2018 ELECTRON DIFFRACTION AND APPLICATIONS

ELECTRON DIFFRACTION AND APPLICATIONS

1. Electron Diffraction
(ED)
DR. HARSH MOHAN
DEPARTMENT OF APPLIED
PHYSICS
M. L. N. COLLEGE
YAMUNA NAGAR
HARYANA

2. M.Sc.Chemistry
Electron diffraction (LEED); Basics,
Measurement Technique, applications in
structure determination.

3. Low energy electron diffraction
(LEED); Principle, Schematic of low
energy electron diffraction, Leed
pattern applications,

4. Applications in structure determination

5. Historical in Short
1897 Discovery of electron beams

(J. J. Thomson)
1924 Wave mechanics postulated
(L. de Broglie)
1927 Prove of electron diffraction
at an atomic lattice (Ni
(111)-
surface) (C. J. Davisson / L.
H. Germer)
(1937 Nobel Prize for Davisson
and Thomson)

10. LEED is Surface Sensitive
Low energy electrons interact
strongly with matter:
Electron mean free path is
small
Only electron scattered from near
surface can leave the surface:
Surface sensitive

11. A beam of electrons of a well-defined low
energy (typically in the range 20 - 200 eV)
is incident normally on the sample. The
diffracted electrons can be observed by a
fluorescent screen after energy-filtering
grids, which selects only the electrons
with the same kinetic energy as the
primary electrons.
Basics

13. Basics
SCATTERING INTENSITY AND ANGLES
a
a
P

14. Basics
SCATTERING INTENSITY AND ANGLES

20. θ θ
δ 2rsinαcos + sin
2 2
f
æ ö
=
ç ¸
è ø

21. In order to add waves that differ in phase
and amplitude ,it is convenient to
represent them in complex plane and to
add vectorically

25. In order to add waves that differ in phase
and amplitude ,it is convenient to
represent them in complex plane and to
add vectorically
2 /
0 0
A A A.
i
e
pdl
= +
2 /
0
(1 )
i
A A e
p d l
= +

26. Where A
o
is called Atomic form
factor and depends on the
nuclear charge of the atom. The
intensity of is proportional to the
square of amplitude or in this
case the amplitude times
complex conjugate Thus
AA

32. THE WIERL EQUATION AND THE MEASUREMENT TECHNIQUES
There are two types of collision which take place between a beam of
electrons and a jet of gas . These are:
1.Elastic collisions, which produce coherent scattering.
2.Inelastic collisions, which produce incoherent scattering.
In other words, scattering of electrons may be divided into two types, viz
coherent and incoherent. Coherent scattering may be regarded as made up
of two components, known as atomic and molecular coherent scattering.
The electrons diffraction experiments involve all the three types of
scattering. It should be noted that incoherent scattering plus the atomic
component of the coherent scattering are responsible for the sharply falling
background while the molecular coherent scattering give rise to the
concentric ring. The molecular coherent scattering depends on the structure
of the molecule.
The coherent or elastic scattering is represented by an equation devised by
the Mark and Wierl.

33. sin 4 1
( ) , sin θ
2
ij
i j
ij ij
sR
I f f s
sR
p
q
l
= =å
Where λ is the wavelength of the electron in the
beam and θ is the scattering angle. The electron
scattering factor, f is a measure of the intensity of
electron scattering powers of the atoms. The
Wierl equation indicates the appearance of
diffraction pattern caused by a molecule in a path
of electron.

34. I (θ) can be calculated only at discrete, equally spaced values of
scattering angle. However Wierl equation does not allow the
direct calculation of internuclear distance from the
measurement of I (θ) at various values of diffraction angle .
Molecular representation of electron diffraction pattern using extended
Wierl equation
To calculate the molecular structure Wierl equation is given by:
1
02 1
sin
( ) ()
N i
i j ij
i j
sR
I K f f P r dr
sR
a
q
-
= =
= SS ò
I (θ)=intensity at diffraction angle θ, K is a experimental
constant, =form factor of i atom , = Probability of the
distribution of the vibrational variation in the distance
between i and j.

35. is scattering angle in dependence of the
wavelength. Equation is modified to:
The Equation assumes the interatomic distances to be constant
and thus the molecule is said to be rigid, Replace the form
factor of atom by an atomic property in above equation.
Atomic properties such as atomic number partial charge or
Atomic polarizability allow to code 3D molecular representation
of electron diffraction pattern.

36. Measurement Technique

42. LOW ELECTRON DIFFRACTION (LEED) AND LOW ELECTRON DIFFRACTION (LEED) AND
STRUCTURE OF SURFACESSTRUCTURE OF SURFACES
 Low energy electron diffraction is one of the most informative
technique for determining the arrangement of the atoms close to
the surface. LEED is generally electron diffraction but the sample
is now the surface of a solid. The use of low energy (10 to 200eV)
electrons corresponding to wavelengths in the range 100 to 400
pm ensures that the diffraction is caused only by atom close to
the surface. LEED is generally electron diffraction but the sample
is now the surface of the solid. The use of low energy tend to
200eV electrons corresponding to wavelengths in the range 100-
400pm ensures that the diffraction is caused only by atoms on
enclosed to the surface. The arrangement used for LEED
experiment consist of a sample container, electron gun, grids and
phosphorous screen. The electron diffracted by the surface layer
are detected by the Fluorescence they produce in the phosphorus
screen

43. Structure of surfaces:Structure of surfaces:
The LEED pattern portrays the 2 dimensional structure of the
surface layer. It is possible to measure the thickness of the
surface later and also infer done details about the vertical
location of the around by studying the the diffraction intensities
which dend on the energy of the electron beam.
1. LEED pattern is sharp if the surface is well ordered for long
distance compared with the wavelength of the incident electron.
Generally, Sharp pattern are obtained for surfaces ordered to
depths of 20nm or more.
2. Diffused LEED pattern shows the poorly ordered surface or the
presence of impurities.
3. If the LEED pattern doesn't corresponds to the pattern
expected by extrapolation of the bulk surface to the surface then
either reconstruction of the surface occurred or there is order in
the arrangement of an adsorbed layer.

44. Measurement Technique

45. Measurement Technique

46. Instrumentation
Electron gun produces focussed e- beam of10 nA-10 mA
and Energy = 20-200 eV.
Magnetic shield expels residual magnetic fields.
Sample positioned at "focus" of hemispherical grids.
Diffracted electrons (elastically scattered) and secondary
electrons (inelastically scattered) back-scattered towards
LEED optics in field free region.
Diffracted electrons – spots
Secondary electrons - diffuse background
After passing through G1 (ground) accelerated towards
phosphor screen.
Negative potentials applied to G2 and G3 to repel
secondary electrons.
 Electrons strike phosphor ® photons.
 LEED. Image captured on photographic film or video
camera.

47. Instrumentation
grid
screen
electron gun

48. For 3D case

49. For 2D case
Normal LEED case with incident e beam
normal to the surface, along one direction
a sin q = n.l

50. k
y
Dy
Real space

versus

reciprocal
space
Real space:
x,y,z
Reciprocal space:
k
x
,

k
y
,

k
z

51. The result is an electron diffraction (ED)
pattern. The pattern one obtains is completely
dependent on the d-spacing and composition
of the crystal that is being analyzed.

52. If an ED is made of an
amorphous structure (i.e.
no crystalline formation)
then one simply gets a
central bright spot
comprised of transmitted
electrons and a single
ring of randomly
forward scattered
electrons.

53. If an ED is made of field of many
crystals, some of which are oriented
at the Bragg’s angle while others are
not, a pattern with well defined
concentric rings, but not spots, will
result.

54. ELECTRON DIFFRACTION PATTERNS
MOSAIC SINGLE CRYSTAL PLATELIKE TEXTURE POLYCRYSTAL

55. Experimental data
LEED pattern
obtained from
Si(111)7x7
reconstructed
surface
Electron gun

63. ADVANTAGES OF ELECTRON DIFFRACTION METHOD
OVER X-RAY METHOD
 The electron diffraction method has got several technical 
advantages over X-ray method. Some of the advantages are 
given below:
1.X-ray method cannot be used under reduced pressure, while 
electron diffraction method can be applied even to gases and 
vapors under reduced pressure. In other electron diffraction is of 
special importance for studying vapors and liquids which boil 
under atmospheric pressure with decomposition.
2.The number of scattering particles are much less in gas and 
hence the exposure required in the x-ray method are quit long, 
but on account of the greater intensity of electron beam, the 
time of exposure is reduced from a few hours (required for the 
X-ray method) to a fraction of second.

65. Summary
Electron diffraction is a technique
which allows users to determine the
atomic arrangement of crystals. When
combined with other analytical
techniques such as EDS it can aid in
the identification of unknown crystals
and/or determine the d-spacing of
newly described crystals.