Introduction to Electron Backscattered Diffraction 1 TEQIP Workshop HREXRD Feb 1 st to Feb 5 th 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 Diffracting plane Cone of intense electrons Diffraction Cones Electron beam EBSD detector Cone of deficient electrons Sample at 70 tilt Kikuchi pattern Kikuchi lines
Interaction of electrons with materials Kikuchi pattern (map) 10
Setup for EBSD in SEM 11 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 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 Angle (hkl) 1 (hkl) 2 25.2 200 311 29.5 111 311 31.5 220 311 35.1 311 311 35.3 111 220 45.0 200 220 50.5 311 311 54.7 111 200 58.5 111 311 60.0 220 202 63.0 311 131 64.8 220 311 70.5 111 111 72.5 200 131 80.0 111 311 84.8 311 131 90.0 111 220 90.0 200 020 90.0 200 022 90.0 220 113 90.0 220 220
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 There are two coordinate systems: Sample (specimen) coordinate system Crystal coordinate system Coordinate systems 23 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 =100 µm; BC; Step=1 µm; Grid300x200 Inverse Pole Figure 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 = Ns 2 For hexagonal grids: A = N 3/2s 2 The diameter (D) is calculated from the area (A) assuming the grain is a circle: D = (4A/p) 1/2.
Pole Figures Consider a cubic crystal in a rolled sheet sample with "laboratory" or "sample" axes as shown below. 31 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 5 o aluminum.matter.org.uk Slices arranged in gird called ODF
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 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 Nothing could be indexed G. Facco; S. Shashank; M.R. Shankar; A.K. Kulovits; J.M.K. Wiezorek, MRS2010 Boston
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
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 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 43