2. 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.

3. 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.

4. 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.

5. Diffraction’s Extinction Distance, xg
The extinction distance is larger for higher order diffracted beams.

6. 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.

7. 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.

8. 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.

9. Double Diffraction

10. Double Diffraction

11. Diffraction From Particles

12. Diffraction From Particles

13. Diffraction From Long Period Superlattices

14. Diffraction From Superlattices

15. Diffraction From Forbidden Reflections.

16. Superlattice Reflections

17. Superlattice Reflections

18. Diffraction from Dislocations

19. Diffraction from Dislocations

20. Diffraction from Dislocations