1. MENA3100, 3/2-10, OBK X-ray diffractionXRD Røntgendiffraksjon Single crystalPowder

2. Diffraction

4. Crystal Atomic arrangementLattice

5. 1848 The 14 Bravais lattices Lattice + base

7. Bragg’s law 2d sin  = n

8. Bragg’s law 2d sin  = n n = 2 But XRD is typically done with monochromatic radiation 2nd. order

9. Bragg’s law 2d sin  = n 2nd. order from 001 1th. order from 002

10. The 14 Bravais lattices Face centered cubic lattice  -iron NaCl  -brass

11. Extinction Example: Face centered cubic Special example: Cubic close packed structure Utslukning

12. Extinction Example: Face centered cubic Special example: Cubic close packed structure Utslukning

13. Don’t confuse with...

14. X-ray diffraction Need X-rays Brehmsstrahlung = white radiation Characteristic X-rays Wavelenght CuK  1 = 1.54056 Å MoK  1 = 0.70930 Å CuK  1 = 1.54056 Å CuK  2 = 1.54433 Å CuK  = 1.5418 Å I(CuK  1 ) = 2·I(CuK  2 )

15. Need sample Single crystal Powder

16. Need experimental setup Diffractometer Bragg-Brentano geometry (Primary monochromator) (Secondary monochromator)

17. Want monochromatic radiation Brehmsstrahlung = white radiation Characteristic X-rays Monochromators: Many possibilities

18. Euclid, The Elements (300 B.C.) Proposition 21, Book III: The angles in the same segment of a circle are equal to another Johansson monochromator

19. Bragg-Brentano geometry The source S can be:

20. Need detector … Need some slits … S Sample Fixed slits: Smaler area at high angle  Smaller area at high angles Variable slits: Same area at all angles

22. The experiment Got some crystals Want a powder Gets lot of small crystals

24. Want powder Random orientation

25. The result The diffractogram Quartz (Don’t call it spectrum)

26. Why?

27. Identification PDF = JCPDS

28. Indexing

29. Lattice dimensions

31. Strain Particle size

32. Fluorescens

33. CuK  1 = 1.54056 Å CuK  2 = 1.54433 Å Primary and secondary monochromators

34. Rietveld refinement