Marc De Graef

Quantitative noninterferometric Lorentz microscopy

Noninterferometric phase reconstruction based on the transport of intensity equation (TIE) is applied to experimental images for a Permalloy thin film and to a computational magnetization pattern for a high density magnetic recording medium. An alternative derivation of the TIE is given, based on linear image formation theory. A compact formal solution, suitable for numerical computation, is given.

Origin of domain structure in hexagonal silicon carbide boules grown by the physical vapor transport method

Transmission electron microscopy (TEM), high-resolution X-ray di!raction, and KOH etching have been used to study the dislocation structure of 4H SiC crystals grown by the physical vapor transport method. Many of the etch pits on the Si(0 0 0 1) surface form arrays extending along the S11 100 T directions. Plan view conventional and high-resolution TEM show that the arrays consist of pure edge dislocations threading along the c-axis with identical Burgers vectors of the a/3S 112 1 0T type. The dislocation arrays constitute low angle [0 0 0 1] tilt boundaries, i.e., [0 0 0 1] is the common axis lying in the boundary. Typical values of the misorientation are in the 60}200 arcsec range. Evidence is presented that such boundaries can form by polygonization of the threading edge dislocations, which have been introduced into SiC crystals by prismatic slip. ( 2000 Published by Elsevier Science B.V.

Introduction and comparison of new EBSD post-processing methodologies

Electron Backscatter Diffraction (EBSD) provides a useful means for characterizing microstructure. However, it can be difficult to obtain index-able diffraction patterns from some samples. This can lead to noisy maps reconstructed from the scan data. Various post-processing methodologies have been developed to improve the scan data generally based on correlating non-indexed or mis-indexed points with the orientations obtained at neighboring points in the scan grid. Two new approaches are introduced (1) a re-scanning approach using local pattern averaging and (2) using the multiple solutions obtained by the triplet indexing method. These methodologies are applied to samples with noise introduced into the patterns artificially and by the operational settings of the EBSD camera. They are also applied to a heavily deformed and a fine-grained sample. In all cases, both techniques provide an improvement in the resulting scan data, the local pattern averaging providing the most improvement of the two. However, the local pattern averaging is most helpful when the noise in the patterns is due to the camera operating conditions as opposed to inherent challenges in the sample itself. A byproduct of this study was insight into the validity of various indexing success rate metrics. A metric based given by the fraction of points with CI values greater than some tolerance value (0.1 in this case) was confirmed to provide an accurate assessment of the indexing success rate.

TIMBIR: A Method for Time-Space Reconstruction From Interlaced Views

Synchrotron X-ray computed tomography (SXCT) is increasingly being used for 3-D imaging of material samples at micron and finer scales. The success of these techniques has increased interest in 4-D reconstruction methods that can image a sample in both space and time. However, the temporal resolution of widely used 4-D reconstruction methods is severely limited by the need to acquire a very large number of views for each reconstructed 3-D volume. Consequently, the temporal resolution of current methods is insufficient to observe important physical phenomena. Furthermore, measurement nonidealities also tend to introduce ring and streak artifacts into the 4-D reconstructions. In this paper, we present a time-interlaced model-based iterative reconstruction (TIMBIR) method, which is a synergistic combination of two innovations. The first innovation, interlaced view sampling, is a novel method of data acquisition, which distributes the view angles more evenly in time. The second innovation is a 4-D model-based iterative reconstruction algorithm (MBIR), which can produce time-resolved volumetric reconstruction of the sample from the interlaced views. In addition to modeling both the sensor noise statistics and the 4-D object, the MBIR algorithm also reduces ring and streak artifacts by more accurately modeling the measurement nonidealities. We present reconstructions of both simulated and real X-ray synchrotron data, which indicate that TIMBIR can improve temporal resolution by an order of magnitude relative to existing approaches.

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.

2. Lorentz microscopy: Theoretical basis and image simulations

Publisher Summary Magnetization configurations in real engineering materials can be studied both qualitatively and quantitatively in a variety of ways. This chapter reviews the basic theory of Lorentz microscopy, a set of observation modes that are commonly used in either a conventional transmission electron microscope (CTEM) or a scanning transmission electron microscope (STEM). The behavior of relativistic electrons in a magnetic field is examined in the chapter, using first a classical and then a quantum mechanical approach. In the chapter, the various observation modes (Fresnel, Foucault, and derived techniques) are presented and the way the transmission electron microscope (TEM) can be used to obtain qualitative pictures of the magnetization configuration in a thin foil is discussed. The chapter presents quantitative observation modes, which produce direct maps of the sample magnetization configuration. These include differential phase contrast, which can be used in CTEM and STEM versions. It also describe the way Lorentz images can be simulated for a given magnetization configuration.

Nanoscale Skyrmions in a Nonchiral Metallic Multiferroic: Ni2MnGa

Magnetic skyrmions belong to a set of topologically nontrivial spin textures at the nanoscale that have received increased attention due to their emergent behavior and novel potential spintronic applications. Discovering materials systems that can host skyrmions at room temperature in the absence of external magnetic field is of crucial importance not only from a fundamental aspect, but also from a technological point of view. So far, the observations of skyrmions in bulk metallic ferromagnets have been limited to low temperatures and to materials that exhibit strong chiral interactions. Here we show the formation of nanoscale skyrmions in a nonchiral multiferroic material, which is ferromagnetic and ferroelastic, Ni2MnGa at room temperature without the presence of external magnetic fields. By using Lorentz transmission electron microscopy in combination with micromagnetic simulations, we elucidate their formation, behavior, and stability under applied magnetic fields at room temperature. The formation of skyrmions in a multiferroic material with no broken inversion symmetry presents new exciting opportunities for the exploration of the fundamental physics of topologically nontrivial spin textures.

Rapid misfit dislocation characterization in heteroepitaxial III-V/Si thin films by electron channeling contrast imaging

Electron channeling contrast imaging (ECCI) is used to characterize misfit dislocations in heteroepitaxial layers of GaP grown on Si(100) substrates. Electron channeling patterns serve as a guide to tilt and rotate sample orientation so that imaging can occur under specific diffraction conditions. This leads to the selective contrast of misfit dislocations depending on imaging conditions, confirmed by dynamical simulations, similar to using standard invisibility criteria in transmission electron microscopy (TEM). The onset and evolution of misfit dislocations in GaP films with varying thicknesses (30 to 250 nm) are studied. This application simultaneously reveals interesting information about misfit dislocations in GaP/Si layers and demonstrates a specific measurement for which ECCI is preferable versus traditional plan-view TEM.

Energy filtered Lorentz microscopy

Abstract Energy-filtered Lorentz microscopy (EFLM) combines a post-column energy filter with a high-resolution TEM, operated with the main objective lens switched off. In this paper we use a magnetostrictive material, Terfenol-D (Tb0.73Dy0.27Fe1.95), to illustrate the benefits of zero-loss filtering on both standard and coherent Fresnel and Foucault modes. It is shown that the signal-to-noise ratio of Foucault images is improved by an order of magnitude. We present a detailed study of magnetic domain configurations in the vicinity of growth twins and show that the magnetic resolution of the system is better than 5 nm. Our observations compare favorably with micromagnetic models. We also show that magnetic induction mapping becomes a viable technique in thicker regions when the inelastically scattered electrons have been removed from the images. Finally, we present simulations of Fresnel and Foucault images, assuming two-dimensional periodic boundary conditions for the computation of the Aharonov-Bohm phase shift.