Orientation dependence of ionization edges in EELS

Site-specific ionisation edge fine-structure of Rutile in the electron microscope

Combined Bloch-wave and density functional theory simulations are performed to investigate the effects of different channelling conditions on the fine-structure of electron energy-loss spectra. The simulated spectra compare well with experiments. Furthermore, we demonstrate that using this technique, the site-specific investigation of atomic orbitals is possible. This opens new possibilities for chemical analyses.

Energy loss by channeled electrons: a quantitative study on transition metal oxides

Electron energy-loss spectroscopy (EELS) attached to current transmission electron microscopes can probe not only element-selective chemical information, but also site-selective information that depends on the position that a specific element occupies in a crystal lattice. The latter information is exploited by utilizing the Bloch waves symmetry in the crystal, which changes with its orientation with respect to the incident electron wave (electron channeling). We demonstrate the orientation dependence of the cross-section of the electron energy-loss near-edge structure for particular crystalline sites of spinel ferrites, by quantitatively taking into account the dynamical diffraction effects with a large number of the diffracted beams. The theoretical results are consistent with a set of experiments in which the transition metal sites in spinel crystal structures are selectively excited. A new measurement scheme for site-selective EELS using a two-dimensional position-sensitive detector is proposed and validated by theoretical predictions and trial experiments.

Theory of free electron vortices

The recent creation of electron vortex beams and their first practical application motivates a better understanding of their properties. Here, we develop the theory of free electron vortices with quantized angular momentum, based on solutions of the Schrödinger equation for cylindrical boundary conditions. The principle of transformation of a plane wave into vortices with quantized angular momentum, their paraxial propagation through round magnetic lenses, and the effect of partial coherence are discussed.

Atomic-resolution spectroscopic imaging: past, present and future

This review examines the development of atomically resolved electron energy loss spectroscopy from the first demonstration of plane-by-plane compositional profiling, through column-by-column spectroscopy to full two-dimensional and potentially three-dimensional spectroscopic imaging. Examples will be presented to highlight the increasing analytical sensitivity and image contrast obtained through each generation of aberration correction, moving towards the ultimate goal of mapping electronic structure inside materials with atomic resolution.

Extending the analysis of EELS spectrum-imaging data, from elemental to bond mapping in complex nanostructures

Multiple least squares fitting has been employed for long time in elemental electron energy-loss spectroscopy (EELS) analysis, in particular in biology, but with the hypothesis of a rather stable shape for the used core-loss signals. In the present case, we explore its use for identifying the variations in the edges' fine structures in complex boron nitride samples and in particular for mapping the bonding types of boron in such samples. Details about this improved procedure applied to data acquired in the spectrum-imaging mode are reported here.

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 3.975theta(E) (theta(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.

Some effects of electron channeling on electron energy loss spectroscopy

As an electron beam (of order 100 keV) travels through a crystalline solid it can be channeled down a zone axis of the crystal to form a channeling peak centered on the atomic columns. The channeling peak can be similar in size to the outer atomic orbitals. Electron energy loss spectroscopy (EELS) measures the losses that the electron experiences as it passes through the solid yielding information about the unoccupied density of states in the solid. The interaction matrix element for this process typically produces dipole selection rules for small angle scattering. In this paper, a theoretical calculation of the EELS cross section in the presence of strong channeling is performed for the silicon L23 edge. The presence of channeling is found to alter both the intensity and selection rules for this EELS signal as a function of depth in the solid. At some depths in the specimen small but significant non-dipole transition components can be produced, which may influence measurements of the density of states in solids.

Channeling, localization and the density matrix in inelastic electron scattering

Building on the relationship between the mixed dynamic form factor (MDFF) for inelastic electron scattering and the one-particle density matrices of the initial and final states of the scatterer it is shown that the MDFF contains information both on the spatial density and the spatial coherence of excitations. We discuss how the MDFF can-at least partly-be measured in scattering geometries invoking channeling conditions. Therefrom, the localization of inelastic events can be determined.

A proposal for dichroic experiments in the electron microscope

Building upon the similarities between inelastic electron scattering and X-ray absorption we show that dichroism can be observed in electron energy loss spectrometry (EELS) in the transmission electron microscope (TEM). Natural or magnetic linear dichroism can be studied in electron scattering experiment with definite wave vector transfer in the interaction.The detection of circular dichroism in the TEM relies on interferometric EELS in a particular scattering geometry that allows extraction of the mixed dynamic form factor from energy loss spectra. Similarities between dichroic signals in energy loss near edge structures and X-ray absorption near edge structures are discussed, and a new experimental setup for dichroic measurements in the TEM is proposed.

Improved comparison of low energy loss spectra with band structure calculations: the example of BN filaments

Electron energy loss spectra have been recorded from BN filaments for energy losses between 2 and 50eV. They compare well with other BN shapes (nanotubes, sheets, etc). The interpretation of all the peaks in the spectra has been made via an ab initio calculation using the FLAPW code WIEN97 (A full potential linearized augmened plane wave package for calculating crystal properties, Karlheinz Schwarz, Techn. Universität Wien, Austria, 1999. ISBN 3-9501031-0-4). In order to fully simulate the observed spectra, the geometry particular to the EELS experiment has been taken into account making use of Wessjohann's relativistic formula for thin anisotropic slabs (Phys. Stat. Sol. B 77 (1976) 535). Furthermore, the effect of the convergent beam has been introduced into the simulation and has been proven to be an important parameter in obtaining the corresponding peak intensities.