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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 (in this case the incident electron)
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.
Electron diffraction is most frequently used in solid state physics and chemistry
to study the crystal structure of solids. Experiments are usually performed in a
transmission electron microscope (TEM), or a scanning electron microscope
(SEM) as electron backscatter diffraction. In these instruments, electrons are
accelerated by an electrostatic potential in order to gain the desired energy and
determine their 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 may be possible to deduce the structure of the
crystal producing the diffraction pattern. However, the technique is limited by
the phase problem.
Apart from the study of crystals i.e. electron crystallography, electron
diffraction is also a useful technique to study the short range order of
amorphous solids, and the geometry of gaseous molecules.
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History
The de Broglie hypothesis, formulated in 1924, predicts that particles should
also behave as waves. 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. At the University of Aberdeen George Paget
Thomson passed a beam of electrons through a thin metal film and observed the
predicted interference patterns. At Bell Labs Clinton Joseph Davisson and
Lester Halbert Germer guided their beam through a crystalline grid. Thomson
and Davisson shared the Nobel Prize for Physics in 1937 for their work.
Theory
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 forces. In addition, the magnetic moment of neutrons is non-zero,
and they are therefore also scattered by magnetic fields. Because of these
different forms of interaction, the three types of radiation are suitable for
different studies.
Intensity of diffracted beams
In the kinematical approximation for electron diffraction, the intensity of a
diffracted beam is given by:
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where \mathbf{g} is the scattering vector of the diffracted beam, \mathbf{r}_i
is the position of an atom i in the unit cell, and f_i is the scattering power of the
atom, also called the atomic form factor. The sum is over all atoms in the unit
cell.
The structure factor describes the way in which an incident beam of electrons is
scattered by the atoms of a crystal unit cell, taking into account the different
scattering power of the elements through the factor f_i. Since the atoms are
spatially distributed in the unit cell, there will be a difference in phase when
considering the scattered amplitude from two atoms. This phase shift is taken
into account by the exponential term in the equation.
The atomic form factor, or scattering power, of an element depends on the type
of radiation considered. Because electrons interact with matter though different
processes than for example X-rays, the atomic form factors for the two cases are
not the same.