X-ray diffraction – the experiment

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

X-ray Source Sample Detector Methods and Instruments All are based on: • 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. 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”

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, fj, 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. http://www.ruppweb.org/xray/comp/scatfac.htm

(sin ) / Deflection angle / atomic number Different elements show the same trend: note the starting value http://www.ruppweb.org/xray/comp/scatfac.htm

f  Z (ish) For  = 0, f is equal to the total number of electrons in the atom, so f=0 = Z Ca2+ and Cl- both have 18 electrons. So at =0 fCa = 18 = fCl 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.

Scattering: angle and Z hkl 1000’s of planes (1000Å = 1m) Bragg (again!!) • Look at Bragg set-up with different emphasis Thus the scattering from this plane will reflect which atoms are in the plane. Turn the crystal….

Scattering: angle and Z hkl Bragg (again!!) 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 d expands

Detector photographic film or area detector White X-ray source Collimator Fixed single crystal Laue Method Max Von Laue 1879-1960 Nobel Prize 1914 http://www.matter.org.uk/diffraction/x-ray/laue_method.htm

Laue Method http://www-xray.fzu.cz/xraygroup/www/laue.html

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 Movingsingle crystal Crystal can be oriented so that intensities for any (hkl) value can be measured

Actual instrument http://www.lks.physik.uni-erlangen.de/equipmen/equipmen.html

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 1000’s of data points needed

Uses • 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!!

Detector - • Film • Counter Monochr. X-rays 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

Film - Debye Scherrer Camera Camera radius = R

Debye-Scherrer Camera Now obsolete! Peter Debye, 1884-1966 Nobel Prize 1936

Counter - Diffractometer • Bruker D8 Advance detector X-ray tube sample

More detail

Not all are the same… X-ray tube Stoe Stadi/P Furnace Detector Sample 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

X-ray diffraction – the experiment

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