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Purpose of this lecture
At the end of this lecture, you should be able to
1) index SAED patterns if the cell parameters are known
2) know how to determine unknown cell parameters from SAED patterns
3) determine the possible space groups from SAED patterns
4) determine possible point groups from CBED patterns
5) solve a simple structure ab initio from PED patterns
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Example materials used in this lecture
Aluminum
Rutile-type SnO2
Slides are on http://www.slideshare.net/johader
The pages with the ED for the exercises can be found at the end of this ppt.
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1. Selected areaelectron diffraction
(SAED)
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Example 1: a known material, e.g. SnO2
Tetragonal, a=b= 4.72 Å, c=3.16 Å
4.72
4.72
3.34
2.36
2.63
1.58
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List of hkl – d
Powdercell
Input:P42/mnma=b=4.72 Åc= 3.17 Å
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010
100
110
200
101
002
Determine the zone-axis
[001] [010]
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If cell parameters/material unknown
Shortest vectors, high symmetry, ...
best during TEM experiment
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Starting from nothing: aluminum First determine the cell parameters
Make a tilt series
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Do you recognize any typical symmetry?Only 2-fold2- and 4-fold2-, 4- and 6-fold
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Do you recognize any typical symmetry?Only 2-fold2- and 4-fold2-, 4- and 6-fold
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What crystal class has both 4-fold and 6-fold axes?cubichexagonalnone
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What crystal class has both 4-fold and 6-fold axes?cubichexagonalnone
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In SAED patterns there is always an inversion centre due to the diffraction geometry!
+ =
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What crystal class has both 4-fold and 3-fold axes?cubichexagonalnone
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What crystal class has both 4-fold and 3-fold axes?cubichexagonalnone
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How many possible choices for the basic vectors are there on this square pattern?
12more
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How many possible choices for the basic vectors are there on this square pattern?
12more
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100
010
a*
b*
200
020 a*
b*
200020
a*b*
There can be a reflection condition!
hk0:
no cond.h=2n,k=2n
h+k=2nChoose simplest first and see if ok with other zones.
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hk0:
no cond.
Measure RCalculate d from R.d=λL (known)Determine a, b, cMake list of d-spacingsCheck if you can index the other patterns with this
100
010
a*
b*
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What will be the value of a and b with this choice?1.432.034.06
2.03
2.03
1.430.78
2.03 2.03
2.032.03
0.91
1.22
2.342.34
1.43
a*b*
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What will be the value of a and b with this choice?1.432.034.06
2.03
2.03
1.430.78
2.03 2.03
2.032.03
0.91
1.22
2.342.34
1.43
a*b*
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If no reflection condition:a=b= c=2.03 Å
list of d-spacings freeware: Powdercell
H K L d/Å_____________
1 0 0 2.030001 1 0 1.435431 1 1 1.172022 0 0 1.015002 1 0 0.907842 1 1 0.82874
Can you index all observed reflections using these cell parameters?
yesno
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If no reflection condition:a=b= c=2.03 Å
list of d-spacings freeware: Powdercell
H K L d/Å_____________
1 0 0 2.030001 1 0 1.435431 1 1 1.172022 0 0 1.015002 1 0 0.907842 1 1 0.82874
Can you index all observed reflections using these cell parameters?
yesno
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200020
a*b*
hk0:
no cond.h=2n,k=2n
h+k=2n
Increase the cell parameters to the next possibility...
Which one has second smallest cell parameters?
topleft
100
010
a*
b*
200
020 a*
b*
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200020
a*b*
hk0:
no cond.h=2n,k=2n
h+k=2n
Increase the cell parameters to the next possibility...
Which one has second smallest cell parameters?
topleft
100
010
a*
b*
200
020 a*
b*
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200020
a*b*h+k=2n
2.03
2.03
1.431.43
In this case, a=b=1.43 Å 2.03 Å2.86 Å
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200020
a*b*h+k=2n
2.03
2.03
1.431.43
In this case, a=b=1.43 Å 2.03 Å2.86 Å
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If hk0:h+k=2n, then a=b= 2.86 Ålist of d-spacings, Powdercell:
Can you index all observed reflections using these cell parameters?
yesno
H K L d/Å ______________1 0 0 2,860001 1 0 2,022331 1 1 1,651222 0 0 1,430002 1 0 1,279032 1 1 1,167592 2 0 1,011163 0 0 0,953332 2 1 0,953333 1 0 0,904413 1 1 0,862322 2 2 0,825613 2 0 0,79322
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If hk0:h+k=2n, then a=b= 2.86 Ålist of d-spacings, Powdercell:
Can you index all observed reflections using these cell parameters?
yesno
H K L d/Å ______________1 0 0 2,860001 1 0 2,022331 1 1 1,651222 0 0 1,430002 1 0 1,279032 1 1 1,167592 2 0 1,011163 0 0 0,953332 2 1 0,953333 1 0 0,904413 1 1 0,862322 2 2 0,825613 2 0 0,79322
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If hk0:h+k=2n, then a=b= 2.86 Ålist of d-spacings, Powdercell:
I show also the reflections not in agreement with hk0: h+k=2n. Will they be seen on any of the SAED patterns of the tilt series?
it is possiblealwaysnever
H K L d/Å ______________1 0 0 2,860001 1 0 2,022331 1 1 1,651222 0 0 1,430002 1 0 1,279032 1 1 1,167592 2 0 1,011163 0 0 0,953332 2 1 0,953333 1 0 0,904413 1 1 0,862322 2 2 0,825613 2 0 0,79322
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If hk0:h+k=2n, then a=b= 2.86 Ålist of d-spacings, Powdercell:
I show also the reflections not in agreement with hk0: h+k=2n. Will they be seen on any of the SAED patterns of the tilt series?
it is possiblealwaysnever
H K L d/Å ______________1 0 0 2,860001 1 0 2,022331 1 1 1,651222 0 0 1,430002 1 0 1,279032 1 1 1,167592 2 0 1,011163 0 0 0,953332 2 1 0,953333 1 0 0,904413 1 1 0,862322 2 2 0,825613 2 0 0,79322
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200020
a*b*
hk0:
no cond.h=2n,k=2n
h+k=2n
Next possibility...
100
010
a*
b*
200
020 a*
b*
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In this case, a=b=2.03 Å 4.06 Å5.92 Å
200
020 a*
b*
2.03
2.03
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In this case, a=b=2.03 Å 4.06 Å5.92 Å
200
020 a*
b*
2.03
2.03
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If hk0:h,k=2n, then a=b= 4.06 Ålist of d-spacings, Powdercell:H K L d/Å___________
1 0 0 4,060001 1 0 2,870851 1 1 2,344042 0 0 2,030002 1 0 1,815692 1 1 1,657492 2 0 1,435433 0 0 1,353332 2 1 1,353333 1 0 1,283883 1 1 1,224142 2 2 1,17202
3 2 0 1,126043 2 1 1,085084 0 0 1,015004 1 0 0,984693 2 2 0,984694 1 1 0,956953 3 0 0,956953 3 1 0,931434 2 0 0,907844 2 1 0,885963 3 2 0,865594 2 2 0,828745 0 0 0,812004 3 0 0,812005 1 0 0,79623
4 3 1 0,796235 1 1 0,781353 3 3 0,78135
Can you index all observed reflections with these cell parameters?
yesno
Do it now.
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If hk0:h,k=2n, then a=b= 4.06 Ålist of d-spacings, Powdercell:H K L d/Å___________
1 0 0 4,060001 1 0 2,870851 1 1 2,344042 0 0 2,030002 1 0 1,815692 1 1 1,657492 2 0 1,435433 0 0 1,353332 2 1 1,353333 1 0 1,283883 1 1 1,224142 2 2 1,17202
3 2 0 1,126043 2 1 1,085084 0 0 1,015004 1 0 0,984693 2 2 0,984694 1 1 0,956953 3 0 0,956953 3 1 0,931434 2 0 0,907844 2 1 0,885963 3 2 0,865594 2 2 0,828745 0 0 0,812004 3 0 0,812005 1 0 0,79623
4 3 1 0,796235 1 1 0,781353 3 3 0,78135
Can you index all observed reflections with these cell parameters?
yesno
Do it now.
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1.430.78
2.03
2.032.03
0.91
1.22
2.342.34
1.43
200
020
The index of this reflection is110220440
2.03
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1.430.78
2.03
2.032.03
0.91
1.22
2.342.34
1.43
200
020
The index of this reflection is110220440
2.03
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0.78
2.03 2.03
2.032.03
0.91
1.22
2.342.34
1.43
200
020
The index of this reflection is200010020
220
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0.78
2.03 2.03
2.032.03
0.91
1.22
2.342.34
1.43
200
020
The index of this reflection is200010020
220
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0.78
0.91
1.22
2.342.34
1.43
020
The index of this reflection is
020 020
020 020
333511511
-
How to decide this?
200220
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0.78
0.91
1.22
2.342.34
1.43
020
The index of this reflection is
020 020
020 020
333511511
-
How to decide this?
200220
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The index of this reflection is
020
333511511
-
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511 and 511?
511 and 511?- -
-
-
Calculate angles etc (lectures Mon-Wed)or
just do it graphically...
115 and 115?
115 and 115?- -
-
-
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c*
b* a*
100 200 300 400 500
501401301201101001
002 102 202 302 402 502
503403303203103003
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The index of this reflection is
020
333511511
-
511511-
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0.91
1.22
2.342.34
1.43
020 020 020
020 020
511-511
200220
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c*
b* a*
100 200 300 400 500
501401301201101001
002 102 202 302 402 502
503403303203103003
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0.91
1.22
2.342.34
1.43
020 020 020
020 020
511-511
200220
The index of this reflection is411311401
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0.91
1.22
2.342.34
1.43
020 020 020
020 020
511-511
200220
The index of this reflection is411311401
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0.912.342.34
1.43
020 020 020
020 020
511-511
311200220
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c*
b* a*
100 200 300 400 500
501401301201101001
002 102 202 302 402 502
503403303203103003
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2.342.34
1.43
020 020 020
020 020
511-511
311
402
200220
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020 020 020
020 020
511-511
311
402111 111
-
200220
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020 020 020
020 020
511-511
311
402111 111
-
202- -
200220
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020 020 020
020 020
511-511
311
402111 111
-
202- -
200220
Zone axes for this zone for example? 103301103-
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020 020 020
020 020
511-511
311
402111 111
-
202- -
200220
Zone axes for this zone for example? 103301103-
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020 020 020
020 020
511-511
311
402111 111
-
202- -
200220
[001] [105][103]
--
[102]- [101]-
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Indexed-> cell parameter: a=4.06 Å
Space group?Possibility from SAED: extinction symbol.-> Determine reflection conditions.
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020 020 020
020 020
511-511
311
402111 111
-
202- -
hkl: h+k+l=2nall odd, all evenno conditions
Bravais lattice: FPI
200220
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020 020 020
020 020
511-511
311
402111 111
-
202- -
hkl: h+k+l=2nall odd, all evenno conditions
Bravais lattice: FPI
200220
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020 020 020
020 020
511-511
311
402111 111
-
202- -
hkl: h+k+l=2nall odd, all evenno conditions
Bravais lattice: FPI
200220
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020 020 020
020 020
511-511
311
402111 111
-
202- -
We know: hk0: h=2n, k=2n. Is this an extra condition, or is it a consequence of F also?
ConsequenceExtra
200220
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020 020 020
020 020
511-511
311
402111 111
-
202- -
We know: hk0: h=2n, k=2n. Is this an extra condition, or is it a consequence of F also?
ConsequenceExtra
200220
![Page 67: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/67.jpg)
020 020 020
020 020
511-511
311
402111 111
-
202- -
Are there àny extra conditions, i.e. conditions that are not already implied by hkl: all odd, all even? Yes
No200220
![Page 68: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/68.jpg)
020 020 020
020 020
511-511
311
402111 111
-
202- -
Are there àny extra conditions, i.e. conditions that are not already implied by hkl: all odd, all even? Yes
No200220
![Page 69: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/69.jpg)
Possible space groups: F23, Fm3, F432, F43m, Fm3m- - -
from: International Tables for Crystallography Volume A, ed. Theo Hahn, Kluwer Ac. Pub., 2002
![Page 70: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/70.jpg)
Possible space groups: F23, Fm3, F432, F43m, Fm3m- - -
Same extinctions.
Difference: 1, 2, m; give no extinctions.
Convergent beam electron diffractionCBED
-
![Page 71: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/71.jpg)
2. Convergent beamelectron diffraction
(CBED)
![Page 72: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/72.jpg)
SAED CBED
Example: rutile-type SnO2
![Page 73: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/73.jpg)
Projection symmetry: 2D, diffuse features
Full symmetry: 3D, sharp features
BF
WP
Lots of tables!
![Page 74: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/74.jpg)
![Page 75: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/75.jpg)
6mm1R
3m1R
6mm
6mRmR
61R
31R
6
6RmmR
3m
3mR
6R
3
4mm1R
4RmmR
4mm
4mRmR
41R
4R
4
2mm1R
2RmmR
2mm
2mRmR
m1R
m
mR
21R
2R
2
1R
1
-1 1 2 m 2/m
22
2
mm
2
mm
m
4 -4 4/m
42
2
4m
m
-42
m
4/m
mm
3 -3 32
3m
-3m
6 -6 6/m
62
2
6m
m
-6m
2
6/m
mm
23
m3
43
2
-43
m
m3
m
![Page 76: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/76.jpg)
WPproj
WP
![Page 77: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/77.jpg)
Projection whole pattern symmetry [001]
44mm2mm
![Page 78: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/78.jpg)
Projection whole pattern symmetry [001]
44mm2mm
![Page 79: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/79.jpg)
Table from: J.A. Eades, Convergent beam diffraction, in: Electron Diffraction Techniques, volume 1, ed. J. Cowley, Oxford University Press, 1992
Projection WP: 4mm
Projection diffraction group:Table Eades
44RmmR
4mm1R
![Page 80: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/80.jpg)
Table from: J.A. Eades, Convergent beam diffraction, in: Electron Diffraction Techniques, volume 1, ed. J. Cowley, Oxford University Press, 1992
Projection WP: 4mm
Projection diffraction group:Table Eades
44RmmR
4mm1R
![Page 81: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/81.jpg)
Projection diffraction group: 4mm1R
Possible diffraction groups:
4mRmR
4mm4RmmR
4mm1R
Table from: J.A. Eades, Convergent beam diffraction, in: Electron Diffraction Techniques, volume 1, ed. J. Cowley, Oxford University Press, 1992
![Page 82: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/82.jpg)
6mm1R
3m1R
6mm
6mRmR
61R
31R
6
6RmmR
3m
3mR
6R
3
4mm1R
4RmmR
4mm
4mRmR
41R
4R
4
2mm1R
2RmmR
2mm
2mRmR
m1R
m
mR
21R
2R
2
1R
1
-1 1 2 m 2/m
22
2
mm
2
mm
m
4 -4 4/m
42
2
4m
m
-42
m
4/m
mm
3 -3 32
3m
-3m
6 -6 6/m
62
2
6m
m
-6m
2
6/m
mm
23
m3
43
2
-43
m
m3
m
Table redrawn from B.F. Buxton, J.A. Eades, J.W. Steeds, G.M. Rackham: Phil. Trans. R. Soc. London, 281 (1976) 171
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What will be useful to narrow it down further?
look at the bright field symmetrylook at the whole pattern symmetry
[...] [...]
![Page 84: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/84.jpg)
What will be useful to narrow it down further?
look at the bright field symmetrylook at the whole pattern symmetry
[...] [...]
![Page 85: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/85.jpg)
WP symmetry
44mm2mm
![Page 86: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/86.jpg)
WP symmetry
44mm2mm
![Page 87: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/87.jpg)
[...] [...]
![Page 88: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/88.jpg)
6mm1R
3m1R
6mm
6mRmR
61R
31R
6
6RmmR
3m
3mR
6R
3
4mm1R
4RmmR
4mm
4mRmR
41R
4R
4
2mm1R
2RmmR
2mm
2mRmR
m1R
m
mR
21R
2R
2
1R
1
-1 1 2 m 2/m
22
2
mm
2
mm
m
4 -4 4/m
42
2
4m
m
-42
m
4/m
mm
3 -3 32
3m
-3m
6 -6 6/m
62
2
6m
m
-6m
2
6/m
mm
23
m3
43
2
-43
m
m3
m
![Page 89: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/89.jpg)
Another pattern
SAED
Index it.
This is:
[101][110][111]
4.72
2.63
=010
=101-
![Page 90: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/90.jpg)
Another pattern
SAED
Index it.
This is:
[101][110][111]
4.72
2.63
=010
=101-
![Page 91: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/91.jpg)
Projection whole pattern [101]
2m2mm
(smaller cond.ap.)
![Page 92: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/92.jpg)
Projection whole pattern [101]
2m2mm
(smaller cond.ap.)
![Page 93: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/93.jpg)
Possible projection diffraction group:
21R
m1R
2mm1R
![Page 94: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/94.jpg)
Possible projection diffraction group:
21R
m1R
2mm1R
![Page 95: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/95.jpg)
Whole pattern [101]
2m2mm
(smaller cond.ap.)
![Page 96: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/96.jpg)
Whole pattern [101]
2m2mm
(smaller cond.ap.)
![Page 97: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/97.jpg)
Diffraction group:
2mm2RmmR
2mm1R
![Page 98: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/98.jpg)
Diffraction group:
2mm2RmmR
2mm1R
![Page 99: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/99.jpg)
6mm1R
3m1R
6mm
6mRmR
61R
31R
6
6RmmR
3m
3mR
6R
3
4mm1R
4RmmR
4mm
4mRmR
41R
4R
4
2mm1R
2RmmR
2mm
2mRmR
m1R
m
mR
21R
2R
2
1R
1
-1 1 2 m 2/m
22
2
mm
2
mm
m
4 -4 4/m
42
2
4m
m
-42
m
4/m
mm
3 -3 32
3m
-3m
6 -6 6/m
62
2
6m
m
-6m
2
6/m
mm
23
m3
43
2
-43
m
m3
m
![Page 100: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/100.jpg)
Possible point groups
4/mmm
m3m
![Page 101: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/101.jpg)
from: International Tables for Crystallography Volume A, ed. Theo Hahn, Kluwer Ac. Pub., 2002
CBED
![Page 102: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/102.jpg)
Combine with information about reflection conditions from SAED patterns
020
200
110
020
011002
hkl: no conditionsh+k+l=2n
002
110-
![Page 103: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/103.jpg)
Combine with information about reflection conditions from SAED patterns
020
200
110
020
011002
hkl: no conditionsh+k+l=2n
002
110-
![Page 104: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/104.jpg)
Combine with information about reflection conditions from SAED patterns
020
200
110
020
011002
hk0: no conditionsh+k=2n
0kl: no conditionsk+l=2nk=2n or l=2n
002
110-
hhl: no conditionsl=2n
![Page 105: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/105.jpg)
Combine with information about reflection conditions from SAED patterns
020
200
110
020
011002
hk0: no conditionsh+k=2n
0kl: no conditionsk+l=2nk=2n or l=2n
002
110-
hhl: no conditionsl=2n
![Page 106: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/106.jpg)
Combine with information about reflection conditions from SAED patterns
020
200
110
020
011002
hk0: no conditionsh+k=2n
0kl: no conditionsk+l=2nk=2n or l=2n
002
110-
hhl: no conditionsl=2n
![Page 107: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/107.jpg)
Combine with information about reflection conditions from SAED patterns
020
200
110
020
011002
hk0: no conditionsh+k=2n
0kl: no conditionsk+l=2nk=2n or l=2n
002
110-
hhl: no conditionsl=2n
![Page 108: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/108.jpg)
International Tables
CBED
SAED
Space Group P42/mnm
![Page 109: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/109.jpg)
3. Precession electron diffraction
(PED)
![Page 110: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/110.jpg)
110
Ab initio solution of structures using electron diffraction:
You have as experimental data:only electron diffraction patterns
You get:the structure
Trouble: dynamical diffraction
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Demonstration of the precession technique with EMAP
Precession electron diffractionExample: SnO2
![Page 112: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/112.jpg)
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Intensities of the reflections from several zones+cell parameters and space group from SAED-CBED+composition from EDX/EELS or nominal composition
STRUCTURE
![Page 115: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/115.jpg)
Extract the intensities usingEDMEXTRAXCRISP...
Possibilities to introduce mistakes:
not well orientedtoo thicktoo small precession angletoo large precession angle…
![Page 116: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/116.jpg)
Apply symmetry
![Page 117: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/117.jpg)
117
Combine separate lists
Many possibilities to introduce mistakes!!
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Direct methods, or optimisation methods made for single crystal data
SIR2008FoxEndeavour...
Right structure càn come out (GIGO).
![Page 119: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/119.jpg)
Purpose of this lecture
At the end of this lecture, you should be able to
1) index SAED patterns if the cell parameters are known
2) know how to determine unknown cell parameters from SAED patterns
3) determine the possible space groups from SAED patterns
4) determine possible point groups from CBED patterns
5) determine a simple structure ab initio from PED patterns
![Page 120: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/120.jpg)
![Page 121: TEM Winterworkshop 2011: electron diffraction](https://reader034.vdocument.in/reader034/viewer/2022042518/559380831a28ab1c218b4669/html5/thumbnails/121.jpg)
ED patterns for the exercises
These ED are the same as those on the previous slides, but the contrast has
been reversed to enable easy writing.
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SAED and CBED SnO2 second zone