Page 1 of 4

www.AssignmentPoint.com

Electron Diffraction

www.AssignmentPoint.com

Page 2 of 4

www.AssignmentPoint.com

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.

Page 3 of 4

www.AssignmentPoint.com

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:

Page 4 of 4

www.AssignmentPoint.com

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.