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Introduction to diffraction

Introduction to diffraction. Øystein Prytz January 21 2009. Interference of waves. Constructive and destructive interference Sound, light, ripples in water etc etc. =(2n+1). =2n. Nature of light. Newton: particles ( corpuscles) Huygens: waves

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Introduction to diffraction

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  1. Introduction to diffraction Øystein Prytz January 21 2009

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

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

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

  8. 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. von Laue formulation Vector normal to a plane θ θ

  10. 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

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