strain analysis

Being more precise

Dr. Stuart Wright, Senior Scientist, Gatan/EDAX

The precision and accuracy of orientation measurements by electron backscatter diffraction (EBSD) have been of interest since the advent of EBSD [1, 2]. In contrast, reliability (in terms of correctly identifying the orientation at least within 5°) was of greater concern when indexing was first automated (there is a section of my thesis [3] devoted to precision, as well as Krieger Lassen’s thesis [4]). I’ve written a few papers on the subject [5 – 7], and there have been several more by other authors [8 – 11]. High-resolution EBSD (HREBSD) has shown success in markedly improving precision [12]. Now that dictionary indexing (DI) has become more common; there has been a resurgence in papers on the precision that can be achieved using DI [13 – 15]. I know that is a lot of references for a blog post, but I wanted to give you an idea of how many different research groups have studied angular precision in EBSD measurements – the references given are only a sampling; there are certainly more.

Will Lenthe and I have been working hard to improve the dictionary indexing capabilities in the EDAX OIM Matrix™ add-on module to EDAX OIM Analysis™. In addition, Will has added the ability to perform spherical indexing within OIM Matrix [16 – 17] (see Will’s “New Tools for EBSD Data Collection and Analysis” webinar for more information). These new capabilities will be available soon in OIM Analysis 9. I’m excited about the progress we’ve made. You will find OIM Matrix much easier to use and more robust. In addition, we’ve sped up many aspects of OIM Analysis, which will help with the big datasets routinely obtained with the EDAX Velocity™ cameras.

The precision of indexing via spherical indexing has recently been explored [18]. Using OIM Analysis 9, we’ve been exploring what we can achieve in terms of orientation precision with orientation refinement [19 – 21] applied to initial indexing results obtained by Hough transform-based indexing, dictionary indexing, and spherical indexing. We haven’t quantified our results yet. Still, the KAM maps (which indicate the orientation precision) we’ve obtained are so promising that I want to show our preliminary results. Our refinement method is essentially a hybrid of that proposed by Singh, Ram, and De Graef [19] and Pang, Larsen, and Schuh [21]. But for the spherical indexing, we also have implemented an additional refinement in the harmonic frequency space. Figure 1 shows some results I am excited to share.

Figure 1. KAM maps from nickel [22]. (Top row) As-indexed, (middle row) with NPAR for Hough-based indexing and refinement in the spherical harmonics for spherical indexing, and (bottom row) after real-space refinement. The first column is for Hough-based indexing, columns 2 – 4 are for dictionary indexing with different dictionary target disorientations, and columns 5 – 6 are for SI with different harmonic bandwidths.

It is pretty interesting that the KAM maps after refinement are all nearly the same, no matter which type of indexing was used to obtain the initial orientation measurements. We do not expect much plastic strain or permanent deformation in these samples, so the reduced KAM values are more of what we expect for the sample.

Here is another set of results for a silicon single crystal. The scan is approximately 1 x 1 mm with a 30 m step size. You can see the dramatic improvement in these results. Unfortunately, the two points with the largest KAM values are due to some dust particles on the sample’s surface.

Figure 2. KAM maps were constructed using Hough-based indexing, SI, and SI followed by refinement.

We are very excited to get these advancements into your hands and are putting in extra hours to get the software ready for release. We hope you are as precisely excited as we are to apply it to your samples!

[1] Harland CJ, Akhter P, Venables JA (1981) Accurate microcrystallography at high spatial resolution using electron backscattering patterns in a field emission gun scanning electron microscope. Journal of Physics E 14:175-182
[2] Dingley DJ (1981) A Comparison of Diffraction Techniques for the SEM. Scanning Electron Microscopy IV: 273-286
[3] Wright SI (1992) Individual Lattice Orientation Measurements Development and Applications of a Fully Automatic Technique. Ph.D. Thesis., Yale University.
[4] Krieger Lassen NC (1994) Automated Determination of Crystal Orientations from Electron Backscattering Patterns. Ph.D. Thesis, Danmarks Tekniske Universitet.
[5] Wright S, Nowell M (2008) High-Speed EBSD. Advanced Materials and Processes 66: 29-31
[6] Wright SI, Basinger JA, Nowell MM (2012) Angular precision of automated electron backscatter diffraction measurements. Materials Science Forum 702: 548-553
[7] Wright SI, Nowell MM, de Kloe R, Chan L (2014) Orientation Precision of Electron Backscatter Diffraction Measurements Near Grain Boundaries. Microscopy and Microanalysis 20:852-863
[8] Humphreys FJ, Huang Y, Brough I, Harris C (1999) Electron backscatter diffraction of grain and subgrain structures – resolution considerations. Journal of Microscopy – Oxford 195:212-216.
[9] Demirel MC, El-Dasher BS, Adams BL, Rollett AD (2000) Studies on the Accuracy of Electron Backscatter Diffraction Measurements. In: Schwartz AJ, Kumar M, Adams BL (eds) Electron Backscatter Diffraction in Materials Science. Kluwer Academic/Plenum Publishers, New York, pp 65-74.
[10] Godfrey A, Wu GL, Liu Q (2002) Characterisation of Orientation Noise during EBSP Investigation of Deformed Samples. In: Lee DN (ed) ICOTOM 13, Seoul, Korea, Textures of Materials. Trans Tech Publications Inc., pp 221-226.
[11] Ram F, Zaefferer S, Jäpel T, Raabe D (2015) Error analysis of the crystal orientations and disorientations obtained by the classical electron backscatter diffraction technique. Journal of Applied Crystallography 48: 797-813
[12] Wilkinson AJ, Britton TB (2012) Strains, planes, and EBSD in materials science. Materials Today 15: 366-376
[13] Ram F, Singh S, Wright SI, De Graef M (2017) Error Analysis of Crystal Orientations Obtained by the Dictionary Approach to EBSD Indexing. Ultramicroscopy 181:17-26.
[14] Nolze G, Jürgens M, Olbricht J, Winkelmann A (2018) Improving the precision of orientation measurements from technical materials via EBSD pattern matching. Acta Materialia 159:408-415
[15] Shi Q, Loisnard D, Dan C, Zhang F, Zhong H, Li H, Li Y, Chen Z, Wang H, Roux S (2021) Calibration of crystal orientation and pattern center of EBSD using integrated digital image correlation. Materials Characterization 178:111206
[16] Lenthe W, Singh S, De Graef M (2019) A spherical harmonic transform approach to the indexing of electron backscattered diffraction patterns. Ultramicroscopy 207:112841
[17] Hielscher R, Bartel F, Britton TB (2019) Gazing at crystal balls: Electron backscatter diffraction pattern analysis and cross-correlation on the sphere. Ultramicroscopy 207:112836
[18] Sparks G, Shade PA, Uchic MD, Niezgoda SR, Mills MJ, Obstalecki M (2021) High-precision orientation mapping from spherical harmonic transform indexing of electron backscatter diffraction patterns. Ultramicroscopy 222:113187
[19] Singh S, Ram F, De Graef M (2017) Application of forward models to crystal orientation refinement. Journal of Applied Crystallography 50:1664-1676.
[20] Winkelmann A, Jablon BM, Tong V, Trager‐Cowan C, Mingard K (2020) Improving EBSD precision by orientation refinement with full pattern matching. Journal of Microscopy 277:79-92
[21] Pang EL, Larsen PM, Schuh CA (2020) Global optimization for accurate determination of EBSD pattern centers. Ultramicroscopy 209:112876
[22] Wright SI, Nowell MM, Lindeman SP, Camus PP, De Graef M, Jackson MA (2015) Introduction and comparison of new EBSD post-processing methodologies. Ultramicroscopy 159:81-94

“Strained” Friendship

Dr. Stuart Wright, Senior Scientist EBSD, EDAX

Don’t just read the title of this post and skip to the photos or you might think it is some soap opera drama about strained relations – instead, the title is, once again, my feeble attempt at a punny joke!

I was recently doing a little reference checking and ended up on the website for Microscopy and Microanalysis (the journal, not the conference). On my first glance, I was surprised to see my name in the bottom right corner. Looking closer, I noticed that the paper Matt Nowell, David Field and I wrote way back in 2011 entitled “A Review of Strain Analysis Using Electron Backscatter Diffraction” is apparently the most cited article in Microscopy and Microanalysis. I am pleased that so many readers have found it useful. I remember, at the time, that we were getting a lot of questions about the tools within OIM Analysis™ for characterizing local misorientation and how they relate to strain. It was also a time when HREBSD was really starting to gain some momentum and we were getting a lot of questions on that front as well. So, we thought it would be helpful to write a paper that hopefully would answer some practical questions on using EBSD to characterize strain. From all the citations, it looks as though we actually managed to achieve what we had strived for.

My co-authors on that paper have been great to work with professionally; but I also count them among my closest personal friends. David Field joined Professor Brent Adams’ research group at BYU way back in 1987 if my memory is correct. We both completed master’s degrees at BYU and then followed Brent to Yale in 1988 to do our PhDs together. David then went on to Alcoa and I went to Los Alamos National Lab. Brent convinced David to leave and join the new startup company TSL and I joined about a year later. David left TSL for Washington State University shortly after EDAX purchased TSL.

Before, I joined TSL, Matt Nowell* had joined the company and he has been at TSL/EDAX ever since. Even with all the comings and goings we’ve remained colleagues and friends.

I’ve been richly blessed by both their excellent professional talents and their fun spirited friendship. We’ve worked, traveled and attended conferences together. We’ve played basketball, volleyball and golf together. I must also brag that we formed the core of the soccer team to take on the Seoul National University students after ICOTOM 13 in Seoul. Those who attended ICOTOM 13 may remember that it was held shortly after the 2002 World Cup hosted jointly by Korea and Japan; in which Korea had such a good showing – finishing 4th. A sequel was played at SNU where the students pretty much trounced the rest of the world despite our best efforts 😊. Here are a few snapshots of us with our Korean colleagues at ICOTOM 13 – clearly, we were always snappy dressers!

* Don’t miss Matt’s upcoming webinar: “Applications of High-Speed CMOS Cameras for EBSD Microstructural Analysis”