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: Can be calculated for all scattering vectors (angles) Δk, but usually we only concern ourselves with Δk=g (destructive interference in all other cases)

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]

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

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?

Introduction to diffraction 2

Introduction to diffraction 2

Presentation Transcript

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