1. X-ray diffraction

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

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

4. Braggs' law  = 2dhkl sin hkl
X-ray diffraction
Braggs' law  = 2dhkl sin hkl
X-rays
As d —> small,
—> large ( is constant) 
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. Looking down on one plane of points.... the equatorial plane
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. Looking down on one plane of points.... the equatorial plane
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. Looking down on one plane of points.... the equatorial plane
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. Looking down on one plane of points.... the equatorial plane
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 on a cone.

24. Ewald construction
hk0 reflected rays all lie in the equatorial plane.
hk1 reflected rays lie on 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
Ewald construction
To see reflections:
move sphere
move crystal
change sphere size
use polycrystalline sample
real space
reciprocal space
only one set
of planes -
one (hkl)

28. Ewald construction
reciprocal
lattice
representation
Ewald sphere

29. Ewald construction