1. X-ray diffraction – the experiment
Learning Outcomes
By the end of this section you should:
understand some of the factors influencing X-ray diffraction output
be aware of some X-ray diffraction experiments and the information they provide
know the difference between single crystal and powder methods

2. Methods and Instruments
All are based on:
X-ray Source
Sample
Detector
Sample can be:
Single crystal
Powder - (what is a powder?!)

3. X-rays - interactions
First assumption: X-rays elastically scattered by electrons.
Second assumption: Spherical, discrete atoms
J. J. Thomson’s classical theory of X-ray scattering.
X-ray output is defined through the scattering cross-section.
where r0 is the classical electron radius.
Very weak interaction. Thus need lots of electrons, and thus many atoms.
J. J. Thomson, “Conduction of Electricity through Gases”

4. Scattering factor More electrons means more scattering ( Z)
Scattering per electron adds together, so helium scatters twice as strongly as H
We define an atomic (X-ray) scattering factor, fj, which depends on:
the number of electrons in the atom (Z)
the angle of scattering

5. Function of deflection angle
f varies as a function of angle , usually quoted as a function of (sin )/
The more diffuse the electron cloud, the more rapid the reduction in the scattering function with scattering angle.

6. Deflection angle / atomic number
Different elements show the same trend: note the starting value
(sin ) /

7. f  Z (ish)
For  = 0, f is equal to the total number of electrons in the atom, so
f=0 = Z
Ca2+ and Cl- both have 18 electrons.
So at =0 fCa = 18 = fCl
But as  increases, Cl- has smaller f as it has a more diffuse electron cloud

8. What is important? Lots of scattering centres
Large enough crystals (lots of planes)
Long range order (otherwise??)
Glass crystallising with temperature
Broad, featureless pattern. Some information can be retrieved (e.g. average atomic distances) but no structure.

9. Bragg (again!!) Look at Bragg set-up with different emphasis
hkl
1000’s of planes (1000Å = 1m)
Scattering:
angle and Z
Thus the scattering from this plane will reflect which atoms are in the plane. Turn the crystal….

10. Bragg (again!!) Scattering: angle and Z hkl d expands
Changes d-spacing and atoms within the planes
So we need to either (a) rotate the crystal or (b) have lots of crystals at different orientations simultaneously

11. Detector photographic film or area detector
Laue Method
White X-ray source
Collimator
Fixed single crystal
Detector photographic film or area detector
Max Von Laue
Nobel Prize 1914

12. Laue Method

13. Laue Method Each spot corresponds to a different crystal plane USES:
alignment of single crystal
info on unit cell
info on imperfections, defects in crystal
Not so common these days…

14. 4-circle Method Monochromatic X-rays Moving detector
Movingsingle crystal
Crystal can be oriented so that intensities for any (hkl) value can be measured

15. Actual instrument

16. Now more common to use area detector which removes one circle.

17. Bruker SMART
Area detector

18. Output List of hkl (each spot represents a plane) and intensity
1000’s of data points needed

19. Uses Unit cell determination
Crystal structure determination (primary method)
We will come to the theory later on…
We’ve also used ours to get information on vertebral disks!!

20. Powder Diffraction
By “powder”, we mean polycrystalline, so equally we can use a piece of metal, bone, etc.
We assume that the crystals are randomly oriented so that there are always some crystals oriented to satisfy the Bragg condition for any set of planes
Monochr.
X-rays
Detector -
Film
Counter

21. Film - Debye Scherrer Camera
Camera radius = R

22. Debye-Scherrer Camera
Now obsolete!
Peter Debye,
Nobel Prize 1936

23. Counter - Diffractometer
Bruker D8 Advance
detector
X-ray tube
sample

24. More detail

25. Not all are the same… X-ray tube Furnace Detector Sample Detector
Stoe Stadi/P

26. Output
Plot of intensity of diffracted beam vs. scattering angle (2)

27. The Powder Pattern
The whole pattern is a representation of the crystal structure
Not like some other techniques like spectroscopy
Next section we will examine the uses in more detail, then the details behind the pattern

28. Summary
Diffraction experiments consist of a source, a sample and a detector
Samples can be single crystal or “powder” (polycrystalline)
Single crystal is a primary technique for structure determination
Powder diffraction relies on a random orientation of (small) crystallites