Advances in EBSD Analysis Using Novel Dynamical Pattern Simulation Software

Transcription

1 Advances in EBSD Analysis Using Novel Dynamical Pattern Simulation Software Bruker Nano GmbH, Berlin Webinar, November 5 th, 2014 Innovation with Integrity

2 Presenters Dr. Daniel Goran Product Manager EBSD, Bruker Nano, Berlin Dr. Aimo Winkelmann Senior Scientist EBSD, Bruker Nano, Berlin 2

3 Dynamical simulations Dynamical simulations capability of ESPRIT 2.0 (main EBSD product) and ESPRIT DynamicS (new standalone product): ESPRIT DynamicS - Platform for development of new analytical tools based on full information contained in a Kikuchi pattern Standalone software involve the whole EBSD community in this process Compatible with all EBSP formats regardless of the EBSD hardware used Using ESPRIT DynamicS in combination with our QUANTAX EBSD system has certain advantages 3

4 Dynamical simulations e - Flash HR EBSD detector - High quality phosphor screen - High end optics system (low aberrations/distortions) - 12 bit images (4096 gray levels) - High pixel resolution CCD chip (native res. 1600x1200 pixels) - High Definition EBSPs high correlation coefficients more accurate results: - Ultra accurate phase ID, unit cell refinement, etc. 4

5 Dynamical simulations ESPRIT 2.0: Flexible interface for creating & editing phase files Dynamical and Kinematic simulations Capable to display and rotate in real time EBSPs using gnomonic, stereographic and spherical projections Compatible with.cif,.cel and.cry format files 5

6 Dynamical simulations ESPRIT 2.0: Flexible interface for creating & editing phase files Dynamical and Kinematic simulations Capable to display and rotate in real time EBSPs using gnomonic, stereographic and spherical projections Compatible with.cif,.cel and.cry format files 6

7 ESPRIT 2.0 Advanced Phase ID on functional materials: Search with Ba, Fe & O - 55 candidate phases 7

8 ESPRIT 2.0 Advanced Phase ID on functional materials: Search with Ba, Fe, O & any other element(s) candidate phases 8

9 ESPRIT DynamicS 9

10 ESPRIT DynamicS Cross correlation tests using: Kinematic and dynamical simulated patterns vs. Experimental patterns from same phase (8 different orientations) Candidate phases were from the same space group (R -3m) but with slightly different lattice parameters (c/a ratios: (A); (B); (C) and (D)) 10

11 ESPRIT DynamicS Cross correlation coefficients between kinematic (left) and dynamical (right) simulated patterns vs. experimental patterns Cross correlation with kinematic simulations inconsistent results Cross correlation with dynamical simulations highly reproducible results 11

12 ESPRIT DynamicS High resolution EBSD Pattern Simulation Aimo Winkelmann Innovation with Integrity

13 Contents 1. Introduction 2. Models of Diffraction in Crystals 3. ESPRIT DynamicS Kikuchi Pattern Simulation Software 4. Application Examples 13

14 Electron Backscatter Diffraction (EBSD) Experimental Setup SEM EDS Chemical Analysis (Energy-dispersive X-ray Spectroscopy) electron beam EBSD Crystallographic Analysis sample Kikuchi pattern 14

15 The raw data 15

16 Geometry of Wave Interference in Crystals λ θ B lattice planes θ B θ B gnomonic projection of Kossel cones θ B Bragg s Law d Kossel cones 16

17 Realistic EBSD Simulations Geometric model High resolution pattern acquired with the Bruker e Flash 17

18 Realistic EBSD Simulations Geometric model High resolution pattern acquired with the Bruker e Flash 18

19 Realistic EBSD Simulations Geometric model High resolution pattern acquired with the Bruker e Flash 19

20 Realistic EBSD Simulations High resolution pattern acquired with the Bruker e Flash 20

21 Realistic EBSD Simulations Realistic simulation using the dynamical theory of electron diffraction High resolution pattern acquired with the Bruker e Flash 21

22 Modelling the Physics of EBSD 22

23 Bloch Wave Model of Electron Diffraction Wave function is sum of Bloch waves ( N ) ( j) Ψ( r ) = c j exp( ik r ) C j Schrödinger Equation ( j) g exp( igr ) Matrix Eigenvalue Problem + Boundary Conditions Wave Function of Diffracted Electrons g 2 2m ( N ) V ( r ) = V 2 K Ψ( r ) ev ( r ) Ψ( r ) = 2m c, C exp( igr ) Bloch wave approach: see e.g. M. De Graef: Introduction to Conventional Transmission Electron Microscopy 2 Fourier expansion of crystal potential j g ( j) g g, k ( j) 2 0 Ψ( r ) Backscattering proportional to probability density of electrons near atomic sites 2 i j* I Z B ( t) C C exp( M )exp[ i( h g) r ] ECP n n ij i, j g, h g h C.J. Rossouw, P.R. Miller, T.W. Josefsson and L.J. Allen, Phil. Mag. A 70, 985 (1994) n 23

24 Do I need to know all this theory? 24

25 ESPRIT DynamicS Kinematic simulation Cr 3 Si pattern acquired with the Bruker e Flash 25

26 ESPRIT DynamicS Realistic dynamical simulation Cr 3 Si pattern acquired with the Bruker e Flash 26

27 ESPRIT DynamicS Overview Easy access to realistic simulations of EBSD patterns Independent of EBSD hardware: stand-alone software load EBSD patterns from any system automatic single-pattern calibration, indexing and fine-tuning Comparison of different simulation models all common models of EBSD patterns included up to full dynamical theory quantification of the agreement between simulation and experiment Import / Export Phase data from/to ESPRIT Import of external crystallographic data (CIF) 27

28 Bragg Reflections Simulation Models Hematite Fe 2 O 3 G. Nolze, A. Winkelmann Exploring structural similarities between crystal phases using EBSD pattern comparison Cryst. Res. Tech. 49, 490 (2014) DOI: /crat Kinematic Model Experiment Dynamical Simulation 20kV 28

29 Visualization Options Experimental pattern Gnomonic projection: dynamical simulation Stereographic projection Gnomonic projection: kinematic simulation Crystal structure Diffraction sphere 29

30 Load any EBSD pattern and simulate GaN TIMEPIX direct electron detection C. Trager-Cowan University of Strathclyde, Glasgow 30

31 Quantification: cross correlation coefficient Experiment Simulation Simulation can depend on: phase, orientation, physical parameters f t Normalized Cross Correlation r= see e.g. "Digital Image Processing" Gonzalez & Woods random 0 < r < 1 perfect fit Application to HR-EBSD: A. Wilkinson, G. Meaden, D. Dingley, Ultramicroscopy 106, 307 (2006) EBSD Image Segmentation: S.U. Park, D. Wei, M. De Graef, M. Shah, J. Simmons and A.O. Hero, Microsc. Microanal. 19, 734 (2013) 31

32 Application Example Distinguishing Iron Oxide Phases Wuestite (FeO) Magnetite (Fe 3 O 4 ) Fm3m, no. 225, cubic Fd3m, no. 227, cubic } Crystal structures and symmetry groups Kinematic simulations show very similar patterns Experimental patterns 160 pixels x 120 pixels, 140 pps Dynamical simulations reproduce the differences between phases 32

33 Application Example Distinguishing Iron Oxide Phases Wuestite (FeO) Magnetite (Fe 3 O 4 ) Fm3m, no. 225, cubic Fd3m, no. 227, cubic } Crystal structures and symmetry groups r Wuestite = 0.62 r Magnetite = 0.53 r Wuestite = 0.41 r Magnetite = 0.64 Pairwise cross-correlation coefficient indicates correct phase Experimental patterns 160 pixels x 120 pixels, 140 pps Dynamical simulations reproduce the differences between phases 33

34 Application Example Simulation of Cr 3 Si HOLZ Rings Dynamical pattern simulations can accurately reproduce HOLZ (Higher- Order Laue Zone) rings Kinematic simulation Crystal structure High resolution pattern acquired with the Bruker e Flash Experimental pattern Pattern fine structure is accurately reproduced: Characteristic HOLZ rings are found around prominent zone axes Dynamical simulation 34

35 Application Example Energy-dependent EBSD:Nickel fcc Experimental patterns Dynamical simulations 5 kv 10kV 15 kv 20kV Energy-dependent zone axis fine structure Sensitivity to lattice parameters 35

36 Application Example Discrimination of Quartz Chirality α-quartz SiO 2 left-handed vs. right-handed Comparison to Experiment: Left-right asymmetry of Kikuchi band profile near [210] direction Normalized Difference of Simulations Dynamical pattern simulations predict and confirm chirality effects in EBSD 36

37 ESPRIT DynamicS: Summary Crystallographic phase analysis via EBSD pattern comparison Direct visual verification of results + numerical quantification investigation of the influence of various parameters in the experiment: lattice parameters (e.g. presence of strain, phase transitions) chemical composition symmetry of crystal structure energy-dependent Kikuchi pattern features User areas: advanced microscale crystallographic characterization of complex functional materials & minerals metals, semiconductors, ceramics, photovoltaic, piezoelectric, magnetic, multiferroic materials 37

38 Copyright 2014 Bruker Corporation. All rights reserved. Innovation with Integrity