Incident Beam Convergence Research Articles

Trichroism in energy-loss near-edge structure spectroscopy: Polarization dependence of near-edge fine structures

The goal of this paper is to relate the current of inelastically scattered electrons collected in a transmission electron microscope (TEM) to the double differential electron energy-loss cross section. Up to now, this relationship, which depends on the point symmetry around the probed atom site, has been essentially studied in a situation called dichroism. This situation can be encountered when a principal threefold, fourfold, or sixfold rotation axis through the probed atom site exists. The electron energy-loss cross section is then a linear combination of longitudinal and transversal cross sections, and the weights of these components are cos{sup 2} {theta}{sub q} and sin{sup 2} {theta}{sub q}, where {theta}{sub q} is the angle between the scattering wave vector q and the principal rotation axis. The first aim of this paper is to find the dependence on q of the cross section in all other cases, that is to say, when the symmetry around the probed atom site is described with one of the eight low symmetry point groups C{sub 1}, S{sub 2}, C{sub 1h}, C{sub 2}, C{sub 2h}, C{sub 2v}, D{sub 2}, and D{sub 2h}. In these eight cases of low symmetry, three distinct situations called trichroism can be distinguished. Inmore » these situations, the cross section is expressed in terms of the cross sections obtained for six, four, or three particular orientations of the scattering wave vector. The second aim of this paper is to provide an expression of the inelastically scattered electron current collected in a TEM for these three situations of trichroism. This current is expressed in terms of experimental parameters, such as the incident beam convergence, the collector acceptance, the electron beam kinetic energy, and the sample orientation. As in the case of dichroism, magic conditions can be found, for which the collected current becomes independent of the single-crystal sample orientation. The case of the C K edge in the nonstoichiometric V{sub 6}C{sub 5} metallic carbide with a trigonal symmetry is given as an illustration.« less

Polarization dependence in ELNES: Influence of probe convergence, collector aperture and electron beam incidence angle

The differential scattering cross section in electron energy loss near edge spectroscopy (ELNES) generally depends on the orientation of the Q wave vector transferred from the incident electron to an atomic core electron. In the case where the excited atom belongs to a threefold, fourfold or sixfold main rotation axis, the dipole cross section depends on the angle of Q with respect to this axis. In this paper, we restrict to this situation called dichroism. Furthermore, if we take into account the relativistic effects due to the high incident electron velocity, this dipole cross section also depends on the angle of Q with respect to the electron beam axis. It is due to these dependences that the shape of measured electron energy loss spectra varies with the electron beam incidence, the collector aperture, the incident beam convergence and the incident electron energy. The existence of a particular beam incidence angle for which the scattering cross section becomes independent of collection and beam convergence semi-angles is clearly underscored. Conversely, it is shown that EELS spectra do not depend on the beam incidence angle for a set of particular values of collection and convergence semi-angles. Particularly, in the case of a parallel incident beam, there is a collection semi-angle (often called magic angle) for which the cross section becomes independent of the beam orientation. This magic angle depends on the incident beam kinetic energy. If the incident electron velocity V is small compared with the light velocity c, this magic angle is about 3.975 θ E ( θ E is the scattering angle). It decreases to 0 when V approaches c. These results are illustrated in the case of the K boron edge in the boron nitride.

Synthesis of Electron Energy Loss Spectra and Application to Quantifying Detection Limits in Materials Science

Electron energy loss spectroscopy (EELS) is a powerful microanalytical tool that can be used to characterize the composition and other properties of a wide range of materials. The compositional information is retrievable from the pattern of edges displayed in the energy-loss spectrum [1]. Under favorable experimental conditions, concentrations below 1000 ppm of many different elements can be detected on a nanometer scale [2].The minimum detectable mass (MDM) and the minimum detectable mass fraction (MDF) attainable in practice depend on many parameters (sample thickness, incident beam convergence / acceptance angles, primary energy, electron dose, probe size, detector efficiency, etc.), and there are no easy rules that can be used to predict them. For instance, a minority element that gives rise to an edge situated at an energy just lower than a major edge due to a principal constituent is much easier to detect than a minority element that gives rise to an edge just above the major edge.

Advances in image simulation for high-resolution TEM

The original high-resolution transmission electron microscope (HRTEM) image simulation program was written as a tool to confirm interpretation of HRTEM images of niobium oxides. Thorough testing on known structures showed that image simulation could reliably duplicate the imaging process occurring in the HRTEM, and could thus be confidently used to interpret images of unknown structures. Mainstream application of image simulation to routine structure determination by HRTEM was ushered in by the establishment of the wide applicability of the SHRLI (simulated high-resolution lattice image) programs. Structure determination of the mineral takéuchiite by HRTEM and image simulation was the first such determination accepted by the KJCr without x-ray data. Of course, once the reliability of image simulation had been established, it was realized that the technique could be put to work for applications other than structure determination. Early on, simulations were used to explore various HRTEM imaging parameters, including specimen ionicity, validity of the projection approximation, and the resolutionlimiting effects of incident-beam convergence. Since the inception of HRTEM image simulation, its range of uses has continued to expand, and so has the number of programs available; distribution of the SHRLI code spawned improved versions as well as some new programs.

Using convergence and spread-of-focus parameters to model spatial and temporal coherence in HRTEM image simulations

In all HRTEM images, the incident electron beam suffers from the effects of limited spatial and temporal coherence. These effects produce a smearing of the image, and provide the ultimate limits as to how high a spatial frequency can be transferred to the image (i.e. resolution). The effect of partial temporal coherence is manifested as a spread of focus, and that of partial spatial coherence as incident beam convergence. The effects of partial coherence can be included in HRTEM image simulations by summing images in real space, or by applying an appropriate transmission cross-coefficient (TCC) when computing the image intensity spectrum in reciprocal space. Figure 1 shows a method of including the effects of incident beam convergence by real-space summation. The degree of convergence is estimated by measuring the spot size in the experimental diffraction pattern (a). Each spot in the diffraction pattern is sub-sampled (b), and a series of images is computed at incident beam angles appropriately sampling the convergence cone.

Parallel Electron Energy Loss Spectroscopy of a Cu-Be Alloy

Although the Cu-Be binary system has been studied by previous investigators and recently reviewed, no direct measurements have been made concerning the chemistry of the γ-phase, which has a nominal stoichiometry CuBe. Quantitative parallel electron energy loss spectroscopy (PEELS) has been used in this investigation of a Cu, 1.8 wt.% Be, 0.3 wt.% Co alloy to determine a section of the γ/(α+γ) phase boundary of the Cu-Be phase diagram. Sections of alloy (in sheet form) were encapsulated in evacuated quartz capsules to prevent oxidation and isothermally aged in the temperature range 400 - 600°C. TEM specimens were prepared by punching disks from the sheet, dimpling and ion milling. Spectra were acquired using a Philips EM400 TEM/STEM in the TEM image mode, and with a Gatan parallel recording EELS spectrometer. The acquisition mode allowed for the use of a relatively large (yet accurately known) collection angle. The incident beam convergence angle was also determined, so that a beam convergence correction could be used to calculate the true collection angle.