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Introduction to diffraction 2

Introduction to diffraction 2. Øystein Prytz. Summary from last time. θ. Vector normal to a plane. The structure factor. Incoming wave:. B. Wave scattered from atom A:. A. Equivalent expression for atom B. Origin. Total scattered wave detected far away:.

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Introduction to diffraction 2

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  1. Introduction to diffraction 2 Øystein Prytz

  2. Summary from last time θ Vector normal to a plane

  3. The structure factor Incoming wave: B Wave scattered from atom A: A Equivalent expression for atom B Origin 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)

  4. The structure factor for copper • fcc lattice with one atom in [000] relative to the lattice point. • r1= [0,0,0], r2= [1/2,1/2,0], r3= [1/2,0,1/2], r4= [0,1/2,1/2]

  5. The structure factor for copper • Result: • hkl even: F=fCu(1+1+1+1)=4fCu • hkl odd: F=fCu(1+1+1+1)=4fCu • h odd, k and l even: F=fCu(1-1+1-1)=0 • h and k odd, l even: F=fCu(1+1-1-1)=0 • Conclusion: hkl even or odd gives allowed reflections, hkl mixed gives forbidden reflections

  6. 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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