Efficiency and accuracy of HR EBSD in measuring inhomogeneity of elastic strains and rotations commonly are demonstrated by imaging GND densities as indicative of dislocation substructure within grains. Not withdrawing the HR EBSD as such, I cannot understand the motivation for such activity. The confusion is in what follows.
1. What we actually search for in substructures is not the Nye's tensor, but LOCATION of dislocation agglomerations (low-angle boundaries, slip bands, etc) as well as related MISORIENTATIONS and STRESS fields. All of them may be shown by inhomogeneous rotation and (elastic) strain fields or by appropriate scalar measures of them.
2. Achievement of the SAME goal through INTERMEDIATE artificial terms gives no additional information, more so that underlying computational procedures involve strong assumptions and their results strongly depend on EBSD routine such as the scanning step.
3. Apart from the above issue, thus derived GNDs could be thought as some estimate for actual dislocation densities [cm^-2], however an APPARENT proportion between GNDs and SSDs will too strongly depend on scanning step again!
A good question - which I take to mean as what use is the determination of (apparent) GND densities from EBSD misorientation maps? And are these apparent values too sensitive to scan step?. I think there have been a few papers on the influence of scan step in recent years so this question is treated in the literature but will have to find them.
The more fundamental problem is what can you do with apparent GND density maps? when they are just derived from misorientation maps? I think the important issue is to determine the ratio of GND to total dislocation densities for different types of dislocation substructures. For example in high SFE materials deformed at high temperatures almost all the dislocations are in LAGBs and contribute to local misorientations so this ratio is close to 1 (and therefore GND maps are useful). However low SFE materials deformed at low temperatures have dislocations in configurations like pile-ups etc with little misorientation so the ratio is close to zero and GND measurements are useless. Most situations are intermediate between these two extremes. And therefore further work on this problem would be of interest.
Thanks, Julian! I know papers on the step effect and my main interest is of course in a fundamental aspect you mention. Well, if you can get the total disl density, your idea would be productive. However to get that you have to employ something other than SEM EBSD. My hint was to directly differentiate the primary data (orientation vectors) in order to get a valuable mapping with no artificial assumptions.
Meanwhile I hope to hear about a certainly justified application of EBSD GND from these special and respected people...
I agree with you and Julian and only want point out again that one has to consider several experimental artifacts like sample prep, pattern center accuracy (improper tilt, out-of-plane tilt of the sample), systematic errors (orientation dependent) in band detection etc. Moreover, the GND model is a very simple geometrical assumption which might be a step-in into this more complex problem but for more complicated crystal structures (no fcc, bcc or hcp) I doubt that it works well.
I think it would work in say semiconductors with very low ro [ cm^-2] where even with a real step GND become lattice disl. However the sensitivity level 10^-8 cm^_2 is still rough for that. As to metals, it is hardly justifiedjustified
for the above considered reason. As to curvature mapping in metals, a possible way to image substructure with no assumptions is given in my paper in MSE-A (2008) available in RG
Since the discussion seems to complete, I'd clear up my position to be understood properly. 1. There is difference between Nye's tensor merely mapping the Burgers vector distributions and its detailsation in terms of CERTAIN rectilinear dislocation families-GNDs. The former (curl of rotation) Is rational as any differentiation stronger maps heterogeneous fields. The latter seems to be only confusing for above reasons...
2. One may also use the former idea by the orientation divergence (not curl) term that is easier to implement.
Further to your comments: in my opinion there are good reasons for experimentally measuring the Nye's tensor (or any equivalent information) and get an approximate measure of the GND local content, because you can get information on the local redundant dislocation density and its hardening effect, that you can compare with predictions from gradient-dependent crystal plasticity models which distinguish between the evolution of the statistically stored and geometrically necessary dislocation densities.
I agree, to distinguish between physical dislocation line density and "mechanistic" Nye's tensor (let alone its representations with particular GND families) would be ideal. The problem is in whether or not the restored (...EBSD) virtual GND lines have a sense. Indeed:
(a) real dislocations are not always rectilinear and consequently are usually mixed (screw/edge) rather than rectilinear edge or srew ones, (b) even if rectilinear, the LOCAL "neutral background" by SSD for the "charged" GND dislocations may have quite various physical densities that is ignored in the GND restoration procedure. That is why minimization of length-scaled energy of GND, as involved in this procedure, becomes completely speculative. in my opinion.
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