Bulk Structure Characterization Apurva Mehta Linda Lim Outline  What do diffraction peaks tell us?  Structure Refinement Intro  Refinement Details - Linda Diffraction Physics X-ray lens with resolution better than ~10nm don’t exist image sample light lens Sample Image SRceactitperroincga l Space Space SSppaaccee X-ray Scattering/diffraction is about probing the structure without a lens Diffraction 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 Diffraction Physics e f iwt 0 e iwt 2pi (r1sin(2q)/l) e e iwt f 1 Phase r1 difference 2pi (r2sin(2q)/l) e e iwt f 2 r2 Phase difference DK = Q = 4p sin(q) /l 2pi (risin(2q)/l) A(DK = (s-s0)) = ei wt Sf e i amplitude A(Q) = Fourier Transform ( r ) i i (ri Q) S e A(DK) = f i Fourier Transform Recap  FT (large) ~ 1/large  small la rge structures in real space  small in reciprocal space  FT (periodic fn) ~ periodic Rec iprocal and space have the same point group symmetry  FT (FT (S) ) ~ S FT FT FT (r eal space)  reciprocal space: FT (rec. space)  image of real space  Convolution Theorem:  FT (a multiply b) = FT (a) conv FT (b)  FT (a conv b) = FT (a) mult FT (b) Diffraction Physics FT FT Sample Scattering Space Space Fourier Transform Multiplication vs Convolution x FT (a multiply b) = FT (a) conv FT (b) Convolution FT (a conv b) = FT (a) mult FT (b) Multiplication Deconstructing the Sample space Sample = S x P * M = x * M o t i f Sample size Infinite Periodic Lattice (S) (M) (P) Reciprocal Space Peaks I (Q) = FT(sample) x FT(sample) = FT ( S x P * M) x FT ( S x P * M) = {FT (S x P) x FT (M)} { ….} = {FT(S) * FT(P) x FT(M)} {…..}