structure analysis.ppt
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The document outlines the procedure for determining a crystal structure from diffraction data. It discusses that lattice parameters and space group must be determined simultaneously with reflection positions. Additional information like crystal system, symmetry, and density can provide insight. Intensities of many reflections need to be measured and corrected. Atom positions can be found using techniques like Patterson functions, heavy atoms, and direct methods. The structure is then refined by adjusting positional and thermal parameters to minimize differences between observed and calculated structure factors.
structure analysis.ppt
- 1. Procedure for structure analysis Overview of strategy What is needed lattice parameters space group equipoint occupation positional parameters reflection positions reflection intensities
- 2. Procedure for structure analysis Overview of strategy What is needed lattice parameters space group done simultaneously reflection positions
- 3. Procedure for structure analysis Overview of strategy What is needed lattice parameters space group done simultaneously need crystal system for size & shape of UC some info on symmetry also acquired reflection positions
- 4. Procedure for structure analysis Overview of strategy What is needed lattice parameters space group done simultaneously need crystal system for size & shape of UC some info on symmetry also acquired small no. reflections needed for crystal system and approx. LPs reflection positions
- 5. Procedure for structure analysis Overview of strategy What is needed lattice parameters space group done simultaneously need crystal system for size & shape of UC some info on symmetry also acquired small no. reflections needed for crystal system and approx. LPs large no. for precise LPs reflection positions
- 6. Examples for LP detn Get a-value for each reflection Which one is correct? or best?
- 7. Examples for LP detn Depends upon Consider effect of expt'l error on a-values at different s Braggs' law says error in d depends on error in sin
- 8. Examples for LP detn Braggs' law says error in d depends on error in sin d eqn says error in a (cubic) depends on error in d d2 = a2/(h2 + k2 + l2) Thus, error in a depends on error in sin
- 9. Precise LPs Best a-value at = 90° extrapolate a-values vs. cos2
- 10. Precise LPs Best a-value at = 90° extrapolate a-values vs. cos2
- 11. Precise LPs Best a-value at = 90° extrapolate a-values vs. cos2
- 12. Precise LPs Another common extrapolation fcn - Nelson-Riley fcn
- 13. Procedure for structure analysis Overview of strategy LPs & SG done simultaneously need crystal system for size & shape of UC some info on symmetry also acquired systematic extinctions ––> Bravais lattice glide planes, screw axes space group - almost ex: Imma (centric) ––– Im21a (non-centric) get correct SG in final structure detn
- 14. Techniques for structure detn 1. Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume)
- 15. Techniques for structure detn 1. Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume) atom sizes
- 16. Techniques for structure detn 1. Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume) atom sizes properties (centric?) isostructural materials (use databases) Ex: Al9Co3Ce do search on LPs
- 17. Techniques for structure detn 1. Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume) atom sizes properties (centric?) isostructural materials (use databases) Ex: Al9Co3Ce do search on LPs
- 18. Techniques for structure detn 1. Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume) atom sizes properties (centric?) isostructural materials (use databases) Ex: Al9Co3Ce do search on LPs Ga9Co3Nd (structure known) only need to "refine" Al9Co3Ce structure
- 19. Techniques for structure detn 1. Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume) atom sizes properties (centric?) isostructural materials (use databases) 2. Measure intensities of as many reflections as possible - correct for LP, absorption
- 20. Techniques for structure detn 1. Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume) atom sizes properties (centric?) isostructural materials (use databases) 2. Measure intensities of as many reflections as possible - correct for LP, absorption 3. Determine atom positions a. Patterson techniques b. heavy atom method
- 21. Techniques for structure detn 3. Determine atom positions a. Patterson techniques b. heavy atom method
- 22. Techniques for structure detn 3. Determine atom positions a. Patterson techniques b. heavy atom method c. isomorphous replacement, anomalous scattering
- 23. Techniques for structure detn 3. Determine atom positions a. Patterson techniques b. heavy atom method c. isomorphous replacement, anomalous scattering d. direct methods Unitary structure factors
- 24. Techniques for structure detn 3. Determine atom positions d. direct methods Unitary structure factors Example: center of symmetry Additional symmetry elements give other relationships
- 25. Techniques for structure detn 4. Refine structure adjust positional parameters to get best agreement betwn Fobs & Fcalc use least squares technique FOM – the R factor
- 26. Techniques for structure detn 4. Refine structure adjust positional parameters to get best agreement betwn Fobs & Fcalc use least squares technique FOM – the R factor Include thermal parameters for each atom
- 27. Techniques for structure detn 4. Refine structure Include thermal parameters for each atom or
- 28. Techniques for structure detn 4. Refine structure Include thermal parameters for each atom or For anisotropic vibration, thermal ellipsoid for each atom
- 29. Techniques for structure detn Rietveld refinement For powder diffraction data Not a structure determination procedure Whole pattern used Need to model peak shapes
- 30. Techniques for structure detn Rietveld refinement For powder diffraction data Not a structure determination procedure Whole pattern used Need to model peak shapes Many data, many parameters: lattice params, backgrd curve coeffs, positional params,temp factors, peak shape params, texture factor, etc.
- 31. Techniques for structure detn Rietveld refinement