Tem for incommensurately modulated materials
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Transcript of Tem for incommensurately modulated materials
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Í Î ÂÛÅ Í ÈÇØÈÅ ÑÌ ÅØÀÍ Í Û Å ÁËÎ ×Í ÛÅ ÕÀËÜÊÎ ÃÅÍ ÈÄÛ Í ÈÊÅËß
Московский Государственный Университетим. М.В. ЛомоносоваФакультет Наук о Материалах
Исаева А.А.
Научные руководителид.х.н., проф. Б.А. Поповкинк.х.н., асс. ФНМ А.И. Баранов
КАФЕДРА НЕОРГАНИЧЕСКОЙ ХИМИИЛаборатория Направленного Неорганического Синтеза
Ë Î Ì Î Í Î ÑÎ Â -2 0 0 3
Examples of incommensurately
modulated structures and
composites studied using
transmission electron
microscopy
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Purpose of this lecture
At the end of this lecture you should be able to:
• Understand the TEM paragraph in papers about IMS and CS
• Be able to make solid comments about conclusionsclaimed from TEM by different sources (collaborators, papers,…) by knowing some possible pitfalls
• Decide whether it would be useful to do TEM on your ownIMS or CS
• Make basic interpretations of TEM data on your ownmaterials by yourself
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Outline of the lecture
The three most frequently usedtechniques in case of IMS/CS:
• Electron diffraction
• HAADF-STEM
• HRTEM
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ED: the main differences withXRD
• Shorter wavelength, almost flat sectionsthrough reciprocal space
• A nanometer size particle is enough
• Multiple diffraction
• Can be combined with direct imaging and compositional analysis
Appearance very much like single crystal XR patterns
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Incommensurately modulatedstructure example
Sb1.155Pb1.216Mn0.628O4
Related commensuratestructure
Sb2MnO4
Abakumov et al., Chemistry of Materials, 17, 5, 2005, 1123-1134
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IMS: indexing the subcell reflections• Related commensurate structure Sb2MnO4
• P42/mbc; a=b=8.7 Å, c= 6.0 Å
• Measure R, calculate d with R.d=C (know instrument constant)
• Index each reflection according to list of d-values for each reflection (cf. XRD)
4.35 4.35
4.353.0 3.06.15
All distances in Å
6.15
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Dangers of double diffraction!• P42/mbc
• Reflection conditions: 0kl: k=2n; hhl: l=2n; 00l: l=2n; h00: h=2n
• In contradiction: 001,003,…,100,300,…,010, 030, … all caused by double diffraction
• Tilt around the row: forbidden reflections will disappear
Abakumov et al., Chemistry of Materials, 17, 5, 2005, 1123-1134
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Subcell vs. IMS
Sb1.155Pb1.216Mn0.628O4
Sb2MnO4
Abakumov et al., Chemistry of Materials, 17, 5, 2005, 1123-1134
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Indexing the IMS
Sb1.155Pb1.216Mn0.628O4
0200 0201 020202010202--
c02110211
-
0000 0001 000200010002--
c
021
001 00110011-
022002210222
--
002000210022
--
q≈3/4c*
02
0
022 020 022
002
000
002-
-
Abakumov et al., Chemistry of Materials, 17, 5, 2005, 1123-1134
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Reflection conditions for m
Sb1.155Pb1.216Mn0.628O4
For thís material: no special conditions for m: if subcell reflection is seen, also hklm with m=1 and m=2 is seen.
02100200
0201 0202
0211-
0211
02210222--
0220
1100
1101 11021122-
1120-
1121
q≈3/4c*
Abakumov et al., Chemistry of Materials, 17, 5, 2005, 1123-1134
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Reflection conditions
Sb1.155Pb1.216Mn0.628O4
0klm: k=2n
hhlm: l=2n
P42/mbc(00γ)
P42/mbc
0kl: k=2n
hhl: l=2n
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• Index the commensurate structure LaSrCuO4, this will help you with indexing the next, incommensurate one.
6.50 Å1.85 Å
6.50 Å2.61 Å
2.61 Å
(Simulated ED patterns)
Given data: cell parameters of LaSrCuO4: a=b=3.7 Å, c=13 Å.
1.85 Å
Exercise 1-1: IMS: index the non-
modulated phase
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6.50 Å1.85 Å
6.50 Å2.61 Å
2.61 Å
(Simulated ED patterns)
Given data: cell parameters of LaSrCuO4: a=b=3.7 Å, c=13 Å.
1.85 Å
001
002
200
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6.50 Å1.85 Å
6.50 Å2.61 Å
2.61 Å
(Simulated ED patterns)
Given data: cell parameters of LaSrCuO4: a=b=3.7 Å, c=13 Å.
1.85 Å
001
002
200
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0021.85 Å
0022.61 Å
2.61 Å
(Simulated ED patterns)
Given data: cell parameters of LaSrCuO4: a=b=3.7 Å, c=13 Å.
1.85 Å
010
020
110
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0021.85 Å
0022.61 Å
2.61 Å
(Simulated ED patterns)
Given data: cell parameters of LaSrCuO4: a=b=3.7 Å, c=13 Å.
1.85 Å
010
020
110
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002020
0022.61 Å
2.61 Å
(Simulated ED patterns)
Given data: cell parameters of LaSrCuO4: a=b=3.7 Å, c=13 Å.
1.85 Å
010
020
110
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002020
0022.61 Å
2.61 Å
(Simulated ED patterns)
Given data: cell parameters of LaSrCuO4: a=b=3.7 Å, c=13 Å.
1.85 Å
100
200
020
020
1.85 Å
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002020
0022.61 Å
2.61 Å
(Simulated ED patterns)
Given data: cell parameters of LaSrCuO4: a=b=3.7 Å, c=13 Å.
1.85 Å
100
200
020
020
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002020
0022.61 Å
2.61 Å
(Simulated ED patterns)
Given data: cell parameters of LaSrCuO4: a=b=3.7 Å, c=13 Å.
200
110
220
½ ½ 0
020
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002020
0022.61 Å
2.61 Å
(Simulated ED patterns)
Given data: cell parameters of LaSrCuO4: a=b=3.7 Å, c=13 Å.
200
110
220
½ ½ 0
020
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Indexed solution
002200
002110 200
110
020
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Zone indices
002200
002110 200
110
020
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Exercise 1-2: IMS: determine the reflection condition h0l
002200
002110 200
110
h0l: h+l=2n
h = 2n
l = 2n
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002200
002110 200
110
h0l: h+l=2n
Exercise 1-2: IMS: determinethe reflection condition h0l
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Exercise 1-2: IMS: determinethe reflection condition hhl
002200
002110 200
110
hhl: h+l=2n
h = 2n
l = 2n
h0l: h+l=2n
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Exercise 1-2: IMS: determinethe reflection condition hhl
002200
002110 200
110
hhl:
l = 2n
h0l: h+l=2n
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Exercise 1-2: IMS: determinethe reflection condition hk0
002200
002110 200
110
hhl: l = 2nh0l: h+l=2n hk0: h+k=2n
h = 2n
k = 2n
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Exercise 1-2: IMS: determinethe reflection condition hk0
002200
002110 200
110
hhl: l = 2nh0l: h+l=2n hk0: h+k=2n
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Solved reflection conditions
002200
002110
h0l:h+l=2n hhl:l=2n hk0:h+k=2n
Also (from rest of the zones) hkl: h+k+l=2n.
110-
200
110
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Determine space group
• International Tables: I---
• Most symmetrical I4/mmm
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Incommensurate vs. basiccell
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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Exercise 1-3: index the IMS
Identify and index the subcell reflections.
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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Propose a modulation vector.
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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• q=αa*
• α<0.5
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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• q=αa*
• α<0.5
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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• q=αa*
• α<0.5
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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Possible solution
• q=αa*
• α<0.5
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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Index the satellite indicated in green
-001
0001
100
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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Index the satellite indicated in green
0001
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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Index the next indicatedsatellite
0002
2002-
2001-
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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Index the next indicatedsatellite
2002-
-
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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Exercise 1-4: IMS with more complete data
• Which of the indicatedvectors corresponds to the modulation vector chosen on the previousslides?
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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Exercise 1-4: IMS with more complete data
• Which of the indicatedvectors corresponds to the modulation vector chosen on the previousslides?
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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Is the proposedvector still valid?
yes
no
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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Indicate the correct modulationvector(s) on the central white area.
You need
q1
q2
q1 ànd q2
q1=αa*+βb*
q2= -αa*+βb*
α=β<0.25
hklmnHadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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20011
20011-
20011-
Index the reflection indicatedin red
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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20011-
Index the reflection indicatedin red
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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Index the others patternsconsistently with this new choice.
Hadermann et al., Journal of Materials Chemistry, 17, 22, 2007, 2344-2350
LaSrCuO3.52
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Index the reflection indicatedin green
20011
20011
20011-
-
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Index the reflection indicatedin green
LaSrCuO3.52
20011-
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Index the reflection indicatedin green
LaSrCuO3.52
10110
10111
10111-
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Index the reflection indicatedin green
LaSrCuO3.52
10111-
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Index the reflection indicatedin green
LaSrCuO3.52
00002
00002
00001-
-
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Index the reflection indicatedin green
LaSrCuO3.52
00002-
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Look out for twinning!
Y0.8Sr2.2Mn2GaO8-
Gillie et al., Journal of Physics and Chemistry of Solids, 65, 1 (2004) 87-93
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Exercise 1-5: twinning?
• Could it be twinning and thus sufficient to useonly one q-vector?
yes
no
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Exercise 1-5: twinning?
• Could it be twinning and thus sufficient to useonly one q-vector?
yes
no
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Exercise 1-6: derive the reflection conditions
hklmn:
h+k+l+m+n=2i
h+k+l=2i
m+n=2i
hhl:l=2n
hkl:h+k+l=2n
LaSrCuO3.52
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Exercise 1-6: derive the reflection conditions
hklmn:
h+k+l=2i
LaSrCuO3.52
hhl:l=2n
hkl:h+k+l=2n
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Exercise 1-6: derive the reflection conditions
hhlm0: l=2i
h=2i
l,m=2i
LaSrCuO3.52
hhl:l=2n
hkl:h+k+l=2n
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Exercise 1-6: derive the reflection conditions
LaSrCuO3.52
hhl:l=2n
hkl:h+k+l=2n
hhlm0:
l,m=2i
buthhlm0:m=2iis sufficient
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Exercise 1-6: derive the reflection conditions
• hklmn:h+k+l=2i
• hhlm0:m=2i
(-hhl0n: n=2i)
LaSrCuO3.52
hhl:l=2n
hkl:h+k+l=2n
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Determining the superspace group
• Online tables Yamamoto (ActaCryst.A 1996, A52, 509)
• I4/mmm(α α0, -αα0)00mg
LaSrCuO3.52
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Use of doing ED
• Deriving approximate cell parameters, modulation vector and superspace group
• Not useful for: precise parameters, precisemodulation vector
• Excellent if multiphase sample or satellitesvery weak in XRD/ND
• Be aware of:
– Twinning
– Multiple diffraction (for forbidden refls., for usingintensities,…)
– The possibility of missing important sections of reciprocal space
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66(Abakumov et al., Chem. Mater. 20
(13), pp. 4457-4467)
Relation composition –modulation vector• Most TEM have EDX available for composition
determination
• Determination of direct links between composition and modulation vector, also in multiphased samples
q q q
2q 2q 2q
a* a* a*
b* b* b*
Ba4In6-xMgxO13-x/2
x = 0 x = 0.2 x = 0.4
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ED of a composite structure (CS)
a1= a2, b1=b2, с1 с2, q = c1* = c2*
hk00 average cellhkl0 first subsystemhk0m second subsystemhklm satellites
Sr1.3Co0.8Mn0.2O3
A1+xA’xB1-xO3 first subsystem[(B, A’)O3]second subsystem [A]
Mandal et al., Chem. Mater., 19, 25 (2007) 6158
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ED of a composite structure (CS)
Sr1.3Co0.8Mn0.2O3
2022-
Mandal et al., Chem. Mater., 19, 25 (2007) 6158
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Exercise 2: compositestructure: index the pattern
[SrF0.82(OH)0.18]2.5[Mn6O12]
Which reflection is 0011?-
Abakumov et al., Chem.Mater. 19, 5 (2007) 1181-1189
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Exercise 2: compositestructure: index the pattern
Which reflection is 0011?-
[SrF0.82(OH)0.18]2.5[Mn6O12]
Abakumov et al., Chem.Mater. 19, 5 (2007) 1181-1189
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Exercise 2: compositestructure: index the pattern
Which reflection is 0012?-
[SrF0.82(OH)0.18]2.5[Mn6O12]
Abakumov et al., Chem.Mater. 19, 5 (2007) 1181-1189
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Exercise 2: compositestructure: index the pattern
Which reflection is 0012?-
[SrF0.82(OH)0.18]2.5[Mn6O12]
Abakumov et al., Chem.Mater. 19, 5 (2007) 1181-1189
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Exercise 2: compositestructure: index the pattern
Which reflection does the blue arrow point at? 002200210012
---
[SrF0.82(OH)0.18]2.5[Mn6O12]
Abakumov et al., Chem.Mater. 19, 5 (2007) 1181-1189
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Exercise 2: compositestructure: index the pattern
Which reflection does the blue arrow point at? 0022
-
[SrF0.82(OH)0.18]2.5[Mn6O12]
Abakumov et al., Chem.Mater. 19, 5 (2007) 1181-1189
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Exercise 2: compositestructure: index the pattern -solution
[SrF0.82(OH)0.18]2.5[Mn6O12]
Abakumov et al., Chem.Mater. 19, 5 (2007) 1181-1189
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Streaks
• order in the plane, disorder betweenthese planes: streak on ED pattern
• disorder in twodirections: diffuse intensity plane: streak or background intensity depending onthe intersection
[SrF0.82(OH)0.18]2.5[Mn6O12]
Abakumov et al., Chem.Mater. 19, 5 (2007) 1181-1189
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HRTEM and HAADFSTEM-images
– contrast related to Zn
– direct information about the heavy atom positions
– brighter with thickness also
– correct orientation veryimportant!
– scanned image: positionsimprecise
HRTEM– complicated phase transfer
function
– no direct interpretationpossible
– contrast changes withthickness and defocus
– correct orientation veryimportant!
– one-shot image: position of the contrast objects reliable
HAADF-STEM
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cm
am
Heavy atoms from HAADF-STEM
“Pb2Fe2O5” Abakumov et al., Ang.Chemie-Int.Ed., 45, 40 (2006) 6697-6700
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High resolution transmissionelectron microscopy (HREM)
Bi2Sr1.2La0.8CuO6.46-xF2x Hadermann et al., JSSC, 156, 2 (2001) 455-451
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image influenced by contrast transfer function of the
microsope
no direct correspondence
visual comparison with simulations needed
PbFe
O
Defocus
Th
ick
nes
s
-700 Å -500 Å -300 Å -100 Å
10
Å3
0 Å
50
Å7
0 Å
90
Å
Relation structure – image in HRTEM
simple perovskite
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Exercise 3: predict what the ED pattern will roughly look like
Hadermann et al., Solid State Sciences, 10; 4 (2008) 382-389
“Pb2Fe2O5”
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Exercise 3: predict what the ED pattern will roughly look like
What will be the subcell reflections?
Hadermann et al., Solid State Sciences, 10; 4 (2008) 382-389
“Pb2Fe2O5”
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Exercise 3: predict what the ED pattern will roughly look like
What will be the subcell reflections?
Hadermann et al., Solid State Sciences, 10; 4 (2008) 382-389
“Pb2Fe2O5”
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Exercise 3: predict what the ED pattern will roughly look like
Hadermann et al., Solid State Sciences, 10; 4 (2008) 382-389
“Pb2Fe2O5”
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Exercise 3: predict what the ED pattern will roughly look like
Hadermann et al., Solid State Sciences, 10; 4 (2008) 382-389
“Pb2Fe2O5”
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Exercise 3: predict what the ED pattern will roughly look like
Hadermann et al., Solid State Sciences, 10; 4 (2008) 382-389
“Pb2Fe2O5”
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Exercise 3: predict what the ED pattern will roughly look like
Hadermann et al., Solid State Sciences, 10; 4 (2008) 382-389
“Pb2Fe2O5”
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88Hadermann et al., Solid State Sciences, 10; 4 (2008) 382-389
“Pb2Fe2O5”
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Domains with varying q
Sr1.3Co0.8Mn0.2O3Mandal et al., Chem. Mater., 19, 25 (2007) 6158
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Comments to the applicabilityof conclusions from TEM• If the satellites cannot be seen on the XRPD-NPD patterns
it is no use to try to refine the structure using the ED cell.
• Precision of parameters determined from ED is not high. ED is good for determining parameters (cell parameters and direction and length of q) qualitatively.
• Good for determining symmetry.
• Can give direct space information and compositionalinformation also.
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Purpose of this lecture
At the end of this lecture you should be able to:
• Understand the TEM paragraph in papers about IMS and CS
• Be able to make solid comments about conclusionsclaimed from TEM by different sources (collaborators, papers,…) by knowing some possible pitfalls
• Decide whether it would be useful to do TEM on your ownIMS or CS
• Make basic interpretations of TEM data on your ownmaterials by yourself