xrd slides/intro from penn state university

xrd slides penn state university

1. X-ray diffraction

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

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

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

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

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

7. 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
Ewald construction

8. 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
Ewald construction

9. Ewald construction

10. Ewald construction

11. Ewald construction

12. Ewald construction

13. Ewald construction

14. Ewald construction

15. Ewald construction

16. 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
Ewald construction

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

18. 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
Ewald construction

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

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

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

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

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

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

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

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

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

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

29. Ewald construction
reciprocal
lattice
representationEwald sphere

30. Ewald construction