Introduction to Electron
Backscattered Diffraction
1
TEQIP Workshop HREXRD
Feb 1st to Feb 5th 2016
SE vs BSE
2
Ranges and interaction volumes
3
(1-2m)
http://www4.nau.edu/microanalysis/Microprobe/Interact-Effects.html
Backscattered Electrons
4
Topographic Contrast
5
Image from Characterization Facility Manual, University of Minnesota
Secondary and backscattered Electrons
6
 Backscattered electrons can also produce secondary electrons.
 Secondary electrons are generated throughout the interaction
volume, but only secondary electrons produced near the surface
are able to escape (~5 nm in metals). For this reason, secondary
electron imaging (SEI) yields high resolution images of surface
features.
By definition, secondary
electrons have energy
<50 eV, with most <10
eV.
EBSD: Theory to Technique
7
Some slides borrowed from Prof. Sudhanshu Shekhar
Singh and TSL OIM Training Program
Electron backscattered Diffraction (EBSD)
8
EBSD Setup
9
SEM vacuum chamber
Electron
beam
Cone of intense
Diffraction
electrons
Cones
Diffracting
plane
EBSD detector
Cone of deficient
electrons
Sample at
70° tilt
Kikuchi pattern
Kikuchi lines
10
Interaction of electrons with materials
Kikuchi pattern
(map)
11
Setup for EBSD in SEM
Principal system components
• Sample tilted at 70° from the horizontal
• phosphor screen (interaction of electrons)
• Sensitive CCD video camera (capture the image on
phosphor screen)
T. Maitland et. al., 2007
V. Randle et. al, 2000
Bragg’s Law
12
d
n = 2d sin B
Formation of Kikuchi lines
13
Conic Sections to Kikuchi Bands
14
The cones of diffracted
electrons form hyperbolae
on the phosphor screen
Properties of Kikuchi pattern
15
•
•
•
•
Each band : diffraction of a family of planes
Intersections of bands : intersections of planes = zone axes
Angles between bands : angles between planes
Band widths : proportional to d(hkl) related to lattice
parameters Middle line of a kikuchi band represents plane
Excess line
Zone axis
Deficient line
Kikuchi lines
Kikuchi/EBSP pattern at a point
Indexing: Identifying various planes
16
Look
Up Tablethese
(LUT)
 The angles
between
bands formed
Angle
(hkl)1
(hkl)2
by planes
from the Kikuchi
25.2are measured
200
311
111
311
pattern29.5
31.5
220
311
 These values
are
compared
against
35.1
311
311
theoretical
formed by
35.3 values
111of all angles
220
200 a given
220crystal system
various45.0
planes for
50.5
311
311
 When the
h-k-l
values
of
a pair of lines are
54.7
111
200
58.5 it gives
111information
311
identified,
about the
60.0
220
202
pair of planes,
but
this
does
63.0
311
131 not
64.8 between
220
distinguish
the 311
two planes and
70.5
111
111
hence this
alone
cannot
be
used to
72.5
200
131
identify80.0
the orientation
of
111
311the sample
 At least84.8
3 sets of311
lines are131required to
90.0
111
220
completely
identify
the
individual
planes
90.0
200
020
90.0 find the
200 orientation
022
and hence
of the
90.0
220
113
sample,90.0
as shown
in
Figure
220
220
Band Identification: Image processing
17
Hough Transform
18
Hough Transform
19
Hough Transform
20
Hough Transform
21
EBSD Analysis
22
Coordinate systems
23
In order to specify an orientation, it is necessary to set up terms of reference,
each of which is known as a coordinate system
There are two coordinate
systems:
• Sample (specimen) coordinate
system
• Crystal coordinate system
Specimen coordinate system: Coordinate
system chosen as the geometry of the
sample
Crystal coordinate system: Coordinate
system based on crystal orientation. In
general [100], [010], [001] are adopted
V. Randle et. al., 2000
24
orientation is then defined as 'the position of the crystal coordinate
system with respect to the specimen coordinate system', i.e.
where Cc and CS are the crystal and specimen coordinate systems
respectively and g is the orientation matrix
The fundamental means for expressing g is the rotation or orientation
matrix
The first row of the matrix is given by
the cosines of the angles between the
first crystal axis, [l00], and each of the
three specimen axes, X, Y, Z, in turn
In general sample coordinate system
is the reference system
Orientation Maps
25
=100 µm; IPF; Step=1 µm; Grid300x200
Inverse Pole Figure
=100 µm; BC; Step=1 µm; Grid300x200
Image Quality Map
Phase Maps
26
Titanium Aluminate
Alumina
Erbium Oxide
Zirconium Oxide
Various kinds of boundaries
27
Charts: Misorientation Angle Distribution
28
Charts: Misorientation Profile
29
Charts: Grain Size
30
The area (A) of a grain is the number
(N) of points in the grain multiplied by
a factor of the step size (s).
For square grids: A = Ns2
For hexagonal grids: A = N3/2s2
The diameter (D) is calculated from
the area (A) assuming the grain is a
circle: D = (4A/p)1/2.
Pole Figures
31
Consider a cubic crystal in a rolled sheet sample with "laboratory" or
"sample" axes as shown below.
The Pole Figure plots the orientation of a given plane normal (pole) with
respect to the sample reference frame. The example below is a (001) pole
figure. Note the three points shown in the pole figure are for three
symmetrically equivalent planes in the crystal.
Pole Figure: Texture Analysis
32
Orientation Distribution Function (ODF)
33
Although an orientation can be uniquely defined by a single point in Euler space, 3D
graphs are hard to interpret
Therefore ODF is a 2D representation of Euler Space
Euler Space is divided into
slices with interval of 5o
Slices arranged in gird called ODF
aluminum.matter.org.uk
t-EBSD
34
SEM – EBSD analysis of the microstructure in 316L
chips formed with both the 0 and 20o raking angle
20 o tool angle: g = 1.5
not indexable
a=+20°
0 o tool angle: g = 1.9
a=0°
tool
indexable
Large areas where the orientation cannot be
Nothing could be indexed
determined (by indexing of Kikuchi patterns)
1. Due to refinement of the microstructure
beyond the resolution limit of the SEM
2. Introduction of large amounts of colddeformation strain => decreasing the quality of
the Kikuchi pattern
G. Facco; S. Shashank; M.R. Shankar; A.K. Kulovits;
J.M.K. Wiezorek, MRS2010 Boston
TEM based OIM Analysis (+20° rake)
0.4 m
0.4 m
0.4 m
0.4 m
Orientation spread
0.2 m
1. BF images show the formation of
dislocation walls sub cell structure
typical of large amounts of plastic
deformation facilitated by conventional
plastic deformation
2. OIM imaging shows large grains that
contain low angle mis-orientations
3. OIM observations are consistent with BF
image contrast of the dislocation wall
sub cell structure
G. Facco; S. Shashank; M.R. Shankar; A.K. Kulovits;
J.M.K. Wiezorek, MRS2010 Boston
TEM based OIM Analysis (0° rake)
0.4 m
0.4 m
0.4 m
0.4 m
1. OIM imaging shows much
smaller grains separated by High
Angle Grain Boundaries HAGB’s
=> grain refinement took place
2. 0° raking constitutes a severe
plastic deformation process
G. Facco; S. Shashank; M.R. Shankar; A.K. Kulovits;
J.M.K. Wiezorek, MRS2010 Boston
Cross-correlation technique to determine elastic
strain
38
In-situ Recrystallization
39
(a) 26R
(b) 500 °C
(c) 15min
(d) 30min
(e) 90min
(f) 120min
N. Sharma, S. Shashank; submitted to J. Microscopy
Band Contrast Intensity as userindependent parameter
40
N. Sharma, S. Shashank; submitted to J. Microscopy
Recovery Parameter
41
(a) 26R, (b) 200 °C and (c) 450 °C.
N. Sharma, S. Shashank; submitted to J. Microscopy
MAD as user-independent parameter
42
N. Sharma, S. Shashank; submitted to J. Microscopy
Summary
43
 EBSD is a very powerful technique for quantitative
microscopy
 It is based on diffraction and hence can be used for
any crystalline materials
 This method provides trove of data related to
orientation, misorientation and can be extrapolated
to represent strains, extent of recovery,
recrystallization and may more things