# Lesson 6

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## Lesson 6

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1. Lesson 6 • A brief look at the homework • Some history • The reciprocal lattice and cell

2. The matrix for the transformation is: 15.168 0.0 -2.7614 0.0 10.348 0.0 0.0 0.0 15.3658 The Cartesian coordinates are O 14.6659 5.0711 11.0064 C 14.5132 4.3744 10.0307 Distance is 1.209 Homework #4

3. History of Diffraction • Starts in Munich, Germany about 1910 • Involves 3 German physicists • One is a professor, one an instructor, and one a graduate student.

4. Arnold Summerfield

5. Summerfield • Full Professor in Munich • Very Good Classical Physicist (at a time when physics was greatly changing)‏ • Very good pianist. • Today most remembered for suggesting that electron levels were elliptical and not spherical.

6. Paul Peter Ewald

7. Ewald • Ewald was a student of Summerfields. • His thesis dealt with calculating the pattern from a regular two and three dimensional grid of radiation emitters. The interest at the time was in radio waves whose wavelengths are in meters but it could be applied to any radiation • Left Germany and was a professor at the Brooklyn Institute of Technology for many years.

8. Max von Laue

9. von Laue • Was a student of Einstein's • Was German nobility(?)‏ • Was in Munich as a lecturer. • Put the following ideas together • X-rays are radiation with Å wavelength • Crystals are regular arrays with Å separation • The diffraction reported in Ewald's thesis should therefore be observed using crystals and x-rays.

10. Von Laue's Idea • Von Laue tells Summerfield his idea. • Summerfield has many objections • Both the nature of x-rays and crystals is speculative • Since the atoms are vibrating in the crystal this motion will cancel out the regular array • How to turn the atoms into radiation sources. • Summerfield is convinced there can be no x-ray diffraction

11. Onward • Von Laue is not easily discouraged • He decides that if a crystal is exposed to white radiation then the atoms will fluoresce at their characteristic wavelengths • He decides to do the experiment to see if it works • Only one problem—von Laue does not dirty his hand with experiments.

12. The experiment • Von Laue recruits a graduate student named Frederick who is very good with x-rays. • Since the atoms will be producing the x-rays, an atom with an easily detected wavelength should be used. • They chose copper and use CuSO4·12H2O • Since the pattern should come off in all directions the film is placed on the incoming x-ray side • The result—a blank film

13. Never Give Up • Von Laue decides he needs more help • He recruits another graduate student named Knipping. • Knipping suggests they place film all around the crystal since maybe the fluorescence idea is wrong. • They try it again • All this is taking place in 1912

14. The Apparatus

15. The Result

16. One Further Comment • At time von Laue appears to be haughty • After Hitler comes to power he brings the Dutch physicist Peter Debye (another Summerfield student) to Germany. • Debye for a while becomes the chief spokesman for Nazi physics and its attempt to disprove “Jewish physics” (Einstein). • Von Laue bitterly fights the Nazi's and Debye • He is kept out of the concentration camps because of his nobility.

17. Reciprocal Space • This is the Fourier transform of the electron density in the crystal. • There is a certain irony—the real space is inside the crystal and we cannot directly experience it. Reciprocal space is what we see in the diffraction pattern. • Note real space is continuous while reciprocal space is discrete.

18. Real and Reciprocal Space

19. Optical Transforms • The paper contains a magnification of what is on the slide. • The slide represents real space • The spots of light define reciprocal space • The reciprocal relationships can readily be seen. • Remember Bragg's law 2dsin(θ)=nλ

20. Homework • No homework • No class Monday • Have a good and productive MLK Day.