arXiv subjects

Jeremy K. Mason

Publications and source records attributed to Jeremy K. Mason.

16 recordsLinked to original sources

arXiv2025

Dependence of Microstructure Classification Accuracy on Crystallographic Data Representation

Convolutional neural networks are increasingly being used to analyze and classify material microstructures, motivated by the possibility that they will be able to identify relevant microstructural features more efficiently and impartially than human experts. While up to now convolutional neural networks have mostly been applied to light optimal microscopy and scanning electron microscope micrographs, application to EBSD micrographs will be increasingly common as rational design generates materials with unknown textures and phase compositions. This raises the question of how crystallographic orientation should be represented in such a convolutional neural network, and whether this choice has a significant effect on the network's analysis and classification accuracy. Four representations of orientation information are examined and are used with convolutional neural networks to classify five synthetic microstructures with varying textures and grain geometries. Of these, a spectral embedding of crystallographic orientations in a space that respects the crystallographic symmetries performs by far the best, even when the network is trained on small volumes of data such as could be accessible by practical experiments.

physics.comp-ph↗

arXiv2023

Energetic contributions to deformation twinning in magnesium

Modeling deformation twin nucleation in magnesium has proven to be a challenging task. In particular, the absence of a heterogeneous twin nucleation model which provides accurate energetic descriptions for twin-related structures belies a need to more deeply understand twin energetics. To address this problem, molecular dynamics simulations are performed to follow the energetic evolution of $\{10\overline{1}2\}$ tension twin embryos nucleating from an asymmetrically-tilted grain boundary. The line, surface and volumetric terms associated with twin nucleation are identified. A micromechanical model is proposed where the stress field around the twin nucleus is estimated using the Eshelby formalism, and the contributions of the various twin-related structures to the total energy of the twin are evaluated. The reduction in the grain boundary energy arising from the change in character of the prior grain boundary is found to be able to offset the energy costs of the other interfaces. The defect structures bounding the stacking faults that form inside the twin are also found to possibly have significant energetic contributions. These results suggest that both of these effects could be critical considerations when predicting twin nucleation sites in magnesium.

cond-mat.mtrl-sci↗

arXiv2023

Simulated surface diffusion in nanoporous gold and its dependence on surface curvature

The morphological evolution of nanoporous gold is generally believed to be governed by surface diffusion. This work specifically explores the dependence of mass transport by surface diffusion on the curvature of a gold surface. The surface diffusivity is estimated by molecular dynamics simulations for a variety of surfaces of constant mean curvature, eliminating any chemical potential gradients and allowing the possible dependence of the surface diffusivity on mean curvature to be isolated. The apparent surface diffusivity is found to have an activation energy of ~0.74 eV with a weak dependence on curvature, but is consistent with the values reported in the literature. The apparent concentration of mobile surface atoms is found to be highly variable, having an Arrhenius dependence on temperature with an activation energy that also has a weak curvature dependence. These activation energies depend on curvature in such a way that the rate of mass transport by surface diffusion is nearly independent of curvature, but with a higher activation energy of ~1.01 eV. The curvature dependencies of the apparent surface diffusivity and concentration of mobile surface atoms is believed to be related to the expected lifetime of a mobile surface atom, and has the practical consequence that a simulation study that does not account for this finite lifetime could underestimate the activation energy for mass transport via surface diffusion by ~0.27 eV.

cond-mat.mtrl-sci↗

arXiv2023

Dependence of simulated radiation damage on crystal structure and atomic misfit in metals

This study investigates radiation damage in three metals in the low temperature and high radiant flux regime using molecular dynamics and a Frenkel pair accumulation method to simulate up to $2.0$ displacements per atom. The metals considered include Fe, equiatomic CrCoNi, and a fictitious metal with identical bulk properties to the CrCoNi composed of a single atom type referred to as an A-atom. CrCoNi is found to sustain higher concentrations of dislocations than either the Fe or A-atom systems and more stacking faults than the A-atom system. The results suggest that the concentration of vacancies and interstitials are substantially higher for the CrCoNi than the A-atom system, perhaps reflecting that the recombination radius is smaller in CrCoNi due to the roughened potential energy landscape. A model that partitions the major contributions from defects to the stored energy is described, and serves to highlight a general need for higher fidelity approaches to point defect identification.

cond-mat.mtrl-sci↗

arXiv2022

Energy storage under high-rate compression of single crystal tantalum

When a material is plastically deformed the majority of mechanical work is dissipated as heat, and the fraction of plastic work converted into heat is known as the Taylor-Quinney coefficient (TQC). Large-scale molecular dynamics simulations were performed of high strain rate compression of single-crystal tantalum, and the resulting integral and differential TQC values are reported up to true strains of 1.0. A phenomenological model is proposed for the energy stored in the material as a function of time with an asymptotic limit for this energy defined by the deformation conditions. The model reasonably describes the convergence of TQC values to 1.0 with increasing plastic strain, but does not directly address the physical nature of thermo-mechanical conversion. This is instead developed in a second more detailed model that accurately accounts for energy storage in two distinct contributions, one being the growing dislocation network and the other the point defect debris left behind by the moving dislocations. The contribution of the point defect debris is found to lag behind that of the dislocation network but to be substantial under the high-rate straining conditions considered here.

cond-mat.mtrl-sci↗

arXiv2021

Topological transitions during grain growth on a finite element mesh

The topological transitions that occur to the grain boundary network during grain growth in a material with uniform grain boundary energies are believed to be known. The same is not true for more realistic materials, since more general grain boundary energies in principle allow many more viable grain boundary configurations. A simulation of grain growth in such a material therefore requires a procedure to enumerate all possible topological transitions and select the most energetically favorable one. Such a procedure is developed and implemented here for a microstructure represented by a volumetric finite element mesh. As a specific example, all possible transitions for a typical configuration with five grains around a junction point are enumerated, and some exceptional transitions are found to be energetically similar to the conventional ones even for a uniform boundary energy. A general discrete formulation to calculate grain boundary velocities is used to simulate grain growth for an example microstructure. The method is implemented as a C++ library based on SCOREC, an open source massively parallelizable library for finite element simulations with adaptive meshing.

cond-mat.mtrl-sci↗

arXiv2020

Classification of atomic environments via the Gromov-Wasserstein distance

Interpreting molecular dynamics simulations usually involves automated classification of local atomic environments to identify regions of interest. Existing approaches are generally limited to a small number of reference structures and only include limited information about the local chemical composition. This work proposes to use a variant of the Gromov-Wasserstein (GW) distance to quantify the difference between a local atomic environment and a set of arbitrary reference environments in a way that is sensitive to atomic displacements, missing atoms, and differences in chemical composition. This involves describing a local atomic environment as a finite metric measure space, which has the additional advantages of not requiring the local environment to be centered on an atom and of not making any assumptions about the material class. Numerical examples illustrate the efficacy and versatility of the algorithm.

cond-mat.mtrl-sci↗

arXiv2020

Distribution of Topological Types in Grain-Growth Microstructures

An open question in studying normal grain growth concerns the asymptotic state to which microstructures converge. In particular, the distribution of grain topologies is unknown. We introduce a thermodynamic-like theory to explain these distributions in two- and three-dimensional systems. In particular, a bending-like energy $E_i$ is associated to each grain topology $t_i$, and the probability of observing that particular topology is proportional to $\frac{1}{s(t_i)}e^{-βE_i}$, where $s(t_i)$ is the order of an associated symmetry group and $β$ is a thermodynamic-like constant. We explain the physical origins of this approach, and provide numerical evidence in support.

cond-mat.mtrl-sci↗

arXiv2019

Basis functions on the grain boundary space: Theory

With the increasing availability of experimental and computational data concerning the properties and distribution of grain boundaries in polycrystalline materials, there is a corresponding need to efficiently and systematically express functions on the grain boundary space. A grain boundary can be described by the rotations applied to two grains on either side of a fixed boundary plane, suggesting that the grain boundary space is related to the space of rotations. This observation is used to construct an orthornormal function basis, allowing effectively arbitrary functions on the grain boundary space to be written as linear combinations of the basis functions. Moreover, a procedure is developed to construct a smaller set of basis functions consistent with the crystallographic point group symmetries, grain exchange symmetry, and the null boundary singularity. Functions with the corresponding symmetries can be efficiently expressed as linear combinations of the symmetrized basis functions. An example is provided that shows the efficacy of the symmetrization procedure.

cond-mat.mtrl-sci↗

arXiv2019

Continuous and Optimally Complete Description of Chemical Environments Using Spherical Bessel Descriptors

Recently, machine learning potentials have been advanced as candidates to combine the high-accuracy of quantum mechanical simulations with the speed of classical interatomic potentials. A crucial component of a machine learning potential is the description of local atomic environments by some set of descriptors. These should ideally be continuous throughout the specified local atomic environment, twice-differentiable with respect to atomic positions and complete in the sense of containing all possible information about the neighborhood. An updated version of the recently proposed Spherical Bessel descriptors satisfies all three of these properties, and moreover is optimally complete in the sense of encoding all configurational information with the smallest possible number of descriptors. The Smooth Overlap of Atomic Position descriptors that are frequently visited in the literature and the Zernike descriptors that are built upon a similar basis are included into the discussion as being the natural counterparts of the Spherical Bessel descriptors, and shown to be incapable of satisfying the full list of core requirements for an accurate description. Aside being mathematically and physically superior, the Spherical Bessel descriptors have also the advantage of allowing machine learning potentials of comparable accuracy that require roughly an order of magnitude less computation time per evaluation than the Smooth Overlap of Atomic Position descriptors, which appear to be the common choice of descriptors in recent studies.

physics.comp-ph↗

arXiv2019

A Novel Approach to Describe Chemical Environments in High Dimensional Neural Network Potentials

A central concern of molecular dynamics simulations are the potential energy surfaces that govern atomic interactions. These hypersurfaces define the potential energy of the system, and have generally been calculated using either predefined analytical formulas (classical) or quantum mechanical simulations (ab initio). The former can accurately reproduce only a selection of material properties, whereas the latter is restricted to short simulation times and small systems. Machine learning potentials have recently emerged as a third approach to model atomic interactions, and are purported to offer the accuracy of ab initio simulations with the speed of classical potentials. However, the performance of machine learning potentials depends crucially on the description of a local atomic environment. A set of invariant, orthogonal and differentiable descriptors for an atomic environment is proposed, implemented in a neural network potential for solid-state silicon, and tested in molecular dynamics simulations. Neural networks using the proposed descriptors are found to outperform ones using the Behler Parinello and SOAP descriptors currently in the literature.

physics.comp-ph↗

arXiv2017

Roundness of grains in cellular microstructures

Many physical systems are composed of polyhedral cells of varying sizes and shapes. These structures are simple in the sense that no more than three faces meet at an edge and no more than four edges meet at a vertex. This means that individual cells can usually be considered as simple, three-dimensional polyhedra. This paper is concerned with determining the distribution of combinatorial types of such polyhedral cells. We introduce the terms \emph{fundamental} and \emph{vertex-truncated} types and apply these concepts to the grain growth microstructure as a testing ground. For these microstructures we demonstrate that most grains are of particular fundamental types, whereas the frequency of vertex-truncated types decreases exponentially with the number of truncations. This can be explained by the evolutionary process through which grain growth structures are formed, and in which energetically unfavorable surfaces are quickly eliminated. Furthermore, we observe that these grain types are `round' in a combinatorial sense: there are no `short' separating cycles that partition the polyhedra into two parts of similar sizes. A particular microstructure derived from the Poisson--Voronoi initial condition is identified as containing an unusually large proportion of round grains. This Round microstructure has an average of $14.036$ faces per grain, and is conjectured to be more resistant to topological change than the steady-state grain growth microstructure.

cond-mat.mtrl-sci↗

arXiv2017

Improved conditioning of the Floater--Hormann interpolants

The Floater--Hormann family of rational interpolants do not have spurious poles or unattainable points, are efficient to calculate, and have arbitrarily high approximation orders. One concern when using them is that the amplification of rounding errors increases with approximation order, and can make balancing the interpolation error and rounding error difficult. This article proposes to modify the Floater--Hormann interpolants by including additional local polynomial interpolants at the ends of the interval. This appears to improve the conditioning of the interpolants and allow higher approximation orders to be used in practice.

math.NA↗

arXiv2015

Geometric and topological properties of the canonical grain growth microstructure

Many physical systems can be modeled as large sets of domains "glued" together along boundaries - biological cells meet along cell membranes, soap bubbles meet along thin films, countries meet along geopolitical boundaries, and metallic crystals meet along grain interfaces. Each class of microstructures results from a complex interplay of initial conditions and particular evolutionary dynamics. The statistical steady-state microstructure resulting from isotropic grain growth of a polycrystalline material is canonical in that it is the simplest example of a cellular microstructure resulting from a gradient flow of a simple energy, directly proportional to the total length or area of all cell boundaries. As many properties of polycrystalline materials depend on their underlying microstructure, a more complete understanding of the grain growth steady-state can provide insight into the physics of a broad range of everyday materials. In this paper we report geometric and topological features of these canonical two- and three-dimensional steady-state microstructures obtained through large, accurate simulations of isotropic grain growth.

cond-mat.mtrl-sci↗

arXiv2014

Statistical Topology of Three-Dimensional Poisson-Voronoi Cells and Cell Boundary Networks

Voronoi tessellations of Poisson point processes are widely used for modeling many types of physical and biological systems. In this paper, we analyze simulated Poisson-Voronoi structures containing a total of 250,000,000 cells to provide topological and geometrical statistics of this important class of networks. We also report correlations between some of these topological and geometrical measures. Using these results, we are able to corroborate several conjectures regarding the properties of three-dimensional Poisson-Voronoi networks and refute others. In many cases, we provide accurate fits to these data to aid further analysis. We also demonstrate that topological measures represent powerful tools for describing cellular networks and for distinguishing among different types of networks.

physics.comp-ph↗

arXiv2012

Complete topology of cells, grains, and bubbles in three-dimensional microstructures

We introduce a general, efficient method to completely describe the topology of individual grains, bubbles, and cells in three-dimensional polycrystals, foams, and other multicellular microstructures. This approach is applied to a pair of three-dimensional microstructures that are often regarded as close analogues in the literature: one resulting from normal grain growth (mean curvature flow) and another resulting from a random Poisson-Voronoi tessellation of space. Grain growth strongly favors particular grain topologies, compared with the Poisson-Voronoi model. Moreover, the frequencies of highly symmetric grains are orders of magnitude higher in the the grain growth microstructure than they are in the Poisson-Voronoi one. Grain topology statistics provide a strong, robust differentiator of different cellular microstructures and provide hints to the processes that drive different classes of microstructure evolution.

cond-mat.mtrl-sci↗