![Page 1: Bulk Structural Analysis Apurva Mehta J. Stubbs J. Lezama ... · J. Lezama will explore this further. Diffraction Physics FT FT A(DK) = S f e2pi (risin(2q)/l) i A(DK) = S f ei (ri](https://reader034.vdocument.in/reader034/viewer/2022050109/5f469ffbb5ff297efb5f1484/html5/thumbnails/1.jpg)
Bulk Structural Analysis
Apurva Mehta
J. Stubbs
J. Lezama Pacheco
M. Michel
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Outline
Peak Shape & Width:
crystallite size
Strain gradient
Peak Positions:
Phase identification
Lattice symmetry
Lattice strain
Peak Intensity:
Structure solution
Crystallite orientation
Apurva
Joanne
Juan
Marc
Misra
Joanna
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Outline
Peak Shape & Width:
crystallite size
Strain gradient
Peak Positions:
Phase identification
Lattice symmetry
Lattice strain
Peak Intensity:
Structure solution
Crystallite orientation
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Q1
Q0
QD
Scattering from a Single crystal
4
Ewald’s Sphere
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Q1
Diffraction for Polycrystals
5
Ewald
Sphere
Reciprocal
Sphere
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s
s
Deformation of Reciprocal Sphere
Strain Ellipsoid
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χ
Q0
s s
Q
Coordinate Transformation
Q
c
χ
Q
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Experimental Setup – 11-3 SSRL
X-ray Beam
Detector
Sample
DIC Camera
Sample
Dogbone
Force Transducer
3 mm
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Strain Determination
110 200 211
c c
Q (nm-1) Q (nm-1)Q (nm-1)
c
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110 Em = 167 GPa
0.3
400
300
200
100
0
Str
ess
(MP
a)
0-.10 .05 .05 .10 .15 .20 .25
% Strain
00
Pois
son’s
Rat
io
Stress (MPa) 400
eyyezz
shear
1
200 211Em = 211 GPa Em = 218 GPa
Elastic Strain Tensors for Iron
eyy
ezz
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Outline
Peak Shape & Width:
crystallite size
Strain gradient
Peak Positions:
Phase identification
Lattice symmetry
Lattice strain
Peak Intensity:
Structure solution
Crystallite orientation
![Page 12: Bulk Structural Analysis Apurva Mehta J. Stubbs J. Lezama ... · J. Lezama will explore this further. Diffraction Physics FT FT A(DK) = S f e2pi (risin(2q)/l) i A(DK) = S f ei (ri](https://reader034.vdocument.in/reader034/viewer/2022050109/5f469ffbb5ff297efb5f1484/html5/thumbnails/12.jpg)
Strain Gradient : example
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Outline
Peak Shape & Width:
crystallite size
Strain gradient
Peak Positions:
Phase identification
Lattice symmetry
Lattice strain
Peak Intensity:
Structure solution
Crystallite orientation
![Page 14: Bulk Structural Analysis Apurva Mehta J. Stubbs J. Lezama ... · J. Lezama will explore this further. Diffraction Physics FT FT A(DK) = S f e2pi (risin(2q)/l) i A(DK) = S f ei (ri](https://reader034.vdocument.in/reader034/viewer/2022050109/5f469ffbb5ff297efb5f1484/html5/thumbnails/14.jpg)
Structure Solution
Single Crystal
Protein Structure
Sample with heavy Z problems Due to
Absorption/extinction effects
Mostly used in Resonance mode
Site specific valence
Orbital ordering.
Powder
Due to small crystallite size kinematic equations valid
Many materials can not be readily prepared in single-crystal form: their structures obtained via synchrotron powder diffraction
Peak overlap a problem – high resolution setup helps
Much lower intensity – loss on super lattice peaks from small symmetry breaks. (Fourier difference helps)
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Diffraction from Polycrystals
Long range order ----> diffraction pattern periodic
crystal rotates ----> diffraction pattern rotates
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From 4 crystallites
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From Powder
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Powder Pattern
Loss of angular information
Not a problem as peak
position = fn(a, b & a )
Peak Overlap :: A problem
But can be useful for precise lattice parameter measurements
J. Lezama will explore
this further
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Diffraction Physics
FT FT
S e2pi (risin(2q)/l)
A(DK) = fi
S ei (ri Q)
A(DK) = fi
A(Q) = Fhkl = Fourier Transform ( ri )
ei (r Qi)
A(r) = FhklSA(Q )/Fhkl is a complex number
We measure A(Q ) * A(Q )
amplitude but not the phase of
A(Q ) is known
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Phase Problem
Amplitude unknown Phase Unknown
-200 0 200 400 600 800 1000 1200 1400 1600
-1.0
-0.5
0.0
0.5
1.0
-200 0 200 400 600 800 1000 1200 1400 1600
-1.0
-0.5
0.0
0.5
1.0
0 200 400 600 800
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
1+1
1+ 0.5
0 200 400 600 800
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 + 45
0 + 0
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Solution to Phase Problem
Phase/Structure must be guessed
And then refined.
How to guess?
Heavy atom substitution, SAD or MAD
Structure with one stronge scatterer – e.g. U in Phosphates matrix - Stubbs
Similarity to homologous compounds, e.g. NaCl KCl
Patterson function or pair distribution analysis.
M. Michel
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Inverse Modeling Method 1
Reitveld Method Data
ModelRefined Structure
40 60 80 100 120 140 160
0
1000
2000
3000
4000
5000
6000
7000
Inte
nsity
q
Profile
shape
Background
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Inverse Modeling Method 2
Fourier Method Data
ModelRefined Structure
40 60 80 100 120 140 160
0
1000
2000
3000
4000
5000
6000
7000
Inte
nsity
q
Profile
shape
Background
subtract
phases
Integrated
Intensities
Fhkl
Fhkl
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Inverse Modeling Methods
Rietveld Method
More precise
Yields Statistically reliable uncertainties
Fourier Method
Picture of the real space
Shows “missing” atoms, broken symmetry, positional disorder
Should iterate between Rietveld and Fourier.
Be skeptical about the Fourier picture if Rietveld refinement does not significantly improve the fit with the “new” model.