Download - TEM workshop 2013: Electron diffraction
![Page 1: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/1.jpg)
Electron Diffraction
![Page 2: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/2.jpg)
At the end of this lecture you should be able to
(1) index SAED patterns in case the cell parameters are already known
(2) determine the possible space groups from SAED patterns
(3) determine possible point groups from CBED patterns
Combine (2) and (3) to find the space group.
![Page 3: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/3.jpg)
Reflections: what do they represent? What is their origin? What information
can they give us?
![Page 4: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/4.jpg)
Constructive vs. destructive interference reflection – no reflection
position distances between the planes (d-values) intensity occupation in the planes
both symmetry of the structure
![Page 5: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/5.jpg)
Single phase?
Crystalline or amorphous?
Orientation crystals/film
?
Targeted phase?
Domain formation?
Crystal parameters?
![Page 6: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/6.jpg)
Selected Area Electron Diffraction
SAED
![Page 7: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/7.jpg)
One atom type A
a b
Basic cell, one plane
b>a
a=3 Å b=5 Å
![Page 8: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/8.jpg)
One atom type A
a b
Basic cell, one plane
b>a
(100)
100
000
a=3 Å b=5 Å
![Page 9: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/9.jpg)
One atom type A
a b
Basic cell, one plane
b>a
(100)
100
000
1/3Å
a=3 Å b=5 Å
![Page 10: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/10.jpg)
One atom type A
a b
Basic cell, one plane
b>a
(100)
100
a*
a=3 Å b=5 Å
![Page 11: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/11.jpg)
One atom type A
a b
Basic cell, one plane
b>a
(010)
a=3 Å b=5 Å
![Page 12: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/12.jpg)
One atom type A
a b
Basic cell, one plane
b>a
(010)
010
a=3 Å b=5 Å
![Page 13: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/13.jpg)
One atom type A
a b
Basic cell, one plane
b>a
(010)
010
a=3 Å b=5 Å
1/5Å
![Page 14: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/14.jpg)
One atom type A
a b
Basic cell, one plane
b>a
(010)
010 b*
a=3 Å b=5 Å
![Page 15: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/15.jpg)
One atom type A
010
100
a b
[001]
Basic cell EDP
b>a a*>b*
a*
b*
a=3 Å b=5 Å
![Page 16: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/16.jpg)
One atom type A
010
100
a b
[001]
Basic cell EDP
b>a a*>b*
a*
b*
Central reflection
is always 000.
000
a=3 Å b=5 Å
![Page 17: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/17.jpg)
One atom type A
010
100
a b
[001]
Basic cell EDP
a=3 Å b=5 Å
![Page 18: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/18.jpg)
One atom type A
010
100
a b
[001]
Basic cell EDP
1/3Å 1/5Å
a=3 Å b=5 Å
![Page 19: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/19.jpg)
010
100
[001]
Basic cell EDP
Indices all other reflections:
vector addition
110
020
200 210
120
![Page 20: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/20.jpg)
1/3Å
1/5Å
Experimentally: the other way around:
010
100
[001]
*
![Page 21: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/21.jpg)
*How?
Make a list of all reflections with hkl and their d-values.
• use Excel to make the list yourself
• use free software like Powdercell
• ...
d hkl
7.68 001
5.64 010
5.46 100
4.55 011
4.45 101
3.92 110
... ...
![Page 22: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/22.jpg)
010
100
Zone-index: [001]
obtained by vector multiplication.
Circle ACW around 000.
1 0 0 1 0 0 0 1 0 0 1 0
0*0-0*1 0*0-1*0 1*1-0*0
[ 0 0 1 ]
0 01 0
0 10 0
1 00 1
![Page 23: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/23.jpg)
(010)
(100)
(110)
[001]
010
100 110
[001]
110 -
(110) -
![Page 24: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/24.jpg)
Exercise: index the given patterns taken
from a CaF2 mineral
![Page 25: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/25.jpg)
a
b
c
b
a
c
CaF2
cubic
a=5.46 Å
Fm3m -
![Page 26: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/26.jpg)
h k l d I F 1 1 1 3.15349 83.73 61.89 2 0 0 2.731 0.11 3.07 2 2 0 1.93111 100 96.55 3 1 1 1.64685 31.44 46.49 2 2 2 1.57674 0.2 6.81 4 0 0 1.3655 12.69 74.25 3 3 1 1.25307 11.35 38.65 4 2 0 1.22134 0.54 8.67 4 2 2 1.11493 23.75 61.87 5 1 1 1.05116 6.88 34.2 3 3 3 1.05116 2.29 34.2
You need this table made for CaF2
![Page 27: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/27.jpg)
We are going to index these patterns. They are obtained by tilting around the diagonal row.
(Online version: working page can be found at the end.)
![Page 28: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/28.jpg)
We are going to index these patterns. They are obtained by tilting around the diagonal row.
(Online version: workpage can be found at the end.)
![Page 29: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/29.jpg)
Start with easiest: highest symmetry or smallest interreflection distances = usually lower zone indices (“main zones”)
(Online version: workpage can be found at the end.)
![Page 30: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/30.jpg)
h k l d I F 1 1 1 3.15349 83.73 61.89 2 0 0 2.731 0.11 3.07 2 2 0 1.93111 100 96.55 3 1 1 1.64685 31.44 46.49 2 2 2 1.57674 0.2 6.81 4 0 0 1.3655 12.69 74.25 3 3 1 1.25307 11.35 38.65 4 2 0 1.22134 0.54 8.67 4 2 2 1.11493 23.75 61.87 5 1 1 1.05116 6.88 34.2 3 3 3 1.05116 2.29 34.2
Why go for smaller interreflection distances?
=higher d = less choices
![Page 31: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/31.jpg)
First pattern:
Apparent symmetry: 4-fold
4,4,0
4,2,0
4,0,0
4,-2,0
4,-4,0
2,4,0
2,2,0
2,0,0
2,-2,0
2,-4,0
0,4,0
0,2,0
0,-2,0
0,-4,0
-2,4,0
-2,2,0
-2,0,0
-2,-2,0
-2,-4,0
-4,4,0
-4,2,0
-4,0,0
-4,-2,0
-4,-4,0
Zone axis : [0,0,1]
Go for highest symmetry
![Page 32: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/32.jpg)
a
b
c
Along which direction does the 4-fold axis lie in a cubic system? <001>
<011> <111>
b
a
c
CaF2
![Page 33: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/33.jpg)
a
b
c
Along which direction does the 4-old axis lie in a cubic system? <001>
<011> <111>
b
a
c
CaF2
![Page 34: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/34.jpg)
probably this is <001>
(Cubic: [100], [010], [001] equivalent = <001>)
4,4,0
4,2,0
4,0,0
4,-2,0
4,-4,0
2,4,0
2,2,0
2,0,0
2,-2,0
2,-4,0
0,4,0
0,2,0
0,-2,0
0,-4,0
-2,4,0
-2,2,0
-2,0,0
-2,-2,0
-2,-4,0
-4,4,0
-4,2,0
-4,0,0
-4,-2,0
-4,-4,0
Zone axis : [0,0,1]
![Page 35: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/35.jpg)
To do: measure the distances, compare to list d-hkl, index consistently.
Scalebar = R (in mm)
Step 1: Use the scalebar for the conversion factor to 1/d-values.
equal to 1/0.08 nm R.d=L
L
42 43 44
34.4 mmÅ 53.8 mmÅ 0.02 mmÅ
![Page 36: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/36.jpg)
To do: measure the distances, compare to list d-hkl, index consistently.
Scalebar = R (in mm)
Step 1: Use the scalebar for the conversion factor to 1/d-values.
equal to 1/0.08 nm R.d=L
L
42 43 44
34.4 mmÅ 53.8 mmÅ 0.02 mmÅ
![Page 37: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/37.jpg)
To do: measure the distances, compare to list d-hkl, index consistently.
Scalebar = R (in mm)
Step 1: Use the scalebar for the conversion factor to 1/d-values.
equal to 1/0.08 nm R.d=L
L
42 43 44
34.4 mmÅ 53.8 mmÅ 0.02 mmÅ
![Page 38: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/38.jpg)
Step 2: measure the distance of two reflections, not on the same line, calculate the corresponding
d-value
Point 1 d 5.46 Å 3.15 Å 2.73 Å
Point 2 d
4,4,0
4,2,0
4,0,0
4,-2,0
4,-4,0
2,4,0
2,2,0
2,0,0
2,-2,0
2,-4,0
0,4,0
0,2,0
0,-2,0
0,-4,0
-2,4,0
-2,2,0
-2,0,0
-2,-2,0
-2,-4,0
-4,4,0
-4,2,0
-4,0,0
-4,-2,0
-4,-4,0
Zone axis : [0,0,1]
5.46 Å 3.15 Å 2.73 Å
1 2
![Page 39: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/39.jpg)
Step 2: measure the distance of two reflections, not on the same line, calculate the corresponding
d-value
Point 1 d 5.46 Å 3.15 Å 2.73 Å
Point 2 d
4,4,0
4,2,0
4,0,0
4,-2,0
4,-4,0
2,4,0
2,2,0
2,0,0
2,-2,0
2,-4,0
0,4,0
0,2,0
0,-2,0
0,-4,0
-2,4,0
-2,2,0
-2,0,0
-2,-2,0
-2,-4,0
-4,4,0
-4,2,0
-4,0,0
-4,-2,0
-4,-4,0
Zone axis : [0,0,1]
5.46 Å 3.15 Å 2.73 Å
1 2
![Page 40: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/40.jpg)
Step 2: measure the distance of two reflections, not on the same line, calculate the corresponding
d-value
Point 1 d 5.46 Å 3.15 Å 2.73 Å
Point 2 d
4,4,0
4,2,0
4,0,0
4,-2,0
4,-4,0
2,4,0
2,2,0
2,0,0
2,-2,0
2,-4,0
0,4,0
0,2,0
0,-2,0
0,-4,0
-2,4,0
-2,2,0
-2,0,0
-2,-2,0
-2,-4,0
-4,4,0
-4,2,0
-4,0,0
-4,-2,0
-4,-4,0
Zone axis : [0,0,1]
5.46 Å 3.15 Å 2.73 Å
1 2
![Page 41: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/41.jpg)
To do: measure the distances, compare to list d-hkl, index.
Step 3: look up in the table to which reflection this corresponds
100 110 200
Point 1 d
Point 2 d
Point 1 hkl
Point 2 hkl
1 2
5.46 Å 3.15 Å 2.73 Å
5.46 Å 3.15 Å 2.73 Å
100 110 200
![Page 42: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/42.jpg)
To do: measure the distances, compare to list d-hkl, index.
Step 3: look up in the table to which reflection this corresponds
100 110 200
Point 1 d
Point 2 d
Point 1 hkl
Point 2 hkl
1 2
5.46 Å 3.15 Å 2.73 Å
5.46 Å 3.15 Å 2.73 Å
100 110 200
![Page 43: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/43.jpg)
To do: measure the distances, compare to list d-hkl, index.
Step 3: look up in the table to which reflection this corresponds
100 110 200
Point 1 d
Point 2 d
Point 1 hkl
Point 2 hkl
1 2
5.46 Å 3.15 Å 2.73 Å
5.46 Å 3.15 Å 2.73 Å
100 110 200
![Page 44: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/44.jpg)
Keep in mind: d-values valid for all equivalent {hkl}!
Step 4: make the indexation consistent
100
010 1
2
If point 1 is 200 then point 2 is 020 or 002.
Choose and stick with your choice.
![Page 45: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/45.jpg)
100
010
200 020
![Page 46: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/46.jpg)
Step 5: calculate the zone-index
[100] [010] [001]
010
200 020
![Page 47: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/47.jpg)
Step 5: calculate the zone-index
[100] [010] [001]
200 020
![Page 48: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/48.jpg)
Next zone
Which one would be easiest next?
2 3 4
![Page 49: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/49.jpg)
Next zone
Which one would be easiest next?
2 3 4
![Page 50: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/50.jpg)
Next zone: with reflections closest to the central beam.
Reflections closer to the central beam: higher d-values
smaller amount of possible matches of hkl to this d
5,5,5
5,3,3
5,1,1
5,-1,-1
5,-3,-3
5,-5,-5
4,4,4
4,2,2
4,0,0
4,-2,-2
4,-4,-4
3,5,5
3,3,3
3,1,1
3,-1,-1
3,-3,-3
3,-5,-5
2,4,4
2,2,2
2,0,0
2,-2,-2
2,-4,-4
1,5,5
1,3,3
1,1,1
1,-1,-1
1,-3,-3
1,-5,-5
0,4,4
0,2,2
0,-2,-2
0,-4,-4
-1,5,5
-1,3,3
-1,1,1
-1,-1,-1
-1,-3,-3
-1,-5,-5
-2,4,4
-2,2,2
-2,0,0
-2,-2,-2
-2,-4,-4
-3,5,5
-3,3,3
-3,1,1
-3,-1,-1
-3,-3,-3
-3,-5,-5
-4,4,4
-4,2,2
-4,0,0
-4,-2,-2
-4,-4,-4
-5,5,5
-5,3,3
-5,1,1
-5,-1,-1
-5,-3,-3
-5,-5,-5
![Page 51: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/51.jpg)
Measure the distance of two reflections, not on the same line, calculate the corresponding d-value
Point 1 d 2.57 Å 2.75 Å 3.15 Å
Point 2 d
1 2
2.57 Å 2.73 Å 3.15 Å
![Page 52: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/52.jpg)
Measure the distance of two reflections, not on the same line, calculate the corresponding d-value
Point 1 d 2.57 Å 2.75 Å 3.15 Å
Point 2 d
1 2
2.57 Å 2.73 Å 3.15 Å
![Page 53: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/53.jpg)
Measure the distance of two reflections, not on the same line, calculate the corresponding d-value
Point 1 d 2.57 Å 2.75 Å 3.15 Å
Point 2 d
1 2
2.57 Å 2.73 Å 3.15 Å
![Page 54: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/54.jpg)
Look up in the table to which reflection this corresponds
110 200 111
110 200 111
Point 1 d = 3.15 Å
Point 2 d = 2.73 Å
hkl hkl
1 2
![Page 55: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/55.jpg)
Look up in the table to which reflection this corresponds
110 200 111
110 200 111
Point 1 d = 3.15 Å
Point 2 d = 2.73 Å
hkl hkl
1 2
![Page 56: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/56.jpg)
Look up in the table to which reflection this corresponds
110 200 111
110 200 111
Point 1 d = 3.15 Å
Point 2 d = 2.73 Å
hkl hkl
1 2
![Page 57: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/57.jpg)
Make the indexation in a consistent manner.
1 2
Point 2 should be indexed as 200 020 200 all are correct
-
![Page 58: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/58.jpg)
Make the indexation in a consistent manner.
1 2
Point 2 should be indexed as 200 020 200 all are correct
-
![Page 59: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/59.jpg)
Consistency: This is a tilt series...
...so the common row needs to have the same indices in all patterns
200 200
200 200
![Page 60: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/60.jpg)
Consistency:
5,5,5
5,3,3
5,1,1
5,-1,-1
5,-3,-3
5,-5,-5
4,4,4
4,2,2
4,0,0
4,-2,-2
4,-4,-4
3,5,5
3,3,3
3,1,1
3,-1,-1
3,-3,-3
3,-5,-5
2,4,4
2,2,2
2,0,0
2,-2,-2
2,-4,-4
1,5,5
1,3,3
1,1,1
1,-1,-1
1,-3,-3
1,-5,-5
0,4,4
0,2,2
0,-2,-2
0,-4,-4
-1,5,5
-1,3,3
-1,1,1
-1,-1,-1
-1,-3,-3
-1,-5,-5
-2,4,4
-2,2,2
-2,0,0
-2,-2,-2
-2,-4,-4
-3,5,5
-3,3,3
-3,1,1
-3,-1,-1
-3,-3,-3
-3,-5,-5
-4,4,4
-4,2,2
-4,0,0
-4,-2,-2
-4,-4,-4
-5,5,5
-5,3,3
-5,1,1
-5,-1,-1
-5,-3,-3
-5,-5,-5
200 1
Point 1 should be indexed as 111 111 111 all of the above are allowed
- - -
![Page 61: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/61.jpg)
Consistency:
5,5,5
5,3,3
5,1,1
5,-1,-1
5,-3,-3
5,-5,-5
4,4,4
4,2,2
4,0,0
4,-2,-2
4,-4,-4
3,5,5
3,3,3
3,1,1
3,-1,-1
3,-3,-3
3,-5,-5
2,4,4
2,2,2
2,0,0
2,-2,-2
2,-4,-4
1,5,5
1,3,3
1,1,1
1,-1,-1
1,-3,-3
1,-5,-5
0,4,4
0,2,2
0,-2,-2
0,-4,-4
-1,5,5
-1,3,3
-1,1,1
-1,-1,-1
-1,-3,-3
-1,-5,-5
-2,4,4
-2,2,2
-2,0,0
-2,-2,-2
-2,-4,-4
-3,5,5
-3,3,3
-3,1,1
-3,-1,-1
-3,-3,-3
-3,-5,-5
-4,4,4
-4,2,2
-4,0,0
-4,-2,-2
-4,-4,-4
-5,5,5
-5,3,3
-5,1,1
-5,-1,-1
-5,-3,-3
-5,-5,-5
200 1
Point 1 should be indexed as 111 111 111 all of the above are allowed
- - -
![Page 62: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/62.jpg)
Consistency:
200 111
111 -
If 111 for point 1 -
311 -
Point 3 is 311 111
![Page 63: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/63.jpg)
Consistency:
If 111 for point 1 -
311 -
Point 3 is 311 111
200 1
![Page 64: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/64.jpg)
Consistency:
200 111
111 -
1 200
3
If 111 for point 1 -
point 3 = 311 -
![Page 65: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/65.jpg)
Consistency:
200 111
111 -
1 200
3
If 111 for point 1 -
point 3 = 311 -
d311 ≠ dpoint3 - but
![Page 66: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/66.jpg)
Consistency:
200 111
111 -
1 200
3
If 111 for point 1 -
point 3 = 311 -
d311 ≠ dpoint3 - but
![Page 67: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/67.jpg)
Consistency:
200 111
111 - 1
200
3
1 and 3 have the same d-value +
relation between 1 and 3 = vector 200 you need two indices such that
h3+2 = h1 k3+0 = k1 l3+0 = l1
(also possible 111 and 111, make a choice and stick to it for the following patterns) - - -
= h1 k1 l1
![Page 68: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/68.jpg)
Consistency:
200 111
111 -
Sum = 022.
Indeed consistent: if 𝑔 perpendicular to 𝑔 200 then type of reflection needs to be 0kl.
022 200 022
![Page 69: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/69.jpg)
Calculate the zone-index
The zone-index is: [011] [011]
200 111
111 -
022
-
![Page 70: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/70.jpg)
Calculate the zone-index
The zone-index is: [011] [011]
200 111
111 -
022
-
![Page 71: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/71.jpg)
...this helps to index the two remaining patterns!!!
Consistency: This is a tilt series...
![Page 72: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/72.jpg)
a
b
c
The crystallite is threedimensional.
![Page 73: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/73.jpg)
0,4,0
0,4,2
1,5,1
0,4,4
1,5,3
0,2,0
0,2,2
1,3,1
0,2,4
2,4,0
1,3,3
2,4,2
3,5,1
0,0,2
2,4,4
1,1,1
3,5,3
0,0,4
2,2,0
1,1,3
2,2,2
3,3,1
2,2,4
4,4,0
3,3,3
2,0,0
4,4,2
5,5,1
2,0,2
4,4,4
3,1,1
5,5,3
2,0,4
4,2,0
3,1,3
4,2,2
5,3,1
4,2,4
5,3,3
4,0,0
4,0,2
5,1,1
4,0,4
5,1,3
Zone axis : [0,0,0] So, the reciprocal lattice is threedimensional.
![Page 74: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/74.jpg)
0,4,0
0,4,2
1,5,1
0,4,4
1,5,3
0,2,0
0,2,2
1,3,1
0,2,4
2,4,0
1,3,3
2,4,2
3,5,1
0,0,2
2,4,4
1,1,1
3,5,3
0,0,4
2,2,0
1,1,3
2,2,2
3,3,1
2,2,4
4,4,0
3,3,3
2,0,0
4,4,2
5,5,1
2,0,2
4,4,4
3,1,1
5,5,3
2,0,4
4,2,0
3,1,3
4,2,2
5,3,1
4,2,4
5,3,3
4,0,0
4,0,2
5,1,1
4,0,4
5,1,3
Zone axis : [0,0,0]
ED patterns are sections of reciprocal space.
[001]
This section is the [001] zone.
![Page 75: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/75.jpg)
0,4,0
0,4,2
1,5,1
0,4,4
1,5,3
0,2,0
0,2,2
1,3,1
0,2,4
2,4,0
1,3,3
2,4,2
3,5,1
0,0,2
2,4,4
1,1,1
3,5,3
0,0,4
2,2,0
1,1,3
2,2,2
3,3,1
2,2,4
4,4,0
3,3,3
2,0,0
4,4,2
5,5,1
2,0,2
4,4,4
3,1,1
5,5,3
2,0,4
4,2,0
3,1,3
4,2,2
5,3,1
4,2,4
5,3,3
4,0,0
4,0,2
5,1,1
4,0,4
5,1,3
Zone axis : [0,0,0]
[011] -
This section is the [011] zone: -
![Page 76: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/76.jpg)
0,4,0
0,4,2
1,5,1
0,4,4
1,5,3
0,2,0
0,2,2
1,3,1
0,2,4
2,4,0
1,3,3
2,4,2
3,5,1
0,0,2
2,4,4
1,1,1
3,5,3
0,0,4
2,2,0
1,1,3
2,2,2
3,3,1
2,2,4
4,4,0
3,3,3
2,0,0
4,4,2
5,5,1
2,0,2
4,4,4
3,1,1
5,5,3
2,0,4
4,2,0
3,1,3
4,2,2
5,3,1
4,2,4
5,3,3
4,0,0
4,0,2
5,1,1
4,0,4
5,1,3
Zone axis : [0,0,0]
[001]
[011] -
We tilt from [001] to [011]: -
![Page 77: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/77.jpg)
0,4,0
0,4,2
1,5,1
0,4,4
1,5,3
0,2,0
0,2,2
1,3,1
0,2,4
2,4,0
1,3,3
2,4,2
3,5,1
0,0,2
2,4,4
1,1,1
3,5,3
0,0,4
2,2,0
1,1,3
2,2,2
3,3,1
2,2,4
4,4,0
3,3,3
2,0,0
4,4,2
5,5,1
2,0,2
4,4,4
3,1,1
5,5,3
2,0,4
4,2,0
3,1,3
4,2,2
5,3,1
4,2,4
5,3,3
4,0,0
4,0,2
5,1,1
4,0,4
5,1,3
Zone axis : [0,0,0]
[001]
[011] -
So the tilt series gives pattern of consecutive sections between these two end zones
Closest is 020.
![Page 78: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/78.jpg)
0,4,0
0,4,2
1,5,1
0,4,4
1,5,3
0,2,0
0,2,2
1,3,1
0,2,4
2,4,0
1,3,3
2,4,2
3,5,1
0,0,2
2,4,4
1,1,1
3,5,3
0,0,4
2,2,0
1,1,3
2,2,2
3,3,1
2,2,4
4,4,0
3,3,3
2,0,0
4,4,2
5,5,1
2,0,2
4,4,4
3,1,1
5,5,3
2,0,4
4,2,0
3,1,3
4,2,2
5,3,1
4,2,4
5,3,3
4,0,0
4,0,2
5,1,1
4,0,4
5,1,3
Zone axis : [0,0,0]
[001]
[015] -
[011] -
x 051
Closest is 151.
![Page 79: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/79.jpg)
0,4,0
0,4,2
1,5,1
0,4,4
1,5,3
0,2,0
0,2,2
1,3,1
0,2,4
2,4,0
1,3,3
2,4,2
3,5,1
0,0,2
2,4,4
1,1,1
3,5,3
0,0,4
2,2,0
1,1,3
2,2,2
3,3,1
2,2,4
4,4,0
3,3,3
2,0,0
4,4,2
5,5,1
2,0,2
4,4,4
3,1,1
5,5,3
2,0,4
4,2,0
3,1,3
4,2,2
5,3,1
4,2,4
5,3,3
4,0,0
4,0,2
5,1,1
4,0,4
5,1,3
Zone axis : [0,0,0]
[011]
[001]
[013] - x
031
Closest is 131.
![Page 80: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/80.jpg)
0,4,0
0,4,2
1,5,1
0,4,4
1,5,3
0,2,0
0,2,2
1,3,1
0,2,4
2,4,0
1,3,3
2,4,2
3,5,1
0,0,2
2,4,4
1,1,1
3,5,3
0,0,4
2,2,0
1,1,3
2,2,2
3,3,1
2,2,4
4,4,0
3,3,3
2,0,0
4,4,2
5,5,1
2,0,2
4,4,4
3,1,1
5,5,3
2,0,4
4,2,0
3,1,3
4,2,2
5,3,1
4,2,4
5,3,3
4,0,0
4,0,2
5,1,1
4,0,4
5,1,3
Zone axis : [0,0,0]
[011]
[001]
x 021
[012] -
042
Closest is 042.
![Page 81: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/81.jpg)
0,4,0
0,4,2
1,5,1
0,4,4
1,5,3
0,2,0
0,2,2
1,3,1
0,2,4
2,4,0
1,3,3
2,4,2
3,5,1
0,0,2
2,4,4
1,1,1
3,5,3
0,0,4
2,2,0
1,1,3
2,2,2
3,3,1
2,2,4
4,4,0
3,3,3
2,0,0
4,4,2
5,5,1
2,0,2
4,4,4
3,1,1
5,5,3
2,0,4
4,2,0
3,1,3
4,2,2
5,3,1
4,2,4
5,3,3
4,0,0
4,0,2
5,1,1
4,0,4
5,1,3
Zone axis : [0,0,0]
[011]
[001]
[035] -
x 053
Closest is 153.
![Page 82: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/82.jpg)
0,4,0
0,4,2
1,5,1
0,4,4
1,5,3
0,2,0
0,2,2
1,3,1
0,2,4
2,4,0
1,3,3
2,4,2
3,5,1
0,0,2
2,4,4
1,1,1
3,5,3
0,0,4
2,2,0
1,1,3
2,2,2
3,3,1
2,2,4
4,4,0
3,3,3
2,0,0
4,4,2
5,5,1
2,0,2
4,4,4
3,1,1
5,5,3
2,0,4
4,2,0
3,1,3
4,2,2
5,3,1
4,2,4
5,3,3
4,0,0
4,0,2
5,1,1
4,0,4
5,1,3
Zone axis : [0,0,0]
[001]
[011] -
Closest is 111. Perpendicular is 022.
![Page 83: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/83.jpg)
0,4,0
0,4,2
0,4,4
0,2,0
1,5,1
0,2,2
1,5,3
0,2,4
1,3,1
0,0,2
1,3,3
0,0,4
2,4,0
1,1,1
2,4,2
1,1,3
2,4,4
2,2,0
3,5,1
2,2,2
3,5,3
2,2,4
2,0,0
3,3,1
2,0,2
3,3,3
2,0,4
4,4,0
3,1,1
4,4,2
3,1,3
4,4,4
4,2,0
5,5,1
4,2,2
5,5,3
4,2,4
4,0,0
5,3,1
4,0,2
5,3,3
4,0,4
5,1,1
5,1,3
Zone axis : [0,0,0]
We can also see this in projection
![Page 84: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/84.jpg)
0,4,4
0,4,2
0,4,0
1,5,3
1,5,1
0,2,4
0,2,2
0,2,0
1,3,3
1,3,1
0,0,4
0,0,2
2,4,4
2,4,2
2,4,0
1,1,3
1,1,1
3,5,3
3,5,1
2,2,4
2,2,2
2,2,0
3,3,3
3,3,1
2,0,4
2,0,2
2,0,0
4,4,4
4,4,2
4,4,0
3,1,3
3,1,1
5,5,3
5,5,1
4,2,4
4,2,2
4,2,0
5,3,3
5,3,1
4,0,4
4,0,2
4,0,0
5,1,3
5,1,1
Zone axis : [0,0,0]
We can also see this in projection
![Page 85: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/85.jpg)
0,4,4
0,4,2
0,4,0
0,2,4
0,2,2
0,2,0
0,0,4
0,0,2
1,5,3
1,5,1
1,3,3
1,3,1
1,1,3
1,1,1
2,4,4
2,4,2
2,4,0
2,2,4
2,2,2
2,2,0
2,0,4
2,0,2
2,0,0
3,5,3
3,5,1
3,3,3
3,3,1
3,1,3
3,1,1
4,4,4
4,4,2
4,4,0
4,2,4
4,2,2
4,2,0
4,0,4
4,0,2
4,0,0
5,5,3
5,5,1
5,3,3
5,3,1
5,1,3
5,1,1
Zone axis : [0,0,0]
We can also see this in projection
![Page 86: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/86.jpg)
0,0,4
0,0,2
0,2,4
0,2,2
0,4,4
0,2,0
0,4,2
0,4,0
1,1,3
1,1,1
1,3,3
1,3,1
1,5,3
1,5,1
2,0,4
2,0,2
2,2,4
2,0,0
2,2,2
2,4,4
2,2,0
2,4,2
2,4,0
3,1,3
3,1,1
3,3,3
3,3,1
3,5,3
3,5,1
4,0,4
4,0,2
4,2,4
4,0,0
4,2,2
4,4,4
4,2,0
4,4,2
4,4,0
5,1,3
5,1,1
5,3,3
5,3,1
5,5,3
5,5,1
Zone axis : [0,0,0]
We can also see this in projection which is easier to draw manually...
![Page 87: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/87.jpg)
0,0,4
0,0,2
0,2,4
0,2,2
0,4,4
0,2,0
0,4,2
0,4,0
1,1,3
1,1,1
1,3,3
1,3,1
1,5,3
1,5,1
2,0,4
2,0,2
2,2,4
2,0,0
2,2,2
2,4,4
2,2,0
2,4,2
2,4,0
3,1,3
3,1,1
3,3,3
3,3,1
3,5,3
3,5,1
4,0,4
4,0,2
4,2,4
4,0,0
4,2,2
4,4,4
4,2,0
4,4,2
4,4,0
5,1,3
5,1,1
5,3,3
5,3,1
5,5,3
5,5,1
Zone axis : [0,0,0]
[001]
![Page 88: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/88.jpg)
0,0,4
0,0,2
0,2,4
0,2,2
0,4,4
0,2,0
0,4,2
0,4,0
1,1,3
1,1,1
1,3,3
1,3,1
1,5,3
1,5,1
2,0,4
2,0,2
2,2,4
2,0,0
2,2,2
2,4,4
2,2,0
2,4,2
2,4,0
3,1,3
3,1,1
3,3,3
3,3,1
3,5,3
3,5,1
4,0,4
4,0,2
4,2,4
4,0,0
4,2,2
4,4,4
4,2,0
4,4,2
4,4,0
5,1,3
5,1,1
5,3,3
5,3,1
5,5,3
5,5,1
Zone axis : [0,0,0]
[001]
[015] -
![Page 89: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/89.jpg)
0,0,4
0,0,2
0,2,4
0,2,2
0,4,4
0,2,0
0,4,2
0,4,0
1,1,3
1,1,1
1,3,3
1,3,1
1,5,3
1,5,1
2,0,4
2,0,2
2,2,4
2,0,0
2,2,2
2,4,4
2,2,0
2,4,2
2,4,0
3,1,3
3,1,1
3,3,3
3,3,1
3,5,3
3,5,1
4,0,4
4,0,2
4,2,4
4,0,0
4,2,2
4,4,4
4,2,0
4,4,2
4,4,0
5,1,3
5,1,1
5,3,3
5,3,1
5,5,3
5,5,1
Zone axis : [0,0,0]
[001]
[015] -
[013] -
![Page 90: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/90.jpg)
0,0,4
0,0,2
0,2,4
0,2,2
0,4,4
0,2,0
0,4,2
0,4,0
1,1,3
1,1,1
1,3,3
1,3,1
1,5,3
1,5,1
2,0,4
2,0,2
2,2,4
2,0,0
2,2,2
2,4,4
2,2,0
2,4,2
2,4,0
3,1,3
3,1,1
3,3,3
3,3,1
3,5,3
3,5,1
4,0,4
4,0,2
4,2,4
4,0,0
4,2,2
4,4,4
4,2,0
4,4,2
4,4,0
5,1,3
5,1,1
5,3,3
5,3,1
5,5,3
5,5,1
Zone axis : [0,0,0]
[001]
[015] -
[013] -
[012] -
![Page 91: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/91.jpg)
0,0,4
0,0,2
0,2,4
0,2,2
0,4,4
0,2,0
0,4,2
0,4,0
1,1,3
1,1,1
1,3,3
1,3,1
1,5,3
1,5,1
2,0,4
2,0,2
2,2,4
2,0,0
2,2,2
2,4,4
2,2,0
2,4,2
2,4,0
3,1,3
3,1,1
3,3,3
3,3,1
3,5,3
3,5,1
4,0,4
4,0,2
4,2,4
4,0,0
4,2,2
4,4,4
4,2,0
4,4,2
4,4,0
5,1,3
5,1,1
5,3,3
5,3,1
5,5,3
5,5,1
Zone axis : [0,0,0]
[001]
[015] -
[013] -
[012] -
[035] -
![Page 92: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/92.jpg)
0,0,4
0,0,2
0,2,4
0,2,2
0,4,4
0,2,0
0,4,2
0,4,0
1,1,3
1,1,1
1,3,3
1,3,1
1,5,3
1,5,1
2,0,4
2,0,2
2,2,4
2,0,0
2,2,2
2,4,4
2,2,0
2,4,2
2,4,0
3,1,3
3,1,1
3,3,3
3,3,1
3,5,3
3,5,1
4,0,4
4,0,2
4,2,4
4,0,0
4,2,2
4,4,4
4,2,0
4,4,2
4,4,0
5,1,3
5,1,1
5,3,3
5,3,1
5,5,3
5,5,1
Zone axis : [0,0,0]
[001]
[015] -
[013] -
[012] -
[035] -
[011] -
![Page 93: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/93.jpg)
Right upper zone:
Point 2 d
1.22 Å 1.11 Å 1.05 Å
Measure the distance of two reflections, not on the same line, calculate the corresponding d-value
5,5,1
5,-5,-1
4,0,0
3,5,1
3,-5,-1
2,0,0
1,5,1
1,-5,-1
-1,5,1
-1,-5,-1
-2,0,0
-3,5,1
-3,-5,-1
-4,0,0
-5,5,1
-5,-5,-1
We already know the first point: 200.
200 2
![Page 94: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/94.jpg)
Right upper zone:
Point 2 d
1.22 Å 1.11 Å 1.05 Å
Measure the distance of two reflections, not on the same line, calculate the corresponding d-value
5,5,1
5,-5,-1
4,0,0
3,5,1
3,-5,-1
2,0,0
1,5,1
1,-5,-1
-1,5,1
-1,-5,-1
-2,0,0
-3,5,1
-3,-5,-1
-4,0,0
-5,5,1
-5,-5,-1
We already know the first point: 200.
200 2
![Page 95: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/95.jpg)
Look up in the table to which reflection this corresponds: We know already it is either 151 or 131 or 042 or 153
1.05 Å 151 131 042
Point 2 d
Point 2 hkl
200 2
![Page 96: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/96.jpg)
Look up in the table to which reflection this corresponds: We know already it is either 151 or 131 or 042 or 153
1.05 Å 151 131 042
Point 2 d
Point 2 hkl
200 2
![Page 97: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/97.jpg)
If this were not a tilt series...
Point 2 could have been at first sight both 115 and 333...
In this case: Can compare the experimental angles between reflections to the theoretical angles -either formulas from any standard crystallography work -or simply simulate the different zones calculated for the different options (JEMS, CrystalKit, Carine,...) to check this
Or in this particular case of 333: you would need to see 111 and 222 at 1/3 and 2/3 of the distance.
![Page 98: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/98.jpg)
Calculate the zone-index
The zone-index is: [0 2 10] [0 1 5] [0 1 5]
200 151
-
![Page 99: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/99.jpg)
Calculate the zone-index
The zone-index is: [0 2 10] [0 1 5] [0 1 5]
200 151
-
![Page 100: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/100.jpg)
[001]
[015] -
[013] -
[012] - [035] -
[011] -
010
031 051
053
What if you didn’t know the material?
You would just need to check more possibilities:
043
032
041 021
[025] -
052 [014] -
[023] - [034] -
When indexed correctly, the patterns in between have to give you one of these as zone-index.
011
![Page 101: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/101.jpg)
Pattern bottom left:
5,3,1
5,-3,-1
4,0,0
3,3,1
3,-3,-1
2,0,0
1,3,1
1,-3,-1
-1,3,1
-1,-3,-1
-2,0,0
-3,3,1
-3,-3,-1
-4,0,0
-5,3,1
-5,-3,-1
Point 2 d
Measure the distance of two reflections, not on the same line, calculate the corresponding d-value
200 2
1.65 Å 1.58 Å 1.37 Å
![Page 102: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/102.jpg)
Pattern bottom left:
5,3,1
5,-3,-1
4,0,0
3,3,1
3,-3,-1
2,0,0
1,3,1
1,-3,-1
-1,3,1
-1,-3,-1
-2,0,0
-3,3,1
-3,-3,-1
-4,0,0
-5,3,1
-5,-3,-1
Point 2 d
Measure the distance of two reflections, not on the same line, calculate the corresponding d-value
200 2
1.65 Å 1.58 Å 1.37 Å
![Page 103: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/103.jpg)
Look up in the table to which reflection this corresponds. We know already it is either: 151 or 131 or 042 or 153
1.65 Å 042 131 153
Point 2 d
Point 2 hkl
200 2
![Page 104: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/104.jpg)
Look up in the table to which reflection this corresponds. We know already it is either: 151 or 131 or 042 or 153
1.65 Å
Point 2 d
Point 2 hkl
200 2
042 131 153
![Page 105: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/105.jpg)
The indexation is indeed consistent.
200 131 062
131 -
![Page 106: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/106.jpg)
200 131 062
131 -
[013] -
![Page 107: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/107.jpg)
Make your analysis easier by not taking ED patterns from separate crystals, but taking different ED patterns from the
same crystallite, if possible.
=“Tilt series”
![Page 108: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/108.jpg)
So now you have indexed these four patterns.
200 131
200 151
200 111
200 020
[001] [015] -
[013] -
[011] -
![Page 109: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/109.jpg)
...indexed patterns give you info on fase, orientation, cell parameters,...
200 131
200 151
200 111
200 020
[001] [015] -
[013] -
[011] -
![Page 110: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/110.jpg)
What if you do not have any prior knowledge when you have to
index?
Analyse the patterns try to propose basis vectors (For example reflections closest to the central beam)
Same system as previous slides: can you index all reflections?
If not, adapt your choice of basis vectors and try again.
![Page 111: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/111.jpg)
If we do not know the space group, the next step would be to determine it!
(maybe you started from 0 or you had only cell parameters from XRD or...)
200 131
200 151
200 111
200 020
[001] [015] -
[013] -
[011] -
![Page 112: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/112.jpg)
Reflection conditions (SAED)
Space group?
P no reflection conditions
F h+k=2n, k+l=2n, h+l=2n
I h+k+l=2n
A/B/C k+l=2n/h+k=2n/h+k=2n
Point Group (CBED)
glide planes conditions on hk0/h0l/0kl
screw axes conditions on h00/0k0/00l
mirror planes, inversion centre, rotation axes
no extra conditions
CBED
SAED
+
![Page 113: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/113.jpg)
Reflection conditions can be looked up in tables in International Tables for Crystallography Vol. A
Or using freeware such as Space Group Explorer
![Page 114: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/114.jpg)
Be careful: forbidden reflections can occur because of dynamical diffraction
Incident electron wave
![Page 115: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/115.jpg)
When reflection conditions say this:
For example possible
020
100
Can see this:
010
100
![Page 116: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/116.jpg)
020
100
F(100)≠0
F(1 10) ≠0
F(010)=0
Need to tilt to remove these paths...
![Page 117: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/117.jpg)
Destroy double diffraction paths by tilting.
If becomes
If stays
then extinct, was due to DD
then not extinct.
![Page 118: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/118.jpg)
You will need this table (from IT volume A)
Figure out reflection conditions for these sets.
![Page 119: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/119.jpg)
hkl: h+k+l=2n h+k, k+l, h+l=2n h+k=2n
Step 1: determine the reflection conditions from the patterns.
200 131
200 151
200 111
200 020
[001] [015] -
[013] -
[011] -
![Page 120: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/120.jpg)
hkl: h+k+l=2n h+k, k+l, h+l=2n h+k=2n
Step 1: determine the reflection conditions from the patterns.
200 131
200 151
200 111
200 020
[001] [015] -
[013] -
[011] -
For these patterns both would be good....!?
![Page 121: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/121.jpg)
This means we do not have sufficient information.
we missed [012], which will make the difference. -
By coincidence
4,4,2
4,0,0
4,-4,-2
2,4,2
2,0,0
2,-4,-2
0,4,2
0,-4,-2
-2,4,2
-2,0,0
-2,-4,-2
-4,4,2
-4,0,0
-4,-4,-2
200
042
![Page 122: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/122.jpg)
0,0,4
0,0,2
0,2,4
0,2,2
0,4,4
0,2,0
0,4,2
0,4,0
1,1,3
1,1,1
1,3,3
1,3,1
1,5,3
1,5,1
2,0,4
2,0,2
2,2,4
2,0,0
2,2,2
2,4,4
2,2,0
2,4,2
2,4,0
3,1,3
3,1,1
3,3,3
3,3,1
3,5,3
3,5,1
4,0,4
4,0,2
4,2,4
4,0,0
4,2,2
4,4,4
4,2,0
4,4,2
4,4,0
5,1,3
5,1,1
5,3,3
5,3,1
5,5,3
5,5,1
Zone axis : [0,0,0]
[001]
[015] -
[013] -
[012] -
[035] -
[011] -
![Page 123: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/123.jpg)
This means we do not have sufficient information.
we missed [012], which will make the difference. -
By coincidence
4,4,2
4,0,0
4,-4,-2
2,4,2
2,0,0
2,-4,-2
0,4,2
0,-4,-2
-2,4,2
-2,0,0
-2,-4,-2
-4,4,2
-4,0,0
-4,-4,-2
200
042 hkl:
h+k+l=2n h+k, k+l, h+l=2n h+k=2n
![Page 124: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/124.jpg)
This means we do not have sufficient information.
we miss [012], which will make the difference. -
By coincidence
4,4,2
4,0,0
4,-4,-2
2,4,2
2,0,0
2,-4,-2
0,4,2
0,-4,-2
-2,4,2
-2,0,0
-2,-4,-2
-4,4,2
-4,0,0
-4,-4,-2
200
042 hkl:
h+k+l=2n h+k, k+l, h+l=2n h+k=2n
For only h+k=2n there is no reason why 021 would be absent.
![Page 125: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/125.jpg)
It is possible to draw the wrong conclusions if you do not have
enough zones!
![Page 126: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/126.jpg)
0kl: k=2n k,l=2n k+l=2n
Step 1: determine the reflection conditions from the patterns.
200 131
200 151
200 111
200 020
[001] [015] -
[013] -
[011] -
200
042
![Page 127: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/127.jpg)
0kl: k=2n k,l=2n k+l=2n
Step 1: determine the reflection conditions from the patterns.
200 131
200 151
200 111
200 020
[001] [015] -
[013] -
[011] -
200
042
![Page 128: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/128.jpg)
hhl: h=2n h,l=2n h+l=2n
Step 1: determine the reflection conditions from the patterns.
200 131
200 151
200 111
200 020
[001] [015] -
[013] -
[011] -
200
042
![Page 129: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/129.jpg)
hhl: h=2n h,l=2n h+l=2n
Step 1: determine the reflection conditions from the patterns.
200 131
200 151
200 111
200 020
[001] [015] -
[013] -
[011] -
200
042
![Page 130: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/130.jpg)
00l: no condition l=2n l=4n
Step 1: determine the reflection conditions from the patterns.
200 131
200 151
200 111
200 020
[001] [015] -
[013] -
[011] -
200
042
![Page 131: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/131.jpg)
00l: no condition l=2n l=4n
Step 1: determine the reflection conditions from the patterns.
200 131
200 151
200 111
200 020
[001] [015] -
[013] -
[011] -
200
042
![Page 132: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/132.jpg)
Step 2: look up the matching extinction symbol in the International Tables of
Crystallography.
? ?
![Page 133: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/133.jpg)
200 and 020 could be due to double diffraction...
200 131
200 151
200 111
200 020
[001] [015] -
[013] -
[011] -
![Page 134: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/134.jpg)
200 and 020 could be due to double diffraction...
Tilt around 200 until all other reflections gone except h00 axis:
200 131
200 151
200 111
200 020
[001] [015] -
[013] -
[011] -
![Page 135: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/135.jpg)
200 and 020 could be due to double diffraction...
Tilt around 200 until all other reflections gone except h00 axis:
200 does not disappear It is not double diffraction 00l: l=2n not 00l: l=4n
![Page 136: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/136.jpg)
Step 2: look up the matching extinction symbol in
the International Tables of Crystallography.
![Page 137: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/137.jpg)
From the reflection conditions you get the extinction symbol:
F - - -
![Page 138: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/138.jpg)
From the reflection conditions you get the extinction symbol:
F - - -
This still leaves 5 possible space groups
F23 Fm3 F432 F43m Fm3m
- - -
![Page 139: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/139.jpg)
From the reflection conditions you get the extinction symbol:
F - - -
This still leaves 5 possible space groups
F23 Fm3 F432 F43m Fm3m
Only difference: rotation axes and mirror planes
cannot be derived from reflection conditions
need CBED
- -
![Page 140: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/140.jpg)
Convergent Beam Electron Diffraction
CBED
![Page 141: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/141.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
Diffraction groups vs. Point groups
![Page 142: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/142.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
Diffraction groups vs. Point groups
![Page 143: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/143.jpg)
For CBED you need sufficiently thick crystals:
10 nm 20 nm 30 nm
40 nm 50 nm
![Page 144: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/144.jpg)
Table from: J.A. Eades, Convergent beam diffraction, in: Electron Diffraction Techniques, volume 1, ed. J. Cowley, Oxford University Press, 1992
![Page 145: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/145.jpg)
Symmetry is 4mm.
Whole pattern projection symmetry
![Page 146: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/146.jpg)
Table from: J.A. Eades, Convergent beam diffraction, in: Electron Diffraction Techniques, volume 1, ed. J. Cowley, Oxford University Press, 1992
![Page 147: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/147.jpg)
Table from: J.A. Eades, Convergent beam diffraction, in: Electron Diffraction Techniques, volume 1, ed. J. Cowley, Oxford University Press, 1992
![Page 148: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/148.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
Diffraction groups vs. Point groups
![Page 149: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/149.jpg)
[111]
![Page 150: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/150.jpg)
6mm
[111]
![Page 151: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/151.jpg)
Table from: J.A. Eades, Convergent beam diffraction, in: Electron Diffraction Techniques, volume 1, ed. J. Cowley, Oxford University Press, 1992
![Page 152: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/152.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
Diffraction groups vs. Point groups
![Page 153: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/153.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
Diffraction groups vs. Point groups
![Page 154: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/154.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
Diffraction groups vs. Point groups
![Page 155: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/155.jpg)
![Page 156: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/156.jpg)
![Page 157: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/157.jpg)
CBED
SAED
![Page 158: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/158.jpg)
So, sometimes just whole pattern projection symmetry is enough if you combine it with the
reflection conditions from SAED.
![Page 159: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/159.jpg)
Try it yourself on example SnO2
![Page 160: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/160.jpg)
SAED CBED
Example: rutile-type SnO2
![Page 161: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/161.jpg)
Projection whole pattern symmetry [001]
4 4mm 2mm
![Page 162: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/162.jpg)
Projection whole pattern symmetry [001]
4 4mm 2mm
![Page 163: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/163.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
4 4RmmR
4mm1R
![Page 164: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/164.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
4 4RmmR
4mm1R
![Page 165: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/165.jpg)
Projection diffraction group: 4mm1R
Possible diffraction groups:
4mRmR
4mm 4RmmR
4mm1R
Table from: J.A. Eades, Convergent beam diffraction, in: Electron Diffraction Techniques, volume 1, ed. J. Cowley, Oxford University Press, 1992
![Page 166: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/166.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
![Page 167: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/167.jpg)
What will be useful to narrow it down further?
look at the bright field symmetry look at the whole pattern symmetry
[...] [...]
![Page 168: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/168.jpg)
What will be useful to narrow it down further?
look at the bright field symmetry look at the whole pattern symmetry
[...] [...]
![Page 169: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/169.jpg)
Whole Pattern projection symmetry
Whole pattern symmetry
![Page 170: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/170.jpg)
WP symmetry
4 4mm 2mm
![Page 171: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/171.jpg)
WP symmetry
4 4mm 2mm
![Page 172: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/172.jpg)
[...] [...]
![Page 173: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/173.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 174: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/174.jpg)
Projection whole pattern [101]
2 m 2mm
(smaller cond.ap.)
![Page 175: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/175.jpg)
Projection whole pattern [101]
2 m 2mm
(smaller cond.ap.)
![Page 176: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/176.jpg)
Possible projection diffraction group:
21R
m1R
2mm1R
Projection whole pattern:
2mm
![Page 177: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/177.jpg)
Possible projection diffraction group:
21R
m1R
2mm1R
Projection whole pattern:
2mm
![Page 178: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/178.jpg)
Possible projection diffraction group:
21R
m1R
2mm1R
Projection whole pattern:
2mm
![Page 179: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/179.jpg)
Whole pattern [101]
2 m 2mm
(smaller cond.ap.)
![Page 180: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/180.jpg)
Whole pattern [101]
2 m 2mm
(smaller cond.ap.)
![Page 181: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/181.jpg)
Diffraction group:
2mm
2RmmR
2mm1R
Whole pattern m
![Page 182: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/182.jpg)
Diffraction group:
2mm
2RmmR
2mm1R
Whole pattern m
![Page 183: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/183.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 184: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/184.jpg)
Possible point groups
4/mmm
m3m
![Page 185: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/185.jpg)
What would make a difference further?
For example: -cell parameters -look for a third zone etc. -SAED for reflection conditions
![Page 186: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/186.jpg)
For example, if you need
cell parameters a=b= 4.72 Å, c=3.16 Å
to be able to index all patterns,
the point group is
4/mmm
m3m
![Page 187: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/187.jpg)
For example, if you need
cell parameters a=b= 4.72 Å, c=3.16 Å
to be able to index all patterns,
the point group is
4/mmm
m3m
![Page 188: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/188.jpg)
CBED
SAED
Space Group P42/mnm
Then you would combine this again with reflection conditions (not derived in this exercise) to get the space group.
![Page 189: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/189.jpg)
At the end of this lecture you should be able to
(1) index SAED patterns in case the cell parameters are already known
(2) determine the possible space groups from SAED patterns
(3) determine possible point groups from CBED patterns
Combine (2) and (3) to find the space group.
![Page 190: TEM workshop 2013: Electron diffraction](https://reader033.vdocuments.site/reader033/viewer/2022051323/549e7326ac795947768b479a/html5/thumbnails/190.jpg)
Working page for indexing