1. Powder X-ray diffraction – the uses
Learning Outcomes
By the end of this section you should:
be able to describe the uses of powder X-ray diffraction and why these “work”
be aware of diffraction/structure databases
understand the limitations in each method

2. Powder XRD – the equipment

3. Uses: fingerprinting Single or multi-phase
Two different crystalline phases are present in this pattern – one in a very small amount
NOT like spectroscopy. Whole patterns match.

4. Databases To match, we need a very large database of powder patterns
ICDD (International Centre for Diffraction Data) Powder Diffraction File contains (2007) 199,574 entries (172,360 inorganic & 30,728 organic)
In ye olden days it was called JCPDS…(Joint Committee for Powder Diffraction Standards) and before that ASTM

5. ICDD
Example
Why d and not 2 ??

6. ICDD
Good….

7. ICDD
Bad….

8. Search/Match
Search programs assist in identifying phase mixtures:

9. Inorganic Crystal Structure Database
ICSD: ICSD

10. Fingerprinting.. Advantages:
relatively quick and easy, can be non-destructive
Problems:
need reliable standards - new phases will not be in the PDF
some things in the database are rubbish!
often need other (chemical) information to narrow down searches
not very sensitive - can “hide” up to 10% impurities (depending on relative “weights” – see later)
problems from preferred orientation, etc.
not much good for organics, organometallics.

11. Preferred Orientation
Remember: we rely on a random orientation of crystallites.
When crystals are platey or needle-shaped (acicular) they will pack in a non-random fashion, preferentially exposing some planes to the incident radiation.
Thus some diffraction peaks will be enhanced relative to others.
This can also happen if a sample is packed down, or a thin film, etc.
Brushite plates, SEM by Anna Fotheringham

12. Preferred Orientation
Intensity mismatch – due to using single crystal
So e.g. all (n00) peaks may be enhanced…

13. Uses: different structures
NaCl
KCl
Even if two structures are the same (and they are chemically similar) differences can be observed:
Peak positions (unit cell changes) and relative intensities (atoms)
There is another major point here:
K+ and Cl- are isoelectronic

14. Uses: different structures
BUT, sometimes you can’t really see any changes on visual inspection…
Zeolite A
This often happens in “open” structures where there is space for change of light atoms

15. Different polymorphs will have different powder patterns
Uses: polymorphs
Different polymorphs will have different powder patterns
e.g. Zn S

16. Uses: polymorphs
K3SO4F: tetragonal & cubic forms

17. Peak Broadening In an X-ray diffraction pattern, peak width depends on
the instrument
radiation not pure monochromatic
Heisenberg uncertainty principle
focussing geometry
the sample…
- a crystalline substance gives rise to sharp lines, whereas a truly amorphous material gives a broad “hump”.
What happens between the two?

18. Peak Broadening
If crystal size < 0.2 m, then peak broadening occurs
At <50nm, becomes significant.
Why?
Bragg’s law gives the condition for constructive interference.
At slightly higher  than the Bragg angle, each plane gives a “lag” in the diffracted beam.
For many planes, these end up cancelling out and thus the net diffraction is zero.
In small crystals, there are relatively fewer planes, so there is a “remanent” diffraction

19. Peak Broadening
We can calculate the average size of the crystals from the broadening:
Scherrer formula
t is the thickness of the crystal,  the wavelength, B the Bragg angle.
B is the line broadening, by reference to a standard, so that
where BS is the halfwidth of the standard material in radians. (A normal halfwidth is around 0.1o)

20. Peak Broadening Halfwidth: “Full width at half-maximum” - FWHM
This can be different in different directions (anisotropic), so by noting which peaks are broadened we can also infer the shape of the crystals.

21. Uses: particle size determination
Here we see particle size increasing with temperature
30oC
1050oC

22. Particle size determination: Example
Peak at 28.2° 2 with FWHM of 0.36° 2
Standard material has FWHM of 0.16° 2
 = CuK = Å
0.36 ° = 0.36 x /180 = rad
0.16 ° = 0.16 x /180 = rad
B = rad
t = 255 Å = m

23. Particle size determinaton
An estimate, rather than an absolute value - also will be dominated by smallest particles.
Good for indication of trends.
A useful complement to other measurements such as surface area, electron microscopy etc.

24. Amorphous / micro-crystalline?
It can be difficult to distinguish between an amorphous material and a crystalline sample with very small particle size.
BUT the idea of such a small size “crystal” being crystalline doesn’t make sense!
5nm = 50Å = e.g. 10 unit cells
Is this sufficient for long range order??

25. Unit cell refinement
As the peak positions reflect the unit cell dimensions, it is an “easy” task to refine the unit cell.
2d sin =  and e.g.
Thus if we can assign hkl values to each peak, we can gain accurate values for the unit cell
We minimise the difference, e.g.
This is known as “least squares” refinement. We will come back to this later.

26. Variable temperature/pressure
Need special apparatus
Here (see previous) we could follow a phase transition as we heated the sample up – following the change in unit cell parameters.
J. M .S. Skakle, J. G. Fletcher, A. R. West, Dalton

27. BaTiO3 T/P Variable pressure hard to do: neutron diffraction (later)
Much of these data actually from dielectric measurements.
T. Ishidate, PRL (1997)
S. A. Hayward, S. A. T. Redfern, H. J. Stone, M. G. Tucker, K. R. Whittle, W. G. Marshall, Z. Krist. (2005)

28. Uses: more advanced Structure refinement – the Rietveld method
A refinement technique, not determination
Whole-pattern fitting - not just the Bragg reflections
Needs a MODEL - pattern calculated from model, compared point-by-point with observed pattern.
Originally developed (1967,1969) for use with neutron data
- good reproducible peak shapes
first report of application to X-ray data
Hugo Rietveld, b1932

29. Uses: Rietveld Refinementx y z
Ca/Ce
0.3333
0.6667
(18) Ce
0.2337(4)
0.25 Si
0.403(3)
0.380(3) O1
0.316(4)
0.467(4) O2
0.597(5) O3
0.340(2)
0.252(3)
0.071(3) O4
Here there was a similarity between the powder pattern of this phase and an existing one – also chemical composition similar.
J. M. S. Skakle, C. L. Dickson, F. P. Glasser, Powder Diffraction (2000) 15,

30. Uses: more advanced Quantitative phase analysis (how much of each)
Naïve approach - relative intensity of peak maxima?
- Consider mixture of Ba,Si,O
- Ba component would scatter more than Si component (e.g. Ba2SiO4 c.f. SiO2)
Thus uses Rietveld method and takes into account relative scattering from each crystalline phase

31. Summary Many different uses for powder X-ray diffraction!
Fingerprinting: identifying phases, distinguishing similar materials, identifying polymorphs, (following chemical reactions)
Indication of particle size from peak broadening
Unit cell refinement
Variable temperature/pressure measurements
Crystal structure refinement
Quantitative analysis