Electron diffraction ystein Prytz Prytz Summary from last

Electron diffraction Øystein Prytz Ø. Prytz

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

Wave nature of electrons • Wavelength of the electrons determined by the de Broglie formula: • Electrons accellerated in 200 k. V potential travel at ~0. 7 c, need to consider relativistic effects: Ø. Prytz

Electron diffraction from polycrystalline sample Electron source e. Polycrystalline sample Detector/film/screen Ø. Prytz

Electron diffraction from polycrystalline sample Ø. Prytz

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

Simple beam path Ø. Prytz

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

The Ewald Sphere is flat (almost) Cu Kalpha X-ray: = 150 pm => small k Electrons at 200 k. V: = 2. 5 pm => large k Ø. Prytz

50 nm Ø. Prytz

Camera constant R=L tan 2θB ~ 2 LsinθB 2 dsinθB =λ ↓ R=Lλ/d Film plate Ø. Prytz

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

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

Bravais-lattice and cell parameters 011 111 001 c 101 b 010 a Ø. Prytz 110 100 [011] [100] d=Lλ/R [101]