Presentation on theme: "X-ray diffraction – the experiment"— Presentation transcript:
1X-ray diffraction – the experiment Learning OutcomesBy the end of this section you should:understand some of the factors influencing X-ray diffraction outputbe aware of some X-ray diffraction experiments and the information they provideknow the difference between single crystal and powder methods
2Methods and Instruments All are based on:X-ray SourceSampleDetectorSample can be:Single crystalPowder - (what is a powder?!)
3X-rays - interactionsFirst assumption: X-rays elastically scattered by electrons.Second assumption: Spherical, discrete atomsJ. J. Thomson’s classical theory of X-ray scattering.X-ray output is defined through the scattering cross-section.where r0 is the classical electron radius.Very weak interaction. Thus need lots of electrons, and thus many atoms.J. J. Thomson, “Conduction of Electricity through Gases”
4Scattering factor More electrons means more scattering ( Z) Scattering per electron adds together, so helium scatters twice as strongly as HWe define an atomic (X-ray) scattering factor, fj, which depends on:the number of electrons in the atom (Z)the angle of scattering
5Function of deflection angle f varies as a function of angle , usually quoted as a function of (sin )/The more diffuse the electron cloud, the more rapid the reduction in the scattering function with scattering angle.
6Deflection angle / atomic number Different elements show the same trend: note the starting value(sin ) /
7f Z (ish)For = 0, f is equal to the total number of electrons in the atom, sof=0 = ZCa2+ and Cl- both have 18 electrons.So at =0 fCa = 18 = fClBut as increases, Cl- has smaller f as it has a more diffuse electron cloud
8What is important? Lots of scattering centres Large enough crystals (lots of planes)Long range order (otherwise??)Glass crystallising with temperatureBroad, featureless pattern. Some information can be retrieved (e.g. average atomic distances) but no structure.
9Bragg (again!!) Look at Bragg set-up with different emphasis hkl1000’s of planes (1000Å = 1m)Scattering:angle and ZThus the scattering from this plane will reflect which atoms are in the plane. Turn the crystal….
10Bragg (again!!) Scattering: angle and Z hkl d expands Changes d-spacing and atoms within the planesSo we need to either (a) rotate the crystal or (b) have lots of crystals at different orientations simultaneously
11Detector photographic film or area detector Laue MethodWhite X-ray sourceCollimatorFixed single crystalDetector photographic film or area detectorMax Von LaueNobel Prize 1914
18Output List of hkl (each spot represents a plane) and intensity 1000’s of data points needed
19Uses Unit cell determination Crystal structure determination (primary method)We will come to the theory later on…We’ve also used ours to get information on vertebral disks!!
20Powder DiffractionBy “powder”, we mean polycrystalline, so equally we can use a piece of metal, bone, etc.We assume that the crystals are randomly oriented so that there are always some crystals oriented to satisfy the Bragg condition for any set of planesMonochr.X-raysDetector -FilmCounter
25Not all are the same… X-ray tube Furnace Detector Sample Detector Stoe Stadi/P
26OutputPlot of intensity of diffracted beam vs. scattering angle (2)
27The Powder PatternThe whole pattern is a representation of the crystal structureNot like some other techniques like spectroscopyNext section we will examine the uses in more detail, then the details behind the pattern
28SummaryDiffraction experiments consist of a source, a sample and a detectorSamples can be single crystal or “powder” (polycrystalline)Single crystal is a primary technique for structure determinationPowder diffraction relies on a random orientation of (small) crystallites