The definition of a high-angle grain boundary

[Omero Felipe Orlandini]

Hello, all! 

I have a general question for all of the folks here who have an interest in an experience with the concept of grain boundaries: how the heck can a grain boundary be defined in a defensible, reality-based manner?

From my literature review of geological EBSD studies, my sense is that generally I could choose 10 degrees misorientation for quartz grains, 15 degrees misorientation for grains of anything else, or (cynically) simply not even mention how grains are defined in my scripts and stand a good chance of avoiding censure. I'd rather avoid the last strategy, but I've had a very hard time justifying ANY specific misorientation angle! 

 - The 10 degree misorientation definition for a high-angle grain boundary in quartz seems to stem ultimately from a book by Derek Hull written in 1965 called 'Introduction to dislocations', where Hull suggests that one definition of a high-angle grain boundary would be when dislocations become so close to one another that they cease to be meaningfully discrete, and then suggests that such a condition might be defined as when the dislocation spacing becomes less than five lattice spacings:

"The atomic mismatch at the boundary is accommodated by regions of good and bad fit: the latter are dislocations. In a simple cubic lattice with edge dislocations b=[100], the boundary will consist of a sheet of equally spaced dislocations lying parallel to the z-axis; the plane of the sheet will be the symmetry plane x=0, i.e. (100). The extra half-planes of the dislocations terminate at the boundary from the left- and right-hand sides alternately. The crystals on each side of the boundary are rotated by equal and opposite amounts about the z-axis and differ in orientation by the angle θ (Fig. 2.12(b)). If the spacing of the dislocations is D, then:

(9.1)

and for small values of θ (in radians)

(9.2)

If θ=1° and b=0.25 nm the spacing between dislocations will be 14 nm. When the spacing is less than a few lattice spacings, say five, θ ~ 10° and the individual identity of the dislocations is in doubt, the boundary is called a large-angle boundary." (from section 9.2 of the book)

This was picked up by White, 1976 in 'The effects of strain on the microstructures, fabrics, and deformation mechanisms in quartzites' published in the Philosophical Transactions of the Royal Society of London, and has since propagated into more modern literature as justification for using 10 degrees to define quartz grains. That's all well and good, but the original ratio of dislocations to lattice spacing being less than or equal to five as suggested by Hull seems very arbitrary.

 - Then, we have the 15 degree camp, which seems to be based entirely on the Read-Shockley model for grain boundary energy as a function of misorientation angle, which predicts an energy maximum around 15 degrees [Read W.T., Shockley W.: Dislocation models of crystal grain boundaries. Phys. Rev. 78(3), 275–289 (1950)]. This model was calibrated on observations of silicon ferrite only, and was shown by Gjostein and Rhines in 1959 to be wildly inaccurate for copper crystals above 6 degrees misorientation. Even as recently as 2011, the Read-Shockley model seems to be known to be inaccurate to an unknown extent above 6 degree misorientations, but is still basically the best general model anyone has? [Rohrer, Gregory S. "Grain boundary energy anisotropy: a review." Journal of materials science 46, no. 18 (2011): 5881.] All of the more recent work on grain boundary energy calculations imply to me that the Read-Shockley model is too simplistic and very likely inaccurate, and that a great deal of fundamental work still needs to be done in order to predict grain boundary energy accurately in both metals and geological materials. 

So my observation to all of you fellow MTEXers (and you are all probably vastly smarter and better read that myself) is that there seems to be no real theoretical basis for choosing either 10 degrees, 15 degrees, or any other number to meaningfully define a high-angle boundary between two grains of the same mineral. Are the 'justifications' listed above just... good enough?

Thank you all for your time and consideration!

Best,

Phil Orlandini, University of Colorado at Boulder

[ruediger Kilian]

Hi Phil,
generally speaking, I think you are totally correct to assume that within a certain angle range, there is no justification that 8 degree might be more or less correct than 10 or 12 or 15. My gut feeling would be that the higher angles are rather ok for highly symmetric phases while for all these low symmetry minerals, a smaller angle angle might apply- however I do not have any evidence for this speculation.
For a certain misorientation, there might be no coincidence between two lattices while for another misorientation with the same misorientation angle, this might still be the case. The choice of angle may also depend on your problem; for example, if you were interested in a transport property of high angle boundaries, hence you want to know the rain boundary density, one might probably rather use a larger angle, so the result will not overestimate this property. At the other hand, if one would be interested in e.g. the nature of misorientation axes of low angle boundaries, one would probably want to use a small angle, to make sure that no “true” high angle boundaries are accidentally selected. For quartz, there’s Shigematsu et al. 2006 (First combined electron backscatter diffraction and transmission electron microscopy study of grain boundary structure of deformed quartzite. J. Microsc.-Oxf., 224:306–321, December 2006. ISSN 0022-2720. doi: 10.1111/j.1365-2818.2006.01697.x.) where they conclude that the transition form low to high angle boundaries in quartz occurs between 9 and 14°, based on the loss of TEM grain boundary fringes - meaning, within this range you may find both types of boundaries.
Apart from a purely angle based segmentation, one can always think of additional information e.. grain shape or whatever fits you grain “model”. If you work on quartz, you will find pretty interesting results if you compare an EBSD map and associated gb angles with your optical impression from the light microscope.
So, with regard to your question, reporting how segmentation was done should always be mentioned and I think it’s always good to have some sort of reasonable justification why one or the other angle was chosen. Apart from that, you are totally correct to assume that we are stuck with misorientation angle concept.
Cheers,
Rüdiger

[Omero Felipe Orlandini]

Hi Rüdiger! 

Thank you for your response! I had seen the Shigematsu et al 2006 paper before, but missed reviewing it in this most recent rabbit-hole into grain boundaries. Thank you for reminding me, I think that actually if I combine that with the Fitz Gerald et al 1983 TEM study of plagioclase boundaries that observes a misorientation range of 3-5 degrees for the same dislocation-based criteria that Shigematsu et al 2006 uses, I should have my two rheologically significant phases covered. Seems a bit weird to use multiple definitions for high-angle grain boundaries simultaneously in one sample, but that seems to be the most honest way to treat a polymineralic sample. At least MTEX makes that process quite straightforward! 

I suppose that what I REALLY should do in the name of scientific rigor is go try to find similar TEM observations of grain boundaries and misorientations for every single mineral in my maps and give each mineral an individual, justified HAGB definition where possible. Because who knows, maybe that pyroxene porphyroclast is doing something very interesting with subgrains that I would otherwise be oblivious to... 

Thank you for your response and helping me to think this process through! 

Best,

Phil

[Fitz Gerald, J.D., Etheridge, M.A., and Vernon, R.H., 1983, Dynamic recrystallization in a naturally deformed albite: Textures and Microstructures Textures and Microstructures, v. 5, p. 219–237.]