lecture13-fingerprinting of xrd result
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8/10/2019 Lecture13-Fingerprinting of Xrd Result
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Fingerprinting..
Advantages: relatively quick and easy, can be non-destructive
Problems:
need reliable standards - new phases will not be in thePDF
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 frompreferred orientation, etc. not much good for organics, organometallics.
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Preferred Orientation
Remember: we rely on a randomorientation of crystallites. When crystals are platey or needle-shaped (acicular) they
will pack in a non-random fashion, preferentially exposingsome planes to the incident radiation.
This can also happen if asample is packed down,or a thin film, etc.
Brushite plates, SEM by Anna Fotheringham
Thus some diffraction
peaks will be enhanced
relative to others.
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Preferred OrientationIntensity mismatchdue to using single crystal
So e.g. all (n00) peaks may be enhanced
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Uses: different structures
20 30 40 50 60 70
53816-ICSD
Lambd a: 1.54 178 Magnif: 1 .0 FWHM: 0.200
Space grp: F m -3 m Direct cell: 5.6400 5.6400 5.640 0 90.00 90.00 90.00
20 30 40 50 60 70
53825-ICSD
Lambd a: 1.54 178 Magnif: 1 .0 FWHM: 0.200
Space grp: F m -3 m Direct cell: 6.2800 6.2800 6.280 0 90.00 90.00 90.00
NaCl
KCl
Even if two structures are thesame (and they are chemicallysimilar) differences can beobserved:
Peak positions (unit cell changes)and relative intensities (atoms)
There is another major pointhere:
K+and Cl-are isoelectronic
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Uses: different structures
BUT, sometimes you cantreally see any changes onvisual inspection
This often happens in open
structures where there is space
for change of light atoms
Zeolite A
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Uses: polymorphs
Differentpolymorphs willhave different
powder patternse.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 broadhump.
What happens between the two?
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Peak Broadening
If crystal size < 0.2 m, then peak broadening occurs
At
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Peak Broadening
We can calculate the average size of the crystalsfrom the broadening:
BcosB
9.0t
Scherrer formula
t is the thickness of the crystal, the wavelength, BtheBragg angle.
B is the line broadening, by reference to a standard, so
that 2S
2
M
2BBB
where BSis the halfwidth of the standard material inradians. (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 inferthe shape of the crystals.
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Uses: particle size determination
Here we see particle size increasing with temperature
0
50
100
150
200
15 20 25 30 35 40 45 50 55 60
20 /o
30oC
1050oC
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Particle size determination: ExamplePeak at 28.2 2with FWHM of 0.36 2
Standard material has FWHM of 0.16 2
= CuK= 1.540
0.36 = 0.36 x /180 = 0.0063 rad (Bm)
0.16 = 0.16 x /180 = 0.0028 rad (Bs)
B = 0.0056 rad
t = 255 = 0.0255 m
1.14cos0056.0540.19.0
t
BcosB
9.0
t
2
S
2
M
2BBB
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Particle size determinaton
An estimate, rather than an absolute value - also will bedominated by smallest particles.
Good for indication of trends.
A useful complement to other measurements suchas surface area, electron microscopy etc.
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Amorphous / micro-crystalline?
It can be difficult to distinguish between anamorphous material and a crystalline samplewith very small particle size.
BUT the idea of such a small size crystal being
crystalline doesnt make sense!5nm = 50 = e.g. 10 unit cellsIs this sufficient for longrange order??
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Unit cell refinementAs the peak positions reflect the unit cell
dimensions, it is an easy task to refine theunit cell.
2d sin= and e.g. 1d
h
a
k
b
l
c2
2
2
2
2
2
2
Thus if we can assign hkl values to each peak, we cangain accurate values for the unit cell
2
calcobs ddWe 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 aswe heated the sample upfollowing the change in unit cell
parameters. J. M .S. Skakle, J. G. Fletcher, A. R. West, Dalton 1996 2497
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BaTiO3T/P
S. A. Hayward, S. A. T. Redfern, H. J. Stone, M. G. Tucker,K. R. Whittle, W. G. Marshall, Z. Krist. (2005) 220735.
T. Ishidate, PRL (1997) 78 2397
Variable pressure hard to do: neutron diffraction (later)
Much of these data actually from dielectric measurements.
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Uses: more advanced
Structure refinementthe Rietveld method
A refinementtechnique, not determination
Whole-pattern fitting - not just the Bragg reflections
Needs a MODEL - pattern calculated from model, comparedpoint-by-point with observed pattern.
Originally developed (1967,1969) for use with neutron data- good reproducible peak shapes1977 - first report of application to X-ray data
Hugo Rietveld,
b1932
http://home.wxs.nl/~rietv025/
http://home.wxs.nl/~rietv025/http://home.wxs.nl/~rietv025/ -
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Uses: Rietveld Refinement
x y z
Ca/Ce 0.3333 0.6667 -0.0038(18)
Ce 0.2337(4) -0.0108 0.25
Si 0.403(3) 0.380(3) 0.25
O1 0.316(4) 0.467(4) 0.25
O2 0.597(5) 0.467(4) 0.25
O3 0.340(2) 0.252(3) 0.071(3)
O4 0 0 0.25
Here there was a similarity
between the powder patternof this phase and anexisting onealso chemicalcomposition similar.
J. M. S. Skakle, C. L. Dickson, F. P. Glasser, Powder Diffraction (2000) 15, 234-238
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605040302010
1,600
1,400
1,200
1,000
800600
400
200
0
-200
-400
HA 80.18 %
b-TCP 19.82 %
Uses: more advanced
Quantitative phase analysis (how much of each)
Nave approach - relative intensity of peak maxima?- Consider mixture of Ba,Si,O- Ba component would scatter more than Si component
(e.g. Ba2SiO4c.f. SiO2)
Thus uses Rietveldmethod and takesinto account relativescattering from eachcrystalline phase
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Summary
Many different uses for powder X-ray diffraction!
Fingerprinting: identifying phases, distinguishingsimilar materials, identifying polymorphs, (followingchemical reactions)
Indication of particle size from peak broadening
Unit cell refinement
Variable temperature/pressure measurements Crystal structure refinement
Quantitative analysis
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