Powder Xray diffraction the uses

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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

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Powder XRD the equipment
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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.
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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

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ICDD

• Example

Why d and not 2? ??
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ICDD

• Good.

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ICDD

• Bad.

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Search/Match

• Search programs assist in identifying phase
  mixtures

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Inorganic Crystal Structure Database

• ICSD ICSD

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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.

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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
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Preferred Orientation

• Intensity mismatch due to using single crystal

So e.g. all (n00) peaks may be enhanced
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Uses different structures

• 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
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Uses different structures

• BUT, sometimes you cant really see any changes
  on visual inspection

Zeolite A
This often happens in open structures where
there is space for change of light atoms
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Uses polymorphs

• Different polymorphs will have different powder
  patterns
• e.g. Zn S

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Uses polymorphs

• K3SO4F tetragonal cubic forms

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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?

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Peak Broadening

• If crystal size lt 0.2 ?m, then peak broadening
  occurs
• At lt50nm, becomes significant.
• Why?

Braggs 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
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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)
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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.
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Uses particle size determination

• Here we see particle size increasing with
  temperature

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Particle size determination Example

• Peak at 28.2 2? with FWHM of 0.36 2?
• Standard material has FWHM of 0.16 2?
• ? CuK? 1.540 Å

0.36 0.36 x ?/180 0.0063 rad 0.16 0.16
x ?/180 0.0028 rad B 0.0056 rad
t 255 Å 0.0255 ?m
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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.

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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 doesnt make sense! 5nm 50Å e.g.
10 unit cells Is this sufficient for long range
order??
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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.
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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 1996 2497
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BaTiO3 T/P
Variable pressure hard to do neutron diffraction
(later) Much of these data actually from
dielectric measurements.
T. Ishidate, PRL (1997) 78 2397
S. A. Hayward, S. A. T. Redfern, H. J. Stone, M.
G. Tucker, K. R. Whittle, W. G. Marshall, Z.
Krist. (2005) 220 735.
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Uses more advanced

• Structure refinement the Rietveld method

A refinement technique, not determination Whole-p
attern 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 1977 - first report of application to
X-ray data
Hugo Rietveld, b1932
http//home.wxs.nl/rietv025/
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Uses Rietveld Refinement
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, 234-238
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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
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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