TEQIP Workshop HREXRD
Feb 1st to Feb 5th 2016
1
Introduction to Electron Backscattered Diffraction
SE vs BSE2
http://www4.nau.edu/microanalysis/Microprobe/Interact-Effects.html
Ranges and interaction volumes
3
(1-2m)
Backscattered Electrons4
Topographic Contrast
Image from Characterization Facility Manual, University of Minnesota
5
Secondary and backscattered Electrons
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.
6
Some slides borrowed from Prof. Sudhanshu ShekharSingh and TSL OIM Training Program
EBSD: Theory to Technique
7
Electron backscattered Diffraction (EBSD)8
EBSD Setup9
Kikuchi pattern
EBSD detectorElectron
beam
Sample at
70° tilt Kikuchi lines
Cone of deficient
electrons
Cone of intense
electronsDiffracting
plane
SEM vacuum chamberDiffraction
Cones
Interaction of electrons with materials Kikuchi pattern
(map)
10
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., 2007V. Randle et. al, 2000
11
Bragg’s Law
d
n = 2d sin B
12
Formation of Kikuchi lines13
Conic Sections to Kikuchi Bands14
The cones of diffracted
electrons form hyperbolae
on the phosphor screen
Properties of Kikuchi pattern
• 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
Zone axis
Kikuchi linesDeficient line
Excess line
Kikuchi/EBSP pattern at a point
15
Indexing: Identifying various planes16
Angle (hkl)1 (hkl)225.2 200 31129.5 111 311 31.5 220 311 35.1 311 311 35.3 111 220 45.0 200 220 50.5 311 311 54.7 111 20058.5 111 31160.0 220 202 63.0 311 131 64.8 220 31170.5 111 111 72.5 200 13180.0 111 311 84.8 311 131 90.0 111 220 90.0 200 020 90.0 200 022 90.0 220 113 90.0 220 220
Look Up Table (LUT) The angles between these bands formed
by planes are measured from the Kikuchi pattern
These values are compared against theoretical values of all angles formed by various planes for a given crystal system
When the h-k-l values of a pair of lines are identified, it gives information about the pair of planes, but this does not distinguish between the two planes and hence this alone cannot be used to identify the orientation of the sample
At least 3 sets of lines are required to completely identify the individual planes and hence find the orientation of the sample, as shown in Figure
Band Identification: Image processing
17
Hough Transform
18
Hough Transform
19
Hough Transform
20
Hough Transform
21
EBSD Analysis
22
In order to specify an orientation, it is necessary to set up terms of reference, each of which is known as a 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
There are two coordinate systems:• Sample (specimen) coordinate system• Crystal coordinate system
V. Randle et. al., 2000
Coordinate systems23
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
24
Orientation Maps
=100 µm; BC; Step=1 µm; Grid300x200
=100 µm; IPF; Step=1 µm; Grid300x200
Image Quality MapInverse Pole Figure
25
Titanium Aluminate
Alumina
Erbium Oxide
Zirconium Oxide
Phase Maps26
Various kinds of boundaries27
Charts: Misorientation Angle Distribution28
Charts: Misorientation Profile29
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 = N3/2s2
The diameter (D) is calculated from
the area (A) assuming the grain is a
circle: D = (4A/p)1/2.
Charts: Grain Size30
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 Figures31
Pole Figure: Texture Analysis32
Orientation Distribution Function (ODF)
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
33
t-EBSD34
20 o tool angle: g = 1.50 o tool angle: g = 1.9
a=+20° a=0°
tool
not indexable
indexable
Large areas where the orientation cannot be
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 cold-
deformation strain => decreasing the quality of
the Kikuchi pattern
Nothing could be indexed
G. Facco; S. Shashank; M.R. Shankar; A.K. Kulovits;
J.M.K. Wiezorek, MRS2010 Boston
SEM – EBSD analysis of the microstructure in 316L chips formed with both the 0 and 20o raking angle
0.2 m
0.4 m 0.4 m 0.4 m 0.4 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
Orientation spread
TEM based OIM Analysis (+20° rake)
G. Facco; S. Shashank; M.R. Shankar; A.K. Kulovits;
J.M.K. Wiezorek, MRS2010 Boston
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
TEM based OIM Analysis (0° rake)
G. Facco; S. Shashank; M.R. Shankar; A.K. Kulovits;
J.M.K. Wiezorek, MRS2010 Boston
Cross-correlation technique to determine elastic strain
38
(a) 26R (b) 500 °C (c) 15min
(d) 30min (e) 90min (f) 120min
In-situ Recrystallization39
N. Sharma, S. Shashank; submitted to J. Microscopy
Band Contrast Intensity as user-independent parameter
40
N. Sharma, S. Shashank; submitted to J. Microscopy
Recovery Parameter
(a) 26R, (b) 200 °C and (c) 450 °C.
41
N. Sharma, S. Shashank; submitted to J. Microscopy
MAD as user-independent parameter42
N. Sharma, S. Shashank; submitted to J. Microscopy
Summary43
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