Presentation on theme: "Powder X-ray diffraction – the uses"— Presentation transcript:
1Powder X-ray diffraction – the uses Learning OutcomesBy 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 databasesunderstand the limitations in each method
3Uses: fingerprinting Single or multi-phase Two different crystalline phases are present in this pattern – one in a very small amountNOT like spectroscopy. Whole patterns match.
4Databases 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
10Fingerprinting.. Advantages: relatively quick and easy, can be non-destructiveProblems: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.
11Preferred 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
12Preferred Orientation Intensity mismatch – due to using single crystalSo e.g. all (n00) peaks may be enhanced…
13Uses: different structures NaClKClEven 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
14Uses: different structures BUT, sometimes you can’t really see any changes on visual inspection…Zeolite AThis often happens in “open” structures where there is space for change of light atoms
15Different polymorphs will have different powder patterns Uses: polymorphsDifferent polymorphs will have different powder patternse.g. Zn S
16Uses: polymorphsK3SO4F: tetragonal & cubic forms
17Peak Broadening In an X-ray diffraction pattern, peak width depends on the instrumentradiation not pure monochromaticHeisenberg uncertainty principlefocussing geometrythe sample…- a crystalline substance gives rise to sharp lines, whereas a truly amorphous material gives a broad “hump”.What happens between the two?
18Peak BroadeningIf crystal size < 0.2 m, then peak broadening occursAt <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
19Peak 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)
20Peak 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.
21Uses: particle size determination Here we see particle size increasing with temperature30oC1050oC
22Particle size determination: Example Peak at 28.2° 2 with FWHM of 0.36° 2Standard material has FWHM of 0.16° 2 = CuK = Å0.36 ° = 0.36 x /180 = rad0.16 ° = 0.16 x /180 = radB = radt = 255 Å = m
23Particle 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.
24Amorphous / 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??
25Unit 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.
26Variable temperature/pressure Need 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
27BaTiO3 T/P Variable pressure hard to do: neutron diffraction (later) Much of these data actually from dielectric measurements.T. Ishidate, PRL (1997)S. A. Hayward, S. A. T. Redfern, H. J. Stone, M. G. Tucker, K. R. Whittle, W. G. Marshall, Z. Krist. (2005)
28Uses: more advanced Structure refinement – the Rietveld method A refinement technique, not determinationWhole-pattern fitting - not just the Bragg reflectionsNeeds 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 shapesfirst report of application to X-ray dataHugo Rietveld, b1932
29Uses: Rietveld Refinement xyzCa/Ce0.33330.6667(18)Ce0.2337(4)0.25Si0.403(3)0.380(3)O10.316(4)0.467(4)O20.597(5)O30.340(2)0.252(3)0.071(3)O4Here 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,
30Uses: 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
31Summary 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 broadeningUnit cell refinementVariable temperature/pressure measurementsCrystal structure refinementQuantitative analysis