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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
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Outline
List of programs for Rietveld refinement
Rietveld refinement using GSAS
Fourier method
Summary
References
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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
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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
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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
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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
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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
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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)
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Add screenshot for previous slide on how to load data
and instrument parameter file
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Powpref genles
Run genles until convergence is achieved
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liveplot
First fit!
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3. Background
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3. Background Choose a suitable background function, then refine
background (powpref genles)
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Background has improved
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Lstview
Chi-squared value = 253.5
Shows the
output of the
refined
parameters
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Refine: Scale
Powpref
genles liveplot
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Refine: Scale
Fit has improved!
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Refine: Scale
Chi-squared value = 13.59
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Refine: diffractometer zero
correction
Powpref
genles liveplot
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Refine: Zero
Chi-squared value = 5.543
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Refine: Scale
Chi-squared value = 13.59
Before refining zero
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Refine: cell
Powpref
genles liveplot
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Refine: cell
Chi-squared value = 5.076
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Refine: profile
Peak shapes
K. Stone
Thursday afternoon
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Refine: profile
Chi-squared value = 4.944
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Progress so far
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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
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Fourier Difference Map
z
x
y
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Add constraints
Now, we’re adding Mn in octahedral site
and Ga in tetrahedral site
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Add constraintsWe want to see the occupancy of Mn in
octahedral site
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Refine site occupancy
Fix site occupancies after each refinement
F= site occupancy
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Refine fractional coordinates and thermal parameterConstrain x,y,z,u for Td and Oct sites
respectively.
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Refine fractional coordinates and thermal parameter
X= fractional coordinates
U = thermal parameter
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Final Parameters
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Chi-squared value = 2.835Rp = 0.0382
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Fourier difference map
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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
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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”
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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)
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Acknowledgments
Oak Ridge National Laboratory SNS
US Department of Energy
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Thank You