1. Electron diffraction
Øystein Prytz

2. Summary from last time θ
Reciprocal lattice of FCC structure is BCC

3. Wave nature of electrons
Wavelength of the electrons determined by the de Broglie formula:
Electrons accellerated in 200 kV potential travel at ~0.7c, need to consider relativistic effects:

4. Electron diffraction from polycrystalline sample
Detector/film/screen
Electron source e-
Polycrystalline sample

5. Electron diffraction from polycrystalline sample

6. Basic architecture of a TEM
Electron source
Electron beam
Specimen
Electromagnetic lenses
Viewing screen

7. Simple beam path

8. The Ewald Sphere (’limiting sphere construction’)
Elastic scattering: k k’
The observed diffraction pattern is the part of the reciprocal lattice that is intersected by the Ewald sphere g

9. The Ewald Sphere is flat (almost)
Cu Kalpha X-ray:  = 150 pm => small k
Electrons at 200 kV:  = 2.5 pm => large k

10. 50 nm

11. Camera constant
Film plate
R=L tan2θB ~ 2LsinθB
2dsinθB =λ ↓
R=Lλ/d

12. Indexing diffraction patterns
The g vector to a reflection is normal to the corresponding (h k l) plane and IgI=1/dnh nk nl
Measure Ri and the angles between
the reflections
- Calculate di , i=1,2,3 (=K/Ri)
Compare with tabulated/theoretical
calculated d-values of possible phases
Compare Ri/Rj with tabulated values for
cubic structure.
g1,hkl+ g2,hkl=g3,hkl (vector sum must be ok)
Perpendicular vectors: gi ● gj = 0
Zone axis: gi x gj =[HKL]z
All indexed g must satisfy: g ● [HKL]z=0
(h2k2l2)
Orientations of corresponding
planes in the real space

13. Determination of the Bravais-lattice of an unknown crystalline phase
50 nm
Tilting series around common axis

14. Bravais-lattice and cell parameters
100
110
111
010
011
001
101
[011]
[100]
[101]
d = L λ / R