Anuradha Verma

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

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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

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.

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.

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