Electron diffraction Øystein Prytz.

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Presentation transcript:

Electron diffraction Øystein Prytz

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

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:

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

Electron diffraction from polycrystalline sample

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

Simple beam path

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

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

50 nm

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

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

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

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