direct numerical simulations for two classes of metamaterial unit cells: namely phononic crystals and locally resonant metamaterials. We then use this model to demonstrate how spatially arranging multiple unit cells into metastructures can lead to tailored and unique properties such as spatially-dependent broadband wave attenuation, rainbow trapping, and pulse shaping. In the case of the broadband wave attenuation application, we show that by building layered metastructures from different metamaterial unit cells, we can slow down or stop wave packets in an enlarged frequency range, while letting other frequencies through. In the case of the rainbow-trapping application, we show that spatial arrangements of different unit cells can be designed to progressively slow down and eventually stop waves with different frequencies at different spatial locations. Finally, in the case of the pulse-shaping application, our results show that heterogeneous metastructures can be designed to tailor the spatial profile of a propagating wave packet. Collectively, these results show the versatility of the relaxed micromorphic model for effectively and accurately simulating wave propagation in heterogeneous metastructures, and how this model can be used to design heterogeneous metastructures with tailored wave propagation functionalities.
Ni-Cr alloys exhibit oscillatory segregation behaviors near low index surfaces, in which the preferred segregation species changes from Ni in the first layer to Cr in the second layer. In many dilute-alloy systems, this oscillatory pattern is attributed to the elastic release of stresses in the local lattice around the segregating solute or impurity atom. These stresses are mostly thought to originate from mismatches in the atomic size of the solute and host atoms. In Ni-Cr alloys, however, an appreciable mismatch in atomic size is not present, leading to questions about the origins of the oscillatory behavior in this alloy. Using density functional theory, we have modeled the segregation of a single Cr atom in the (100) and (111) surfaces of FCC Ni, an alloy which exhibits this oscillatory behavior. Using Bader charge analysis, we show that the negative energy correlates directly with the amount of charge on the Cr atom. As Ni atoms strip valence charge from the Cr, the Cr contracts slightly in size. The greatest contraction and highest positive charge for the Cr occurs when it is in the second layer of the surface where the system exhibits the oscillating negative segregation energy. We then find that this behavior persists in other alloy systems (Ag-Nb, Cu-Cr, Pt-Nb, and Pt-V), which exhibit similar atomic radii and electronegativity differences between host and solute to Ni-Cr. These represent alloys in which the host metal exhibits an FCC ground-state structure while the solute metal exhibits a BCC ground-state structure.
Co-deposited, immiscible alloy systems form hierarchical microstructures under specific deposition conditions that accentuate the difference in constituent element mobility. The mechanism leading to the formation of these unique hierarchical morphologies during the deposition process is difficult to identify, since the characterization of these microstructures is typically carried out post-deposition. We employ phase-field modeling to study the evolution of microstructures during deposition combined with microscopy characterization of experimentally deposited thin films to reveal the origin of the formation mechanism of hierarchical morphologies in co-deposited, immiscible alloy thin films. Our results trace this back to the significant influence of a local compositional driving force that occurs near the surface of the growing thin film. We show that local variations in the concentration of the vapor phase near the surface, resulting in nuclei (i.e., a cluster of atoms) on the film’s surface with an inhomogeneous composition, can trigger the simultaneous evolution of multiple concentration modulations across multiple length scales, leading to hierarchical morphologies. We show that locally, the concentration must be above a certain threshold value in order to generate distinct hierarchical morphologies in a single domain.
Designing next generation thin films, tailor-made for specific applications, relies on the availability of robust processing-structure-property relationships. Traditional structure zone diagrams are limited to low-dimensional mappings, with machine-learning methods only recently attempting to relate multiple processing parameters to the final microstructure. Despite this progress, structure-processing relationships are unknown for processing conditions that vary during thin-film deposition, limiting the range of microstructures and properties achievable. In this project, we employed a phase-field computational model combined with a genetic algorithm (GA) to identify and design time-dependent processing protocols that achieve tailor-made microstructures. We simulate the physical vapor deposition of a binary-alloy thin film by employing a phase-field model, where deposition rates and diffusivities are controlled via the genetic algorithm. Our GA-guided protocols achieve targeted microstructures with lateral and vertical concentration modulations, as well as more complex, hierarchical microstructures previously not described in simple structure zone diagrams. Our algorithm provides insight to experimentalists looking for additional avenues to design novel thin-film microstructures.
With the rapid proliferation of additive manufacturing and 3D printing technologies, architected cellular solids including truss-like 3D lattice topologies offer the opportunity to program the effective material response through topological design at the mesoscale. The present report summarizes several of the key findings from a 3-year Laboratory Directed Research and Development Program. The program set out to explore novel lattice topologies that can be designed to control, redirect, or dissipate energy from one or multiple insult environments relevant to Sandia missions, including crush, shock/impact, vibration, thermal, etc. In the first 4 sections, we document four novel lattice topologies stemming from this study: coulombic lattices, multi-morphology lattices, interpenetrating lattices, and pore-modified gyroid cellular solids, each with unique properties that had not been achieved by existing cellular/lattice metamaterials. The fifth section explores how unintentional lattice imperfections stemming from the manufacturing process, primarily sur face roughness in the case of laser powder bed fusion, serve to cause stochastic response but that in some cases such as elastic response the stochastic behavior is homogenized through the adoption of lattices. In the sixth section we explore a novel neural network screening process that allows such stocastic variability to be predicted. In the last three sections, we explore considerations of computational design of lattices. Specifically, in section 7 using a novel generative optimization scheme to design novel pareto-optimal lattices for multi-objective environments. In section 8, we use computational design to optimize a metallic lattice structure to absorb impact energy for a 1000 ft/s impact. And in section 9, we develop a modified micromorphic continuum model to solve wave propagation problems in lattices efficiently.
This project focused on providing a fundamental physico-chemical understanding of the coupling mechanisms of corrosion- and radiation-induced degradation at material-salt interfaces in Ni-based alloys operating in emulated Molten Salt Reactor(MSR) environments through the use of a unique suite of aging experiments, in-situ nanoscale characterization experiments on these materials, and multi-physics computational models. The technical basis and capabilities described in this report bring us a step closer to accelerate the deployment of MSRs by closing knowledge gaps related to materials degradation in harsh environments.
We investigate the unitary mechanisms related to the surface migration of vacancies in dilute Ni-Cr alloys via first-principle calculations. We survey a complete set of surface and sub-surface migration paths for vacancies near the (100) free surface and calculate the corresponding migration barriers. Our results show that a vacancy migrating towards the free surface will face lower energy barriers to migrate via atomic exchange with a neighboring Cr atom rather than with a Ni atom. Once a vacancy reaches the free surface, it will be trapped there. Our results also reveal that, when a Cr atom sits in the atomic plane just below the free surface, any in-plane vacancy hopping jump that would result in the vacancy sitting on top a subsurface Cr atom is energetically unfavorable. Taken together, these fundamental unitary surface migration mechanisms offer insights into the complex interactions between surface segregation and vacancy migration phenomena in Ni-Cr-based alloys.
Nanostructures with a high density of interfaces, such as in nanoporous materials and nanowires, resist radiation damage by promoting the annihilation and migration of defects. This study details the size effect and origins of the radiation damage mechanisms in nanowires and nanoporous structures in model face-centered (gold) and body-centered (niobium) cubic nanostructures using accelerated multi-cascade atomistic simulations and in-situ ion irradiation experiments. Our results reveal three different size-dependent mechanisms of damage accumulation in irradiated nanowires and nanoporous structures: sputtering for very small nanowires and ligaments, the formation and accumulation of point defects and dislocation loops in larger nanowires, and a face-centered-cubic to hexagonal-close-packed phase transformation for a narrow range of wire diameters in the case of gold nanowires. Smaller nanowires and ligaments have a net effect of lowering the radiation damage as compared to larger wires that can be traced back to the fact that smaller nanowires transition from a rapid accumulation of defects to a saturation and annihilation mechanism at a lower dose than larger nanowires. These irradiation damage mechanisms are accompanied with radiation-induced surface roughening resulting from defect-surface interactions. Comparisons between nanowires and nanoporous structures show that the various mechanisms seen in nanowires provide adequate bounds for the defect accumulation mechanisms in nanoporous structures with the difference attributed to the role of nodes connecting ligaments in nanoporous structures. Taken together, our results shed light on the compounded, size-dependent mechanisms leading to the radiation resistance of nanowires and nanoporous structures.
Twin boundaries play an important role in the thermodynamics, stability, and mechanical properties of nanocrystalline metals. Understanding their structure and chemistry at the atomic scale is key to guide strategies for fabricating nanocrystalline materials with improved properties. We report an unusual segregation phenomenon at gold-doped platinum twin boundaries, which is arbitrated by the presence of disconnections, a type of interfacial line defect. By using atomistic simulations, we show that disconnections containing a stacking fault can induce an unexpected transition in the interfacial-segregation structure at the atomic scale, from a bilayer, alternating-segregation structure to a trilayer, segregation-only structure. This behavior is found for faulted disconnections of varying step heights and dislocation characters. Supported by a structural analysis and the classical Langmuir-McLean segregation model, we reveal that this phenomenon is driven by a structurally induced drop of the local pressure across the faulted disconnection accompanied by an increase in the segregation volume.
Temperature- and irradiation-assisted failure mechanisms in miscible phase boundaries are clarified via atomistic calculations. We first establish the temperature-dependent brittle-to-ductile transition in U–Zr miscible phase boundaries. Our results confirm that these boundaries are mostly brittle at low temperatures and ductile at elevated temperatures. We then investigate the changes induced by irradiation on the fracture mechanisms in such phase boundaries. The irradiation-induced defect accumulation follows a multi-stage process that starts with the accumulation of isolated small dislocation loops before transitioning to the saturation and growth of larger dislocation loops and end up with a reorganization into forest dislocations. The accumulation of loops is the primary feature to participate in the delineation between brittle and ductile interfacial fracture in irradiated phase boundaries. At low damage levels, radiation defect interactions with the crack tip are limited and U–Zr miscible boundaries fail through the emission of dislocations ahead of the crack tip followed by brittle cleavage in agreement with the classical Griffith’s criterion for crack stability. At higher damage levels, the failure mode transitions from brittle crack growth to ductile void growth. In this case, the microcrack tip is blunted by the high density of pre-existing, radiation-induced defects in the vicinity of the crack. This interaction leads to the development and growth of a cavity at the interface as opposed to interfacial cleavage.
Grain boundaries in metallic materials can exist in a wide range of stable and metastable structures. In addition, the properties of a grain boundary may be altered through solute segregation. In this work, we present a formulation that combines the spectrum of embrittling potencies associated with solute segregation with site-occupancy statistics. As a prototype problem, we illustrate the relation between segregation and embrittlement in the case of S segregation to grain boundaries in Ni. To obtain a population of site segregation energies, we perform molecular statics calculations on 378 different symmetric-tilt grain boundaries and their free surface equivalents, using an embedded-atom method interatomic potential developed specifically for studying embrittlement. Our results show that it is important to consider both the energies associated with embrittlement and the probability of occupancy to describe the general embrittling nature of a grain boundary. When analyzed in isolation, certain grain boundaries show large embrittling potencies; however, that effect is diminished when the probability of S segregation to that grain boundary is considered within a polycrystal. We propose a new quantity, the embrittling estimator, which not only categorizes grain boundaries as embrittling or strengthening, but also considers site occupancy probabilities, so that the embrittlement behavior of grain boundaries within a network of grain boundaries can be compared. Finally, we examine the relationship between embrittlement behavior and innate grain boundary properties, such as the free volume, and find statistical evidence that the complex nature of embrittlement cannot be explained by linear correlations with excess volumes or energies. Ultimately, this combined approach provides a theoretical tool to assist grain boundary engineering of metastable alloys.
Predicting the properties of grain boundaries poses a challenge because of the complex relationships between structural and chemical attributes both at the atomic and continuum scales. Grain boundary systems are typically characterized by parameters used to classify local atomic arrangements in order to extract features such as grain boundary energy or grain boundary strength. The present work utilizes a combination of high-throughput atomistic simulations, macroscopic and microscopic descriptors, and machine-learning techniques to characterize the energy and strength of silicon carbide grain boundaries. A diverse data set of symmetric tilt and twist grain boundaries are described using macroscopic metrics such as misorientation, the alignment of critical low-index planes, and the Schmid factor, but also in terms of microscopic metrics, by quantifying the local atomic structure and chemistry at the interface. These descriptors are used to create random-forest regression models, allowing for their relative importance to the grain boundary energy and decohesion stress to be better understood. Results show that while the energetics of the grain boundary were best described using the microscopic descriptors, the ability of the macroscopic descriptors to reasonably predict grain boundaries with low energy suggests a link between the crystallographic orientation and the resultant atomic structure that forms at the grain boundary within this regime. For grain boundary strength, neither microscopic nor macroscopic descriptors were able to fully capture the response individually. However, when both descriptor sets were utilized, the decohesion stress of the grain boundary could be accurately predicted. These results highlight the importance of considering both macroscopic and microscopic factors when constructing constitutive models for grain boundary systems, which has significant implications for both understanding the fundamental mechanisms at work and the ability to bridge length scales.
The phase-field method is a powerful and versatile computational approach for modeling the evolution of microstructures and associated properties for a wide variety of physical, chemical, and biological systems. However, existing high-fidelity phase-field models are inherently computationally expensive, requiring high-performance computing resources and sophisticated numerical integration schemes to achieve a useful degree of accuracy. In this paper, we present a computationally inexpensive, accurate, data-driven surrogate model that directly learns the microstructural evolution of targeted systems by combining phase-field and history-dependent machine-learning techniques. We integrate a statistically representative, low-dimensional description of the microstructure, obtained directly from phase-field simulations, with either a time-series multivariate adaptive regression splines autoregressive algorithm or a long short-term memory neural network. The neural-network-trained surrogate model shows the best performance and accurately predicts the nonlinear microstructure evolution of a two-phase mixture during spinodal decomposition in seconds, without the need for “on-the-fly” solutions of the phase-field equations of motion. We also show that the predictions from our machine-learned surrogate model can be fed directly as an input into a classical high-fidelity phase-field model in order to accelerate the high-fidelity phase-field simulations by leaping in time. Such machine-learned phase-field framework opens a promising path forward to use accelerated phase-field simulations for discovering, understanding, and predicting processing–microstructure–performance relationships.
Understanding phase transformations in 2D materials can unlock unprecedented developments in nanotechnology, since their unique properties can be dramatically modified by external fields that control the phase change. Here, experiments and simulations are used to investigate the mechanical properties of a 2D diamond boron nitride (BN) phase induced by applying local pressure on atomically thin h-BN on a SiO2 substrate, at room temperature, and without chemical functionalization. Molecular dynamics (MD) simulations show a metastable local rearrangement of the h-BN atoms into diamond crystal clusters when increasing the indentation pressure. Raman spectroscopy experiments confirm the presence of a pressure-induced cubic BN phase, and its metastability upon release of pressure. Å-indentation experiments and simulations show that at pressures of 2–4 GPa, the indentation stiffness of monolayer h-BN on SiO2 is the same of bare SiO2, whereas for two- and three-layer-thick h-BN on SiO2 the stiffness increases of up to 50% compared to bare SiO2, and then it decreases when increasing the number of layers. Up to 4 GPa, the reduced strain in the layers closer to the substrate decreases the probability of the sp2-to-sp3 phase transition, explaining the lower stiffness observed in thicker h-BN.
The accumulation of point defects and defect clusters in materials, as seen in irradiated metals for example, can lead to the formation and growth of voids. Void nucleation is derived from the condensation of supersaturated vacancies and depends strongly on the stress state. It is usually assumed that such stress states can be produced by microstructural defects such dislocations, grain boundaries or triple junctions, however, much less attention has been brought to the formation of voids near microcracks. In this paper, we investigate the coupling between point-defect diffusion/recombination and concentrated stress fields near mode-I crack tips via a spatially-resolved rate theory approach. A modified chemical potential enables point-defect diffusion to be partially driven by the mechanical fields in the vicinity of the crack tip. Simulations are carried out for microcracks using the Griffith model with increasing stress intensity factor K1. Our results show that below a threshold for the stress intensity factor, the microcrack acts purely as a microstructural sink, absorbing point defects. Above this threshold, vacancies accumulate at the crack tip. These results suggest that, even in the absence of plastic deformation, voids can form in the vicinity of a microcrack for a given load when the crack’s characteristic length is above a critical length. While in ductile metals, irradiation damage generally causes hardening and corresponding quasi-brittle cleavage, our results show that irradiation conditions can favor void formation near microstructural stressors such as crack tips leading to lower resistance to crack propagation as predicted by traditional failure analysis.
This report details the current benchmark results to verify, validate and demonstrate the capabilities of the in-house multi-physics phase-field modeling framework Mesoscale Multiphysics Phase Field Simulator (MEMPHIS) developed at the Center for Integrated Nanotechnologies (CINT). MEMPHIS is a general phase-field capability to model various nanoscience and materials science phenomena related to microstructure evolution. MEMPHIS has been benchmarked against a suite of reported classical phase-field benchmark problems to verify and validate the correctness, accuracy and precision of the models and numerical methods currently implemented into the code.
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.
The self-interstitial atom (SIA) is one of two fundamental point defects in bulk Si. Isolated Si SIAs are extremely difficult to observe experimentally. Even at very low temperatures, they anneal before typical experiments can be performed. Given the challenges associated with experimental characterization, accurate theoretical calculations provide valuable information necessary to elucidate the properties of these defects. Previous studies have applied Kohn-Sham density functional theory (DFT) to the Si SIA, using either the local density approximation or the generalized gradient approximation to the exchange-correlation (XC) energy. The consensus of these studies indicates that a Si SIA may exist in five charge states ranging from -2 to +2 with the defect structure being dependent on the charge state. This study aims to re-examine the existence of these charge states in light of recently derived "approximate bounds"on the defect levels obtained from finite-size supercell calculations and new DFT calculations using both semi-local and hybrid XC approximations. We conclude that only the neutral and +2 charge states are directly supported by DFT as localized charge states of the Si SIA. Within the current accuracy of DFT, our results indicate that the +1 charge state likely consists of an electron in a conduction-band-like state that is coulombically bound to a +2 SIA. Furthermore, the -1 and -2 charge states likely consist of a neutral SIA with one and two additional electrons in the conduction band, respectively.
While lattice metamaterials can achieve exceptional energy absorption by tailoring periodically distributed heterogeneous unit cells, relatively little focus has been placed on engineering heterogeneity above the unit-cell level. In this work, the energy-absorption performance of lattice metamaterials with a heterogeneous spatial layout of different unit cell architectures was studied. Such multi-morphology lattices can harness the distinct mechanical properties of different unit cells while being composed out of a single base material. A rational design approach was developed to explore the design space of these lattices, inspiring a non-intuitive design which was evaluated alongside designs based on mixture rules. Fabrication was carried out using two different base materials: 316L stainless steel and Vero White photopolymer. Results show that multi-morphology lattices can be used to achieve higher specific energy absorption than homogeneous lattice metamaterials. Additionally, it is shown that a rational design approach can inspire multi-morphology lattices which exceed rule-of-mixtures expectations.
The interaction of energetic ions with the electronic and ionic system of target materials is an interesting but challenging multiscale problem, and understanding of the early stages after impact of heavy, initially charged ions is particularly poor. At the same time, energy deposition during these early stages determines later formation of damage cascades. We address the multiscale character by combining real-time time-dependent density functional theory for electron dynamics with molecular dynamics simulations of damage cascades. Our first-principles simulations prove that core electrons affect electronic stopping and have an unexpected influence on the charge state of the projectile. We show that this effect is absent for light projectiles, but dominates the stopping physics for heavy projectiles. By parametrizing an inelastic energy loss friction term in the molecular dynamics simulations using our first-principles results, we also show a qualitative influence of electronic stopping physics on radiation-damage cascades.
This report details the current benchmark results to verify, validate and demonstrate the capabilities of the in-house multi-physics phase-field modeling framework Mesoscale Multiphysics Phase Field Simulator (MEMPHIS) developed at the Center for Integrated Nanotechnologies (CINT). MEMPHIS is a general phase-field capability to model various nanoscience and materials science phenomena related to microstructure evolution. MEMPHIS has been benchmarked against a suite of reported 'classical' phase-field benchmark problems to verify and validate the correctness, accuracy and precision of the models and numerical methods currently implemented into the code.
Atomistic modeling of radiation damage through displacement cascades is deceptively non-trivial. Due to the high energy and stochastic nature of atomic collisions, individual primary knock-on atom (PKA) cascade simulations are computationally expensive and ill-suited for length and dose upscaling. Here, we propose a reduced-order atomistic cascade model capable of predicting and replicating radiation events in metals across a wide range of recoil energies. Our methodology approximates cascade and displacement damage production by modeling the cascade as a core-shell atomic structure composed of two damage production estimators, namely an athermal recombination corrected displacements per atom (arc-dpa) in the shell and a replacements per atom (rpa) representing atomic mixing in the core. These estimators are calibrated from explicit PKA simulations and a standard displacement damage model that incorporates cascade defect production efficiency and mixing effects. We illustrate the predictability and accuracy of our reduced-order atomistic cascade method for the cases of copper and niobium by comparing its results with those from full PKA simulations in terms of defect production as well as the resulting cascade evolution and structure. We provide examples for simulating high energy cascade fragmentation and large dose ion-bombardment to demonstrate its possible applicability. Finally, we discuss the various practical considerations and challenges associated with this methodology especially when simulating subcascade formation and dose effects.
Since the landmark development of the Scherrer method a century ago, multiple generations of width methods for X-ray diffraction originated to non-invasively and rapidly characterize the property-controlling sizes of nanoparticles, nanowires, and nanocrystalline materials. However, the predictive power of this approach suffers from inconsistencies among numerous methods and from misinterpretations of the results. Therefore, we systematically evaluated twenty-two width methods on a representative nanomaterial subjected to thermal and mechanical loads. To bypass experimental complications and enable a 1:1 comparison between ground truths and the results of width methods, we produced virtual X-ray diffractograms from atomistic simulations. These simulations realistically captured the trends that we observed in experimental synchrotron diffraction. To comprehensively survey the width methods and to guide future investigations, we introduced a consistent, descriptive nomenclature. Alarmingly, our results demonstrated that popular width methods, especially the Williamson-Hall methods, can produce dramatically incorrect trends. We also showed that the simple Scherrer methods and the rare Energy methods can well characterize unloaded and loaded states, respectively. Overall, this work improved the utility of X-ray diffraction in experimentally evaluating a variety of nanomaterials by guiding the selection and interpretation of width methods.
The predictions of scaling laws for the structure and properties of defect clusters are generally limited to small defect clusters in their ground-state configurations. We investigated the size and geometrical configuration dependence of nano-sized defect clusters in niobium (Nb) using molecular dynamics. We studied the structure and stability of large clusters of size up to fifty defects for vacancies and one hundred defects for interstitials, as well as the role of helium and metastable configurations on the stability of these clusters. We compared three different interatomic potentials in order to determine the relative stability of these clusters as a function of their size and geometrical configurations. Additionally, we conducted a statistical analysis to predict the formation and binding energies of interstitial clusters as a function of both their size and configuration. We find that the size dependence of vacancy and interstitial clusters can be approximated by functional forms that account for bulk and surface effects as well as some considerations of elastic interactions. We also find that helium and metastable configurations can make vacancy and interstitial clusters thermally stable depending on the configuration. Our parameterized functional forms for the formation and binding energies are valid for a very broad range of defect sizes and configurations making it possible to be used directly in a coarse-grained modeling strategy such as Monte Carlo, cluster dynamics or dislocation dynamics which look at defect accumulation and evolution in microstructures.
The embrittling or strengthening effect of solute atoms at grain boundaries (GBs), commonly known as the embrittling potency, is an essential thermodynamic property for characterizing the effects of solute segregation on GB fracture. One of the more technologically relevant material systems related to embrittlement is the Ni-S system where S has a deleterious effect on fracture behavior in polycrystalline Ni. In this work, we develop a Ni-S embedded-atom method (EAM) interatomic potential that accounts for the embrittling behavior of S at Ni GBs. Results using this new interatomic potential are then compared to previous density functional theory studies and a reactive force-field potential via a layer-by-layer segregation analysis. Our potential shows strong agreement with existing literature and performs well in predicting properties that are not included in the fitting database. Finally, we calculate embrittling potencies and segregation energies for six [100] symmetric-tilt GBs using the new EAM potential. We observe that embrittling potency is dependent on GB structure, indicating that specific GBs are more susceptible to sulfur-induced embrittlement.
Irradiation resistance of metallic nanostructured multilayers is determined by the interactions between defects and phase boundaries. However, the dose-dependent interfacial morphology evolution can greatly change the nature of the defect-boundary interaction mechanisms over time. In the present study, we used atomistic models combined with a novel technique based on the accumulation of Frenkel pairs to simulate irradiation processes. We examined dose effects on defect evolutions near zirconium-niobium multilayer phase boundaries. Our simulations enabled us to categorize defect evolution mechanisms in bulk phases into progressing stages of dislocation accumulation, saturation, and coalescence. In the metallic multilayers, we observed a phase boundary absorption mechanism early on during irradiation, while at higher damage levels, the increased irradiation intermixing triggered a phase transformation in the Zr-Nb mixture. This physical phenomenon resulted in the emission of a large quantity of small immobile dislocation loops from the phase boundaries.
The ability of nanoporous metals to avoid accumulation of damage under ion beam irradiation has been the focus of several studies in recent years. The width of the interconnected ligaments forming the network structure typically is on the order of tens of nanometers. In such confined volumes with high amounts of surface area, the accumulation of damage (defects such as stacking-fault tetrahedra and dislocation loops) can be mitigated via migration and annihilation of these defects at the free surfaces. In this work, in situ characterization of radiation damage in nanoporous gold (np-Au) was performed in the transmission electron microscope. Several samples with varying average ligament size were subjected to gold ion beams having three different energies (10 MeV, 1.7 MeV and 46 keV). The inherent radiation tolerance of np-Au was directly observed in real time, for all ion beam conditions, and the degree of ion-induced damage accumulation in np-Au ligaments is discussed here.
This study was initiated to quantify and characterize the uncertainty associated with the degradation mechanisms impacting normal dry storage operations for used nuclear fuel (UNF) and normal conditions of transport in support of the Spent Fuel and Waste Science & Technology Campaign (SFWST) and its effectiveness to rank the data needs and parameters of interest. This report describes the technical basis and guidance resulting from the development of software to perform uncertainty quantification (UQ) by developing and describing a holistic model that integrates the various processes controlling Atmospheric Stress Corrosion Cracking (ASCC) in the specific context of Interim Spent Fuel Storage Installations (ISFSIs). These processes include the daily and annual cycles of temperature and humidity associated with the environment, the deposition of chloride-containing aerosol particles, pit formation, pit-to-crack transition, and crack propagation.
For long-term storage, spent nuclear fuel (SNF) is placed in dry storage systems, commonly consisting of welded stainless steel canisters enclosed in ventilated overpacks. Choride-induced stress corrosion cracking (CISCC) of these canisters may occur due to the deliquescence of sea-salt aerosols as the canisters cool. Current experimental and modeling efforts to evaluate canister CISCC assume that the deliquescent brines, once formed, persist on the metal surface, without changing chemical or physical properties. Here we present data that show that magnesium chloride rich-brines, which form first as the canisters cool and sea-salts deliquesce, are not stable at elevated temperatures, degassing HCl and converting to solid carbonates and hydroxychloride phases, thus limiting conditions for corrosion. Moreover, once pitting corrosion begins on the metal surface, oxygen reduction in the cathode region surrounding the pits produces hydroxide ions, increasing the pH under some experimental conditions, leads to precipitation of magnesium hydroxychloride hydrates. Because magnesium carbonates and hydroxychloride hydrates are less deliquescent than magnesium chloride, precipitation of these compounds causes a reduction in the brine volume on the metal surface, potentially limiting the extent of corrosion. If taken to completion, such reactions may lead to brine dry-out, and cessation of corrosion.
Safety basis analysts throughout the U.S. Department of Energy (DOE) complex rely heavily on the information provided in the DOE Handbook, DOE-HDBK-3010, Airborne Release Fractions/Rates and Respirable Fractions for Nonreactor Nuclear Facilities, to determine radionuclide source terms from postulated accident scenarios. In calculating source terms, analysts tend to use the DOE Handbook's bounding values on airborne release fractions (ARFs) and respirable fractions (RFs) for various categories of insults (representing potential accident release categories). This is typically due to both time constraints and the avoidance of regulatory critique. Unfortunately, these bounding ARFs/RFs represent extremely conservative values. Moreover, they were derived from very limited small-scale bench/laboratory experiments and/or from engineered judgment. Thus, the basis for the data may not be representative of the actual unique accident conditions and configurations being evaluated. The goal of this research is to develop a more accurate and defensible method to determine bounding values for the DOE Handbook using state-of-art multi-physics-based computer codes. This enables us to better understand the fundamental physics and phenomena associated with the types of accidents in the handbook. In this fourth year, we improved existing computational capabilities to better model fragmentation situations to capture small fragments during an impact accident. In addition, we have provided additional new information for various sections of Chapters 4 and 5 of the Handbook on free fall powders and impacts of solids, and have provided the damage ratio simulations for containers (7A drum and standard waste box) for various drops and impact scenarios. Thus, this work provides a low-cost method to establish physics-justified safety bounds by considering specific geometries and conditions that may not have been previously measured and/or are too costly to perform during an experiment.
We performed a systematic study of the threshold displacement energy (Ed) in metallic uranium as a function of both the recoil direction and temperature using Molecular Dynamics simulations. We developed a novel orientation sampling scheme that utilizes crystallographic symmetrical geodesic grids to select directions from the orientation fundamental zone to study the directional dependency. Additionally, we studied the temperature dependency by considering both the α-uranium phase, corresponding to the ground state for temperatures ranging from 0 K to 600 K, and the γ-uranium phase, corresponding to high-temperature state for temperatures above 900 K. In this study, we compared several definitions of the threshold energy: a direction-specific threshold displacement energy (Ed (θ,Φ)), an angle-averaged threshold energy ($E_d^{ave}$), a production probability threshold displacement energy ($E_d^{pp}$), and a defect count threshold displacement energy ($E_d^{dc}$). The direction-specific threshold displacement energies showed large angular anisotropy and variations in Ed results in accordance with crystallographic considerations. Specifically, preferred defect channeling directions were observed in the [120], [1$\bar{2}$0], [1$\bar{1}$1] directions for the α-uranium, and [001], [111] directions for the γ-uranium. The production probability threshold displacement energy ($E_d^{pp}$) is calculated as approximately 99.2659 eV at 10 K (α-U), 103.4980 eV at 300 K (α-U), 76.0915 eV at 600 K (α-U), and 42.9929 eV at 900 K (γ-U). With exception of those calculated at 10 K, threshold displacement energies decrease with increasing temperature. Analyses of the stable defect structures showed that the most commonly observed interstitial configuration in α-uranium consists of a ( 0 1 0 ) dumbbell-like interstitial; while in γ-uranium no preferential defect configuration could be identified due to thermally-induced lattice instabilities at the elevated temperatures.
Semi-coherent cube-on-cube miscible U–Zr interfaces were studied using molecular dynamics simulations. The misfit accommodation of such semi-coherent phase boundaries was characterized by a two-dimensional dislocation network model utilizing a combination of theoretical predictions and analysis of the atomic system. The dislocation networks were discussed for various stacking orientation of the adjoining phases in terms of the composition of the dislocation sets, the partitioning between edge and screw components and the associated residual elastic fields. These analyses showed that the patterning of the network of dislocations forming these phase boundaries results from the competition between a structurally-driven process (i.e., function of the lattice misfit) and a chemically-driven process (i.e., due to the miscibility between U and Zr).
This project focused on providing a fundamental mechanistic understanding of the complex degradation mechanisms associated with Pellet/Clad Debonding (PCD) through the use of a unique suite of novel synthesis of surrogate spent nuclear fuel, in-situ nanoscale experiments on surrogate interfaces, multi-modeling, and characterization of decommissioned commercial spent fuel. The understanding of a broad class of metal/ceramic interfaces degradation studied within this project provided the technical basis related to the safety of high burn-up fuel, a problem of interest to the DOE.
The evolution and characterization of single-isolated-ion-strikes are investigated by combining atomistic simulations with selected-area electron diffraction (SAED) patterns generated from these simulations. Five molecular dynamics simulations are performed for a single 20 keV primary knock-on atom in bulk crystalline Si. The resulting cascade damage is characterized in two complementary ways. First, the individual cascade events are conventionally quantified through the evolution of the number of defects and the atomic (volumetric) strain associated with these defect structures. These results show that (i) the radiation damage produced is consistent with the Norgett, Robinson, and Torrens model of damage production and (ii) there is a net positive volumetric strain associated with the cascade structures. Second, virtual SAED patterns are generated for the resulting cascade-damaged structures along several zone axes. The analysis of the corresponding diffraction patterns shows the SAED spots approximately doubling in size, on average, due to broadening induced by the defect structures. Furthermore, the SAED spots are observed to exhibit an average radial outward shift between 0.33% and 0.87% depending on the zone axis. This characterization approach, as utilized here, is a preliminary investigation in developing methodologies and opportunities to link experimental observations with atomistic simulations to elucidate microstructural damage states.
The two-dimensional elastic Green’s function is calculated for a general anisotropic elastic bimaterial containing a line dislocation and a concentrated force while accounting for the interfacial structure by means of a generalized interfacial elasticity paradigm. The introduction of the interface elasticity model gives rise to boundary conditions that are effectively equivalent to those of a weakly bounded interface. The equations of elastic equilibrium are solved by complex variable techniques and the method of analytical continuation. The solution is decomposed into the sum of the Green’s function corresponding to the perfectly bonded interface and a perturbation term corresponding to the complex coupling nature between the interface structure and a line dislocation/concentrated force. Such construct can be implemented into the boundary integral equations and the boundary element method for analysis of nano-layered structures and epitaxial systems where the interface structure plays an important role.
The complexity of radiation effects in a material’s microstructure makes developing predictive models a difficult task. In principle, a complete list of all possible reactions between defect species being considered can be used to elucidate damage evolution mechanisms and its associated impact on microstructure evolution. However, a central limitation is that many models use a limited and incomplete catalog of defect energetics and associated reactions. Even for a given model, estimating its input parameters remains a challenge, especially for complex material systems. Here, we present a computational analysis to identify the extent to which defect accumulation, energetics, and irradiation conditions can be determined via forward and reverse regression models constructed and trained from large data sets produced by cluster dynamics simulations. A global sensitivity analysis, via Sobol’ indices, concisely characterizes parameter sensitivity and demonstrates how this can be connected to variability in defect evolution. Based on this analysis and depending on the definition of what constitutes the input and output spaces, forward and reverse regression models are constructed and allow for the direct calculation of defect accumulation, defect energetics, and irradiation conditions. Here, this computational analysis, exercised on a simplified cluster dynamics model, demonstrates the ability to design predictive surrogate and reduced-order models, and provides guidelines for improving model predictions within the context of forward and reverse engineering of mathematical models for radiation effects in a materials’ microstructure.
Diffusion of point defects during irradiation is simulated via a two-way coupling between mechanical stress and defect diffusion in iron. This diffusion is based on a modified chemical potential that includes not only the local concentration of radiation-induced defects, but also the influence of the residual stress field from both the microstructure (i.e. dislocations or grain boundaries) and the eigenstrain caused by the defects themselves. Defect flux and concentration rates are derived from this chemical potential using Fick's first and second laws. Mean field rate theory is incorporated to model the annihilation of Frenkel pairs, and increased annihilation near grain boundaries is included based on the elastic energy of each grain boundary. Mechanical equilibrium is coupled with diffusion by computing eigenstrain from point defects and adding this to the total strain. Intrinsic stresses associated with the dislocations and grain boundaries are calculated using dislocation and disclination mechanics. Through this two-way-coupled model, regions of low concentration are seen near grain boundaries, and sink efficiency is calculated for different types of microstructure. The results show that the two-way mechanical coupling has a strong influence on sink efficiency for dislocation loops. The results also suggest that misorientation is a poor metric for determining sink efficiency, with sink density and elastic energy being much more informative.
All grain boundaries are not equal in their predisposition for fracture due to the complex coupling between lattice geometry, interfacial structure, and mechanical properties. The ability to understand these relationships is crucial to engineer materials resilient to grain boundary fracture. Here, a methodology is presented to isolate the role of grain boundary structure on interfacial fracture properties, such as the tensile strength and work of separation, using atomistic simulations. Instead of constructing sets of grain boundary models within the misorientation/structure space by simply varying the misorientation angle around a fixed misorientation axis, the proposed method creates sets of grain boundary models by means of isocurves associated with important fracture-related properties of the adjoining lattices. Such properties may include anisotropic elastic moduli, the Schmid factor for primary slip, and the propensity for simultaneous slip on multiple slip systems. This approach eliminates the effect of lattice properties from the comparative analysis of interfacial fracture properties and thus enables the identification of structure-property relationships for grain boundaries. As an example, this methodology is implemented to study crack propagation along Ni grain boundaries. Segregated H is used as a means to emphasize differences in the selected grain boundary structures while keeping lattice properties fixed.
