EM Course – Diffraction Effects
Professor Rodney Herring
Diffraction
As mentioned in class, there are 10 chapters dedicated to
electron diffraction in Williams and Carter. There’s no way we’ll
have enough time to cover all of this material, as well as, reach
some imaging and analytical methods so I will summarize some
of the material that I believe is very important that is presented in
these chapters in order for you to have a base to explore further
concepts necessary for you to understand your diffraction
measurements in the future.
Diffraction’s Extinction Distance, xg
• The amplitude or intensity of diffracted beams depends on many
factors.
• One important factor is a characteristic length called the extinction
distance, xg, which is a dynamic diffraction effect where the intensity from
the direct beam is transferred to the diffracted beams, which then transfer
the intensity back into the direct beam.
• The extinction distance is thus dependent on Bragg angle, qB, and the
specific diffracted beam whose characteristics are determined by the
structure factor, Fg.
• The extinction distance can be expressed as:
Vc is the volume of the unit cell of the crystal.
Diffraction’s Extinction Distance, xg
Direct beam
Diffracted beam
Diffracted beam 1
Intensity
Diffracted beam 2
Intensity
Note the difference in amplitude. As the thickness increases adsorption of
the intensity occurs leading to reduced contrast. There is also a difference
in periodicity not obvious here.
Diffraction’s Extinction Distance, xg
The extinction distance is larger for higher order diffracted beams.
Diffraction Extinction Distance, xg
Since dynamic diffraction is a thickness effect, the intensity of the
diffracted beam varies with the thickness of the specimen, t, and the
extinction distance of the specific diffracted beam.
It is a very important equation, expressed as
Where seff is the effective deviation from the exact Bragg
diffraction condition as discussed earlier.
Diffraction Extinction Distance, xg
Direct beam
Diffracted beam
Intensity
Note that the direct beam and diffracted beam are of equal
intensity at a specimen thickness, t, giving p/4, which will vary
depending on the extinction distance of the diffracted beam.
For my method of diffracted beam holography, the interference of
two beams with equal intensity gives the highest contrast fringes
so I aim for this condition in many of my experiments.
I can also use the relative intensity of the direct beam with the
specific diffracted to determine the thickness of my specimen.
Diffraction Extinction Distances
Thus, the intensity in our image varies sinusoidally depending on
the thickness and on the beam or diffracted beam used for
imaging.
Double Diffraction
Double Diffraction
Diffraction From Particles
Diffraction From Particles
Diffraction From Long Period
Superlattices
Diffraction From Superlattices
Diffraction From Forbidden Reflections
.
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Superlattice Reflections
Superlattice Reflections
Diffraction from Dislocations
Diffraction from Dislocations
Diffraction from Dislocations