Phase Shift Of Electron Wave Research Articles

PyHoLo software, a new tool for electron hologram analysis and magnetic investigation

A new tool, PyHoLo software, was developed to help automate the process of determining magnetic field B from a series of holograms, registered at different environmental conditions (e.g. for upside and downside orientations of a sample in a specimen holder). This procedure involves translating single holograms into phase shift of electron wave, but also alignment of holograms (i.e. shift, rotation, magnification) and finally calculation of magnetic field in an area selected for investigation. PyHoLo gives functionality for performing all those steps without having to refer to different programs and tools. The workflow and results of this procedure are discussed using as an example sample of FeCuSiB. Program summaryProgram title: PyHoLoCPC Library link to program files:http://dx.doi.org/10.17632/n4rgzbnbpw.1Licensing provisions: GNU General Public License 3Programming language: PythonNature of problem: (1) Determination of electric and magnetic fields in a sample on the basis of electron holograms, registered on transmission electron microscope during off-axis holography experiment. (2) Alignment of electron holograms acquired for different sample orientations and at different external conditions.Solution method: PyHoLo adapts procedures for all steps required to translate experimental holograms into electric and magnetic signals, i.e. restoration of total phase shift, alignment of electron holograms (shift, rotation, magnification, warping), phase separation. There is no need to refer to different tools and programs.Additional comments: PyHoLo requires Python 3.6 or newer and a number of external libraries to work (see README or manual for details). PyHoLo is a constant work in progress, developed by only one person, so it might be a little rough around the edges.

Reconstruction of the electric charge density in thin films from the contrast transfer function measurements

The radial distribution of the beam-induced charge in thin films is investigated using the contrast transfer properties of the transmission electron microscope. The phase shift due to charging is measured as the phase difference between the contrast transfer functions of two photos taken with and without film at the back focal plane. Solving the inverse Laplace problem with this input data recovers the charge density of the measured film. The electric potential function in the whole area is reconstructed using the boundary integral method and the analytical solution of the Laplace equation for the electric potential is induced from unit step-wise surface charge. The phase shift of electron waves is derived in a weak lens approximation. In this way, the radial dependence of the charge density and the magnitude of the electrostatic potential at the thin film are obtained. The surface charge density reaches quasi-equilibrium state after the first 30 min of the electron beam pre-irradiation. The hydrocarbon contamination layer on the surface of the film is considered to be the main source of charging. An explanation of the qualitative behavior of the charge density, based on the contamination diffusion theory, is proposed.

Electric charging of thin films measured using the contrast transfer function

The phase shift of electron waves due to charging of thin films is investigated using the contrast transfer properties of the microscope. We take two photos, one with film at the back focal plane and the other one without film. The phase difference between the contrast transfer functions of the two photos is evaluated using our theoretical predictions. The theoretical model is based on an analytical solution of the Laplace equation with appropriate boundary conditions. From the resulting electrostatic potential function the phase shift of electron waves is derived in a weak lens approximation. With this method, information about the radius of the electron beam and the magnitude of the electrostatic potential at the thin film is obtained. The excellent agreement between the theoretical model and experimental results is observed.

Sagnac experiment with electrons: Observation of the rotational phase shift of electron waves in vacuum.

A Sagnac experiment with electron waves in vacuum is reported. The phase shift caused by rotation of an electron biprism interferometer placed on a turntable has been measured. It was found to agree with prediction within error margins of about 30%. A compact ruggedized electron interferometer was used. It is based on a high-precision optical bench of 36-cm length. This interferometer is less sensitive by orders of magnitude to mechanical vibrations and electromagnetic stray fields than conventional electron interferometers. A beam of low-energy electrons (150\char21{}3000 eV) emitted by a field-emission electron source was used. For the most part, electrostatic electron optical components were employed. The magnified interference fringe pattern was intensified by a dual-stage multichannel-plate intensifier, recorded by a charge-coupled-device video camera, transmitted from the turntable to the laboratory system via a slip ring, and evaluated by an image-processing system. Both the rotation rate and the area enclosed between the two partial waves were varied (up to values of 0.5 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and 3.9 ${\mathrm{mm}}^{2}$, respectively). Fringe shifts on the order of 5% of a fringe period were attained. Some historical aspects of the Sagnac effect as well as some aspects of its interpretation are mentioned. A brief informal discussion is included of the interpretation of the Sagnac phase shift as a geometric phase (``Berry phase'') caused by the global anholonomy of the local phase factor that is produced by the gauge field induced by rotation.

Phase Shift of Electron Waves in A Rotating Frame of Reference

After the first matter wave version of Sagnac’s classical light optical experiment of 1913, performed by Mercereau and Zimmermann with electron Cooper pairs in 1965, and the Sagnac experiment realized with neutrons by Werner et al. in 1979 , we report here on the first observation of the rotational phase shift of electron waves in vacuum.Theory. The Sagnac effect links classical physics, quantum physics and relativity. Using the special theory of relativity it can be derived that coherent waves, e.g. of light, neutrons or electrons, travelling around a finite area A experience a relative phaseshift

Contribution of Atomic-Level TEM to Resolution of Structure

Atomic Resolution Electron Microscopes are now producing useful results in many fields of science and technology. This success was obtained not only by the improvement of resolution of TEM but also through the developments of theories and experiments of diffraction crystallography, image formation and recording technique over the past 44 years. Boersch (1946-47) discussed the image of atoms and crystals by the phase object approximation; the image contrast is due to the phase shift of electron waves passing through them. Scherzer (1949) discussed the effect of the phase shift by the electron lens and proposed the phase contrast transfer function. He pointed out that the key to observe images of single atoms is by contrast enhancement, which might be possible by dark field images if resolution is improved. This proposal was attempted by improving the resolution using tilted-beam dark fields (Th atoms, Hg & Pt atoms 1971). Crystal lattice fringes were observed by Menter in 1956 who discussed the contrast by kinematical theory. The interpretation of lattice images by dynamical theories were carried out by Hashimoto et al. (Bethe theory) and Cowley (Multi-slice theory) in 1958-60 and noted the correct position of atoms is in neither black fringe regions nor white ones when the images are taken in the Bragg reflecting position. However Miyake et al in 1964, showed that black or white contrast peaks appear at atom positions if the crystal is in symmetry position. Two dimensional lattice structure images were first photographed in 1970-71, which stimulated strongly the application of electron microscopy to materials science, crystallography and engineering at many laboratories such as the National Center at Berkeley. For the identification of correct position of atoms, two types of image contrast calculation have been proposed (e.g. multi-slice 1972, Bethe method 1975). The partially coherent theory originally developed in optics was introduced into the contrast calculation in 1979-80. Around this time, many observations of defect structures have been carried out, some of which are shown in Table 1. In situ observation of moving atoms and atom columns in molecules and crystals have been carried out in 1978 by using a TV system, which enable us to see the transition phenomena with a speed of 1/30 or 1/60 seconds. More recently atomic imaging at 1.8 A-1.6 A played an important role in the structure research of new materials and phenomena such as superconducting materials (metallic A15, 1989, ceramic high Tc, 1988), metal ceramic interface (Nb/Al2O3 1984), superstructure (GaAs/AlAs/GaAs 1985) quasi crystals (1987) etc. Many subsequent observations are presented in this congress. In spite of these developments, there are still some problems to be solved, e.g. imaging of atoms in the correct positions and the identification of different kinds of atoms in the materials especially with unknown crystal structure.

Some remarks on the quantum mechanics of the electron

For didactic as well as historical reasons it does not make much sense for about thirty years to speak of the diffraction of electron waves by microscopic slits as an “imaginary experiment”. The coherence length of electron waves has been measured by the phase shift of a coherent partial electron wave propagating through a metallic micro-tube to which an electric potential is applied. The statement by H. Hora that the phase shift of electron waves due to the magnetic vector potential depends on electron velocity is not supported by experiments. There is no principal upper limit for the electron-optical path length difference due to an enclosed magnetic flux.

An electron optical sagnac experiment

Using an electron biprism interferometer completely different in its technical design compared to conventional instruments, we hope to prove the rotationally induced phase shift of electron waves. Besides its unconventional design, another unique feature of our instrument is a Wien filter incorporated in its beam path which allows to shift the coherent wave packets relative to each other longitudinally. This provides the possibility of (1) reestablishing maximum overlap of the wave packets and in turn maximum contrast of the interference fringes and (2) of measuring coherence lengths of electron waves as well as, via Fourier spectroscopy, the energy distribution of the electrons.

Vacancies and Complexes in the Noble Metals

In part I, the changes in resistivity of a noble metal on the introduction of vacancies into the lattice are calculated, taking into account the relaxation of the lattice around the defect site. The agreement between calculated and experimental resistivities is satisfactory for a particular model of the scattering power of the vacancy. Using this same model, it is then shown how the calculations of Fumi and Brooks concerning vacancy formation energies can be modified in the light of known surface energy data to yield quite reasonable predictions of formation energies of relaxed vacancies in noble metal lattices. The agreement between calculated and experimental resistivity data implies that the phase shift of electron waves at the Fermi surface are accurate and this in turn permits the prediction of the electron density in the neighborhood of the vacancy. In part II, this electron density is used in a treatment of the interaction energy between vacancies and substitutional impurities in the noble metals. The binding energies deduced in this way from scattering theory exhibit a strong dependence on the valence of the solute atom and are invariably positive for positive valence solutes at nearest neighboring lattice sites to a vacancy. The computed binding energies are quantitatively compatible with the available experimental data.The long-range characteristics of interaction between vacancies and both point and extended defects are also investigated in part II. Particular attention is drawn (a) to the oscillatory nature of the interaction as a function of the separation of the defects, and (b) to the different dependence on this separation for interactions concerning the different types of defect. Thus, in every case, the interaction energy oscillates with period $\frac{{k}_{F}}{\ensuremath{\pi}}$, ${k}_{F}$ being the Fermi energy, while the decay of amplitude with separation takes the form ${r}^{\ensuremath{-}3}$, ${r}^{\ensuremath{-}\frac{5}{2}}$, or ${r}^{\ensuremath{-}2}$ contingent upon the vacancy interacting with a second point defect, a dislocation, or a crystal boundary, respectively.