1. Ø. Prytz Introduction to diffraction Øystein Prytz January 21 2009

2. Ø. Prytz Interference of waves Constructive and destructive interference Sound, light, ripples in water etc etc  =2n   =(2n+1) 

3. Ø. Prytz Nature of light Newton: particles (corpuscles) Huygens: waves Thomas Young double slit experiment (1801) Path difference  phase difference Light consists of waves ! But remember blackbody radiation and photoelectric effect !

4. Ø. Prytz Discovery of X-rays Wilhelm Röntgen 1895/96 Nobel Prize in 1901 Particles or waves? Not affected by magnetic fields No refraction, reflection or intereference observed If waves, λ  10 -9 m

5. Ø. Prytz Max von Laue The periodicity and interatomic spacing of crystals had been deduced earlier (e.g. Auguste Bravais). von Laue realized that if X-rays were waves with short wavelength, interference phenomena should be observed like in Young’s double slit experiment. Experiment in 1912, Nobel Prize in 1914

6. Ø. Prytz Bragg’s law William Henry and William Lawrence Bragg (father and son) found a simple interpretation of von Laue’s experiment Consider a crystal as a periodic arrangement of atoms, this gives crystal planes Assume that each crystal plane reflects radiation as a mirror Analyze this situation for cases of constructive and destructive interference Nobel prize in 1915

7. Ø. Prytz Derivation of Bragg’s law θ θ θ x Path difference Δ= 2x => phase shift Constructive interference if Δ=nλ This gives the criterion for constructive interference: d hkl Bragg’s law tells you at which angle θ B to expect maximum diffracted intensity for a particular family of crystal planes. For large crystals, all other angles give zero intensity. But what happens if you place a plane in the middle?

8. Ø. Prytz von Laue formulation Scattering angle related to the inverse plane spacing Waves often described using wave vectors The wave vector points in the direction of propogation, and its length inversely proportional to the wave length

9. Ø. Prytz von Laue formulation θ Vector normal to a plane θ

10. Ø. Prytz The reciprocal lattice g is a vector normal to a set of planes, with length equal to the inverse spacing between them Reciprocal lattice vectors a*,b* and c* These vectors define the reciprocal lattice All crystals have a real space lattice and a reciprocal lattice Diffraction techniques map the reciprocal lattice