1. © Oxford Instruments Analytical Limited 2001 MODULE 3 - About the EBSD Pattern Bragg Diffraction Pattern Formation ‘Background’ Background Subtraction The Hough Transform The information contained in the EBSP

2. © Oxford Instruments Analytical Limited 2001 About the EBSD Pattern - Bragg Diffraction EBSD occurs due to Bragg diffraction Bragg's law: nL = 2d sine theta where n is the order of reflection, L (Lambda) is the electron wavelength, d is the lattice spacing, and theta is the Bragg angle, the angle of incidence of the electron.

3. © Oxford Instruments Analytical Limited 2001 About the EBSD Pattern - Pattern Formation Electron scattering takes place between the crystal planes Bragg diffraction occurs from the crystal planes Bands in the EBSP are called Kikuchi bands.

4. © Oxford Instruments Analytical Limited 2001 About the EBSD Pattern - ‘Background’ Only a small proportion of the electrons arriving at the phosphor screen are diffracted. Therefore the pattern is superimposed on a ‘background’ Background subtraction is required to enhance pattern contrast

5. © Oxford Instruments Analytical Limited 2001 About the EBSD Pattern - ‘Background’ Subtraction Background subtraction greatly enhances pattern contrast and the number of bands detectable

6. © Oxford Instruments Analytical Limited 2001 About the EBSD Pattern - Detecting the Bands - The Hough Transform The Hough Transfrom provides a suitable technique for deriving the parameters of a straight line and thus the band positions in an EBSP. Lines in the pattern are converted to ‘spots’ in Hough Space

7. © Oxford Instruments Analytical Limited 2001 About the EBSD Pattern - Detecting the Bands - The Hough Transform Hough Transform of a single line

8. © Oxford Instruments Analytical Limited 2001 About the EBSD Pattern - Detecting the Bands - The Hough Transform Hough Transform of an EBSP Note the variation of gray scale in Hough Transform

9. © Oxford Instruments Analytical Limited 2001 About the EBSD Pattern - Detecting the Bands - The Hough Transform Filtering the Hough Space image greatly enhances clarity Peak detection is used to find the maxima Band positions are determined and related back into real space

10. © Oxford Instruments Analytical Limited 2001 About the EBSD Pattern - Information contained in the EBSP The EBSP contains the angular relationship between planes the symmetry of the crystal orientation information

11. © Oxford Instruments Analytical Limited 2001 Examples Pyrrhotite (6kV)FerriteAluminium TitaniumOlivine Ge