1. Anuradha Verma

2. What is electron Diffraction ?
History
Use of electron Diffraction Studies
Electron interaction with matter
Intensity of diffracted beams
What is the need of using Electron diffraction ?
Principle involved
Set up for electron diffraction
Interaction of Electron Beam and Gas Molecule
Electron Diffraction pattern
Types of electron diffraction

3. Electron diffraction refers to the wave nature of
electrons. 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 the wave-particle
duality, which states that the behavior of a particle of
matter (in this case the incident electron) can be
described by a wave.
Both properties are used in the electron diffraction
experiment, which gives information about distances
between atoms in gas-phase molecules.

4.  The de Broglie Hypothesis, formulated
in 1924, proposed by French physicist
Louis de Broglie & predicts that
particles should also behave as waves.
 The diffraction of electrons was first
shown by Davisson and Germer in 1927
 The first gas electron diffraction (GED)
investigation of molecular structure,
that of carbon tetrachloride, was
reported by Mark and Wierl in 1930.

5. 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.

6. In the kinematical approximation for electron diffraction, the
intensity of a diffracted beam is given by:
Here is the wave function of the diffracted beam and is
the so called structure factor which is given by:
where g is the scattering vector of the diffracted beam, is
the position of an atom in the unit cell, and is the scattering
power of the atom. 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 term . 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.

7. For a single crystal x-ray diffraction, size
required is 0.05mm (diam) otherwise
intensity of diffracted beam are too weak
to be detected clearly.
Reason:-
1.Efficiency with which x-ray are diffracted
is very low.
2.Crystal as large as 0.05mm cannot be
prepared.
Electron diffraction in such cases is helpful
as it uses wave property of electron and as
its scattering efficiency is high and small
sample may be used.

8.  Molecular geometry: relative position of atomic nuclei in the
molecule
 Energy difference between conformers
 Intramolecular motion
 Information about molecular energetic
 Information about electron density distribution
 Electron diffraction is most frequently used in solid state physics
and chemistry to study the crystal structure of solids.
 Short range order of amorphous solids
 Unit cell & space group determination:
Only reliable method for crystal smaller than 0.01-0.02mm (diam).
 Phase Identification:
Only when x-ray powder diffraction method are unavailable. Useful
when
1.small quantities are available
2.thin film samples
 Detecting small amount of impurity present in the sample.
 Evaluating bond angles and bond length in relatively small gaseous
sample.

9. Secondary diffraction:
As scattering efficiency of electron is high, the
diffracted beams are strong. Secondary
diffraction occurs when these diffracted beam
effectively become the incident beam and are
diffracted by another set of lattice planes.
Consequences:
1.Extra spots may appear in diffraction pattern and
care is needed in interpretation of diffraction data.
New experimental techniques have, however greatly
improved resolution of bands.
2.Intensity of diffracted beams are unreliable and
cannot be used for crystal structure determination.

10. Structure can be determined by analyzing the
scattering pattern produced when a beam of electrons
interacts with the sample.
Electron beam penetrate gases and produce diffraction
pattern as a result of interaction with gas molecules
Since electron are they are scattered strongly by their
interaction with nuclei and electrons of the atoms of
sample. Hence, cannot be used to study the interiors of
sample. However used for studying molecules in the
gaseous state held on surfaces and in thin films.
N.B:- Electron beam fail to penetrate beyond the
surface of solids and liquids.
Strong interaction between electron beam and
atom because charge present on the electron.

11.  Diffraction:
Diffraction refers to various phenomena which occur when a
wave encounters an obstacle.
The diffraction phenomenon is described as the apparent
bending of waves around small obstacles and the spreading out
of waves,
 Scattering:
 Change in direction of electromagnetic waves
 Scattering efficiency and behavior depends on size of
scatterers relative to wavelengths of radiation
Define size parameter as ratio of characteristic particle
diameter to wavelength
Treats particles as identical spheres

12. Scattering efficiency of a particle, customarily denoted by
Qb [non-dimensional], is defined by the following equation:
Qb = Cb / G
where Cb [length2] is the scattering cross section of the
particle, and G [length2] is the area of a geometrical cross
section of the particle in a plane perpendicular to the
direction of the incident light (i.e. the particle shadow).
The scattering efficiency may assume values greater than
unity (which conflicts with the traditionally accepted
meaning of this term, implying that its maximum value is
unity), i.e. a particle may scatter from the incident beam
more light power that falls on its geometrical cross section.

13. Diffraction of x-ray by crystal
depends upon the spacing
between the layers while the
diffraction of electrons by
gaseous molecules depends
upon the distances between the
atoms in a molecule.

14. An electron beam is produced by drawing electrons out of the cathode plate by
means of applied voltage and directing them to anode.
Beam pass across a potential difference of V volts, each electron acquires kinetic
energy as a result of the acceleration in electric field.
mv2 = eV
Thus momentum,
mv =
And for an electron wavelength λ from de Broglie relation is
λ = = = pm
Therefore accelerating voltage of 40 kV corresponds to 6 pm.
Such wavelength leads to interference effect when a accelerated beam passes
through a sample containing scattering centres seperated by the interatomic
distances between the atoms of molecule.

15. When a beam of high energy electrons passes through a
chamber containing gas molecules the charge of nuclei of
molecule will interact with the incoming beam.
Each atom of gas molecule will act as a radiation scattering
center.
Since particles of the electron beam carry a charge , the
amount of scattering resulting from interaction is relatively
large.
SCATTERING OF ELECTRON BEAM:
Coherent Scattering- No energy exchange between the beam
and scattering centre.
Incoherent Scattering- Energy exchange; change in the
wavelength and phase of the scattered electron beam

17. An electron diffraction pattern consists of pattern of rings of varying
intensity. The position of darkened rings on the photographic plate are
estimated visually. For convenient comparison with calculated scattering
curves, a plot is sketched for the plate darkening as a function of parameter
s defined by
s = sin
Diffraction pattern shows that intensity at a scattering angle θ can be
expressed in terms of function s. The expression for net scattering by two
atoms i and j separated by distance rij and randomly oriented in the path of
electron beam is given by Wierl Equation.
I(s) =fifj (1+ sin srij/ srij)
Where f i and fj are the scattering factors for the atom i and j
respy.
It can be extended to polyatomic molecule as
I(s) = ∑ij fifj (sin srij/ srij)
For any assumed molecular structure the contribution from all pairs of atoms
can be calculated and plot of I (s) versus s called a theoritical scattering
curve can be made.
The theoritical curves are then compared with experimental curves.

19.  Gas electron diffraction:
The target of this method is the determination of the
structure of gaseous molecules i.e. the geometrical
arrangement of the atoms from which a molecule is built up.
 Low-energy electron diffraction (LEED):
It is a technique for the determination of the surface
structure of crystalline materials by bombardment with a
collimated beam of low energy electrons (20-200eV) and
observation of diffracted electrons as spots on a fluorescent
screen.
 Reflection high-energy electron diffraction (RHEED):
It is a technique used to characterize the surface of
crystalline materials. RHEED systems gather information only
from the surface layer of the sample, which distinguishes
RHEED from other materials characterization methods that
also rely on diffraction of high-energy electrons.
LEED is also surface sensitive, but LEED achieves surface
sensitivity through the use of low energy electrons.

20.  Physical Chemistry
Gordon M. Barrow
 Principles of physical Chemistry
Puri, Sharma & Pathania
 An Introduction To Crystallography
F.C.Phillips
 spectroscopy.chemistry.ohiostate.edu/institute
/weber1.pdf
 en.wikipedia.org/wiki/Electron_diffraction