1. Research School of Chemistry &
Diffuse Scattering
D. J. Goossens
AINSE Research Fellow,
Research School of Chemistry &
Department of Physics
ANU

2. What is diffuse scattering?
Diffuse scattering is the scattered intensity that lies between the Bragg peaks.
It tells you about short-range order in the crystal. The Bragg peaks tell you about the unit cell -- the regular, long-range order. But that may not be the whole story.
Some example of diffuse scattering:
Bragg peaks only occupy a few pixels at the centre of each bright region. The rest of the pattern is ‘diffuse scattering’ and conventional analysis ignores it all, and ignores all the information in it…
Bragg peak
Diffuse intensity
X-ray diffuse scattering from benzil, C14H10O2

3. Examples of diffuse scattering.
X-ray diffuse scattering from PCNB, C6Cl5NO2
(h k 1)
Neutron diffuse scattering from PZN, PbZn1/3Nb2/3O3
Neutron diffuse scattering from paraterphenyl, C18D14
…etc…
Yttria stabilised cubic zirconia, hk0.5, X-rays

4. What is diffuse scattering?
Usually when you do a structural study you measure the Bragg reflections In powder diffraction, you might get a pattern that looks something like this:
Powder diffraction pattern of deuterated benzil C14D10O2 at 100K. Inset shows boxed peak as a function of temperature.

5. The Reciprocal lattice
In single crystal diffraction, you measure a bunch of integrated intensities of Bragg reflections.
Each reflection is due to a set of planes of atoms in the crystal.
The set of all possible reflections makes up a grid of points in reciprocal space.

6. A perfect crystal b b* a a* 210 reflection
So say we have a perfect (simple cubic) crystal.
We could measure the Bragg reflections that come off it, and we would get a lattice of reflections in reciprocal space. a* b* b a
2-d cut through a simple cubic crystal, looking down (say) c at the ab plane
210 reflection

7. (2-d cut so we’ll take l = 0)
Structure factor
This diffraction pattern is like a slice or cut through reciprocal space, and we can index the diffraction spots as usual with h, k and l
(2-d cut so we’ll take l = 0)
All the intensity is localised on the reciprocal lattice points, an we can calculate the expected intensity for a given point in the usual way:
(k) 4 3 2 1
(h)

8. Adding Disorder...
What happens when we introduce disorder (static or thermal)?
First: what can disorder look like? b a
Disorder in occupancies (‘Occupational disorder’)
Disorder in positions (‘Displacive disorder’)
And plainly both can occur at once.

9. Other types of disorder
If our scatterers are a bit more complicated, we can have other forms of disorder:
Or bits within the molecule can rotate or twist or whatever…
If our scatterer is say a molecule, then we can have orientational disorder:
And these can occur along with displacive and occupational disorder.

10. Displacements, short-range correlated
Three examples
Direct space
(crystal)
Reciprocal space
(diffraction)
No disorder.
Random displacements
Displacements, short-range correlated

11. Displacements short-range correlated
Looks the same?
If we subtract out the scattering from the Bragg peaks and scale up, what is left?
Random displacements
Displacements short-range correlated

12. Looks the same...but it is not!
If we subtract out the scattering from the Bragg peaks and scale up, what is left?
Random displacements
Displacements short-range correlated, Bragg scattering subtracted…

13. Displacements short-range correlated, Bragg scattering subtracted…
Implications...
That’s why we’re interested in diffuse scattering.
Things that look the same to Bragg scattering look different to diffuse scattering.
The local ordering that diffuse scattering can study is what is truly reflective of the crystal chemistry and physics -- an individual atom does not care what ‘average’ it is supposed to obey, just how it interacts with its neighbours.
The average may be completely non-physical. So if we really want to understand how the structures (and properties) arise, sometimes we need to ‘get inside’ the average using diffuse scattering.
Displacements short-range correlated, Bragg scattering subtracted…

14. Displacements short-range correlated, Bragg scattering subtracted…
More implications
The average may be completely non-physical. So if we really want to understand how the structures (and properties) arise, sometimes we need to ‘get inside’ the average using diffuse scattering.
Diffuse scattering lets us look at the population of local configurations that go into making up the average. We can tackle questions like:
Are atoms tending to push apart? Pull together? Are vacancies clustering or anticlustering? What sorts of defects do we have and how do they interact? How does the position/conformation/attitude of one molecule affect the next? What are the key interactions in propagating the correlations?
Displacements short-range correlated, Bragg scattering subtracted…

15. Other Effects... Random occupancies Positively correlated occupancies
Negatively correlated occupancies

16. Other Effects (2)
Random occupancies (Bragg removed, no structured diffuse)
Positively correlated occupancies
(Bragg removed, diffuse on Bragg positions)
Negatively correlated occupancies
(Bragg removed but positions indicated by white dots)

17. Other Effects (3) -ve occ. corr. +ve occ. corr.
Like letting occupancy and displacement interact…
-ve
occ.
corr.
+ve
occ.
corr.
Type 1 atoms pull together
Type 2 push apart
Like atoms push apart
Unlike atoms pull together
Unlike atoms push apart
Like atoms pull together

18. So...
We study diffuse scattering because it give additional information compared to the Bragg peaks.
Particularly, it tells you about the disorder and short-range-order in the material.
There are many materials where disorder is crucial in determining physical properties…
Eg: Relaxor ferroelectrics like PZN, PbZn1/3Nb2/3O3
Colossal magnetoresistance manganites
Host-guest systems and molecular framework materials
Glassy systems
Molecular crystals

19. Collecting the data
Diffuse scattering can be measured using electrons, X-rays and neutrons.
Neutron
X-ray
Electron
Weak sources (big crystals, slow data collections ~days)
Scattering does not depend on atomic number;
Sensitive to magnetism;
Quantitative data;
Good range of sample environments;
Can see inelastic effects
Bright sources (small crystals, faster experiments ~hours); Wide range of sample environments;
Can’t see inelastic effects
Bright sources (very small crystals or even grains, fast experiments);
Non-quantitative data
Limited sample environments
Etc…

20. This is a neutron school so...
Collecting neutron diffuse scattering…
At a spallation source and;
At a reactor (here!)

21. Collecting Diffuse Scattering at a Spallation Source (ISIS)
11 detectors
64  64 pixels per detector
complete t.o.f. spectrum per pixel

22. Neutron Time of Flight Geometry
angle subtended by 90detector bank
volume of reciprocal space recorded simultaneously with one detector bank.
A-A’ and B-B’ given by detector bank
B-A and B’-A’ given by time-of-flight

23. Benzil Diffuse Scattering
3 crystal orientations
1 detector
symmetry applied
3 crystal orientations
4 detectors
symmetry applied
3 crystal orientations
1 detector
1 crystal orientation
6 detectors
1 crystal orientation
2 detectors
1 crystal orientation
3 detectors
1 crystal orientation
1 detector

24. PZN Diffuse Scattering
10 crystal settings
8 detectors
(h k 0)
apply m3m
symmetry
(h k 0.5)
(h k 1)
nb. full 3D
volume

25. Cu1.8Se (Thanks to Andrew Studer and Sergey Danilkin, ANSTO)
At a Reactor...
Cu1.8Se (Thanks to Andrew Studer and Sergey Danilkin, ANSTO)
Wombat

26. ...still at a reactor
Easiest to picture if we just thing of the equatorial pixels on the 2-d detector…
 = sample angle
Some trigonometry

27. Data Analysis
No unit cells!

28. Considerations Unit cells cannot be considered identical.
Need to model a region of the crystal large enough to contain a statistically valid population of local configurations, and to avoid finite-size effects
Usually upwards of 32 × 32 × 32 unit cells
Maybe 150+ atoms per cell
= 32 × 32 × 32 × 3 × 150 = too many coordinates to fit directly

29. The Approach
Work with the parameters which determine the coordinates – the interatomic interactions. These will be the same from cell to cell.
Use ‘contact vectors’ between atoms:
Use torsional springs within molecules:
Use Ising terms to model occupancies:
We equilibrate a real-space model crystal subject to the imposed interactions and then calculate its diffuse diffraction pattern and compare with the observed, then adjust the interactions accordingly.

30. MC algorithm

31. In Summary
Diffuse scattering contains information about short-range order that is not present in the Bragg peaks. This information relates to the local environments of the atoms and molecules, so can be important in relating structure to function. Diffuse scattering is demanding to measure and analyse, but it can be done and it can reveal important insights. It also produces some quite pretty pictures!

32. More examples of diffuse scattering
CaCSZ
PCNB
CePdSb
DCDNB
YCSZ
33’benzil
Benzil
Fe1-xO
PZN
CMA
Oxide
Molecular
Intermetallic

33. Go back to Disordered Materials Go to Home Page