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