Electron diffraction
Selected area diffraction (SAD) in TEM
Electron back scatter diffraction (EBSD) in SEM
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Bragg’s law

 
ko  k  k
2d hkl sin(  )  n
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.
ko  k 
1

The Ewald Sphere
Cu Kalpha X-ray:  = 150 pm
Electrons at 200 kV:  = 2.5 pm
ko
k
The observed diffraction pattern is
the part of the reciprocal lattice that
is intersected by the Ewald sphere
g
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Intensity distribution and Laue zones
Ewald sphere
(Reflecting sphere)
2θ
First order Laue zone
Zero order Laue zone
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The intensity distribution
around each reciprocal
lattice point is spread out
in the form of spikes directed
normal to the specimen
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
Transmitted
Diffracted beam Multiple
diffracted beam beam
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c
Simplified ray diagram
b
a
Parallel incoming electron beam
3,8 Å
Si
Sample
1,1 nm
PowderCell 2.0
Objective lense
Diffraction plane Objective aperture
(back focal plane)
Image plane
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Selected area
aperture
Apertures
Condenser aperture
Objective aperture
Selected area 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.
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The orientation relationship between the
phases can be determined with ED.
MENA3100
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
(h2k2l2)
-
Measure Ri and the angles between
the reflections
-
Calculate di , i=1,2,3
-
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
Orientations of corresponding
planes in the real space
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(=K/Ri)
Zone axis: gi x gj =[HKL]z
All indexed g must satisfy: g ● [HKL]z=0
MENA3100
Example: Study of unknown phase in a BiFeO3 thin film
Metal organic compound on Pt
BiFeO3
Heat treatment at 350oC (10 min) to
remove organic parts.
Pt
TiO2
Lim
Process repeated three times before final
heat treatment at 500-700 oC (20 min) .
(intermetallic phase grown)
SiO2
Bi
Bi
O
O
Si
O
Bi
Bi
Fe
O
Bi
Fe
Fe
O
O
O
200 nm
O
Fe
Bi
Fe
Fe
Bi
O
Bi
O
O
O
Bi
Bi
Bi
Fe
Goal:
Fe
Fe
O
O
O
O
BiFeO3 with space grupe: R3C
and celle dimentions:
a= 5.588 Å c=13.867 Å
c
b
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O
Fe
Bi
Fe
Bi
Bi
O Fe
Bi
Bi
Po wd erCell 2 .0
a
MENA3100
Determination of the Bravais-lattice of an unknown crystalline phase
Tilting series around common axis
27o
15o
50 nm
10o
0o
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Determination of the Bravais-lattice of an unknown crystalline phase
Tilting series around a dens row of
reflections in the reciprocal space
0o
50 nm
19o
Positions of the
reflections in the
reciprocal space
25o
40o
52o
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Bravais-lattice and cell parameters
011
111
001
c
101
b
010
a
110
[011]
[100]
[101]
d=Lλ/R
100
6.04 Å
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
7.94 Å
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α= β= γ= 90o
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Chemical analysis by use of EDS and EELS
Ukjent fase
BiFe2O5
BiFeO3
CCD
counts
x 1000
CCD
counts
x 1000
1_1evprc.PICT
Nr_2_1evprc.PICT
40
14
35
12
O-K
Fe - L2,3
30
10
25
8
BiFeO3
20
6
Ukjent fase
4
15
2
10
-0
5
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500 eV forskyvning, 1 eV pr. kanal
-0
-0
200
200
400
600
Energy
(eV)
400 Loss 600
Energy Loss (eV)
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800
800
1000
1000
Published structure
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, 2014-2017.
Romgruppe: Pbam nr. 55,
celleparametre: 7,94 Å, 8,44 Å, 6.01Å
Bi
Bi
Fe
Fe
O
O
O
O
4g
4h
4f
4g
8i
4h
2b
x
0,176
0,349
0
0,14
0,385
0,133
0
y
0,175
0,333
0,5
0,435
0,207
0,427
0
O
Bi
O
z
0
0,5
0,244
0
0,242
0,5
0,5
O
Bi
O
Bi
Fe
O
O
Fe
Fe
O
O
Fe O
O
Fe
O
O
Fe
O
Fe
O
O
Fe
O
Fe
O
O
O
Fe
Fe
O
O
Fe
Bi
O
Bi
O
O
Bi
O
Bi
c
b
Po wd erCell 2 .0
a
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
Inelastically scattered electrons
give rise to diffuse background in
the ED pattern.
θB
2θB
Kikuchi lines are due to:
-Inelastic+ elastic scattering event
-lattice parameter
Objective lens
Diffraction plane
Excess
line
Deficient
line
1/d
-accelerating voltage
-Burgers vector
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Excess
θB
-Angular distribution of inelastic
scattered electrons falls of rapidly
with angle. I=Iocos2α
Used for determination of:
-crystal orientation
Deficient
MENA3100
http://www.doitpoms.ac.uk/index.html
http://www.doitpoms.ac.uk/tlplib/diffraction-patterns/kikuchi.php
Electron Back Scattered Diffraction (EBSD)
Orientation Image Microscopy (OIM)
in a SEM
• 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.
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Orientation map example
CD-200 Nordiff EBSD Camera
Step=0.2micron
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Overlaid maps
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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.
http://www.ebsd.com/ebsd-explained/anim2.htm
http://www.ebsd.com/ebsd-explained/simulationapplet.htm
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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
20 kV
10 kV
Effect of changing accelerating voltage on diffraction patterns from nickel
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30 kV
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
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Image with tilt compensation and
no dynamic focus compensation
MENA3100
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
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.
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:
2
I hkl




  f i ( ) cos 2 (hxi  kyi  lz i )   f i ( ) sin 2 (hxi  kyi  lz i )
 i
 i


2
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.
Diffraction pattern from the
orthorhombic ceramic mullite
(3Al2O3 2SiO2) collected at
10 kV accelerating voltage.
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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.
MENA3100
Simulation of crystal
orientation giving the
solution shown.
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.
Background
Original pattern
Background subtraction
Background division
http://www.ebsd.com/ebsd-explained/undertakingexperiments3.htm
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