powder x-ray diffraction – the uses learning outcomes by the end of this section you should: be...

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

Powder XRD – the equipment

Uses: fingerprinting

• Single or multi-phase

NOT like spectroscopy. Whole patterns match.

Two different crystalline phases are present in this pattern – one in a very small amount

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

ICDD

Example

Why d and not 2 ??

ICDD

Good….

ICDD

Bad….

Search/Match

Search programs assist in identifying phase mixtures:

Inorganic Crystal Structure Database

ICSD: ICSD

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.

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.

This can also happen if a sample is packed down, or a thin film, etc.

Brushite plates, SEM by Anna Fotheringham

Thus some diffraction peaks will be enhanced relative to others.

Preferred OrientationIntensity mismatch – due to using single crystal

So e.g. all (n00) peaks may be enhanced…

Uses: different structures

20 30 40 50 60 70

53816-ICSDLambda: 1.54178 Magnif: 1.0 FWHM: 0.200Space grp: F m -3 m Direct cell: 5.6400 5.6400 5.6400 90.00 90.00 90.00

20 30 40 50 60 70

53825-ICSDLambda: 1.54178 Magnif: 1.0 FWHM: 0.200Space grp: F m -3 m Direct cell: 6.2800 6.2800 6.2800 90.00 90.00 90.00

NaCl

KCl

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

Uses: different structures

BUT, sometimes you can’t really see any changes on visual inspection…

This often happens in “open” structures where there is space for change of light atoms

Zeolite A

Uses: polymorphs

Different polymorphs will have different powder patterns

e.g. Zn S

Uses: polymorphs

K3SO4F: tetragonal & cubic forms

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?

Peak Broadening

If crystal size < 0.2 m, then peak broadening occurs

At <50nm, becomes significant.

Why?

Bragg’s 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

Peak Broadening

We can calculate the average size of the crystals from the broadening:

BcosB

9.0t

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 2

S2M

2 BBB

where BS is the halfwidth of the standard material in radians. (A normal halfwidth is around 0.1o)

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.

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 6020 / o

30oC

1050oC

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

1.14cos0056.0

540.19.0

t

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.

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 doesn’t make sense!5nm = 50Å = e.g. 10 unit cellsIs this sufficient for long range order??

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. 1d

ha

kb

lc2

2

2

2

2

2

2

Thus if we can assign hkl values to each peak, we can gain accurate values for the unit cell

2calcobs ddWe minimise the difference, e.g.

This is known as “least squares” refinement. We will come back to this later.

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

BaTiO3 T/P

S. A. Hayward, S. A. T. Redfern, H. J. Stone, M. G. Tucker, K. R. Whittle, W. G. Marshall, Z. Krist. (2005) 220 735.

T. Ishidate, PRL (1997) 78 2397

Variable pressure hard to do: neutron diffraction (later)

Much of these data actually from dielectric measurements.

Uses: more advanced

Structure refinement – the Rietveld method

A refinement technique, not determination

Whole-pattern 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 shapes1977 - first report of application to X-ray data

Hugo Rietveld, b1932

http://home.wxs.nl/~rietv025/

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 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

2Th Degrees605040302010

Cou

nts

1,600

1,400

1,200

1,000

800

600

400

200

0

-200

-400

HA 80.18 %b-TCP 19.82 %

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

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