Diffuse Scattering

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• Diffuse Scattering

D. J. Goossens AINSE Research Fellow, Research
School of Chemistry Department of Physics ANU
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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
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Examples of diffuse scattering.
X-ray diffuse scattering from PCNB, C6Cl5NO2
Neutron diffuse scattering from PZN,
PbZn1/3Nb2/3O3
Neutron diffuse scattering from paraterphenyl,
C18D14
etc
Yttria stabilised cubic zirconia, hk0.5, X-rays
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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
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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.
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A perfect crystal
So say we have a perfect (simple cubic) crystal.
b
a
2-d cut through a simple cubic crystal, looking
down (say) c at the ab plane
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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 well take l 0)
(k) 4 3 2 1 0
0 1 2 3 4 (h)
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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.
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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.
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Three examples
Direct space (crystal)
Reciprocal space (diffraction)
No disorder.
Random displacements
Displacements, short-range correlated
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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
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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
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Implications...
Thats why were 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
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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
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Other Effects...
Positively correlated occupancies
Random occupancies
Negatively correlated occupancies
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Other Effects (2)
Positively correlated occupancies (Bragg removed,
diffuse on Bragg positions)
Random occupancies (Bragg removed, no structured
diffuse)
Negatively correlated occupancies (Bragg removed
but positions indicated by white dots)
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Other Effects (3)
Like letting occupancy and displacement
interact
-ve occ. corr.
ve occ. corr.
Type 1 atoms pull together Type 2 push apart
Unlike atoms push apart Like atoms pull together
Like atoms push apart Unlike atoms pull together
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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
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Collecting the data
Diffuse scattering can be measured using
electrons, X-rays and neutrons.
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This is a neutron school so...

• Collecting neutron diffuse scattering
• At a spallation source and
• At a reactor (here!)

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Collecting Diffuse Scattering at a Spallation
Source (ISIS)
11 detectors
64 ? 64 pixels per detector
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Neutron Time of Flight Geometry
A-A and B-B given by detector bank B-A and
B-A given by time-of-flight
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Benzil Diffuse Scattering
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PZN Diffuse Scattering
nb. full 3D volume
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At a Reactor...
Cu1.8Se(Thanks to Andrew Studer and Sergey
Danilkin, ANSTO)
Wombat
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...still at a reactor
Easiest to picture if we just thing of the
equatorial pixels on the 2-d detector
? sample angle
Some trigonometry
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Data Analysis
No unit cells!
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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

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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.

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MC algorithm
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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!
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More examples of diffuse scattering
Intermetallic
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