9/2-10mena3100 electron diffraction selected area diffraction (sad) in tem electron back scatter...
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9/2-10 MENA3100
Electron diffraction
Selected area diffraction (SAD) in TEM
Electron back scatter diffraction (EBSD) in SEM
9/2-10 MENA3100
Bragg’s law ndhkl )sin(2
Bragg’s law tells you at which angle θB to expect maximum diffracted intensity for a particular family of crystal planes. For large crystals, all other angles give zero intensity.
1kko
kkko
The Ewald Sphere
The observed diffraction pattern is the part of the reciprocal lattice that is intersected by the Ewald sphere
kok
g
Cu Kalpha X-ray: = 150 pmElectrons at 200 kV: = 2.5 pm
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2θko k
g
The intensity distributionaround each reciprocal lattice point is spread out in the form of spikes directednormal to the specimen
Ewald sphere(Reflecting sphere)
Intensity distribution and Laue zones
Zero order Laue zone
First order Laue zone
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Multiple scattering
• Multiple scattering (diffraction) leads to oscillations in the diffracted intensity with increasing thickness of the sample
– Forbidden reflection may be observed
– Kinematical intensities with XRD
Incident beam
Diffracted beam Multiplediffracted beam
Transmitted beam
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Simplified ray diagram
Objective lense
Diffraction plane(back focal plane)
Image plane
Sample
Parallel incoming electron beamSi
a
b
cP
ow
derC
ell 2.0
1,1 nm3
,8 Å
Objective aperture
Selected area aperture
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Apertures
Selected area aperture
Condenser aperture
Objective aperture
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Diffraction with large SAD aperture, ring and spot patterns
Poly crystalline sample Four epitaxial phases
Similar to XRD from polycrystalline samples. The orientation relationship between the phases can be determined with ED.
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Camera constant
R=L tan2θB ~ 2LsinθB
2dsinθB =λ ↓ R=Lλ/d
Camera constant: K=λL
Film plate
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Indexing diffraction patterns
The g vector to a reflection is normal to the corresponding (h k l) plane and IgI=1/dnh nk nl
- Measure Ri and the angles between the reflections
- Calculate di , i=1,2,3 (=K/Ri)
- Compare with tabulated/theoretical calculated d-values of possible phases
- Compare Ri/Rj with tabulated values for cubic structure.
- g1,hkl+ g2,hkl=g3,hkl (vector sum must be ok)
- Perpendicular vectors: gi ● gj = 0
- Zone axis: gi x gj =[HKL]z
- All indexed g must satisfy: g ● [HKL]z=0
(h2k2l2)
Orientations of correspondingplanes in the real space
9/2-10 MENA3100
Example: Study of unknown phase in a BiFeO3 thin film
200 nm
Si
SiO2
TiO2
Pt
BiFeO3
Lim
ab
c
BiBi
Fe
O O
Fe
Fe
Bi
O
Bi
Bi
O
Fe
O
O
Bi
O
Fe
Bi
Fe
O
Bi
O
Bi
O
Fe
O
Fe
O
Bi
Bi
O
Fe
O
Bi
Bi
O O
Bi
O
Fe
Fe
O
Fe
BiBi
PowderCell 2.0
Goal:
BiFeO3 with space grupe: R3Cand celle dimentions: a= 5.588 Å c=13.867 Å
Metal organic compound on Pt
Heat treatment at 350oC (10 min) to remove organic parts.
Process repeated three times before final heat treatment at 500-700 oC (20 min) . (intermetallic phase grown)
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Determination of the Bravais-lattice of an unknown crystalline phase
Tilting series around common axis
0o
10o
15o
27o
50 nm
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50 nm
Tilting series around a dens row of reflections in the reciprocal space
0o
19o
25o
40o
52o
Positions of the reflections in the reciprocal space
Determination of the Bravais-lattice of an unknown crystalline phase
9/2-10 MENA3100
Bravais-lattice and cell parameters
From the tilt series we find that the unknown phase has a primitive orthorhombic Bravias-lattice with cell parameters:
a= 6,04 Å, b= 7.94 Å og c=8.66 Å
α= β= γ= 90o
6.0
4 Å
7.94 Å8.66 Å
a
bc
100
110
111
010
011
001 101
[011] [100] [101]
d = L λ / R
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Chemical analysis by use of EDS and EELS
Ukjent faseBiFeO3 BiFe2O5
1_1evprc.PICT
-0 200 400 600 800 10005
10
15
20
25
30
35
40
Energy Loss (eV)
CC
D c
ount
s x
100
0
Nr_2_1evprc.PICT
-0 200 400 600 800 1000
-0
2
4
6
8
10
12
14
Energy Loss (eV)
CC
D c
ount
s x
100
0
Ukjent faseBiFeO3
Fe - L2,3
O - K
500 eV forskyvning, 1 eV pr. kanal
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Published structure
A.G. Tutov og V.N. MarkinThe x-ray structural analysis of the antiferromagnetic Bi2Fe4O9 and the isotypical combinations Bi2Ga4O9 and Bi2Al4O9
Izvestiya Akademii Nauk SSSR, Neorganicheskie Materialy (1970), 6, 2014-2017.
Romgruppe: Pbam nr. 55, celleparametre: 7,94 Å, 8,44 Å, 6.01Å
x y zBi 4g 0,176 0,175 0Fe 4h 0,349 0,333 0,5Fe 4f 0 0,5 0,244O 4g 0,14 0,435 0O 8i 0,385 0,207 0,242O 4h 0,133 0,427 0,5O 2b 0 0 0,5
ab
c
O
Bi
Fe
O
Fe
Bi
O
Fe O
O
O
Fe
Fe
O O
O
O
Fe
Bi
O
O
Bi
O
Bi
O
O
Bi
Fe
O
O
O O
Fe
Fe
O
O
O Fe
O
Bi
Fe
O
Fe
Bi
O
PowderCell 2 .0
Celle parameters found with electron diffraction (a= 6,04 Å, b= 7.94 Å and c=8.66 Å) fits reasonably well with the previously published data for the Bi2Fe4O9 phase. The disagreement in the c-axis may be due to the fact that we have been studying a thin film grown on a crystalline substrate and is not a bulk sample. The conditions for reflections from the space group Pbam is in agreement with observations done with electron diffraction.
Conclusion: The unknown phase has been identified as Bi2Fe4O9 with space group Pbam with cell parameters a= 6,04 Å, b= 7.94 Å and c=8.66 Å.
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Kikuchi pattern
http://www.doitpoms.ac.uk/index.htmlhttp://www.doitpoms.ac.uk/tlplib/diffraction-patterns/kikuchi.php
ExcessDeficient
Used for determination of:-crystal orientation
-lattice parameter
-accelerating voltage
-Burgers vector
Excess line
Deficient line
2θB
θB
θB
Diffraction plane
Objective lens
1/d
Inelastically scattered electronsgive rise to diffuse background in the ED pattern.
-Angular distribution of inelastic scattered electrons falls of rapidly with angle. I=Iocos2α
Kikuchi lines are due to:-Inelastic+ elastic scattering event
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• EBSD– Geometry similar to Kikuchi diffraction in TEM
– Information from nm regions
• OIM– Gives the distribution of crystal orientation for grains intersected by the
sample section that can be presented in various ways. (+/- 0.5o)
– Involves • collection a large sets of EBSD data • Bin the crystallographic data from
each pixel (stereographic triangle)
– Colour codes
– Localized preferred orientation
and residual stress etc.
Electron Back Scattered Diffraction (EBSD)Orientation Image Microscopy (OIM)
in a SEM
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Orientation map example
Step=0.2micron
CD-200 Nordiff EBSD Camera
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Overlaid maps
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http://www.ebsd.com/ebsd-explained/simulationapplet.htm
Electron back scattered diffraction (EBSD)
http://www.ebsd.com/ebsd-explained/anim2.htm
Principal system componentsSample tilted at 70° from the horizontal, a phosphor screen,a sensitive CCD video camera, a vacuum interface for mounting the phosphor and camera in an SEM port. Electronic hardware that controls the SEM, including the beam position, stage, focus,and magnification. A computer to control EBSD experiments, analyse the EBSD pattern and process and display the results.
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Probe current Increased probe current – shorter camera integration time
– increased beam size
Accelerating voltage Increased accelerating voltage – reduced λ - reduced width of the Kikuchi bands
– brighter pattern - shorter integration time
– higher penetration depth
Changing the accelerating voltage may require adjustment to the Hough transform filter size to
ensure the Kikuchi bands are detected correctly
Microscope operating conditions
Effect of changing accelerating voltage on diffraction patterns from nickel
10 kV 20 kV 30 kV
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Working distance and magnification Because the sample is tilted, the SEM working distance will change as the beam position moves up or down the sample, and the image will go out of focus.
Microscope operating conditions
Image with tilt and dynamic focus compensation. The working distance is 14.98 mm at the top and 15.11 mm at the bottom of the image
Image with tilt compensation and no dynamic focus compensation
Image without tilt or dynamic focus
compensation
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Microscope operating conditionsEBSD systems can compensate automatically for shifts in the pattern centre by calibrating at two working distances and interpolating for intermediate working distance values. It is important to know the range of working distances for which the EBSD system will remain accurately calibrated.
With a tilted sample, the pattern centre position will depend on the sample working distance.
The yellow cross shows the pattern centre with working distance 10, 18 and 22 mm
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Band Intensity The mechanisms giving rise to the Kikuchi band intensities and profile shapes are complex. As an approximation, the intensity of a Kikuchi band for the plane (hkl) is given by: 22
)(2sin)()(2cos)(
iii
iiiii
iihkl lzkyhxflzkyhxfI
where fi(θ) is the atomic scattering factor for electrons and (x i yi zi) are the fractional coordinates in
the unit cell for atom i. An observed diffraction pattern should be compared with a simulation to ensure only planes that produce visible Kikuchi bands are used when solving the diffraction pattern.
Simulation of crystal orientation giving the
solution shown.
Simulated diffraction pattern showing all Kikuchi bands with intensity greater than 10% of the most intense band.
Solution overlaid on the diffraction pattern giving the crystal orientation as {370}<7-34>
Diffraction pattern from the orthorhombic ceramic mullite (3Al2O3 2SiO2) collected at 10 kV accelerating voltage.
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The background can be measured by scanning the beam over many grains in the sample to average out the diffraction information.
The background can be removed by subtraction from, or division into, the original pattern.
Background removal
Background division Background subtraction Original pattern
http://www.ebsd.com/ebsd-explained/undertakingexperiments3.htm
Background
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