X-ray diffraction

1. X-ray diffraction

2. X-rays d   set of lattice planes d sin  X-ray diffraction Braggs' law = 2dhkl sin hkl From this set of planes, only get reflection at one angle - 

3. X-rays X-ray diffraction Braggs' law = 2dhkl sin hkl another set of lattice planes

4.   As d —> small, —> large ( is constant) X-ray diffraction Braggs' law = 2dhkl sin hkl X-rays another set of lattice planes Different sets of planes reflect at different  angles

5. Ewald construction Think of set of planes reflecting in x-ray beam

6. Ewald construction Think of set of planes reflecting in x-ray beam Center sphere on specimen origin x-ray beam is a sphere diameter

7. Ewald construction Think of set of planes reflecting in x-ray beam Center sphere on specimen origin x-ray beam is a sphere diameter Construct lines as below

8. Ewald construction Think of set of planes reflecting in x-ray beam Center sphere on specimen origin x-ray beam is a sphere diameter Construct lines as below

9. Ewald construction

10. Ewald construction

11. Ewald construction

12. Ewald construction

13. Ewald construction

14. Ewald construction

15. Ewald construction

16. Ewald construction Most common in single crystal studies is to move (usually rotate) crystal Consider crystal placed at sphere center oriented w/ planes of points in reciprocal lattice as below

17. Ewald construction Looking down on one plane of points.... the equatorial plane:

18. Ewald construction Looking down on one plane of points.... the equatorial plane No points on sphere (here, in 2-D, a circle); must rotate reciprocal lattice to observe reflections. rotate around axis here, perpendicular to screen

19. Ewald construction Looking down on one plane of points.... the equatorial plane Must rotate reciprocal lattice to observe reflections. rotate around axis here, perpendicular to screen

20. Ewald construction Looking down on one plane of points.... the equatorial plane Must rotate reciprocal lattice to observe reflections. rotate around axis here, perpendicular to screen

21. Ewald construction Looking down on one plane of points.... the equatorial plane Must rotate reciprocal lattice to observe reflections. rotate around axis here, perpendicular to screen

22. Ewald construction hk0 reflected rays all lie in the equatorial plane.

23. Ewald construction hk0 reflected rays all lie in the equatorial plane. hk1 reflected rays lie in a cone.

24. Ewald construction hk0 reflected rays all lie in the equatorial plane. hk1 reflected rays lie in a cone.

25. Ewald construction Sheet of film or image paper wrapped cylindrically around crystal....

26. Ewald construction Sheet of film or image paper wrapped cylindrically around crystal.... looks like this after x-ray exposure of oscillating crystal .....when flattened:

27. use polycrystalline sample real space reciprocal space only one set of planes - one (hkl) Ewald construction To see reflections: move sphere move crystal change sphere size

28. use polycrystalline sample real space reciprocal space only one set of planes - one (hkl) Ewald construction To see reflections: move sphere move crystal change sphere size

29. Ewald construction reciprocal lattice representation Ewald sphere

30. Ewald construction