Rubber Bands and Dynamical Diffraction Simulations

Dr. Jordan Moering, Mid-Atlantic Sales Manager, EDAX

Like any nerdy high schooler growing up in the suburbs of North Carolina, I had a lot of weird hobbies growing up. Some of these turned into scientific interests that brought me to grad school, and others just turned into party tricks (Rubik’s cube, anyone?). I’ve recently been thinking about one of these hobbies, especially after hearing our recent webinar on OIM Matrix and Forward Modeling.

When I was 15, I thought that rubber band balls were really cool. I’m not sure why, but I really enjoyed the twists and turns of the multiple layers of bands on top of each other. The aspect ratio of the band thickness to the curvature and angle of the bands was something I found really fascinating. Fast forward a few decades and what used to be a softball-sized rubber band ball is now a 12 kg behemoth that I pass every day while walking to my office. I’ve been giving a lot of thought to this ball recently because of how it mimics the dynamical diffraction simulation used in dictionary indexing.

Figure 1. (left) My 12 kg ball of rubber bands. (right) Simulated Kikuchi patterns for EBSD analysis.

I suppose what really fascinates me the most about these projections is how accurate they are. The fundamentals of diffraction can be so simply described in Bragg’s law, but the implications for these phenomena are profound. Because different crystallographic indices diffract incoming electrons at different intensities, the collected image shows the orientation of the crystal wherever the electron beam was parked. The resulting bands (called Kikuchi lines) are a direct representation of the material’s crystal structure.

Now, I’m not an expert on diffraction, but I find all this to be fascinating. What’s cool to me is that recent developments in computing and modeling have enabled new types of indexing. This includes Dictionary Indexing which utilizes an entirely synthesized library of diffraction patterns to correlate the likely orientation of every collected pattern when obtaining EBSD scans. What’s fascinating to me is that these simulations historically struggle to account for artifacts in the Kikuchi patterns like lens blurring, phosphor illumination, etc. With the advent of direct detection cameras however, there is no need to account for these as individual electrons create the image on the sensor. New techniques like forward model-based indexing are only accelerating the adoption of this new technique. And at the core of these new modeling techniques are simulations – simulations of Kikuchi patterns.

So yeah, I see my rubber band ball every day and think about simulated diffraction patterns. I suspect that it is a very low symmetry system based on the geometry.

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