Lecture13-Fingerprinting of Xrd Result

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


21/222Th Degrees

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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Lecture13-Fingerprinting of Xrd Result