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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
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
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.