Presentation on theme: "X-ray diffraction – the experiment Learning Outcomes By the end of this section you should: understand some of the factors influencing X-ray diffraction."— Presentation transcript:
X-ray diffraction – the experiment Learning Outcomes By the end of this section you should: understand some of the factors influencing X-ray diffraction output be aware of some X-ray diffraction experiments and the information they provide know the difference between single crystal and powder methods
Methods and Instruments All are based on: X-ray Source SampleDetector Sample can be: Single crystal Powder - (what is a powder?!)
X-rays - interactions First assumption: X-rays elastically scattered by electrons. Second assumption: Spherical, discrete atoms J. J. Thomsons classical theory of X-ray scattering. X-ray output is defined through the scattering cross-section. Very weak interaction. Thus need lots of electrons, and thus many atoms. J. J. Thomson, Conduction of Electricity through Gases where r 0 is the classical electron radius.
Scattering factor More electrons means more scattering ( Z) Scattering per electron adds together, so helium scatters twice as strongly as H We define an atomic (X-ray) scattering factor, f j, which depends on: the number of electrons in the atom (Z) the angle of scattering
Function 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.
Deflection angle / atomic number Different elements show the same trend: note the starting value (sin ) /
f Z (ish) For = 0, f is equal to the total number of electrons in the atom, so f =0 = Z Ca 2+ and Cl - both have 18 electrons. So at =0 f Ca = 18 = f Cl But as increases, Cl - has smaller f as it has a more diffuse electron cloud
What is important? Lots of scattering centres Large enough crystals (lots of planes) Long range order (otherwise??) Glass crystallising with temperature Broad, featureless pattern. Some information can be retrieved (e.g. average atomic distances) but no structure.
Bragg (again!!) Look at Bragg set-up with different emphasis hkl 1000s of planes (1000Å = 1 m) Scattering: angle and Z Thus the scattering from this plane will reflect which atoms are in the plane. Turn the crystal….
Bragg (again!!) d expands Changes d-spacing and atoms within the planes So we need to either (a) rotate the crystal or (b) have lots of crystals at different orientations simultaneously hkl Scattering: angle and Z
Laue Method White X- ray source Collimator Fixed single crystal Detector photographic film or area detector Max Von Laue Nobel Prize 1914
Laue Method Each spot corresponds to a different crystal plane USES: alignment of single crystal info on unit cell info on imperfections, defects in crystal Not so common these days…
4-circle Method Monochromatic X-rays Moving detector Moving single crystal Crystal can be oriented so that intensities for any (hkl) value can be measured
Now more common to use area detector which removes one circle.
Bruker SMART Area detector
Output List of hkl (each spot represents a plane) and intensity 1000s of data points needed
Uses Unit cell determination Crystal structure determination (primary method) We will come to the theory later on… Weve also used ours to get information on vertebral disks!!
Powder Diffraction By 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 planes Monochr. X-rays Detector - Film Counter
Film - Debye Scherrer Camera Camera radius = R
Debye-Scherrer Camera Now obsolete! Peter Debye, Nobel Prize 1936
Not all are the same… Stoe Stadi/P DetectorSample X-ray tube Furnace Detector
Output Plot of intensity of diffracted beam vs. scattering angle (2 )
The Powder Pattern The whole pattern is a representation of the crystal structure Not like some other techniques like spectroscopy Next section we will examine the uses in more detail, then the details behind the pattern
Summary Diffraction experiments consist of a source, a sample and a detector Samples can be single crystal or powder (polycrystalline) Single crystal is a primary technique for structure determination Powder diffraction relies on a random orientation of (small) crystallites