Relative dislocation density using the approach of Hirsch et al.
Dislocation Density, ρ = (β2)/(9.b2)
b = Burgers Vector, and
β = Integrated Breadth (computed numerically from XRD profile data)
Let us take the example of SiC 4H (004)s reflection and the use of XRD rocking curve analysis.
How should I figure out b, Burgers Vector?
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One can measure the dislocation density by TEM studies and then use it in your formula to get b, the Burger's vector.
You are right in a sense. Eventually I'd have to calibrate the experimental XRD β, Integrated Breadth, with the dislocation density observed using TEM. However, it is not trivial choosing the TEM samples for such "calibration" from say a 75mm wafer. Besides, how does the β obtained from XRD for a specific (hlk) relate to measurements using TEM or EPD or other methods?
Is β(hkl), a measure of the projection of the dislocation density on the (hkl) plane?
b = Burgers Vector, is a theoretical computation, correct?
Ultimately, everything is an estimate only!! One has to fix the starting coordinates(frame of ref) to get proper projection; but it is all imaginary according to me. Some example is given in the book: Mechanical Behaviour of Materials by Courtney.
So, is it reasonable to assume that somewhere on the 75mm wafer (monocrystalline) exists a 30x30 µm pixel with minimum dislocation density? This may be determined using TEM by selecting the sample from the wafer after imaging with NDE Bragg XRD Microscopy first before "destroying it" for the TEM analyses, right Ganesh :-)
If so, then all other pixel "beta" values may be converted to relative dislocation density, couldn't they?
My fundamental question is, what is the difference between say using the (004)s reflection or another asymmetric or other reflection with different (hkl)? How do they correlate?
We have data for (004)s, (224)-, (113)- reflection from the NIST 2000 standard reference material wafer. How do we correlate these RCP's (rocking curve profiles) for various (hkl)'s?
BTW How do I incorporate "instrumental profile" in my XRD analyses?
All helpful suggestions are deeply appreciated and welcome :-)
Interesting reference correlating TEM and XRD data with Nano powders:
X-ray Line Profile Analysis of Nanoparticles in Proton Exchange Membrane Fuel Cell Electrodes
Matthias Loster,*,† Davor Balzar,‡ K. Andreas Friedrich,§ and Jurgen Garche Center for Solar Energy and Hydrogen Research Baden-Wurttemberg, DiVision 3, Electrochemical Energy Storage and ConVersion, Helmholtzstrasse 8, 89081 Ulm, Germany ReceiVed: March 7, 2007; In Final Form: May 3, 2007
https://www.flickr.com/photos/85210325@N04/15649120475/in/album-72157645018820696/
https://www.researchgate.net/post/What_is_the_best_way_to_interpret_REAL_TIME_3D_X_Y_o-2TH_o_ph_ch_reciprocal_space_relative_intensity_data_from_HRXRD_rocking_curve_analyses
http://mysite.du.edu/~balzar/Loster2007.pdf
Well, you are too good! I can not go further at this time unless I do the complete home work. Sorry for that.
Best,
Ganesh
No problem Ganesh. Thanks for your suggestions.
Do feel free to review my other posts and comment when convenient. LinkedIn is also another good source for information and networking. Check it out!
Here is some recent data from IISc Bengaluru on their Rigaku SmartLab:
https://www.youtube.com/watch?v=nSEkBv6VKXc&list=FL7-u3nABX4YMdHDugoPsYcA
https://www.linkedin.com/today/author/0_3UtsFcd477uzRO6QWOzIay
Hi Ravi,
Can you give me the reference for the Hirsch formula to estimate dislocation density? I would like to estimate dislocation density from X-ray rocking curve data.
Thanks,
gourav
Dislocation Density, ρ=β2/9b2 for a Gaussian distribution, b=Burger’s Vector, ρ-Dislocation Density, integral breadth, β, is related to the FWHM peak width, H, by β = 0.5 H (π / loge2)1/2
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