Jeff P. Simmons

Green's function boundary conditions in two-dimensional and three-dimensional atomistic simulations of dislocations

Abstract A method for dynamically updating the boundary conditions of atomistic simulations is presented. The lattice Greens function boundary relaxation method, originally introduced by Sinclair et al. in 1978, is extended to treat three-dimensional (3D) simulations. The boundary conditions for two-dimensional (2D) and 3D defect cells are evaluated using line and point force distributions respectively. The method is general and has been incorporated into several potential interaction schemes. Examples of the method using embeddedatom method potentials are presented for the following: simulation of a straight (a/2)[110] screw dislocation in Ni; an isolated a kink on an (a/2)[111] screw dislocation in bcc Fe; simulation of a periodic array of a kinks on an (a/2)[111] screw dislocation in bcc Fe. The first simulation is 2D in nature and the last two defects are 3D.

Phase-field modeling of bimodal particle size distributions during continuous cooling

Abstract Microstructures in Nickel-base alloys typically contain a two-phase mixture of γ/γ′. The microstructure having a bimodal size distribution of γ′ is of particular interest because it has important property consequences [1] . In this paper, the phase-field method with an explicit nucleation algorithm is employed to investigate the microstructural development during a continuous cooling with various cooling rates. It is demonstrated that bimodal particle size distributions can be achieved at an intermediate cooling rate due to a coupling between diffusion and undercooling, in which the system experiences two peaks of well-isolated nucleation events. It is suggested that this is caused by soft impingement, followed by a renewal of driving force for nucleation, followed by a subsequent soft impingement. Under very high cooling rates, the microstructure becomes unimodal, because undercooling always outruns diffusion and the microstructure never reaches soft impingement.

Atomistics simulations of structures and properties of ½⟨110⟩ dislocations using three different embedded-atom method potentials fit to γ-TiAl

Abstract Molecular statics simulations were made of dislocations in L10 structures, using three different embedded-atom method (EAM) potentials that were fitted to the bulk properties of γ-TiAl. The three EAM potentials were fitted to produce complex stacking-fault energies of 120, 320 and 580 mJ m−2 so that the effects of variations in fault energies could be investigated parametrically. Core structures were determined for each of the potentials for the following orientations: screw, 30[ddot] mixed, 60[ddot] mixed and edge. These cores were all planar except the screw orientations calculated with the 320 and 580 mJm−2 potentials. These showed substantial amounts of non-planar spreading. The 60[ddot] orientations for these two potentials had a tendency for the screw component of the displacement to spread out of plane and the edge component to spread in the glide plane. The screw orientation of the 320 mJm−2 potential was found to have two possible states: planar and non-planar. The friction stresses were...

A Model Based Iterative Reconstruction Algorithm For High Angle Annular Dark Field-Scanning Transmission Electron Microscope (HAADF-STEM) Tomography

High angle annular dark field (HAADF)-scanning transmission electron microscope (STEM) data is increasingly being used in the physical sciences to research materials in 3D because it reduces the effects of Bragg diffraction seen in bright field TEM data. Typically, tomographic reconstructions are performed by directly applying either filtered back projection (FBP) or the simultaneous iterative reconstruction technique (SIRT) to the data. Since HAADF-STEM tomography is a limited angle tomography modality with low signal to noise ratio, these methods can result in significant artifacts in the reconstructed volume. In this paper, we develop a model based iterative reconstruction algorithm for HAADF-STEM tomography. We combine a model for image formation in HAADF-STEM tomography along with a prior model to formulate the tomographic reconstruction as a maximum a posteriori probability (MAP) estimation problem. Our formulation also accounts for certain missing measurements by treating them as nuisance parameters in the MAP estimation framework. We adapt the iterative coordinate descent algorithm to develop an efficient method to minimize the corresponding MAP cost function. Reconstructions of simulated as well as experimental data sets show results that are superior to FBP and SIRT reconstructions, significantly suppressing artifacts and enhancing contrast.

A Dictionary Approach to Electron Backscatter Diffraction Indexing.

We propose a framework for indexing of grain and subgrain structures in electron backscatter diffraction patterns of polycrystalline materials. We discretize the domain of a dynamical forward model onto a dense grid of orientations, producing a dictionary of patterns. For each measured pattern, we identify the most similar patterns in the dictionary, and identify boundaries, detect anomalies, and index crystal orientations. The statistical distribution of these closest matches is used in an unsupervised binary decision tree (DT) classifier to identify grain boundaries and anomalous regions. The DT classifies a pattern as an anomaly if it has an abnormally low similarity to any pattern in the dictionary. It classifies a pixel as being near a grain boundary if the highly ranked patterns in the dictionary differ significantly over the pixels neighborhood. Indexing is accomplished by computing the mean orientation of the closest matches to each pattern. The mean orientation is estimated using a maximum likelihood approach that models the orientation distribution as a mixture of Von Mises-Fisher distributions over the quaternionic three sphere. The proposed dictionary matching approach permits segmentation, anomaly detection, and indexing to be performed in a unified manner with the additional benefit of uncertainty quantification.

Model-Based Iterative Reconstruction for Bright-Field Electron Tomography

Bright-Field (BF) electron tomography (ET) has been widely used in the life sciences for 3-D imaging of biological specimens. However, while BF-ET is popular in the life sciences, 3-D BF-ET imaging has been avoided in the physical sciences due to measurement anomalies from crystalline samples caused by dynamical diffraction effects such as Bragg scatter. In practice, these measurement anomalies cause undesirable artifacts in 3-D reconstructions computed using filtered back-projection (FBP). Alternatively, model-based iterative reconstruction (MBIR) is a powerful framework for tomographic reconstruction that combines a forward model for the measurement system and a prior model for the object to obtain reconstructions by minimizing a single cost function. In this paper, we present an MBIR algorithm for BF-ET reconstruction from crystalline materials that can account for the presence of anomalous measurements. We propose a new forward model for the acquisition system which accounts for the presence of anomalous measurements and combine it with a prior model for the object to obtain the MBIR cost function. We then propose a fast algorithm based on majorization-minimization to find a minimum of the corresponding cost function. Results on simulated as well as real data show that our method can dramatically improve reconstruction quality as compared to FBP and conventional MBIR without anomaly modeling.

On the use of moment invariants for the automated analysis of 3D particle shapes

A mathematical method is introduced to describe quantitatively the shape and shape evolution of precipitates in a two-phase microstructure. The method relies on the concept of moment invariants, i.e. combinations of second order moments that are invariant with respect to affine and/or similarity transformations. We introduce three invariants, one a shape discriminator, the other two aspect ratio discriminators. A normalized form of the invariants is defined and it is shown explicitly that any 3D shape must belong to a finite region of the normalized moment invariant space. The shape and bounds of this region are defined in terms of isoperimetric inequalities. Two examples of moment invariant applications are given: fitting the shape of second phase precipitates and the time evolution of a bimodal phase field simulation.

Model based iterative reconstruction for Bright Field electron tomography

Bright Field (BF) electron tomography (ET) has been widely used in the life sciences to characterize biological specimens in 3D. While BF-ET is the dominant modality in the life sciences it has been generally avoided in the physical sciences due to anomalous measurements in the data due to a phenomenon called “Bragg scatter” - visible when crystalline samples are imaged. These measurements cause undesirable artifacts in the reconstruction when the typical algorithms such as Filtered Back Projection (FBP) and Simultaneous Iterative Reconstruction Technique (SIRT) are applied to the data. Model based iterative reconstruction (MBIR) provides a powerful framework for tomographic reconstruction that incorporates a model for data acquisition, noise in the measurement and a model for the object to obtain reconstructions that are qualitatively superior and quantitatively accurate. In this paper we present a novel MBIR algorithm for BF-ET which accounts for the presence of anomalous measurements from Bragg scatter in the data during the iterative reconstruction. Our method accounts for the anomalies by formulating the reconstruction as minimizing a cost function which rejects measurements that deviate significantly from the typical Beer’s law model widely assumed for BF-ET. Results on simulated as well as real data show that our method can dramatically improve the reconstructions compared to FBP and MBIR without anomaly rejection, suppressing the artifacts due to the Bragg anomalies.

Model-based iterative reconstruction for synchrotron X-ray tomography

Synchrotron based X-ray tomography is widely used for three dimensional imaging of materials at the micron scale. Tomographic data collected from a synchrotron is often affected by non-idealities in the measurement system and sudden “blinding” of detector pixels during the acquisition. Typically, reconstructions are done using analytical reconstruction techniques combined with pre/post-processing steps to correct for the non-idealities, resulting in loss of detail while still producing noisy reconstructions with some artifacts. In this paper, we present a model-based iterative reconstruction (MBIR) algorithm for synchrotron X-ray tomography that can automatically handle the non-idealities as a part of the reconstruction. First, we develop a forward model that accounts for the non-idealities in the measurement system and for the occurrence of outliers in the measurement. Next, we combine the forward model with a prior model of the object to formulate the MBIR cost function and propose an algorithm to minimize the cost. Results on a real data set show that the MBIR reconstructions are superior to the analytical reconstructions effectively suppressing noise as well as other artifacts.

3D Materials Image Segmentation by 2D Propagation: A Graph-Cut Approach Considering Homomorphism

Segmentation propagation, similar to tracking, is the problem of transferring a segmentation of an image to a neighboring image in a sequence. This problem is of particular importance to materials science, where the accurate segmentation of a series of 2D serial-sectioned images of multiple, contiguous 3D structures has important applications. Such structures may have distinct shape, appearance, and topology, which can be considered to improve segmentation accuracy. For example, some materials images may have structures with a specific shape or appearance in each serial section slice, which only changes minimally from slice to slice, and some materials may exhibit specific inter-structure topology that constrains their neighboring relations. Some of these properties have been individually incorporated to segment specific materials images in prior work. In this paper, we develop a propagation framework for materials image segmentation where each propagation is formulated as an optimal labeling problem that can be efficiently solved using the graph-cut algorithm. Our framework makes three key contributions: 1) a homomorphic propagation approach, which considers the consistency of region adjacency in the propagation; 2) incorporation of shape and appearance consistency in the propagation; and 3) a local non-homomorphism strategy to handle newly appearing and disappearing substructures during this propagation. To show the effectiveness of our framework, we conduct experiments on various 3D materials images, and compare the performance against several existing image segmentation methods.