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X-ray Version of Davisson-Germer Experiment

Bhanumoorthy Pullooru

Published Jul 12, 2021• 5 citations
Publisher

Abstract

Abstract Application of unitcell defined boundary conditions leads to the question on the formation of standing waves within unitcell. We design and propose X-ray version of Davisson-Germer experiment as the answer. In the proposed experiment, a tunable synchrotron beam replaces the variable de Broglie wavelength of incident electron beam. Among the two series of Davisson-Germer peaks from original experiments available in literature, first series shown in figure 1 demonstrates standing wave description and the second series shown in figure 2 demonstrates running wave description. Both running waves and standing waves cannot simultaneously exist within the unitcell and the proposed experiment alone can resolve between the two. The experiment can be conducted on a macromolecular crystal also.

DOI
10.21203/rs.3.rs-653799/v1

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Abstract Application of unitcell defined boundary conditions leads to the question on the formation of standing waves within unitcell. We design and propose X-ray version of Davisson-Germer experiment as the answer. In the proposed experiment, a tunable synchrotron beam replaces the variable de Broglie wavelength of incident electron beam. Among the two series of Davisson-Germer peaks from original experiments available in literature, first series shown in figure 1 demonstrates standing wave description and the second series shown in figure 2 demonstrates running wave description. Both running waves and standing waves cannot simultaneously exist within the unitcell and the proposed experiment alone can resolve between the two. The experiment can be conducted on a macromolecular crystal also.
Abstract We show that the historic Davisson-Germer experiment demonstrates formation of standing waves within nickel crystal unitcell. Cartesian Fourier transform cannot offer description in terms of standing waves because Cartesian Fourier theory cannot accommodate π in place of 2π. Thus, formation of standing waves within unitcell in Davisson-Germer experiment necessarily requires spherical polar coordinate description of crystal diffraction. Description in spherical polar coordinates permits to incorporate precision angles from the experiment for better convergence in structure determination calculations.
Abstract The famed Davisson-Germer Experiments demonstrated the wave phenomenon of electrons similarly to X-Ray scattering from Sir Lawrence Bragg’s X-ray experimentations on crystals c. 1913. Their empirical deduction of electrons behaving as waves (i.e. oscillatory) ignores the possibility of an electron beam behaving harmonically upon elastic collision with a diffraction grating - represented by nickel crystal - in their experiment. However, it is well established in the electrical engineering science that crystals possess piezoelectric effects and are used ubiquitously in electronic circuit designs for causing stable harmonic oscillation responses to direct current voltages. In light of this, the current mathematical model proposes the Davisson-Germer results to be the effect of a nickel crystal oscillator circuit which amplifies a direct voltage source – the electron beam – causing the phenomenon of inductance from the resultant electrical feedback with the crystal atom’s electromagnetic field.
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.
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.