EM Course – Elastic Scattering
Professor Rodney Herring
Elastic Scattering - Introduction
Transverse Waves
particles and waves
Elastic Scattering of Electrons
Elastic Scattering of Electrons
Interference
1 Point Source
2 Point Sources
Elastic Scattering of Electrons
Elastic Scattering of Electrons
Scattering Cross Section of Electrons
For electrons scattering from the nucleus to high angles, the differential
cross-section is given by,
For electrons scattering from the nucleus to high angles, the total nuclear
cross-section is given by,
The beam energy, Eo, the angle of scattering (q) and the atomic number, Z,
all affect the probability that an electron will be scattered by the nuclei of
atoms in the specimen. These expressions cannot calculate the cross
sections exactly because they only consider the particle nature of
electrons and ignore their wave nature.
Scattering Cross Section of Electrons
For C, a 1 MV TEM does very little radiation
damage to the specimen!
Mean Free Path of Electrons
Atomic Scattering Factor, f(q)
The Rutherford expressions of electron scattering could not calculate the cross
sections exactly because they only considered the particle nature of electrons
and ignored their wave nature.
A full wave mechanics treatment of scattering cross sections is well beyond the
scope of this course.
The easiest and most familiar concept used is the atomic-scattering factor, f(q),
which is related to the differential elastic cross section by,
Atomic Scattering Factor, f(q)
Zero-loss & Phonon-loss Intensities for
Gallium Arsenide (GaAs)
50
40
Intensity 30
444
222
20
666
atomic planes
10
0.2
0.4
0.6
0.8
1.0
s (1/Å)
0
10
q (mrad)
Doyle and Turner Acta Cryst. (1968). A24, 390
20
Atomic Scattering Factor, f(q)
THE Structure Factor, F(q)
THE Structure Factor, F(q)
An example follows
THE Structure Factor, F(q)
THE Structure Factor, F(q)
THE Structure Factor, F(q)
Diffraction Equations
Diffraction Equations
(Sir William H. Bragg and Mr. W. Lawrence Bragg)
(father - son team)
1915
Diffraction Equations
• As seen before, the destructive and constructive
interference of a beam of x-rays or electrons off atomic
planes is shown below.
Destructive Interference
Constructive Interference
Chapter Summary