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