I would like to determine the GND for the martensitic steels from KAM measurements. In literature, I am finding the following equation:
GND = (2theta)/(ub)
Where theta is the average misorientation angle across dislocation
boundaries, u is the unit length (namely the ‘‘step size’’ of the EBSD
map) and b the magnitude of the Burgers vector.
Can anyone suggest me how can I obtain theta in the above equation?
Or is there any other formula to estimate the GND from KAM?
Thank you
You are already on the right way...although I am not very convinced which kind of numbers you really get from these equations. Theoretically it is trivial that a rotation can be interpreted as accumulated number of dislocations, but how statistically relevant is this assumption? You have no idea about the statistically stored dislocations SSD (estimations says that SSDs are about 10 times more than GNDs) and you cannot say anything about dislocations compensating the rotations (practically nihilate GND-responsible rotations). For special cases it is a good approach but I am not sure how far you can or realls should go. I know, it is trendy at the moment to use an equation immediately if it has been used soomewhere in a paper, but I would recommend you to think about the meaning and whether this meaning fits to your problem. There were also a few interesting investigations from EDAX-TSL who remarkably showed that a different step size results in different GNDs. How trustful GND can be if it depends on the acquisition conditions?
By the way, MTEX is capable to calculate the GND from EBSD data (without any evaluation). If you have Matlab you should definitely use this free-available toolbox.
https://mtex-toolbox.github.io/files/doc/EBSDsquare.calcGND.html
Let alone the problem of uncertain proportion between GND and SSD mentioned by G.Nolze, there are a lot of troubles with the formula in question as follows...
1) Whether your Theta or KAM is essentially SCALAR number, whereas the sought GND density is TENSOR (curl of distortion or of rotation in a simplified treatment) and should be determined as such. As to the formula, it is generally wrong and this becomes obvious in case of elastically bent crystal domain with NO DISLOCATIONS. Indeed, the proposed treatment of EBSD data will give a senseless NON_ZERO result here.
2) Even if your limit the oversimplified formula use to interfaces only, it still remains ambiguous since different EBSD steps will give different results when crossing an interface.
3) If you still think the matter costs your time, you may have a look on the related formal problems in the paper "Choice of scalar measure..." in my RG page. On the same page there was also a discussion ("Is the GND density....") on various troubles in this field.
Hi you are trying to do GND calculation using EBSD data and you have mentioned some constant how to calculate that constant value. Could you help me to find that @ Dulal Saha
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