The dislocations you are observing are all, i.e. mainly SSDs and only some of them are GNDs. Well, GNDs only describe the visible orientation variation. If this is averaged out by dislocations of different Burgers vectors they don't appear in this analysis. On the other hand, it is more important what GNDs can really tell us? I am quite in doubt about it. Not everything which can be calculated automatically makes sense. You can certainly derive this number but then you should have strong arguments to use it for any kind of interpretation. The accuracy of the calculation (not of the real existence) strongly depends on the precision of the orientation determination. Here is a lot of space for improvements, not only using high resolution EBSD (in the sense of huge single patterns). They describe anyway another effect (locall elastic deformation of the lattice). Summarizing, GND can be useful to find some kind of correlation between the measured misorientation and perhaps mechanical properties. From my very personal point of view they are overestimated at the moment because of  the insufficient orientation precision but also because of the very complex deformation processes in polycrystalline materials, the low statistic (only some grains are scanned mostly, and their low fraction compared to SSDs.   

The dislocations you are observing are all, i.e. mainly SSDs and only some of them are GNDs. Well, GNDs only describe the visible orientation variation. If this is averaged out by dislocations of different Burgers vectors they don't appear in this analysis. On the other hand, it is more important what GNDs can really tell us? I am quite in doubt about it. Not everything which can be calculated automatically makes sense. You can certainly derive this number but then you should have strong arguments to use it for any kind of interpretation. The accuracy of the calculation (not of the real existence) strongly depends on the precision of the orientation determination. Here is a lot of space for improvements, not only using high resolution EBSD (in the sense of huge single patterns). They describe anyway another effect (locall elastic deformation of the lattice). Summarizing, GND can be useful to find some kind of correlation between the measured misorientation and perhaps mechanical properties. From my very personal point of view they are overestimated at the moment because of  the insufficient orientation precision but also because of the very complex deformation processes in polycrystalline materials, the low statistic (only some grains are scanned mostly, and their low fraction compared to SSDs.   

Thanks mate!

Agree with you on the doubts on the EBSD results for GND density measurements.

But in TEM, is there any way to separate SSDs from GNDs? any experience on that?

Well, you can of course use the crystal orientation, calculate all possible dislocations and Burgers vectors and investigate only these g-vector conditions. These are certainly NOT the GND related dislocations, since all are now visible but you will get at least an idea how they are distributed. If there is a significant correlation to lattice rotations dísplayed by EBSD you can at least discuss the size. How statistically relevant this is I do not know.   

Thanks for your comments Gert. Trying to find a way to validate EBSD accuracy on such calculations ....

If you have the patterns I could do this for you. If not it becomes more a statistical problem since you only have the Euler angles derived from your EBSD system. Hough bands have certain limits. Therefore we are preferring a matching of the entire pattern with dynamical pattern simulation. It runs with about 1 patter/s, but can be improved in future, if it is of general interest.  The principle you can see at the attached link. 

Conference Paper EBSD: more reliable and precise

Thanks Gert. I have actually downloaded your presentation and trying to find a free time to read it through.

There are "debaters" out there talking against EBSD being able to calculate GNDs density at all! Therefore, I was looking for another characterization technique to validate the result I get from EBSD.

The dynamic pattern simulation could be an alternative though ... I will discuss with you later on regarding this ... Cheers

The total dislocation density is also an important aspect in terms of accuracy. If you use the standard GND calculation function (e.g. in OIM Analysis or similar software packages) from a relatively fast scan on fully recrystallized Cu or Ni with step a size of 100 - 200nm, you will get a GND "noise floor" which is at least 2 orders of magnitude higher than the total dislocation density (10^10) and maybe 3 orders above the real GND density. However, after a few percent of plastic strain your real dislocation density is already in the range of the above mentioned noise floor or even higher and if the strain is much larger you might even neglect this effect, depending on what you want to derive/learn from the GND density.

I also agree that GNDs are somewhat overrated, especially in terms of estimating the total dislocation density. Unfortunately, the ratio of GNDs to SSDs is not a constant but changes with plastic strain and even crystal orientation.

Dear Ehsan, dear Gert, dear colleagues,

Thank you, Ehsan, for asking this important question, and Gert, for your interesting thoughts and discussion. Concerning the GNDs and SSDs I have two remarks.

1. The term geometrically necessary dislocations (GNDs for short), introduced by Ashby in 1970, has a vague meaning and does not admit an exact statistical interpretation. A much better term is excess (or non-redundant) dislocations. The density of excess dislocations is important in the continuum dislocation theory and crystal plasticity because it characterizes the macroscopically observable average plastic distortion. In contrary, the so-called statistically stored (or redundant) dislocations (which usually exist in form of dislocation dipoles to render low energy to the crystal) do not contribute to this average plastic distortion. However, they play two important roles in crystal plasticity: (i) together with the Frank-Read source they provide additional sources for the nucleation of excess dislocations due to the fact that, when the applied shear stress becomes large enough, the dislocation dipoles dissolve to form the freely moving excess dislocations, (ii) the neutral dislocation dipoles act as obstacles that impede the motion of excess dislocations leading to the nonlinear work hardening.

2. The experimental measurement of excess dislocations by using the electron backscatter diffraction (EBSD for short) is based first of all on the Nye-Bilby-Kröner formula relating the tensor of excess dislocation density with the curl of the average plastic distortion. Since the total distortion (which is the sum of the lattice and plastic distortions) is compatible, this Nye-Bilby-Kröner tensor is equal to the curl of the lattice distortion taken with minus sign. An additional assumption made is that the lattice strain is small compared to the lattice rotation.

Concerning the role of statistically stored dislocations in crystal plasticity you can find a continuum model proposed in our recent paper

https://www.researchgate.net/publication/278048077_Continuum_dislocation_theory_accounting_for_statistically_stored_dislocations_and_Taylor_hardening

Article Continuum dislocation theory accounting for redundant disloc...

I agree with the above points but wish to develop the comment of Enrico who pointed out that in material with a low dislocation density the "EBSD misorientation noise" induces artificially high GND densities. This is, of course, due to the angular error of standard EBSD, typically 0.5-1°, and defines a lower limit of GND density measurement of order 10 exp13 (m-2). It is probable that this error could be significantly reduced by High Angular Resolution EBSD. However, it is quite likely that there is an upper limit of GND density measurement since at high dislocation densities EBSD has difficulties with the spatial resolution. This upper limit might be of order 10exp15 (but should be checked). Then we have the further problem that the GND analysis is based on the spatial derivatives of the misorientation which are only known in the observation  plane. And, as mentioned above we do not really know the relation between GND density and total dislocation density which is the most important parameter.  In summary it would be very nice to use local misorientation measurements obtained by EBSD to derive dislocation densities but we are a long way away from doing this satisfactorily at the moment, except for particular cases where virtually all the dislocations contribute to misorientations (excess dislocations predominate)

I completely agree with Gert, moreover the virtual sharing of actual dislocations among GND and SSD by means of EBSD seems to be deceptive rather than informative. Indeed, we are unable to indicate in TEM image which particular defect is redundant (neutral) and which is GN (charged). If to consider what use still may come from a formal GND density, it is clear that strain hardening is sooner due to actual (total) density normally close to that of SSD. What in rest?! Apparently, the only sense of GND is in real effects such as plastically induced misorientations (boundaries) and stress sources. HOWEVER, these effects are more easy and pertinent  to treat (and measure) directly, without intermediate terms not always reliable. As to excellent accuracy of HR EBSD mentioned by Julian, this performance exceeds practical meaning of GND in my opinion. For more reasoning please have a look at a long discussion (first, a short question) in my RG page where Gert and Julian also actively participated. 

Microtexture Analysis and Modeling of Ambient Fatigue and Creep-Fatigue Damages in Ti-6Al-4V Alloy

Article in Metallurgical and Materials Transactions A 48A(2) · December 2016.

I recommend Jalaj's answer

Best Regards

Hi,

Can you please suggest me some papers where GND is calculated for FCC. I have found some papers but there is some constant relates to twist boundary etc . and I am not able to find how they are using that constant value. So, please suggest me formula and paper for GND calculation using twin and HAGB for FCC