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European Journal of Physics

An experiment on the particle–wave nature of electrons

Gioṙgio Matteucci, A. Migliori, Francisco F. Medina, Román Castañeda

Published Dec 22, 2008• 9 citations
Publisher

Abstract

A primary electron beam of a transmission electron microscope is scattered into secondary beams by the planes of atoms of a single crystal. These secondary beams are focused to form a diffraction pattern on the final screen. This experiment is similar to the Thompson one which, independently by Davisson and Germer, demonstrated the de Broglie hypothesis of the existence of electron waves. Without changing the experimental apparatus, it is possible to realize an interference experiment with electrons coming from two spatially separated sources in analogy with the optical Young set-up. Both experiments are clear evidence of the electron wave-like behaviour. By varying the conditions of illumination, changes of the fringe visibility which reveal the spatial coherence properties of the electron beam, are displayed.

DOI
10.1088/0143-0807/30/1/023

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A primary electron beam of a transmission electron microscope is scattered into secondary beams by the planes of atoms of a single crystal. These secondary beams are focused to form a diffraction pattern on the final screen. This experiment is similar to the Thompson one which, independently by Davisson and Germer, demonstrated the de Broglie hypothesis of the existence of electron waves. Without changing the experimental apparatus, it is possible to realize an interference experiment with electrons coming from two spatially separated sources in analogy with the optical Young set-up. Both experiments are clear evidence of the electron wave-like behaviour. By varying the conditions of illumination, changes of the fringe visibility which reveal the spatial coherence properties of the electron beam, are displayed.
The years of the third decade of the present century were heady times. Old social orders were being swept away, monarchies becoming republics and the United States of America was emerging as a world power. In physics too, revolutions were taking place, none more potent than that which resulted in the emergence of quantum mechanics as a model for the behaviour of sub-atomic particles. It was Newton who first suggested that light was particulate but during the nineteenth century this view had fallen into neglect. Indeed a number of experiments, for example the classic Young's slits experiment, demonstrated quite conclusively that light was a wave motion. How else could interference fringes occur? However, the experiments on the photoelectric effect demonstrated just as conclusively that light energy was carried in packets, or quanta, and that a continuous wave description was not applicable. This ‘wave or particle’ dilemma was not unique to the behaviour of light. J. J. Thompson showed that cathode rays were charged, had a well defined mass and had all the properties expected of a beam of particles. Nevertheless, Davisson and Germer showed that diffraction of electrons could take place, an effect made visually much more dramatic by G. P. Thompson's transmission electron diffraction patterns. Nowadays, electron diffraction is used as a routine analytical tool in all advanced metallurgical and materials science laboratories (Fig. 2.1). Clearly new axioms were required.
The Young-Feynman two-hole interferometer is widely used to present the electron wave-particle duality and in particular the buildup of interference fringes with single electrons. The teaching approach consists of two steps: i) electrons come through only one hole but diffraction effects are disregarded; ii) electrons come through both holes and interference fringes are described. Therefore, a student might believe that wave phenomena are not revealable in case i) but they arise only by the combined effect of electrons from the two holes. To avoid misunderstanding regarding the distribution of electrons passing through one hole, Fresnel and Fraunhofer diffraction patterns are discussed. In particular, an original experiment, realized with a standard electron microscope and a sample with round holes is presented to introduce the wave nature of electrons. The experimental results clearly show that a careful discussion of electron diffraction phenomena from one hole provides students with the evidence that the interference experiment from both holes is not strictly required to show the superposition of electron waves.
An experiment analogous to that devised by Grimaldi and subsequently repeated by Young to study the nature of light has been realized with electrons. Following the Grimaldi and Young line of thought, an original approach is presented to introduce undergraduate physics students to the wave behaviour of electrons. An electron microscope equipped with a low coherent source of electrons and a thin platinum wire, acting as an opaque obstacle, is used to reproduce the experimental conditions adopted by Grimaldi and Young with light. Electron interference fringes produced in the geometrical shadow of the obstacle are interpreted by assuming that electrons behave like a sound or a light wave. This hypothesis is confirmed by the modelling of the experimental electron interference patterns.
Davisson and Germer performed an experiment, in which electrons were reflected from parallel layers of atoms in a crystal. The electrons showed interference, thus demonstrating the wave nature of the electron. Louis de Broglie postulated a wave model of the electron, in which an electron orbit was represented by a group of in-phase waves. The model predicted that the angular momentum of an electron could take on only a limited number of values, a concept that Neils Bohr had introduced some years earlier as an ad hoc assumption. In an electron microscope, electrons stream off a hot filament and are accelerated to high velocity by passing between two electrically charged plates. The electrons' wavelength is related to their velocity and it is easy to obtain electrons with wavelengths near 0.1 nm, which suggests the possibility of obtaining resolution of about the same magnitude.
Electron double-slit experiments, the essence of quantum mechanical “wave/particle duality”, have been extensively and continuously studied because their unrealistic interpretations have attracted many researchers. Here, we discuss recent sophisticated V-shaped double-slit experiments to elucidate electron-path information, i.e., which slit electrons pass through, which path they pursue, and where they arrive and interfere on the image plane. In a transmission electron microscope, an optically zero-propagation distance condition was realized, where the double-slit position was imaged just on the detector plane. Interference fringes composed of dot images were controlled by using two electron biprisms. Using a V-shaped double slit, we confirmed that it is possible to observe interference fringes only when the path information of individual electrons is not available. Furthermore, we studied how the interference fringes would shift their detected positions when electron wave phases were modulated before illumination to the double slit. Phase shifts were generated by tilting electron beams. We confirmed that each single electron as a wave changed its phase even when it traveled alone inside the microscope.