Electron microscope object reconstruction: Retrieval of local variations in mixed type potentials. Part I: Theoretical preliminaries

The direct object retrieval via the linearized inversion of the dynamical scattering matrix is extended using a second order perturbation theory and including mixed type potentials. The higher order perturbation increases the confidence region extracting object thickness and bending directly out of amplitude and phase of an electron wave without using trial-and-error iterative matching. Applying parameterization of a mixed type total scattering potential as a priori information enables a simple extension of the structure retrieval procedure to reconstruct local variations of the object potential, too.     

TEM characterization of precipitates in the segregated regions of a low-carbon, low-manganese, titanium-added steel

A concentric solidification technique has been employed to simulate sulphide precipitation at the centreline of a continuously cast low-carbon, low-manganese, titanium-added steel slab. Selected precipitates were identified using transmission electron microscopy following sample preparation by focused ion beam milling techniques. FeTiS₂ and hexagonal MnS containing iron atoms form in close proximity to each other in super-saturated areas of the concentrically solidified sample. The presence of FeTiS₂ precipitates in low-carbon steel has been verified for the first time, and the crystal structure determined by electron diffraction analysis as a trigonal CdI₂-type with a P 3 m1 space group and lattice parameters of a = 0.341 nm and c = 0.569 nm.     

Electron back‐scattering diffraction (EBSD) measurements of antigorite lattice‐preferred orientations (LPO)

Lattice preferred orientations of serpentines induce a strong anisotropy of various properties in serpentine bearing‐rocks. Lattice preferred orientations had so far been obtained only by X‐ray diffraction techniques. We have applied electron back‐scattering diffraction to the measurement of the lattice preferred orientations of antigorite in a naturally deformed high‐pressure serpentinite. This technique is very sensitive to sample preparation that can lead to surface amorphization in the case of serpentine. A polishing procedure is described that avoids amorphization and allows accurate electron back‐scattering diffraction measurements with optimized experimental conditions in a variable pressure scanning electron microscope. Results indicate that deformation leads to lattice preferred orientations characterized by extremely strong c‐axis clustering perpendicular to the foliation, as expected for a layered silicate. In the foliation plane, a significant clustering of the a‐axis is observed and tentatively attributed to intracrystalline deformation mechanisms. These data suggest that antigorite deforms mostly by gliding along the basal plane of the layered phyllosilicate structure, but that gliding may occur along directions favouring a‐axis alignment. Electron back‐scattering diffraction appears to be a reliable method for determining phyllosilicate lattice preferred orientations in deformed rocks, with potential applications for determining anisotropy of properties like seismic velocities or thermal and electrical conductivities.     

Practical implementation of a direct method for coherent diffractive imaging

We experimentally implement a direct, non-iterative method for recovering the complex wave in the exit-surface plane of a coherently illuminated object. The form of illumination is subject to certain conditions. By satisfying these conditions, the complex exit-surface wave is directly recovered from a single far-field intensity pattern, by solving a set of linear equations. These linear equations, whose coefficients depend on the incident illumination, are obtained by analyzing the autocorrelation function of the exit-surface wave. This autocorrelation is constructed by taking the inverse Fourier transform of the diffraction pattern. We introduce a preconditioning step, for the system of linear equations, which improves the robustness of the method to noise. While the present experimental proof of concept has been performed using a visible-light laser, the method is applicable to diffractive imaging using coherent X-ray and electron sources.     

Electron channelling based crystallography

Electron channelling occurs when the incident electron beam is parallel to the atom columns of an object, such as a crystal or a particular crystal defect. Then, the electrons are trapped in the electrostatic potential of an atom column in which they scatter dynamically. This picture provides physical insight and explains why a one-to-one correspondence is maintained between the exit wave and the projected structure, even in case of strong dynamical scattering. Moreover, the theory is very useful to invert the dynamical scattering, that is, to derive the projected structure from the exit wave. Finally, it can be used to determine the composition of an atom column with single atom sensitivity or to explain dynamical electron diffraction effects. In this paper, an overview of the channelling theory will be given together with some recent applications.     

Crystallographic image processing approach to crystal structure determination

It is shown that the crystallographic image-processing technique based on the weak-phase object approximation and on the combination of high-resolution electron microscopy and electron diffraction is applicable to crystal structure determination. The technique consists of two stages: image deconvolution and phase extension. In the first stage an image taken at an arbitrary defocus condition can be transformed into the structure image with the resolution limited by the resolution of the electron microscope. In the second stage the image resolution is enhanced to the diffraction resolution limit so that most unoverlapped atoms can be resolved individually in the final image. Although the experimental diffraction intensities are available for the image deconvolution, they must be corrected for the phase extension. The proposed empirical method of electron diffraction intensity correction seems effective for obtaining a set of corrected diffraction intensities which are approximately equal to square structure factors.
When the crystal structure under examination belongs to a known typical type, it is easy to propose the structure model by referring to the deconvoluted image which reveals the low-resolution structure, and the high-resolution structure can also be determined by image simulation.     

A method for determining void arrangements in inverse opals

The periodic arrangement of voids in ceramic materials templated by colloidal crystal arrays (inverse opals) has been analysed by transmission electron microscopy. Individual particles consisting of an approximately spherical array of at least 100 voids were tilted through 90° along a single axis within the transmission electron microscope. The bright‐field images of these particles at high‐symmetry points, their diffractograms calculated by fast Fourier transforms, and the transmission electron microscope goniometer angles were compared with model face‐centred cubic, body‐centred cubic, hexagonal close‐packed, and simple cubic lattices in real and reciprocal space. The spatial periodicities were calculated for two‐dimensional projections. The systematic absences in these diffractograms differed from those found in diffraction patterns from three‐dimensional objects. The experimental data matched only the model face‐centred cubic lattice, so it was concluded that the packing of the voids (and, thus, the polymer spheres that composed the original colloidal crystals) was face‐centred cubic. In face‐centred cubic structures, the stacking‐fault displacementvector is . No stacking faults were observed when viewingthe inverse opal structure along the orthogonal <110>‐type directions, eliminating the possibility of a random hexagonally close‐packed structure for the particles observed. This technique complements synchrotron X‐ray scattering work on colloidal crystals by allowing both real‐space and reciprocal‐space analysis to be carried out on a smaller cross‐sectional area.     

Comparison of different models for the generation of electron backscattering patterns in the scanning electron microscope

An electron backscattering pattern (EBSP) is formed on a fluorescent (or other) screen from the faster scattered electrons when a single-crystal region of a solid sample is illuminated by a finely focused electron beam (EB). The EBSP is very similar in appearance to the electron channeling pattern (ECP) that is obtained in the scanning electron microscope (SEM) by rocking the beam about a point on the surface of a single crystal. It has been suggested that the mechanisms that give rise to EBSP and ECP are related by reciprocity. If this is indeed the case, then the models that are used to explain them should be the same except for the direction in which the electrons travel through the specimen. The two-event “diffraction model” for EBSP (diffuse scattering followed by diffraction) fails this condition, leading to the conclusion that the “channeling in and channeling out” model for EBSP is more likely to be correct. This has been described rigorously by Reimer (1979, 1985). It is named after the title used by Joy (1994). An attempt is made here to describe this model in a simple way.     

Lattice-resolution contrast from a focused coherent electron probe. Part I

To develop a Bloch wave framework for lattice-resolution contrast derived from coherent or incoherent scattering of an electron probe focused onto a crystal, boundary conditions which influence the propagation of an arbitrarily distorted coherent electron probe are addressed. These boundary conditions are particularly relevant for a probe focused within a unit cell, and lead to a general theory which hinges on Bloch wave excitation amplitudes being written as a function of beam position and focus. Whereas antisymmetric Bloch states are not excited for an incident plane wave at an exact zone axis orientation, these states may be strongly excited depending on probe focus and position within the unit cell. Equations for both coherent and incoherent lattice image contrast in scanning transmission electron microscopy are derived for any detector configuration in the Bloch wave framework. An equivalent expression amenable to evaluation via multislice techniques is also described. It is shown explicitly how mixed dynamic form factors for incoherent scattering should be taken into account for annular dark field or backscattered electron detectors, as well as for characteristic losses detected by X-ray emissions or by electron energy loss spectroscopy. A background contribution from "absorbed" electrons is included in the theory. The contribution of cross-talk from neighbouring columns to incoherent contrast is examined within the context of this theoretical framework.     

Orientation and phase mapping in the transmission electron microscope using precession‐assisted diffraction spot recognition: state‐of‐the‐art results

A recently developed technique based on the transmission electron microscope, which makes use of electron beam precession together with spot diffraction pattern recognition now offers the possibility to acquire reliable orientation/phase maps with a spatial resolution down to 2 nm on a field emission gun transmission electron microscope. The technique may be described as precession‐assisted crystal orientation mapping in the transmission electron microscope, precession‐assisted crystal orientation mapping technique–transmission electron microscope, also known by its product name, ASTAR, and consists in scanning the precessed electron beam in nanoprobe mode over the specimen area, thus producing a collection of precession electron diffraction spot patterns, to be thereafter indexed automatically through template matching. We present a review on several application examples relative to the characterization of microstructure/microtexture of nanocrystalline metals, ceramics, nanoparticles, minerals and organics. The strengths and limitations of the technique are also discussed using several application examples.     

Retrieving overlapping crystals information from TEM nano‐beam electron diffraction patterns

The diffraction patterns acquired with a transmission electron microscope (TEM) contain Bragg reflections related to all the crystals superimposed in the thin foil and crossed by the electron beam. Regarding TEM‐based orientation and phase characterisation techniques, the nondissociation of these signals is usually considered as the main limitation for the indexation of diffraction patterns. A new method to identify the information related to the distinct but overlapped grains is presented. It consists in subtracting the signature of the dominant crystal before reindexing the diffraction pattern. The method is coupled to the template matching algorithm used in a standard automated crystal orientation mapping tool (ACOM‐TEM). The capabilities of the approach are illustrated with the characterisation of a NiSi thin film stacked on a monocrystalline Si layer. Then, a subtracting‐indexing cycle applied to a 70 nm thick thin foil containing polycrystalline tungsten electrical contacts shows the capability of the technique to recognise small nondominant grains.     

Charge contrast imaging of material growth and defects in environmental scanning electron miscroscopy--linking electron emission and cathodoluminescence

An electron-based technique for the imaging of crystal defect distribution such as material growth histories in non- and poorly conductive materials has been identified in the variable pressure or environmental scanning electron microscope. Variations in lattice coherence at the meso-scale can be imaged in suitable materials. Termed charge contrast imaging (CCI), the technique provides images that correlate exactly with emitted light or cathodoluminescence in suitable materials. This correlation links cathodoluminescence and an electron emission. The specific operating conditions for observation of these images reflect a complex interaction between the electron beam, the positive ions generated by electron-gas interactions in the chamber, a biased detector, and the sample. The net result appears to be the suppression of all but very near surface electron emission from the sample, probably from of the order of a few nanometres. Consequently, CCI are also sensitive to very low levels of surface contaminants. Successful imaging of internal structures in a diverse range of materials indicate that the technique will become an important research tool.     

Method of Finite Differences in Time Domain. Calculating Echo Signals in Anisotropic Inhomogeneous Materials,Pattern Noise

When developing ultrasonic testing techniques for such complex objects as composite welds, the method of finite differences in time domain (FDTD) can be used to calculate echo signals in numerical experiments. Since the FDTD method is based on explicit numerical solution of the wave equation for an elastic medium, it can be used to take account of such effects as the emergence of a run round wave on a volume reflector, the transformation of a longitudinal wave into a lateral one under scattering of ultrasound by a crack, and the rescattering of pulses between reflectors and test-object boundaries. Applying the FDTD method to modeling the propagation of ultrasound in the sample with a high pattern noise and in the samples made of anisotropic inhomogeneous materials is substantiated. The FDTD calculation of the direct problem of propagation of elastic vibrations in a solid may prove useful when solving the inverse problem of ultrasonic nondestructive testing.     

Use of backscattered electron imaging on developed radioautographic emulsions: Application to viewing rat incisor enamel maturation pattern following 45calcium injection

Immunoelectron microscopy techniques were used to localize alpha-actinin within the Z lattice of adult skeletal muscles. Analysis of electron micrographs by direct visualization demonstrated that anti-alpha-actinin Fab fragments bound throughout the Z lattice. A low-resolution scanning densitometry technique was developed to quantitate the visual increase in the density of the Z lattice. These techniques did not allow determination of the particular component of the Z lattice, amorphous matrix, axial filaments, or cross-connecting filaments with which the antibody was associated. Therefore, additional techniques, including direct measurement of filament diameters and optical diffraction, were utilized in determining which components of the Z lattice bound anti-alpha-actinin Fab fragments. These analyses suggest that the antibody binding is distributed evenly throughout the lattice, along the filaments, and between them and is confined to the region of double overlap of the ends of the thin filaments.     

Inverse electronic scattering by singular values decomposition within the Fresnel-Kirchhoff formalism.

The inverse scattering technique we presented previously to enable a sample reconstruction from the diffraction figures obtained by electronic projection microscopy is reforrmulated within the Fresnel-Kirchhoff formalism, which describes the sample as a two-dimensional mask. The method relies on the use of singular values decomposition techniques, thus providing the best least-squares solutions and enabling a reduction of noise. The technique is applied to the analysis of a two-dimensional nanometric sample that is observed in Fresnel conditions with an electronic energy of 40 eV. The algorithm turns out to provide results with a mean relative error around 1% and to be very stable against random noise.     

A graphic description of the interaction of waves with various boundaries

The solution of hyperbolic partial-differential equations has been an area of interest for many years. The original technique proposed for their solution was the method of characteristics, which converted the partial-differential equations into ordinary differential equations. The latter were often solved by graphical techniques and were applied to various problems from water hammer in pipes to the intake and exhaust systems of internal combustion engines.With the advent of the digital computer the tedious graphical techniques lost favour and numerical algorithms replaced them. Some of the numerical techniques were based on method of characteristics whilst others have relied on direct solution of the conservation equations. The proponents of each technique argue the benefits of their approach. The definite disadvantage of all the numerical techniques has been the loss of ‘feel’ for the wave action; this was readily available in the graphical approach because the waves were ‘visible’.This paper describes the application of computer graphics to the solution of the wave equations. It shows how the understanding of wave interaction with various geometric and parametric properties of the pipe and gas can be improved by simple isometric pictures.     

Electron crystal structure analysis of small organic molecules

Electron crystallography of small organic molecules, i.e., electron diffraction crystal structure analysis, has been long recognized to possess definite advantages over neutron and x-ray diffraction techniques for the investigation of microcrystalline preparations. Quantitative application of the technique to real structural problems, on the other hand, had been hindered initially by an inadequate theoretical model. Yet, as demonstrated in this review of the methodology, the adequate recognition of limiting factors due to n-beam dynamical scattering and crystal deformation permits design of optimal diffraction experiments which yield intensity data suitable for ab initio structure analysis. Representative crystallographic analyses discussed here underscore the utility of this technique as a probe of organic molecular structure at atomic resolution.     

Neutron scattering studies of BiFeO3 multiferroics: a review for microscopists

Application of the neutron scattering technique in the study of crystal and magnetic properties of multiferroic BiFeO₃ is presented. The crucial role of the neutron scattering technique, complementary to X-ray diffraction method and transmission electron microscopy, is shown. Especially the ultra high-resolution time-of-flight (TOF) neutron diffraction technique used by Sosnowska et al. to detect the magnetic cycloid ordering and its role in studies of physical properties of BiFeO₃ and its alloys are reviewed. The first inelastic neutron scattering patterns of magnetic excitations in BiFeO₃ are also presented. Applications of different microscopy techniques such as transmission electron microscopy (TEM), scanning electron microscopy ( SEM), field emission TEM and SEM (FESEM and FETEM), magnetic force microscope (MFM) and polarization force microscopy (PFM) bring insight on the fundamental problem of ferroelectricity and confirm the potential of BiFeO₃ multiferroic material for nanoscale devices.     

Refinement of the 200 structure factor for GaAs using parallel and convergent beam electron nanodiffraction data

We present a new method to measure structure factors from electron spot diffraction patterns recorded under almost parallel illumination in transmission electron microscopes. Bloch wave refinement routines have been developed to refine the crystal thickness, its orientation and structure factors by comparison of experimentally recorded and calculated intensities. Our method requires a modicum of computational effort, making it suitable for contemporary personal computers. Frozen lattice and Bloch wave simulations of GaAs diffraction patterns are used to derive optimised experimental conditions. Systematic errors are estimated from the application of the method to simulated diffraction patterns and rules for the recognition of physically reasonable initial refinement conditions are derived. The method is applied to the measurement of the 200 structure factor for GaAs. We found that the influence of inelastically scattered electrons is negligible. Additionally, we measured the 200 structure factor from zero loss filtered two-dimensional convergent beam electron diffraction patterns. The precision of both methods is found to be comparable and the results agree well with each other. A deviation of more than 20% from isolated atom scattering data is observed, whereas close agreement is found with structure factors obtained from density functional theory [A. Rosenauer, M. Schowalter, F. Glas, D. Lamoen, Phys. Rev. B 72 (2005), 085326-1], which account for the redistribution of electrons due to chemical bonding via modified atomic scattering amplitudes.