# Davisson–Germer experiment

Last updated

The Davisson–Germer experiment was a 1923-27 experiment by Clinton Davisson and Lester Germer at Western Electric (later Bell Labs), [1] in which electrons, scattered by the surface of a crystal of nickel metal, displayed a diffraction pattern. This confirmed the hypothesis, advanced by Louis de Broglie in 1924, of wave-particle duality, and was an experimental milestone in the creation of quantum mechanics.

## History and overview

According to Maxwell's equations in the late 19th century, light was thought to consist of waves of electromagnetic fields and matter was thought to consist of localized particles. However, this was challenged in Albert Einstein's 1905 paper on the photoelectric effect, which described light as discrete and localized quanta of energy (now called photons), which won him the Nobel Prize in Physics in 1921. In 1924 Louis de Broglie presented his thesis concerning the wave–particle duality theory, which proposed the idea that all matter displays the wave–particle duality of photons. [2] According to de Broglie, for all matter and for radiation alike, the energy ${\displaystyle E}$ of the particle was related to the frequency of its associated wave ${\displaystyle \nu }$ by the Planck relation:

${\displaystyle E=h\nu \,}$

And that the momentum of the particle ${\displaystyle p}$ was related to its wavelength by what is now known as the de Broglie relation:

${\displaystyle \lambda ={\frac {h}{p}},}$

where h is Planck's constant.

An important contribution to the Davisson–Germer experiment was made by Walter M. Elsasser in Göttingen in the 1920s, who remarked that the wave-like nature of matter might be investigated by electron scattering experiments on crystalline solids, just as the wave-like nature of X-rays had been confirmed through X-ray scattering experiments on crystalline solids. [2] [3]

This suggestion of Elsasser was then communicated by his senior colleague (and later Nobel Prize recipient) Max Born to physicists in England. When the Davisson and Germer experiment was performed, the results of the experiment were explained by Elsasser's proposition. However the initial intention of the Davisson and Germer experiment was not to confirm the de Broglie hypothesis, but rather to study the surface of nickel.

In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow moving electrons at a crystalline nickel target. The angular dependence of the reflected electron intensity was measured and was determined to have the same diffraction pattern as those predicted by Bragg for X-rays. At the same time George Paget Thomson independently demonstrated the same effect firing electrons through metal films to produce a diffraction pattern, and Davisson and Thomson shared the Nobel Prize in Physics in 1937. [2] [4] The Davisson–Germer experiment confirmed the de Broglie hypothesis that matter has wave-like behavior. This, in combination with the Compton effect discovered by Arthur Compton (who won the Nobel Prize for Physics in 1927), [5] established the wave–particle duality hypothesis which was a fundamental step in quantum theory.

## Early experiments

Davisson began work in 1921 to study electron bombardment and secondary electron emissions. A series of experiments continued through 1925.

Davisson and Germer's actual objective was to study the surface of a piece of nickel by directing a beam of electrons at the surface and observing how many electrons bounced off at various angles. They expected that because of the small size of electrons, even the smoothest crystal surface would be too rough and thus the electron beam would experience diffused reflection. [6]

The experiment consisted of firing an electron beam (from an electron gun, an electrostatic particle accelerator) at a nickel crystal, perpendicular to the surface of the crystal, and measuring how the number of reflected electrons varied as the angle between the detector and the nickel surface varied. The electron gun was a heated tungsten filament that released thermally excited electrons which were then accelerated through an electric potential difference, giving them a certain amount of kinetic energy, towards the nickel crystal. To avoid collisions of the electrons with other atoms on their way towards the surface, the experiment was conducted in a vacuum chamber. To measure the number of electrons that were scattered at different angles, a faraday cup electron detector that could be moved on an arc path about the crystal was used. The detector was designed to accept only elastically scattered electrons.

During the experiment, air accidentally entered the chamber, producing an oxide film on the nickel surface. To remove the oxide, Davisson and Germer heated the specimen in a high temperature oven, not knowing that this caused the formerly polycrystalline structure of the nickel to form large single crystal areas with crystal planes continuous over the width of the electron beam. [6]

When they started the experiment again and the electrons hit the surface, they were scattered by nickel atoms in crystal planes (so the atoms were regularly spaced) of the crystal. This, in 1925, generated a diffraction pattern with unexpected peaks.

## Breakthrough

On a break, Davisson attended the Oxford meeting of the British Association for the Advancement of Science in summer 1926. At this meeting, he learned of the recent advances in quantum mechanics. To Davisson's surprise, Max Born gave a lecture that used diffraction curves from Davisson's 1923 research which he had published in Science that year, using the data as confirmation of the de Broglie hypothesis. [7]

He learned that in prior years, other scientists – Walter Elsasser, E. G. Dymond, and Blackett, James Chadwick, and Charles Ellis – had attempted similar diffraction experiments, but were unable to generate low enough vacuums or detect the low-intensity beams needed. [7]

Returning to the United States, Davisson made modifications to the tube design and detector mounting, adding azimuth in addition to colatitude. Following experiments generated a strong signal peak at 65 V and an angle θ = 45°. He published a note to Nature titled, "The Scattering of Electrons by a Single Crystal of Nickel". [8]

Questions still needed to be answered and experimentation continued through 1927. [9]

By varying the applied voltage to the electron gun, the maximum intensity of electrons diffracted by the atomic surface was found at different angles. The highest intensity was observed at an angle θ = 50° with a voltage of 54 V, giving the electrons a kinetic energy of 54  eV . [2]

As Max von Laue proved in 1912, the periodic crystal structure serves as a type of three-dimensional diffraction grating. The angles of maximum reflection are given by Bragg's condition for constructive interference from an array, Bragg's law

${\displaystyle n\lambda =2d\sin \left(90^{\circ }-\theta \right),}$

for n = 1, θ = 50°, and for the spacing of the crystalline planes of nickel (d = 0.091 nm) obtained from previous X-ray scattering experiments on crystalline nickel. [2]

According to the de Broglie relation, electrons with kinetic energy of 54  eV have a wavelength of 0.167  nm . The experimental outcome was 0.165 nm via Bragg's law, which closely matched the predictions. As Davisson and Germer state in their 1928 follow-up paper, "These results, including the failure of the data to satisfy the Bragg formula, are in accord with those previously obtained in our experiments on electron diffraction. The reflection data fail to satisfy the Bragg relation for the same reason that the electron diffraction beams fail to coincide with their Laue beam analogues." [1] However, they add, "The calculated wave-lengths are in excellent agreement with the theoretical values of h/mv as shown in the accompanying table." [1] So although electron energy diffraction does not follow the Bragg law, it did confirm de Broglie's equation.

Davisson and Germer's accidental discovery of the diffraction of electrons was the first direct evidence confirming de Broglie's hypothesis that particles can have wave properties as well.

Davisson's attention to detail, his resources for conducting basic research, the expertise of colleagues, and luck all contributed to the experimental success.

## Practical applications

It wasn't until the 1960s that vacuum tubes were adequately made reliable and available to expand on the electron diffraction technique, but since that time, scientists have used LEED diffraction to explore the surfaces of crystallized elements and the spacing between atoms.[ citation needed ]

## Related Research Articles

Diffraction refers to various phenomena that occur when a wave encounters an obstacle or opening. It is defined as the bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.

In modern physics, the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanical phenomena. This type of experiment was first performed, using light, by Thomas Young in 1801, as a demonstration of the wave behavior of light. At that time it was thought that light consisted of either waves or particles. With the beginning of modern physics, about a hundred years later, it was realized that light could in fact show behavior characteristic of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same behavior, which was later extended to atoms and molecules. Thomas Young's experiment with light was part of classical physics long before the development of quantum mechanics and the concept of wave-particle duality. He believed it demonstrated that the wave theory of light was correct, and his experiment is sometimes referred to as Young's experiment or Young's slits.

Wave–particle duality is the concept in quantum mechanics that every particle or quantum entity may be described as either a particle or a wave. It expresses the inability of the classical concepts "particle" or "wave" to fully describe the behaviour of quantum-scale objects. As Albert Einstein wrote:

It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.

X-ray crystallography (XRC) is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their crystallographic disorder, and various other information.

A timeline of atomic and subatomic physics.

Matter waves are a central part of the theory of quantum mechanics, being an example of wave–particle duality. All matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave. In most cases, however, the wavelength is too small to have a practical impact on day-to-day activities.

Electron diffraction refers to the wave nature of electrons. However, from a technical or practical point of view, it may be regarded as a technique used to study matter by firing electrons at a sample and observing the resulting interference pattern. This phenomenon is commonly known as wave–particle duality, which states that a particle of matter can be described as a wave. For this reason, an electron can be regarded as a wave much like sound or water waves. This technique is similar to X-ray and neutron diffraction.

Neutron diffraction or elastic neutron scattering is the application of neutron scattering to the determination of the atomic and/or magnetic structure of a material. A sample to be examined is placed in a beam of thermal or cold neutrons to obtain a diffraction pattern that provides information of the structure of the material. The technique is similar to X-ray diffraction but due to their different scattering properties, neutrons and X-rays provide complementary information: X-Rays are suited for superficial analysis, strong x-rays from synchrotron radiation are suited for shallow depths or thin specimens, while neutrons having high penetration depth are suited for bulk samples.

In physics, Bragg's law, Wulff–Bragg's condition or Laue-Bragg interference, a special case of Laue diffraction, gives the angles for coherent scattering of waves from a crystal lattice. It encompasses the superposition of wave fronts scattered by lattice planes, leading to a strict relation between wavelength and scattering angle, or else to the wavevector transfer with respect to the crystal lattice. Such law had initially been formulated for X-rays upon crystals but is moreover relevant for all kind of quantum beams, such as neutron and electron waves on atomic spacing, as well as for visual light on artificial periodic micros-scale lattices.

Reflection high-energy electron diffraction (RHEED) is a technique used to characterize the surface of crystalline materials. RHEED systems gather information only from the surface layer of the sample, which distinguishes RHEED from other materials characterization methods that also rely on diffraction of high-energy electrons. Transmission electron microscopy, another common electron diffraction method samples the bulk of the sample due to the geometry of the system. Low-energy electron diffraction (LEED) is also surface sensitive, but LEED achieves surface sensitivity through the use of low energy electrons.

Clinton Joseph Davisson was an American physicist who won the 1937 Nobel Prize in Physics for his discovery of electron diffraction in the famous Davisson–Germer experiment. Davisson shared the Nobel Prize with George Paget Thomson, who independently discovered electron diffraction at about the same time as Davisson.

The Ewald sphere is a geometric construction used in electron, neutron, and X-ray crystallography which demonstrates the relationship between:

Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials. An instrument dedicated to performing such powder measurements is called a powder diffractometer.

Electron scattering occurs when electrons are deviated from their original trajectory. This is due to the electrostatic forces within matter interaction or, if an external magnetic field is present, the electron may be deflected by the Lorentz force. This scattering typically happens with solids such as metals, semiconductors and insulators; and is a limiting factor in integrated circuits and transistors.

Low-energy electron diffraction (LEED) is a technique for the determination of the surface structure of single-crystalline materials by bombardment with a collimated beam of low-energy electrons (30–200 eV) and observation of diffracted electrons as spots on a fluorescent screen.

The history of quantum mechanics is a fundamental part of the history of modern physics. Quantum mechanics' history, as it interlaces with the history of quantum chemistry, began essentially with a number of different scientific discoveries: the 1838 discovery of cathode rays by Michael Faraday; the 1859–60 winter statement of the black-body radiation problem by Gustav Kirchhoff; the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system could be discrete; the discovery of the photoelectric effect by Heinrich Hertz in 1887; and the 1900 quantum hypothesis by Max Planck that any energy-radiating atomic system can theoretically be divided into a number of discrete "energy elements" ε such that each of these energy elements is proportional to the frequency ν with which each of them individually radiate energy, as defined by the following formula:

Helium atom scattering (HAS) is a surface analysis technique used in materials science. HAS provides information about the surface structure and lattice dynamics of a material by measuring the diffracted atoms from a monochromatic helium beam incident on the sample.

Rutherford backscattering spectrometry (RBS) is an analytical technique used in materials science. Sometimes referred to as high-energy ion scattering (HEIS) spectrometry, RBS is used to determine the structure and composition of materials by measuring the backscattering of a beam of high energy ions impinging on a sample.

The Kapitza–Dirac effect is a quantum mechanical effect consisting of the diffraction of matter by a standing wave of light. The effect was first predicted as the diffraction of electrons from a standing wave of light by Paul Dirac and Pyotr Kapitsa in 1933. The effect relies on the wave–particle duality of matter as stated by the de Broglie hypothesis in 1924.

In 1922, American physicist William Duane presented a discrete momentum-exchange model of the reflection of X-Ray photons by a crystal lattice. Duane showed that such a model gives the same scattering angles as the ones calculated via a wave diffraction model, see Bragg's Law.

## References

1. Davisson, C. J.; Germer, L. H. (1928). "Reflection of Electrons by a Crystal of Nickel". Proceedings of the National Academy of Sciences of the United States of America. 14 (4): 317–322. Bibcode:1928PNAS...14..317D. doi:10.1073/pnas.14.4.317. PMC  . PMID   16587341.
2. Eisberg, R.; Resnick, R. (1985). . Quantum Physics: of Atoms, Molecules, Solids, Nuclei, and Particles (2nd ed.). John Wiley & Sons. ISBN   978-0-471-87373-0.
3. Rubin, H. (1995). "Walter M. Elsasser". Biographical Memoirs. 68. National Academy Press. ISBN   978-0-309-05239-9.
4. Davisson, Clinton Joseph; Thomson, George Paget (1937). "Clinton Joseph Davisson and George Paget Thomson for their experimental discovery of the diffraction of electrons by crystals". The Nobel Foundation.
5. The Nobel Foundation (Arthur Holly Compton and Charles Thomson Rees Wilson) (1937). "Arthur Holly Compton for his discovery of the effect named after him and Charles Thomson Rees Wilson for his method of making the paths of electrically charged particles visible by condensation of vapour". The Nobel Foundation 1927.
6. Young, Hugh D. and Freedman, Roger A. (2004) University Physics, Ed. 11. Pearson Education, Addison Wesley, San Francisco, ISBN   0-321-20469-7, pp. 1493–1494.
7. Gehrenbeck, Richard K. (1978). "Electron diffraction: fifty years ago" (PDF). Physics Today. 31 (1): 34–41. Bibcode:1978PhT....31a..34G. doi:10.1063/1.3001830.
8. Davisson, C.; Germer, L. H. (1927). "The Scattering of Electrons by a Single Crystal of Nickel". Nature. 119 (2998): 558. Bibcode:1927Natur.119..558D. doi:10.1038/119558a0. S2CID   4104602.