Powder X-ray diffraction the usesLearning Outcomes

By the end of this section you should:be able to describe the uses of powder X-ray diffraction and why these workbe aware of diffraction/structure databasesunderstand the limitations in each method

Powder XRD the equipment

Uses: fingerprintingSingle or multi-phaseNOT like spectroscopy. Whole patterns match.Two different crystalline phases are present in this pattern one in a very small amount

DatabasesTo 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

ICDDExampleWhy d and not 2 ??

ICDDGood.

ICDDBad.

Search/MatchSearch programs assist in identifying phase mixtures:

Inorganic Crystal Structure DatabaseICSD: ICSD

Fingerprinting..Advantages:relatively quick and easy, can be non-destructive

Problems:need reliable standards - new phases will not be in the PDFsome things in the database are rubbish!often need other (chemical) information to narrow down searchesnot 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 OrientationRemember: 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 FotheringhamThus some diffraction peaks will be enhanced relative to others.

Preferred OrientationIntensity mismatch due to using single crystalSo e.g. all (n00) peaks may be enhanced

Uses: different structuresEven 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 structuresBUT, sometimes you cant really see any changes on visual inspectionThis often happens in open structures where there is space for change of light atomsZeolite A

Uses: polymorphsDifferent polymorphs will have different powder patternse.g. Zn S

Uses: polymorphsK3SO4F: tetragonal & cubic forms

Peak BroadeningIn an X-ray diffraction pattern, peak width depends onthe instrumentradiation not pure monochromaticHeisenberg uncertainty principlefocussing 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 BroadeningIf crystal size < 0.2 m, then peak broadening occursAt

Peak BroadeningWe can calculate the average size of the crystals from the broadening:

Scherrer formulat is the thickness of the crystal, the wavelength, B the Bragg angle.B is the line broadening, by reference to a standard, so thatwhere BS is the halfwidth of the standard material in radians. (A normal halfwidth is around 0.1o)

Peak BroadeningHalfwidth: Full width at half-maximum - FWHMThis 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 determinationHere we see particle size increasing with temperature

Particle size determination: ExamplePeak at 28.2 2 with FWHM of 0.36 2 Standard material has FWHM of 0.16 2 = CuK = 1.540 0.36 = 0.36 x /180 = 0.0063 rad0.16 = 0.16 x /180 = 0.0028 radB = 0.0056 radt = 255 = 0.0255 m

Particle size determinatonAn 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 doesnt make sense!5nm = 50 = e.g. 10 unit cellsIs this sufficient for long range order??

Unit cell refinementAs 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 cellWe minimise the difference, e.g.This is known as least squares refinement. We will come back to this later.

Variable temperature/pressureNeed special apparatusHere (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/PS. 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 advancedStructure refinement the Rietveld methodA 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 dataHugo Rietveld, b1932http://home.wxs.nl/~rietv025/

Uses: Rietveld RefinementHere 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

Uses: more advancedQuantitative 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. Ba2SiO4 c.f. SiO2)Thus uses Rietveld method and takes into account relative scattering from each crystalline phase

SummaryMany different uses for powder X-ray diffraction!Fingerprinting: identifying phases, distinguishing similar materials, identifying polymorphs, (following chemical reactions)Indication of particle size from peak broadeningUnit cell refinementVariable temperature/pressure measurementsCrystal structure refinementQuantitative analysis