Davisson and Germer

It does not provide mueh historieal perspeetive on the development of quantum meehanies. Subjeets sueh as the photoeleetrie effeet, blaek-body radiation, the dual nature of eleetrons and photons, and the Davisson and Germer experiments are not even diseussed. 

The underlying principle of RHEED is that particles of matter have a wave character. This idea was postulated by de Broglie in (1924). He argued that since photons behave as particles, then particles should exhibit wavelike behavior as well. He predicted that a particle s wavelength is Planck s constant h divided by its momentum. The postulate was confirmed by Davisson and Germer s experiments in 1928, which demonstrated the diffraction of low-energy electrons from Ni. ... 

When Davisson and Germer reported in 1927 that the elastic scattering of low-energy electrons from well ordered surfaces leads to diffraction spots similar to those observed in X-ray diffraction [2.238-2.240], this was the first experimental proof of the wave nature of electrons. A few years before, in 1923, De Broglie had postulated that electrons have a wavelength, given in A, of ... 

FIGURE 1.21 Davisson and Germer showed that electrons produce a diffraction pattern when reflected from a crystal G. P. Thomson, working in Aberdeen, Scotland, showed that they also produce a diffraction pattern when they pass through a very thin gold foil. The latter is shown here. G. P. Thomson was the son of J. J. Thomson, who identified the electron (Section B). Both received Nobel prizes 1.1. for showing that the electron is a particle and G. P. for showing that it is a wave. 

All of the other phenomena associated with waves can also be observed in particles. For example, in 1927 Davisson and Germer accelerated a beam of electrons to a known kinetic energy and showed that these electrons could be diffracted off a nickel crystal, just as X-rays are diffracted (see Figure 3.8). Just as with photons, interference is not always seen if the wavelength spread or the slits are large, the fringes wash out. This also explains why interference is not seen with macroscopic objects, such as buckshot—the wavelength is far too small. 

The wave character of electrons was discovered experimentally by Davisson and Germer in 1927, and they found that the wave lengths were just equal to those given by de Broglie s theory. 

It was only in 1927 from the experiments of Davisson and Germer and slightly later from those of G. P. Thomson that it was found that these electron beams exhibit exactly the same diffraction phenomena as those which Von Laue, Friedrich and Knipping had observed with X-rays in 1912. For X-rays this result was in agreement with the prevailing conception of the nature of these rays. With electrons, however, this wave character appeared to be completely in conflict with the ideas which had been supported for more than 50 years, nevertheless only three years before De Broglie had published his fundamental hypothesis on the wave nature of electrons in his thesis (1924). 

This relation found a direct experimental confirmation in the experiments of Davisson and Germer and of Thomson already mentioned on the diffraction of electron beams by crystal lattices. In fact for electrons which have traversed a potential difference P, the energy eP = 1/2 mv2 the kinetic energy, or (mv)2 = 2 meP thus ... 

For a potential difference of 150 V, or 60,000 V we have therefore X = 1 A or 0.05 A respectively, which agrees with the experiments carried out by Davisson and Germer with nickel single crystals or by Thomson with gold foil. With the observed angles of deviation the wave length could be calculated from the lattice spacings in the same way as with X-rays. We can therefore look upon (4 ) also as the purely experimental result of these experiments from which the wave nature of the electron and the correctness of equation (4 ) appear experimentally. 

The solution thus represents a wave along the x axis with a wave length which agrees with that determined in the experiments of Davisson and Germer and of G. P. Thomson (see p. 109) if the electrons have traversed a potential difference P then the total energy W — eP. 

Experimental evidence was obtained by Davisson and Germer in 1927 and later by Thomson which supported the de Broglie relationship. These authors showed that crystals diffracted a beam of electrons in exactly the... 

As an example of the curves obtained by experiment, the reflection at the plane (111) of a single crystal of nickel for 9 = 10 as found by Davisson and Germer f is illustrated in fig. 2. The abscissae represent A or 1/A in Angstrom units. The wavelength 1 A corresponds to an electron beam of 150 volts. 

The small maximum of the third order indicated by an arrow is ascribed by Davisson and Germer to anomalous dispersion of the electrons. Here, however, we shall not inquire further into this exceptional case. 

The variation of S with wave-length has also been much investigated, and anomalous dispersion has definitely been found to exist a natural modification of the classical dispersion theory enables us to account for the latter. But since (according to Davisson and Germer) very few facts about these anomalous phenomena are meanwhile available in the case of electron reflection, we shall not trouble to describe these experiments. 

Even Davisson and Germer s first work on the reflection of slow electrons by crystal lattices made it clear that the facts could not be accurately represented by equations (3) and (5) on the contrary, definite deviations from Bragg s law of reflection occur. These were first explained by Patterson as being due to a diminution of the distance between the lattice planes at the surface. Bethe has shown, however, that better agreement with experiment is obtained by expressing the action of the crystal on the electrons by means of a mean lattice potential V. Schrodinger s equation for the de Broglie waves with an internal lattice potential is then... 

Two years after de Broglie s prediction, C. Davisson (1882-1958) and L. H. Germer (1896-1971) at the Bell Telephone Laboratories demonstrated diffraction of electrons by a crystal of nickel. This behavior is an important characteristic of waves. It shows conclusively that electrons do have wave properties. Davisson and Germer found that the wavelength associated with electrons of known energy is exactly that predicted by de Broglie. Similar diffraction experiments have been successfully performed with other particles, such as neutrons. 

Through the work of de Broglie, Davisson and Germer, and others, we now know that electrons in atoms can be treated as waves more effectively than as small compact particles traveling in circular or elliptical orbits. Large objects such as golf balls and moving automobiles obey the laws of classical mechanics (Isaac Newton s laws), but very small... 

A key motivation for macromolecule interferometry is the question up to which molecular size and complexity non-classical features of quantum mechanics are still observable. How far can the limits of the wave-particle duality be pushed for massive particles, first predicted by de Broglie [de Broglie 1923] and demonstrated by Davisson and Germer [Davisson 1927] for electrons. 

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