1) The purpose of the lecture is to teach how to index and determine cell parameters from SAED patterns, determine possible space groups and point groups, and solve simple structures from PED patterns.
2) Example materials used are aluminum and rutile-type SnO2. The slides and exercises for determining unknown cell parameters from SAED patterns are provided.
3) The document provides a step-by-step example of determining the cell parameters of aluminum from its SAED patterns, starting with no prior knowledge of the material. The correct cell is determined to be cubic with a=b=c=4.06 Angstroms.
2. 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
3. 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.
18. How many possible choices for the basic vectors are
there on this square pattern?
1
2
more
19. How many possible choices for the basic vectors are
there on this square pattern?
1
2
more
20. There can be a reflection condition!
hk0: 100 200
a*
020 a* h=2n,
no cond. 010
b* b* k=2n
020 200
b* a* Choose simplest
h+k=2n first and see if ok
with other zones.
21. hk0: 100
a*
no cond. 010
b*
Measure R
Calculate d from R.d=λL (known)
Determine a, b, c
Make list of d-spacings
Check if you can index the other patterns with this
22. What will be the value of a and b with this choice?
1.43
2.03
4.06
0.78
2.03 1.43 1.22
a*
2.03 2.03 2.03
b*
0.91
2.34 2.34
2.03 2.03
1.43
23. What will be the value of a and b with this choice?
1.43
2.03
4.06
0.78
2.03 1.43 1.22
a*
2.03 2.03 2.03
b*
0.91
2.34 2.34
2.03 2.03
1.43
24. If no reflection condition:
a=b= c=2.03 Å
list of d-spacings freeware: Powdercell
H K L d/Å
_____________ Can you index all
observed
1 0 0 2.03000 reflections using
1 1 0 1.43543 these cell
1 1 1 1.17202 parameters?
2 0 0 1.01500
yes
2 1 0 0.90784
2 1 1 0.82874 no
25. If no reflection condition:
a=b= c=2.03 Å
list of d-spacings freeware: Powdercell
H K L d/Å
_____________ Can you index all
observed
1 0 0 2.03000 reflections using
1 1 0 1.43543 these cell
1 1 1 1.17202 parameters?
2 0 0 1.01500
yes
2 1 0 0.90784
2 1 1 0.82874 no
26. hk0: 100 200
a*
020 a* h=2n,
no cond. 010
b* b* k=2n
Increase the cell
020 200 parameters to the next
b* a* possibility...
h+k=2n
Which one has second
smallest cell parameters?
top
left
27. hk0: 100 200
a*
020 a* h=2n,
no cond. 010
b* b* k=2n
Increase the cell
020 200 parameters to the next
b* a* possibility...
h+k=2n
Which one has second
smallest cell parameters?
top
left
28. 020 2.03 200
1.43 1.43
b* a*
h+k=2n
2.03
In this case, a=b=
1.43 Å
2.03 Å
2.86 Å
29. 020 2.03 200
1.43 1.43
b* a*
h+k=2n
2.03
In this case, a=b=
1.43 Å
2.03 Å
2.86 Å
30. If hk0:h+k=2n, then a=b= 2.86 Å
list of d-spacings, Powdercell:
H K L d/Å
______________
1 0 0 2,86000
1 1 0 2,02233 Can you index all
1 1 1 1,65122 observed
2 0 0 1,43000
2 1 0 1,27903 reflections using
2 1 1 1,16759
2 2 0 1,01116
these cell
3 0 0 0,95333 parameters?
2 2 1 0,95333
3 1 0 0,90441 yes
3 1 1 0,86232 no
2 2 2 0,82561
3 2 0 0,79322
31. If hk0:h+k=2n, then a=b= 2.86 Å
list of d-spacings, Powdercell:
H K L d/Å
______________
1 0 0 2,86000
1 1 0 2,02233 Can you index all
1 1 1 1,65122 observed
2 0 0 1,43000
2 1 0 1,27903 reflections using
2 1 1 1,16759
2 2 0 1,01116
these cell
3 0 0 0,95333 parameters?
2 2 1 0,95333
3 1 0 0,90441 yes
3 1 1 0,86232 no
2 2 2 0,82561
3 2 0 0,79322
32. If hk0:h+k=2n, then a=b= 2.86 Å
list of d-spacings, Powdercell:
H K L d/Å I show also the
______________
1 0 0 2,86000 reflections not in
1 1 0 2,02233
1 1 1 1,65122
agreement with
2 0 0 1,43000 hk0: h+k=2n.
2 1 0 1,27903
2 1 1 1,16759 Will they be seen on any
2 2 0 1,01116 of the SAED patterns of
3 0 0 0,95333
2 2 1 0,95333 the tilt series?
3 1 0 0,90441
3 1 1 0,86232
it is possible
2 2 2 0,82561 always
3 2 0 0,79322
never
33. If hk0:h+k=2n, then a=b= 2.86 Å
list of d-spacings, Powdercell:
H K L d/Å I show also the
______________
1 0 0 2,86000 reflections not in
1 1 0 2,02233
1 1 1 1,65122
agreement with
2 0 0 1,43000 hk0: h+k=2n.
2 1 0 1,27903
2 1 1 1,16759 Will they be seen on any
2 2 0 1,01116 of the SAED patterns of
3 0 0 0,95333
2 2 1 0,95333 the tilt series?
3 1 0 0,90441
3 1 1 0,86232
it is possible
2 2 2 0,82561 always
3 2 0 0,79322
never
61. Indexed Space group?
-> cell parameter: Possibility from SAED:
a=4.06 Å extinction symbol.
-> Determine reflection
conditions.
62. hkl: h+k+l=2n Bravais lattice: F
all odd, all even P
no conditions I
511 -
220 200 511
311
020 020 020
402
111 -
111
020 020
- -
202
63. hkl: h+k+l=2n Bravais lattice: F
all odd, all even P
no conditions I
511 -
220 200 511
311
020 020 020
402
111 -
111
020 020
- -
202
64. hkl: h+k+l=2n Bravais lattice: F
all odd, all even P
no conditions I
511 -
220 200 511
311
020 020 020
402
111 -
111
020 020
- -
202
65. We know: hk0: h=2n, k=2n. Is this an extra
condition, or is it a consequence of F also?
Consequence
511 - Extra
220 200 511
311
020 020 020
402
111 -
111
020 020
- -
202
66. We know: hk0: h=2n, k=2n. Is this an extra
condition, or is it a consequence of F also?
Consequence
511 - Extra
220 200 511
311
020 020 020
402
111 -
111
020 020
- -
202
67. Are there àny extra conditions, i.e. conditions
that are not already implied by hkl: all odd, all
even? Yes
No 511 -
220 200 511
311
020 020 020
402
111 -
111
020 020
- -
202
68. Are there àny extra conditions, i.e. conditions
that are not already implied by hkl: all odd, all
even? Yes
No 511 -
220 200 511
311
020 020 020
402
111 -
111
020 020
- -
202
69. - -
- F432, F43m, Fm3m
Possible space groups: F23, Fm3,
from: International Tables for Crystallography Volume A, ed. Theo Hahn, Kluwer Ac. Pub., 2002
70. - -
- F432, F43m, Fm3m
Possible space groups: F23, Fm3,
Same extinctions.
- 2, m; give no extinctions.
Difference: 1,
Convergent beam electron diffraction
CBED
102. Combine with information about
reflection conditions from SAED patterns
020 002 002
110 011
200 020 -
110
hkl:
no conditions
h+k+l=2n
103. Combine with information about
reflection conditions from SAED patterns
020 002 002
110 011
200 020 -
110
hkl:
no conditions
h+k+l=2n
104. Combine with information about
reflection conditions from SAED patterns
020 002 002
110 011
200 020 -
110
hk0: 0kl: hhl:
no conditions no conditions no conditions
h+k=2n k+l=2n l=2n
k=2n or l=2n
105. Combine with information about
reflection conditions from SAED patterns
020 002 002
110 011
200 020 -
110
hk0: 0kl: hhl:
no conditions no conditions no conditions
h+k=2n k+l=2n l=2n
k=2n or l=2n
106. Combine with information about
reflection conditions from SAED patterns
020 002 002
110 011
200 020 -
110
hk0: 0kl: hhl:
no conditions no conditions no conditions
h+k=2n k+l=2n l=2n
k=2n or l=2n
107. Combine with information about
reflection conditions from SAED patterns
020 002 002
110 011
200 020 -
110
hk0: 0kl: hhl:
no conditions no conditions no conditions
h+k=2n k+l=2n l=2n
k=2n or l=2n
110. Ab initio solution of structures using electron
diffraction:
You have as
experimental data: You get:
only electron the structure
diffraction patterns
Trouble: dynamical diffraction
110
114. Intensities of the reflections
from several zones
+
cell parameters and space
STRUCTURE
group from SAED-CBED
+
composition from EDX/EELS
or nominal composition
115. Extract the intensities using
EDM
EXTRAX
CRISP
...
Possibilities to introduce
mistakes:
not well oriented
too thick
too small precession angle
too large precession angle
…
118. Direct methods, or optimisation methods
made for single crystal data
SIR2008
Fox
Endeavour
...
Right structure càn come out (GIGO).
119. 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
120.
121. 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.
Indexing of SAED patterns: to get information about the structure needed for studying defects needed for HREM imaging
toon in EMAP!
off course can be skipped if you know them
off course can be skipped if you know them
off course can be skipped if you know them
off course can be skipped if you know them
off course can be skipped if you know them
off course can be skipped if you know them
off course can be skipped if you know them
off course can be skipped if you know them
off course can be skipped if you know them
it is possible in other zones, the condition is not a Bravais condition
it is possible in other zones, the condition is not a Bravais condition
it is possible in other zones, the condition is not a Bravais condition
it is possible in other zones, the condition is not a Bravais condition
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
use notepad to explainMany ways, for example, use what you know = 020.both left and right same distance, so 333 or 511 with or without minus signs (-) and cyclic permutation (cp)difference between both has to be 020333 not possible: other one 313 or 353 (-, cp)511 possible: right 5-11, left 511; but also 5-1-1 and 51-1 are possiblehow to choose?use graphyc representation of reciprocal space
use notepad to explainMany ways, for example, use what you know = 020.both left and right same distance, so 333 or 511 with or without minus signs (-) and cyclic permutation (cp)difference between both has to be 020333 not possible: other one 313 or 353 (-, cp)511 possible: right 5-11, left 511; but also 5-1-1 and 51-1 are possiblehow to choose?use graphyc representation of reciprocal space
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
two difficulties: choose between 333 and 511, then assign the minus signs
4mm
4mm
to overcome dynamical effects.So the measured intensities can be just for ab initio structure determination and for refinement of the structure.
Beam precessed on a cone.Descan to keep the central beam stationary.Ewald sphere intersects the plane along an arcLess reflections excited simultaneouslyless dynamical effectsIntegrated pattern pseudo-kinematicalSymmetry improved in for example microdiffraction patterns so intensities can be used.ANIMATION : EMAP: SnO2