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.