Caroline Sorensen and Dr. David Fullwood, Department of Mechanical Engineering

The research I have completed over the past year has been very successful. The results will soon (i.e. in the next week or two) be submitted for publication, most likely to the journal “Metallurgical and Material Transactions A.” Preliminary findings from this research were also presented earlier this year at the annual conference of The Minerals, Metals, & Materials Society in San Diego, CA. In this final report I will overview the initial goal and proposed methods, outline a few of the problems that were encountered and solved in my research, discuss the implications of the results, and suggest further relevant research.

Initial Goal and Proposed Method

The goal of this research was to determine the subsurface orientation of grain boundaries using electron backscatter diffraction (EBSD) images. EBSD images are usually treated as 2D data; however they are in fact the product of a three dimensional volume of interactions between incoming electrons and the sample material. This fact manifests itself in the fact that EBSD images taken near a grain boundary present a blended image of patterns from either grain. If a series of EBSD images are taken in a line across a grain boundary, the scans will show the second grain’s pattern growing increasingly strong. Our research exploited this phenomenon to uncover a piece of previously generally inaccessible data: the inclination of a grain boundary below the surface.

The method involved three general steps. First the electron material interactions were simulated and a curve was created that describes how the strength of either grain’s pattern changes across the grain boundary. This process was repeated for every possible grain boundary plane orientation to create a library of curves. Second a line scan was taken across a grain boundary in a sample to get a real experimental curve analogous to these simulated ones. And thirdly the experimental curve was matched to the best-fitting library curve, whose grain boundary orientation is thus the orientation of the sample’s grain boundary. Finally these results were verified using known methods of determining the subsurface orientation (which are either destructive or have a limited scope).

Problems Encountered and Solved

The main problem we encountered was in the verification process. We needed several grains whose subsurface orientation we knew already to determine the efficacy of the new method. Initially we had supposed that we could use a “FIB-ed” sample. Such a sample is obtained by taking a regular EBSD scan over the surface, removing a layer of material using the Focused Ion Beam (FIB) technique, and then repeating for several layers, giving information from locations deeper and deeper into the sample. By reconstructing this data set the grain boundary plane orientation can be recovered relatively easily. However, producing such a sample is quite expensive. Furthermore, the FIB is only calibrated for silicon samples, meaning that any metallic sample one would wish to use would have some unknown error due to the uncertainty in how much material is removed with each layer.

Thus we had only one, semi-reliable, and quite small sample with which to verify the proposed method. Without another verification plan, it would be impossible to thoroughly confirm the success of our research.

Fortunately, Dr. Fullwood, the faculty mentor for this project, suggested an alternative. In addition to using the information recovered from the FIB data, we would also exploit the that certain types of grains can only be formed at specific orientations in relation to their adjacent, or parent, grain. The best and most easily accessible of such grains are twin grains. Twins are a special type of grain that are generally formed as a result of the sample undergoing deformation (e.g. when the sample is pulled into a slightly elongated shape). Such twins are exclusively formed at a given set of orientations, in relation to their parent grain, and they are easily recognizable by their long, lens-like shape.

Thus we were able to write new MATLAB code to mathematically determine the orientation of any given twin grain boundary plane. This provided the absolutely vital verification on our results.

Results and Implications

Using this less expensive and more accurate, though slightly trickier, verification method, we were able to test our method using 10 different grain boundaries. One of these was from the copper FIB test, while the other nine were twin boundaries in tantalum samples. Our method proved to be accurate to within 11 degrees, with an average error of 3 degrees.

Suggested Further Research

While it is difficult to quantitatively allocate this error to specific problems, the likely sources of error include the following: issues inherent in the Monte Carlo simulations used to model the interaction volume, human inaccuracies and sample inconsistencies in measuring twin boundary orientations, and as mentioned earlier the impossibility of proper calibration of the FIB data.
The first of these three listed errors is the most difficult to eradicate. Though there are several such simulations that can be used, all are based on the same essential algorithms and are thus susceptible to the same weaknesses. The fundamental flaw with this type of simulation is the inability of the computer models to correctly model the wave-particle duality of the electrons used in the microscope. These current models rely solely on the particle nature of the electrons, meaning they are incapable of simulating the wave diffraction that is in fact central to the interaction they try to model.

This underlying problem in the simulation has not prevented the success of our research; however it certainly deserves further inquiry. As a result, my next project in the works is a purely experimental study of the size and shape of the interaction volume. Because the character of the interaction volume is so fundamental to all work done using EBSD images from the SEM, it is crucial to verify these widely-used Monte Carlo models.