Introduction to Quantum Ideas
45
The electron diffraction experiments establish the fact that the electrons
possess wave properties exactly as de Broglie had suggested. To clarify that
the wave property is not because of the simultaneous participation of a large
number of electrons, but is associated with each electron, experiments have
been done with very low intensity electron beams so that the electrons pass
through the instruments essentially one at a time. With sufficiently long exposure,
a diffraction pattern was obtained which differed in no way from the pattern
obtained with normal intensity beams, thus suggesting that the wave-like properties
are to be associated with individual electrons. The de Broglie wavelength has
also been verified for neutral molecules (Estermann and Stern, 1930) and for
neutrons; however, in order that they have the same de Broglie wavelength as
the x-ray wavelength, their energies (E = p
2
/2m) have to be of the order of
~ 0.02 eV, i.e., one uses thermal molecules and neutrons.
Electron and neutron diffraction, along with x-ray diffraction have become
an indispensable tool for the study of the structures of solids. Their diffraction
patterns though qualitatively similar, have important differences which need to
be mentioned.
Since the electrons are sensitive to electrostatic forces, electron beams
have little penetration. With the development of slow electron beams
(10 to 1000 eV) which undergo negligible penetration and for which diffraction
occurs essentially at the first atomic layer, electron diffraction has become an
important tool for the study of surfaces. Electron beams of fairly high energies,
i.e., about 50 keV, have quite small de Broglie wavelengths, and therefore are
used in electron microscopes for high resolution studies of small specimens.
On the other hand neutrons, like x-rays, are fairly insensitive to electrostatic
forces, and therefore penetrate easily. Neutron diffraction has several advantages:
1. Since neutron scattering is essentially by the nucleus and depends quite
distinctively on the structure of the nucleus, neutron diffraction can give
more information about crystals formed from different atoms which have
nearly equal atomic number and which cannot easily be distinguished by
x-rays.
2. The scattering of neutrons by light nuclei such as hydrogen is large, and
hence neutron diffraction is an important technique in the study of structures
of organic compounds. The scattering of x-rays by light atoms is weak
(the coherent cross-section is approximately proportional to Z
2
where Z is
the number of electrons).
3. The magnetic ordering of atoms in a crystal, which have nonzero magnetic
moment, can be studied by neutron diffraction which therefore is a valuable
method of investigating magnetic materials. The main disadvantages of
using neutron diffraction are the low intensity of neutron beams available
45
The electron diffraction experiments establish the fact that the electrons
possess wave properties exactly as de Broglie had suggested. To clarify that
the wave property is not because of the simultaneous participation of a large
number of electrons, but is associated with each electron, experiments have
been done with very low intensity electron beams so that the electrons pass
through the instruments essentially one at a time. With sufficiently long exposure,
a diffraction pattern was obtained which differed in no way from the pattern
obtained with normal intensity beams, thus suggesting that the wave-like properties
are to be associated with individual electrons. The de Broglie wavelength has
also been verified for neutral molecules (Estermann and Stern, 1930) and for
neutrons; however, in order that they have the same de Broglie wavelength as
the x-ray wavelength, their energies (E = p
2
/2m) have to be of the order of
~ 0.02 eV, i.e., one uses thermal molecules and neutrons.
Electron and neutron diffraction, along with x-ray diffraction have become
an indispensable tool for the study of the structures of solids. Their diffraction
patterns though qualitatively similar, have important differences which need to
be mentioned.
Since the electrons are sensitive to electrostatic forces, electron beams
have little penetration. With the development of slow electron beams
(10 to 1000 eV) which undergo negligible penetration and for which diffraction
occurs essentially at the first atomic layer, electron diffraction has become an
important tool for the study of surfaces. Electron beams of fairly high energies,
i.e., about 50 keV, have quite small de Broglie wavelengths, and therefore are
used in electron microscopes for high resolution studies of small specimens.
On the other hand neutrons, like x-rays, are fairly insensitive to electrostatic
forces, and therefore penetrate easily. Neutron diffraction has several advantages:
1. Since neutron scattering is essentially by the nucleus and depends quite
distinctively on the structure of the nucleus, neutron diffraction can give
more information about crystals formed from different atoms which have
nearly equal atomic number and which cannot easily be distinguished by
x-rays.
2. The scattering of neutrons by light nuclei such as hydrogen is large, and
hence neutron diffraction is an important technique in the study of structures
of organic compounds. The scattering of x-rays by light atoms is weak
(the coherent cross-section is approximately proportional to Z
2
where Z is
the number of electrons).
3. The magnetic ordering of atoms in a crystal, which have nonzero magnetic
moment, can be studied by neutron diffraction which therefore is a valuable
method of investigating magnetic materials. The main disadvantages of
using neutron diffraction are the low intensity of neutron beams available