1. Electron diffraction Selected area diffraction (SAD) in TEM
Electron back scatter diffraction (EBSD) in SEM
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2. Bragg’s law The Ewald Sphere Cu Kalpha X-ray:  = 150 pm
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.
The Ewald Sphere ko k g
Cu Kalpha X-ray:  = 150 pm
Electrons at 200 kV:  = 2.5 pm
Hva er forskjell i tetabragg for røntgen og elelktroner for samme d-verdi i en krystall? Elektroner vekselvirker sterkere enn røntgen, mer dynamisk spredning (kinematiske intensiteter med røntgen).
The observed diffraction pattern is the part of the reciprocal lattice that is intersected by the Ewald sphere
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3. Intensity distribution and Laue zones2θ ko k g
Intensity distribution and Laue zones
Ewald sphere
(Reflecting sphere)
The intensity distribution
around each reciprocal
lattice point is spread out
in the form of spikes directed
normal to the specimen
First order Laue zone
Zero order Laue zone
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4. Multiple scattering Incident beam
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
Multiple
diffracted beam
Transmitted
beam
Diffracted beam
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5. Simplified ray diagram
Parallel incoming electron beam
1,1 nm
3,8 Å
Sample
Objective lense
Diffraction plane
(back focal plane)
Objective aperture
Parallel incoming electron beam and a selection aperture in the image plane.
Diffraction from a single crystal in a polycrystalline sample if the aperture is small enough/crystal large enough.
Orientation relationships between grains or different phases can be determined.
~2% accuracy of lattice parameters
Convergent electron beam better
Selected area
aperture
Image plane
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6. Apertures Condenser aperture Objective aperture Selected area aperture
Intermediate and projector lenses. Tilting of sample, beam tilt. Recording on film or CCD camera.
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7. 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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8. Camera constant Film plate R=L tan2θB ~ 2LsinθB 2dsinθB =λ ↓ R=Lλ/d
K=λL
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9. 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 corresponding
planes in the real space
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10. Example: Study of unknown phase in a BiFeO3 thin film
200 nm Si
SiO2
TiO2 Pt
BiFeO3
Lim
Metal organic compound on Pt
Heat treatment at 350oC (10 min) to remove organic parts.
Process repeated three times before final heat treatment at oC (20 min) .
(intermetallic phase grown)
Goal:
BiFeO3 with space grupe: R3C
and celle dimentions:
a= Å c= Å
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11. Determination of the Bravais-lattice of an unknown crystalline phase
50 nm
Tilting series around common axis
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12. Determination of the Bravais-lattice of an unknown crystalline phase
Tilting series around a dens row of
reflections in the reciprocal space
50 nm
Positions of the
reflections in the
reciprocal space
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13. Bravais-lattice and cell parameters
100
110
111
010
011
001
101
[011]
[100]
[101]
d = L λ / R
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
6.04 Å
7.94 Å
8.66 Å
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14. Chemical analysis by use of EDS and EELS
Ukjent fase
BiFeO3
BiFe2O5
Ukjent fase
BiFeO3
Fe - L2,3
O - K
500 eV forskyvning, 1 eV pr. kanal
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15. Published structure 9/2-10 MENA3100 A.G. Tutov og V.N. Markin
The x-ray structural analysis of the antiferromagnetic Bi2Fe4O9 and the isotypical combinations Bi2Ga4O9 and Bi2Al4O9
Izvestiya Akademii Nauk SSSR, Neorganicheskie Materialy (1970), 6,
Romgruppe: Pbam nr. 55, celleparametre: 7,94 Å, 8,44 Å, 6.01Å
x y z
Bi 4g 0,176 0,175 0
Fe 4h 0,349 0,333 0,5
Fe 4f 0 0,5 0,244
O 4g 0,14 0,435 0
O 8i 0,385 0,207 0,242
O 4h 0,133 0,427 0,5
O 2b 0 0 0,5
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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16. Kikuchi pattern Excess line Deficient 1/d
2θB θB
Diffraction plane
Objective lens
1/d
Inelastically scattered electrons
give 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
Deficient
Excess
Used for determination of:
crystal orientation
-lattice parameter
-accelerating voltage
-Burgers vector
Tegn opp Kikuchi mønster for et tenkt SAD mønster (feks. [100] proj)
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17. Electron Back Scattered Diffraction (EBSD) Orientation Image Microscopy (OIM) in a SEM
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.
Presenting the results both quantitatively and in an image format.
The first step is to define a grid of test pixels across the region of interest. The total number of pixel in the image grid is critical, since it determines, with the dwell-time per pixel, the time required to collect data.
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18. Orientation map example
CD-200 Nordiff EBSD Camera
Step=0.2micron
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19. Overlaid maps
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20. Electron back scattered diffraction (EBSD)
Principal system components
Sample 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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21. Microscope operating conditions
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  
It is very important to understand the effect of varying the microscope operating conditions on the diffraction pattern. Increased probe size Must be balanced with the spatial resolution required Also, because more energy is being deposited on the phosphor screen, this will result in a brighter pattern which requires a shorter integration time (Figure 4).
Higher accelerating voltages may be required to penetrate conducting layers, and lower accelerating voltages for restraining the beam to thin layers, or for charging samples.
Note that there is an effect on the bandwidth, sharpness and contrast
Experimental setup
It is important to balance the requirements of total experiment time, orientation accuracy and spatial resolution when designing an EBSD experiment.
The orientation measurement accuracy is typically ±0.5°.
Spatial resolution
The electrons contributing to the diffraction pattern originate within nanometres of the sample surface.
Spatial resolution depend on the electron beam diameter i.e. type of electron source and probe current.
Typical beam diameters at 0.1 nA probe current and 20 kV accelerating voltage are 2 nm for a FEG source and 30 nm for a tungsten source.
Pressure
EBSD patterns can also be collected from samples at low vacuum in environmental SEMs.
This can be useful with specimens which may otherwise charge, such as ceramic or geological materials.
10 kV
20 kV
30 kV
Effect of changing accelerating voltage on diffraction patterns from nickel
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22. Microscope operating conditions
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.
Image without tilt or dynamic focus compensation
Image with tilt compensation and no dynamic focus compensation
Image with tilt and dynamic focus compensation. The working distance is mm at the top and mm at the bottom of the image
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23. Microscope operating conditions
EBSD 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.
With a tilted sample, the pattern centre position will depend on the sample working distance. Middle: The top and bottom of the field of view may have a different working distance and hence pattern centre positions. Right: If the sample is moved, the working distance and hence pattern centre position will change.
The yellow cross shows the pattern centre with working distance 10mm
The pattern centre moves down the screen as the working disance increases to 18mm 
The pattern centre moves down the screen as the working disance increases to 22mm
The yellow cross shows the pattern centre with working distance 10, 18 and 22 mm
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24. 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:
where fi(θ)  is the atomic scattering factor for electrons and (xi 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.
This is especially important when working with materials with more than one atom type.
Diffraction pattern from the orthorhombic ceramic mullite (3Al2O3 2SiO2) collected at 10 kV accelerating voltage.
Solution overlaid on the diffraction pattern giving the crystal orientation as {370}<7-34>
Simulated diffraction pattern showing all Kikuchi bands with intensity greater than 10% of the most intense band.
Simulation of crystal orientation giving the solution shown.
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25. Background removal
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.
Electrons of all energies scattered from the sample form a background to the diffraction pattern. The background intensity can be removed to improve the visibility of the Kikuchi bands
Original pattern
Background subtraction
Background division
Background
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