5 10c exercise_index the aluminum tilt series_ex on saed do not know cell parsJoke Hadermann
This is a tutorial on how to index single crystal (electron) diffraction patterns when the cell parameters are not yet known. This follows after another tutorial for the case of known cell parameters, 5.10a.
5 10b exercise_determine the diffraction symbol of ca_f2_ex on saedJoke Hadermann
These slides follow up on the slides with a tutorial on how to index ED patterns, 5 10a. From the result achieved in those slides, we now derive the reflection conditions and corresponding possible space groups.
Electron diffraction: Tutorial with exercises and solutions (EMAT Workshop 2017)Joke Hadermann
Electron diffraction patterns provide information about the structure of crystalline materials by revealing the diffraction of electrons from crystal planes. Reflections in patterns represent the constructive interference of electrons from different crystal planes, with their position and intensity indicating the d-spacing of planes and occupation/symmetry of the structure. By indexing patterns, determining the d-spacings of reflections and relating them to crystal planes via Braggs law, the zone axis and unit cell parameters can be determined.
Complementarity of advanced TEM to bulk diffraction techniquesJoke Hadermann
Lecture contains some examples of how advanced TEM techniques can help solve the structure if for some reason bulk diffraction techniques do not allow to propose a model.
Scheelite CGEW/MO for luminescence - Summary of the paperJoke Hadermann
This document summarizes a research paper that studied the incommensurate modulation and luminescence properties of CaGd2(1-x)Eu2x(MoO4)4(1-y)(WO4)4y phosphors. The researchers found that these materials exhibit incommensurate modulation of the cation ordering due to vacancies in the scheelite structure, which requires description in superspace. Replacing Mo6+ with W6+ switched the modulation from 3+2D to 3+1D, despite their similar sizes. Variations in Eu content changed luminescence intensity but not the modulation periodicity. The results contradict prior reports of simple ordered structures.
Mapping of chemical order in inorganic compoundsJoke Hadermann
Presentations of some of the possibilities of observing cation and anion order in perosvkite based structures in order to solve their structure or to solve other questions, when they could not be solved by bulk diffraction techniques. The examples include a (Pb,Bi)FeO3-d compound, a solid oxide fuel cell compound Sr(Nb,Co,Fe)O3-d and several brownmillerite related compounds, as well as a "relaxor ferromagnetic". This was an invited lecture given at the Spring meeting of the British Crystallographic Association in 2014.
New oxide structures using lone pairs cations as "chemical scissors"Joke Hadermann
Lone pair cations like Bi3+ and Pb2+ allow for asymmetric coordination environments which can be used to create crystallographic shear planes in perovskite structures. Shear planes involve shifting one part of the structure relative to the other. This results in a new class of anion-deficient perovskite structures called the AnBnO3n-2 homologous series. Unlike other homologous series, these structures have electrically and magnetically active interfaces between perovskite blocks, resulting in frustrated magnetic structures. The orientation and spacing of shear planes can be controlled through composition.
This is a tutorial on indexing diffraction patterns, deriving reflection conditions from SAED, derving point groups from CBED and combining both to find the space group. The slides contain exercises, the page to work on is at the end of the presentation and should be printed first to be able to measure on that page.
This lecture was given at the 2nd International School on Aperiodic Crystals in Bayreuth, Germany. It is an updated version of the lecture given on the 1st school, that can be found between my lectures as "TEM for incommensurately modulated materials".
Contenu connexe
Similaire à 5 10a exercise_index the patterns of ca_f2_ex on saed
5 10c exercise_index the aluminum tilt series_ex on saed do not know cell parsJoke Hadermann
This is a tutorial on how to index single crystal (electron) diffraction patterns when the cell parameters are not yet known. This follows after another tutorial for the case of known cell parameters, 5.10a.
5 10b exercise_determine the diffraction symbol of ca_f2_ex on saedJoke Hadermann
These slides follow up on the slides with a tutorial on how to index ED patterns, 5 10a. From the result achieved in those slides, we now derive the reflection conditions and corresponding possible space groups.
Electron diffraction: Tutorial with exercises and solutions (EMAT Workshop 2017)Joke Hadermann
Electron diffraction patterns provide information about the structure of crystalline materials by revealing the diffraction of electrons from crystal planes. Reflections in patterns represent the constructive interference of electrons from different crystal planes, with their position and intensity indicating the d-spacing of planes and occupation/symmetry of the structure. By indexing patterns, determining the d-spacings of reflections and relating them to crystal planes via Braggs law, the zone axis and unit cell parameters can be determined.
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Lecture contains some examples of how advanced TEM techniques can help solve the structure if for some reason bulk diffraction techniques do not allow to propose a model.
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This document summarizes a research paper that studied the incommensurate modulation and luminescence properties of CaGd2(1-x)Eu2x(MoO4)4(1-y)(WO4)4y phosphors. The researchers found that these materials exhibit incommensurate modulation of the cation ordering due to vacancies in the scheelite structure, which requires description in superspace. Replacing Mo6+ with W6+ switched the modulation from 3+2D to 3+1D, despite their similar sizes. Variations in Eu content changed luminescence intensity but not the modulation periodicity. The results contradict prior reports of simple ordered structures.
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Presentations of some of the possibilities of observing cation and anion order in perosvkite based structures in order to solve their structure or to solve other questions, when they could not be solved by bulk diffraction techniques. The examples include a (Pb,Bi)FeO3-d compound, a solid oxide fuel cell compound Sr(Nb,Co,Fe)O3-d and several brownmillerite related compounds, as well as a "relaxor ferromagnetic". This was an invited lecture given at the Spring meeting of the British Crystallographic Association in 2014.
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Lone pair cations like Bi3+ and Pb2+ allow for asymmetric coordination environments which can be used to create crystallographic shear planes in perovskite structures. Shear planes involve shifting one part of the structure relative to the other. This results in a new class of anion-deficient perovskite structures called the AnBnO3n-2 homologous series. Unlike other homologous series, these structures have electrically and magnetically active interfaces between perovskite blocks, resulting in frustrated magnetic structures. The orientation and spacing of shear planes can be controlled through composition.
This is a tutorial on indexing diffraction patterns, deriving reflection conditions from SAED, derving point groups from CBED and combining both to find the space group. The slides contain exercises, the page to work on is at the end of the presentation and should be printed first to be able to measure on that page.
This lecture was given at the 2nd International School on Aperiodic Crystals in Bayreuth, Germany. It is an updated version of the lecture given on the 1st school, that can be found between my lectures as "TEM for incommensurately modulated materials".
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2. 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
3. We are going to index these patterns:
Start with easiest:
highest symmetry or smallest interreflection distances
= usually lower zone indices (“main zones”)
6. probably this is <001>
(Cubic: [100], [010], [001] equivalent = <001>)
7. To do: measure the distances, compare to list d-hkl, index
consistently.
length scalebar = R (in mm)
here it depends on your print/screen
size, so let us suppose it is 45.5 mm
Step 1: Use the scalebar for the conversion
factor to 1/d-values.
equal to 1/0.08 nm
R.d=L
then L would be
36.4 mmÅ
53.8 mmÅ
0.02 mmÅ
8. Now calculate the L for your own case and use that for
the following slides.
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
5.46 Å
3.15 Å
2.73 Å
1
2
9. 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
10. Keep in mind: d-values 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 to your choice.
14. Next zone: with reflections closest to the central beam.
Because reflections far from the central beam:
lower d-values
larger amount of possible matches of hkl to this d
difficult to conclude which one is correct index!
15. 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
16. 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
17. Make the indexation in a consistent manner.
1 2
Point 2 should be indexed as
200
020
200
all are correct
- (see next slide why)
18. Consistency:
This is a tilt series...
...so the common row needs to have the
same indices in all patterns
200 200
200 200
20. Consistency:
200111
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
h1 k1 l1 = h3+2 k3 l3
(also possible 111 and 111, make a choice and stick to it for the following patterns)
- - - - -
48. 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
We already know the
first point: 200.
200
2
49. 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
50. 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.
52. [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
041021
[025]-
052 [014]-
[023]-
[034]-
When indexed correctly, the patterns in between
have to give you one of these as zone-index.
011
53. Pattern bottom left:
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
54. 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 113
131
311
Point 2
d
Point 2
hkl
200
2
55. The indexation is indeed consistent.
200
2
3
4
Same reasoning: if 2 is 131, then 3 is 131, and 4 is 062.
All consistent with each other
(cf. explanation previous pattern).
-
57. 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”
58. So now you have indexed these four patterns.
200
131
200
151
200111
200020
[001] [015]
-
[013]
-
[011]
-
59. ...indexed patterns give you info on fase,
orientation, cell parameters,...
200
131
200
151
200111
200020
[001] [015]
-
[013]
-
[011]
-
60. 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.
61. 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
200111
200020
[001] [015]
-
[013]
-
[011]
-
Notes de l'éditeur
binnen/buitenrand!!!!
binnen/buitenrand!!!!
binnen/buitenrand!!!!
binnen/buitenrand!!!!
binnen/buitenrand!!!!
eerste voordoen, voor andere zones doen ze het zelf
eerste voordoen, voor andere zones doen ze het zelf
eerste voordoen, voor andere zones doen ze het zelf
binnen/buitenrand!!!!
binnen/buitenrand!!!!
binnen/buitenrand!!!!
eerste voordoen, voor andere zones doen ze het zelf
eerste voordoen, voor andere zones doen ze het zelf
binnen/buitenrand!!!!
eerste voordoen, voor andere zones doen ze het zelf
eerste voordoen, voor andere zones doen ze het zelf
binnen/buitenrand!!!!
binnen/buitenrand!!!!
eerste voordoen, voor andere zones doen ze het zelf