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