Structure Refinement
Linda Lim
Stanford University
Stanford Synchrotron Radiation Lightsource
Stephens’ Law –“A Rietveld refinement is never perfected,
merely abandoned”
Demonstration: Rietveld Refinement of spinel oxide
Outline
List of programs for Rietveld refinement
Rietveld refinement using GSAS
Fourier method
Summary
References
Selected list of Programs
o CCP14 for a more complete list(http://sdpd.univ-lemans.fr/du-sdpd/nexus/ccp14/web/index3.htm)
GSAS
GSAS-II
Fullprof
DBW
MAUD
Topas from Bruker – not free
Example: MnGa2O4
General purpose: to refine a crystal structure
Specific to this example:
Purpose: to find out the site occupancies of
Mn2+ and Ga3+ in octahedral (oct) and
tetrahedral (tet) sites respectively
Why is it significant?
Anti-site defects may affect conductivity due
to generation/compensation of charges
Inverse Modeling Method 1
Rietveld Method
Data
ModelRefined Structure
40 60 80 100 120 140 160
0
1000
2000
3000
4000
5000
6000
7000
Inte
nsity
Profile
shape
Background
1. Model
Sample: MnGa2O4
Spinel AB2O4
Lattice parameter: 8.450 Å
Space group: F d -3 m
Some options:
- Retrieve crystallographic information from powder diffraction database (.cif file)
- Key in the above information directly into
GSAS
Fractional coordinates
- Relative position of a specific atom in the
unit cell
Multiplicity
- How many of a specific atom in the unit cell
UISO
- Isotropic thermal parameter
2. Profile Shape
From instrument parameter file
Obtain from refinement of calibrant (eg.
LaB6)
Gives the initial values for the profile function
(instrumental only parameters)
Add screenshot for previous slide on how to load data
and instrument parameter file
Powpref genles
Run genles until convergence is achieved
liveplot
First fit!
3. Background
3. Background Choose a suitable background function, then refine
background (powpref genles)
Background has improved
Lstview
Chi-squared value = 253.5
Shows the
output of the
refined
parameters
Refine: Scale
Powpref
genles liveplot
Refine: Scale
Fit has improved!
Refine: Scale
Chi-squared value = 13.59
Refine: diffractometer zero
correction
Powpref
genles liveplot
Refine: Zero
Chi-squared value = 5.543
Refine: Scale
Chi-squared value = 13.59
Before refining zero
Refine: cell
Powpref
genles liveplot
Refine: cell
Chi-squared value = 5.076
Refine: profile
Peak shapes
K. Stone
Thursday afternoon
Refine: profile
Chi-squared value = 4.944
Progress so far
Inverse Modeling Method 2
Fourier MethodData
ModelRefined Structure
40 60 80 100 120 140 160
0
1000
2000
3000
4000
5000
6000
7000
Inte
nsity
Profile
shape
Background
subtract
phases
Integrated
Intensities
Fourier Difference Map
z
x
y
Add constraints
Now, we’re adding Mn in octahedral site
and Ga in tetrahedral site
Add constraintsWe want to see the occupancy of Mn in
octahedral site
Refine site occupancy
Fix site occupancies after each refinement
F= site occupancy
Refine fractional coordinates and thermal parameterConstrain x,y,z,u for Td and Oct sites
respectively.
Refine fractional coordinates and thermal parameter
X= fractional coordinates
U = thermal parameter
Final Parameters
Chi-squared value = 2.835Rp = 0.0382
Fourier difference map
Summary of refinement
parameters Final site occupancies
Final formula
(Mn0.76Ga0.24)tet (Mn0.21Ga1.79)octO3.9
Anti-site defects are present
Atom Site Occupancy
Mn Tet 0.7573
Ga Tet 0.2427
Mn Oct 0.1064
Ga Oct 0.8963
O 0.9742
How do you know when to
stop?
Chi-square, liveplot, R factor look good
Most importantly, it has answered the
scientific question you have
Stephens’ Law –“A Rietveld refinement is never perfected,
merely abandoned”
References
Collaborative Computation Project 14: http://sdpd.univ-lemans.fr/du-sdpd/nexus/ccp14/web/index3.htm
Rietveld mailing list: http://lachlan.bluehaze.com.au/stxnews/riet/using.htm
Brian Toby’s EXPGUI mailing list: http://www.aps.anl.gov/mailman/listinfo/expgui
To download EXPGUI and GSAS as a package: https://subversion.xor.aps.anl.gov/trac/EXPGUI
Powder Diffraction: Theory and Practice (RSC Publishings)
Acknowledgments
Oak Ridge National Laboratory SNS
US Department of Energy
Thank You
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