electron diffraction - introduction
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Electron Diffraction - Introduction. Electron diffraction is an important method to characterize materials. The textbook, Transmission Electron Microscopy, dedicates 10 of its chapters to electron diffraction and it’s discussed in many of the other chapters, as well. - PowerPoint PPT PresentationTRANSCRIPT
EM Course – Electron Diffraction
Professor Rodney Herring
Electron Diffraction - IntroductionElectron diffraction is an important method to characterize
materials.
The textbook, Transmission Electron Microscopy, dedicates 10 of its chapters to electron diffraction and it’s discussed in many of the other chapters, as well.
Every time a beam, of any kind, passes through an object, the beam diffracts by some process.
Diffraction has many forms. For example,• The beam can diffract, or scatter, off of individual atoms or
molecules or single, small structures. • If there is a periodic arrangement, the diffraction intensity will
be constructive in some orientations and destructive in other orientations.
• If there is only short range order such as in amorphous materials, the diffraction intensity will be speckled or in rings.
Examples of Electron Diffraction
• The arrangement of “spots” (square, rectangular, hexagonal) gives the crystal structure of the material.
• A lot of other crystal structure information is given by Kikuchi lines and Higher-ordered Laue Zone Lines (HOLZ), which we will discuss in some detail.
• If we open up the spots, we may see crystal structure as in the following slide.
diffracted beam or spotKikuchi linesHigher-ordered Laue Zone Lines
Examples of Electron Diffraction
Electron diffraction from atomic planes of a crystal
Kossel Images of GaAs/ InGaAs Superlattices
Electron Diffraction - Introduction
To understand electron diffraction, we’ll start from first principles, as presented in Williams and Carter.
Electron Diffraction
Electron Diffraction
Electron Scattering
Note the use of incoherent to describe scattered electrons, as used in all EM textbooks. Nothing could be further from the truth!
Inte
nsi
tye-
1/nm
32
33
34
35
36
37
e-
0.00 0.02 0.04 0.06 0.08 0.10 0.121/nm
e-
1/nm
4500
5000
5500
6000
6500
7000
e-
0.00 0.02 0.04 0.06 0.08 0.101/nm
Position 1
Position 2
High-angle diffusely-scattered electrons
Fringes Produced from Elastically and Inelastically Scattered Electrons Ge specimen
Intensityalong white line(essentially constant)
Fringes found > 18 mrad
1
1
2
~ 0.05e-
1/nm
0
50
100
150
200
250
300
e-
0.0 0.5 1.0 1.5 2.0 2.5 3.01/nm
Inte
nsi
ty
Position 1/nm
Inte
nsi
ty2
1
Contrast enhanced image
000/111
2
Interference fringes produced from elastically and inelastically scattered electrons generated from a Ge specimen.
3
1 mrad
Electron Scattering
Electron Scattering Cross Section,
=
Single atom
Electron Scattering Cross Section,
Electron Scattering Cross Section,
O.01 nm is approximately the spatial resolution of UVic’s STEHM.
Mean Free Path, This a common term and concept used in electron microscopy
Mean Free Path,
No is number of atoms is density
Regrettably, also means wavelength, which is more commonly referred to than mean free path.
Fraunhofer and Fresnel Diffraction
In the TEM we can focus the diffraction pattern so that the spots and lines are clear. This condition is considered Fraunhofer diffraction.
Diffraction From Apertures
= wavelength
Constructive Interference
Wavelength
Phase Shift Between Images
x
image 1image 2
phase shift = x/ x 2
Calculation of Temperature
Refractive index, x/
T 103.49/
for air = 103.49 p1/T + 177.4 p2/T + 86.26p3/T x (1+5748/T)
For a 1 mm translation,
x = 12.7 pixels = 67.5 pixels(measured values)
Calculation of Temperature
T 103.49/= 103.49/0.188= 550 K
x/= 12.7/67.5= 0.188
Thus an approximate value of the temperature can be obtained by this simple analysis, which provides an example of confocal holography.
Definition of Angles in TEM
EELS Spectroscopy