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Unveiling Electron Diffraction: Understanding Wave Nature and Lattice Structure in TEM

This summary discusses electron diffraction in Transmission Electron Microscopy (TEM), explaining concepts such as reciprocal lattice, de Broglie wavelength, relativistic effects, Ewald Sphere construction, elastic scattering, Cu Kalpha X-ray, indexing diffraction patterns, crystallographic phases, and Bravais lattice determination.

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Unveiling Electron Diffraction: Understanding Wave Nature and Lattice Structure in TEM

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  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 Electron source e- Polycrystalline sample Detector/film/screen

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

  12. (h2k2l2) 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 Orientations of corresponding planes in the real space

  13. 27o 50 nm 15o 10o 0o Determination of the Bravais-lattice of an unknown crystalline phase Tilting series around common axis

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

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