Powder Diffraction - Spallation Neutron Source

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$Single Crystal Diffraction - Spallation Neutron Source$

Fitting crystallographic data -- what is it all about? We perform an experiment: – Get lots of intensity and position measurements in a diffraction measurement: what do they tell us? Obtain an unit cell that fits the diffraction positions (indexing) “Solve the structure”: determine an approximate model to match the intensities Add/modify the structure for completeness & chemical sense Optimize the structure (model) to obtain the best fit to the observed data – This is usually done with Gauss-Newton least-squares fitting – Parameters to be fit are structural and may account for other experimental effects Least Squares gives us a Hessian matrix; inverse is variance-covariance matrix which gives uncertainties in the parameters 40
Crystallography from powder diffraction: before Rietveld How did crystallographers use powder diffraction data? Avoided powder diffraction Manually integrate intensities – discard peaks with overlapped reflections Or – rewrote single-crystal software to refine using sums of overlapped reflections Simulation of powder diffraction data was commonly done Qualitative reasoning: similarities in patterns implied similar structures Visual comparison between computed and observed structure verifies approximate model Fits, where accurate (& precise) models were rarely obtained Error propagation was difficult to do correctly (but not impossible) 41
Page 1 and 2: A Very Abbreviated Introduction to
Page 3 and 4: Where to go for more… There are m
Page 5 and 6: Basic Crystallography 5
Page 7 and 8: Lattice planes General Indices: la
Page 9 and 10: Diffraction from single crystals D
Page 11 and 12: Powder Diffraction 11
Page 13 and 14: Bragg cones in powder diffraction S
Page 15 and 16: Coherent Atomic Scattering Power (d
Page 18 and 19: Resonant Conditions X-rays X-ray fo
Page 20 and 21: Measuring powder diffraction Angul
Page 22 and 23: Highest resolution requires high co
Page 24 and 25: Powder Instruments: Constant Wavele
Page 26 and 27: Time of Flight Diffraction Time of
Page 28 and 29: Neutron Powder Diffraction with Spa
Page 30 and 31: Materials effects on Powder Diffrac
Page 32 and 33: Crystallite Size Broadening d*=cons
Page 34 and 35: Microstrain Broadening See GSAS Man
Page 36 and 37: Anisotropic strain broadening terms
Page 38 and 39: Fitting of Powder Diffraction Data
Page 42 and 43: Hugo Rietveld’s technique Hugo R
Page 44 and 45: Hugo Rietveld in the Petten Reactor
Page 46 and 47: Hugo Rietveld’s other breakthroug
Page 48 and 49: What sort of data are needed for Ri
Page 50 and 51: Limitations of Rietveld Rietveld c
Page 52 and 53: Approaches to Profile Models Three
Page 54 and 55: Voigt vs. Pseudo-Voigt A Gaussian c
Page 56 and 57: Axial Divergence (Low Angle Asymmet
Page 58 and 59: Sample Displacement & Transparency
Page 60 and 61: The Unit Cell The unit cell descri
Page 62 and 63: Lattice Types Centering causes latt
Page 64 and 65: Space Groups Not all combinations
Page 66: Reciprocal Lattice To simplify mat

Powder Diffraction - Spallation Neutron Source

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