Thinking in Reciprocal Space PDF
Preview Thinking in Reciprocal Space
Thinking in Reciprocal Space Apurva Mehta Outline Introduce Reciprocal Space Reciprocal Space maybe at first appear strange Examples thinking in reciprocal space makes intepretting scattering experiments easier. Why X-ray Scattering? Structure of Materials 10s of nm to A Scattering Physics X-ray lens with resolution better than ~10nm don’t exist image sample light lens Sample Image Scattering Space Space Space X-ray Scattering/diffraction is about probing the structure without a lens Sample to Scattering Space Diffraction Pattern: Contains all the contrast relevant l information at the 4q resolution of l/2sin(q) Transformation of distance into angle Fourier Transform: sample space scattering space Scattering Physics: Bragg’s Law Real Space 2dsin(q) = l 2q 1/2d =sin(q)/l d 1. Distance Angle “Reciprocal” relation 2. Fundamental unit is not q but sin(q)/l Fundamental Units for scattering s = sin(q)/l Q = 4p sin(q)/l Think in Q Or provide both q and l l= hc/E – synchrotron units are E Scattering Physics Elastic Scattering Momentum change DK = 2sin(q) * 2p/l Momentum 2q DK = Q = 4p sin(q) /l K = 2p/l 0 K = 2p/l 0 Reciprocal Space Ordered Lattice can only provide discrete momentum kicks: Bloch X-ray Diffraction Elastic Momentum Transfer Space Scattering Real Space Lattice Reciprocal Lattice Graphical Solution: Single crystal Q Q 1 D Q 0 Ewald’s Sphere 10
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