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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 Sample Detector
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.
Very weak interaction. Thus need lots of electrons, and thus many atoms.
J. J. Thomson, “Conduction of Electricity through Gases”
where r0 is the classical electron radius.
20
2
20
2
3
8
43
8r
cm
e
e
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 )/
http://www.ruppweb.org/xray/comp/scatfac.htm
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
http://www.ruppweb.org/xray/comp/scatfac.htm
0
5
10
15
20
25
30
35
0 0.2 0.4 0.6
sin 0 / (A -1)
f in
ele
ctr
on
s
copper
oxygen
(sin ) /
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.
Bragg (again!!)
• Look at Bragg set-up with different emphasis
hkl1000’s of planes (1000Å = 1m)
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
sourceCollimator
Fixed single crystal
Detector photographic film or area
detector
http://www.matter.org.uk/diffraction/x-ray/laue_method.htm
Max Von Laue 1879-1960
Nobel Prize 1914
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
Movingdetector
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
0 0 -1 0.00 0.11 1 0 0 -2 21.52 0.61 1 0 0 -3 0.15 0.27 1 0 0 -4 245.17 3.01 1 0 0 -5 0.04 0.36 1 0 0 -6 16.09 0.92 1 0 0 -7 0.46 0.40 1 0 0 -8 0.25 0.45 1 0 0 -9 -0.20 0.38 1 0 0 -10 3.44 0.64 1 0 0 -11 -0.31 0.37 1 0 0 -12 -0.04 0.39 1 0 0 -13 -0.15 0.42 1 0 -1 0 0.30 0.15 1 0 -1 -1 237.47 2.80 1 0 1 -1 264.24 2.70 1 0 1 -2 26.53 0.65 1 0 -1 -3 1.63 0.39 1 0 1 -3 2.11 0.32 1 0 -1 -4 2.58 0.46 1 0 1 -4 2.46 0.39 1 0 -1 -5 96.60 2.13 1 0 1 -5 88.31 1.69 1 0 -1 -6 0.65 0.36 1 0 1 -6 0.39 0.38 1 0 -1 -7 2.01 0.58 1 0 1 -7 2.01 0.47 1 0 -1 -8 0.27 0.45 1 0 1 -8 0.32 0.42 1 0 -1 -9 6.73 0.87 1 0 1 -9 6.35 0.68 1 0 -1 -10 -0.46 0.42 1 0 1 -10 0.07 0.38 1 0 -1 -11 0.67 0.51 1 0 1 -11 0.54 0.41 1 0 -1 -12 -0.32 0.47 1 0 1 -12 0.18 0.39 1 0 -1 -13 -0.09 0.47 1 0 1 -13 -0.09 0.45 1 0 -2 0 348.85 3.47 1 0 -2 -1 133.28 2.48 1 0 2 -1 123.01 1.27 1 0 2 -2 148.04 1.54 1 0 -2 -3 60.01 1.75 1 0 2 -3 61.91 1.08 1 0 -2 -4 0.72 0.40 1 0 2 -4 1.20 0.31 1 0 -2 -5 2.93 0.58 1
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!!
Powder 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 planes
Monochr.X-rays
Detector -
• Film
• Counter
Film - Debye Scherrer Camera
Camera radius = R
360
4
R2
S
Debye-Scherrer Camera
Now obsolete!
Peter Debye, 1884-1966
Nobel Prize 1936
Counter - Diffractometer
• Bruker D8 Advance
X-ray tube
detector
sample
More detail
Not all are the same…
Stoe Stadi/P
Detector SampleX-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