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Øystein Prytz Introduction to diffraction 2 Øystein Prytz

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Summary from last time θ Vector normal to a plane

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Øystein Prytz The structure factor B A Origin Incoming wave: Wave scattered from atom A: Equivalent expression for atom B Total scattered wave detected far away: Can be calculated for all scattering vectors (angles) Δk, but usually we only concern ourselves with Δk=g (destructive interference in all other cases)

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Øystein Prytz The structure factor for copper fcc lattice with one atom in [000] relative to the lattice point. r 1 = [0,0,0], r 2 = [1/2,1/2,0], r 3 = [1/2,0,1/2], r 4 = [0,1/2,1/2]

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Øystein Prytz The structure factor for copper Result: hkl even: F=f Cu (1+1+1+1)=4f Cu hkl odd: F=f Cu (1+1+1+1)=4f Cu h odd, k and l even: F=f Cu (1-1+1-1)=0 h and k odd, l even: F=f Cu (1+1-1-1)=0 Conclusion: hkl even or odd gives allowed reflections, hkl mixed gives forbidden reflections

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Øystein Prytz The reciprocal lattice for bcc iron? Body centered cubic lattice One atom per lattice point, [000] relative to the lattice point What is the reciprocal lattice?

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