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 P.; 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 P.; 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.