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Physics Textbooks Boundless Physics Introduction to Quantum Physics History and Quantum Mechanical Quantities
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Concept Version 9
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Diffraction Revisited

De Broglie's hypothesis was that particles should show wave-like properties such as diffraction or interference.

Learning Objective

  • Compare application of X-ray, electron, and neutron diffraction for materials research


Key Points

    • The wavelength of an electron is given by the de Broglie equation $\lambda = \frac{h}{p}$.
    • Because of different forms of interaction involved, X-ray, electron, and neutron are suitable for different studies of material properties.
    • De Broglie's idea completed the wave-particle duality.

Terms

  • photoelectric effect

    The observation of electrons being emitted from matter (metals and non-metallic solids, liquids, or gases) as a consequence of their absorption of energy from electromagnetic radiation.

  • black body radiation

    The type of electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by a black body (an opaque and non-reflective body) held at constant, uniform temperature.

  • grating

    Any regularly spaced collection of essentially identical, parallel, elongated elements.


Full Text

The de Broglie hypothesis, formulated in 1924, predicts that particles should also behave as waves. The wavelength of an electron is given by the de Broglie equation $\lambda = \frac{h}{p}$. Here h is Planck's constant and p the relativistic momentum of the electron. $\lambda$ is called the de Broglie wavelength.

From the work by Planck (black body radiation) and Einstein (photoelectric effect), physicists understood that electromagnetic waves sometimes behaved like particles. De Broglie's hypothesis is complementary to this idea: particles should also show wave-like properties such as diffraction or interference. De Broglie's formula was confirmed three years later for electrons (which have a rest-mass) with the observation of electron diffraction in two independent experiments. George Paget Thomson passed a beam of electrons through a thin metal film and observed the predicted interference patterns. Clinton Joseph Davisson and Lester Halbert Germerguided their beam through a crystalline grid to observe diffraction patterns.

X-ray diffraction is a commonly used tool in materials research. Thanks to the wave-particle duality, matter wave diffraction can also be used for this purpose. The electron, which is easy to produce and manipulate, is a common choice. A neutron is another particle of choice. Due to the different kinds of interactions involved in the diffraction processes, the three types of radiation (X-ray, electron, neutron) are suitable for different kinds of studies.

Electron diffraction is most frequently used in solid state physics and chemistry to study the crystalline structure of solids. Experiments are usually performed using a transmission electron microscope or a scanning electron microscope. In these instruments, electrons are accelerated by an electrostatic potential in order to gain the desired energy and, thus, wavelength before they interact with the sample to be studied. The periodic structure of a crystalline solid acts as a diffraction grating, scattering the electrons in a predictable manner. Working back from the observed diffraction pattern, it is then possible to deduce the structure of the crystal producing the diffraction pattern. Unlike other types of radiation used in diffraction studies of materials, such as X-rays and neutrons, electrons are charged particles and interact with matter through the Coulomb forces. This means that the incident electrons feel the influence of both the positively charged atomic nuclei and the surrounding electrons. In comparison, X-rays interact with the spatial distribution of the valence electrons, while neutrons are scattered by the atomic nuclei through the strong nuclear force.

Electron Diffraction Pattern

Typical electron diffraction pattern obtained in a transmission electron microscope with a parallel electron beam.

Neutrons have also been used for studying crystalline structures. They are scattered by the nuclei of the atoms, unlike X-rays, which are scattered by the electrons of the atoms.  Thus, neutron diffraction has some key differences compared to more common methods using X-rays or electrons. For example, the scattering of X-rays is highly dependent on the atomic number of the atoms (i.e., the number of electrons), whereas neutron scattering depends on the properties of the nuclei. In addition, the magnetic moment of the neutron is non-zero, and can thus also be scattered by magnetic fields. This means that neutron scattering is more useful for determining the properties of atomic nuclei, despite the fact that neutrons are significantly harder to create, manipulate, and detect compared to X-rays and electrons.

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