NEUTRON AND ELECTRON DIFFRACTIONS

.NEUTRON DIFFRACTION

A neutron generated in a reactor and slowed to thermal velocities by repeated collisions with a moderator (eg graphite) until it is travelling at about 4 km s^-1 has a wavelength of about 100 pm thus allowing similar diffraction phenomena than with X-rays. In practice, a range of wavelengths occurs in a neutron beam, but a monochromatic beam can be selected by diffraction from a germanium crystal.

The scattering of X-rays is caused by the oscillation that an incoming electromagnetic wave generates in the electrons of atoms.

The scattering of neutrons is a nuclear phenomenon. Neutrons pass through the electronic structures of atoms and interact with their nuclei. As a result, the intensity with which the neutrons are scattered is independent of the number of electrons (Table 3). Wheras X-ray scattering factors increase strongly with the atomic number, neutron scattering factors vary much less strongly; nor do they vary with angle. As a result, neutron diffraction is not dominated by the heavy atoms present in the molecule.

Table 3. Scattering factors (X-ray vs neutrons)

Element	X-rays sin theta/lamdba =0	X-rays sin theta/lamdba =0.5Å-1	Neutrons (10-12 cm)
H	1.0	0.07	-0.38
D (=2H)	1.0	0.07	0.65
C	6.0	1.7	0.66
54Fe	26.0	11.5	0.42
Co	27.0	12.2	0.25

In particular, neutron diffraction shows up the positions of hydrogen nuclei much more clearly than X-rays. The difference in sensitivity to hydrogens can have a pronounced effect on the measure of the C-H bond lengths. For example, X-ray measurements on sucrose give R(C-H) = 0.96 Å; neutron measurements, which respond to the location of the nuclei, give R(C-H) = 1.095 Å.

Similarly, atoms with similar atomic numbers (almost undistinguishable in X-ray diffraction) may have neutron scattering factors significantly different. As an example, it is possible to distinguish elements like Ni and Co that are present in the same compound.

Beside the nuclear diffraction of neutrons, there is also a magnetic diffraction of neutrons. In contrast with photons (X-ray diffraction) neutrons possess a magnetic moment due to their spin. This magnetic moment can couple with the magnetic field of ions in some crystals and modify the diffraction pattern.

.ELECTRON DIFFRACTION

Electrons are scattered strongly by their interaction with the charges of electrons and nuclei, and so cannot be used to study the interiors of solid samples. However, they can be used to study molecules in the gas phase, on surfaces, and in thin films.

Diffraction by a gaseous sample :

The gaseous sample presents all possible orientations of atom-atom separations to the electron beam and the resulting diffracting pattern is like an X-ray powder photograph. The intensity of the diffracted beam decreases steadily with increasing scattering angle and the overall pattern consists of a series of concentric undulations on a background (Fig 23). The undulations are due to the sharply defined scattering from nuclear positions, and the background is due to scattering from the less well-defined continuous electron density distribution. The contribution of the scattering from the nuclei (undulations) can be experimentally emphasized by eliminating the unwanted background (insertion of a rotating disk, cfr next). The Wierl equation expresses the diffracted intensity in terms of the separation of nuclei (Rij), the scattering angle and the electronic scattering factors f.

Wierl equation : I(theta) = SUM fi fj (sin sRij) / sRij with s = 4pi/lambda sin 1/2 theta

Fig. 23. Scattering intensity as a function of the scattering angle: total signal (a) and pattern after substration of the background (b). Note that in b, the intensity is plotted against s = (4pi/ lambda) sin 1/2 theta.

A schematic electron diffraction apparatus is illustrated in Fig 24. Electrons are emitted from a hot filament and accelerated through a potential gradient. They then pass through the stream of gaseous sample and on to a fluorescent screen. A rotating heart-shaped sector emphasizes the scattering from nuclear positions and suppresses the smoothly varying background due to scattering from the continuous electron distribution in the molecules.

Fig. 24. The diffraction pattern is photographed from the fluorescent screen.

Low-energy electron diffraction (LEED) :

Low-energy electron diffraction is another application of electron diffraction and is one of the most informative techniques for determining the arrangement of atoms close to a surface. It will not be discussed in details here.

The LEED pattern portrays the two-dimensional structure of the surface. In practice, interpretation of LEED data is much more complicated than the interpretation of bulk X-ray data. By studying how the diffraction intensities depend on the energy of the electron beam it is possible to infer some details about the vertical location of atoms and to measure the thickness of the surface layer.

The presence of defects in a surface (steps, terraces) shows up in LEED patterns and their amount can be estimated.

Fuente: http://perso.fundp.ac.be/~jwouters/DRX/diffraction.html#chap%203
Abel Colmenares
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