Procedure for structure analysis Overview of strategy

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 • Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume)

15. Techniques for structure detn • Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume) atom sizes

16. Techniques for structure detn • 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 • 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 • 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 • Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume) atom sizes properties (centric?) isostructural materials (use databases) • Measure intensities of as many reflections as possible - correct for LP, absorption

20. Techniques for structure detn • Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume) atom sizes properties (centric?) isostructural materials (use databases) • 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 • 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 • 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 • Refine structure • Include thermal parameters for each atom • or

28. Techniques for structure detn • 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