Any advice on the calculation of dislocation density using HRXRD rocking curves?

Dear Dr Nagaraja K K,

Angular mosaic tilt or twist spread of the crystals that measured from FWHM value of omega scan which has to be taken in the units of Radians. In this context, which can be considered as unitless.

Dear Nagaraja,

Malleswararao's answer is correct. Just convert your FWHM value to Radians (this makes it a number). It is usually measured in degrees originally. Just multiply your FWHM by (pi/180).

Ravi is correct in noting that you must account for instrumental broadening and not simply convert the rocking curve FWHM to dislocation density.

Actually one needs to define the "dislocation density" first. So if we are measuring say a "line" in a "volume" perhaps, then it would need to be mm/mm^3=mm^(-2). Yes?

In practice, we do need to compare the FWHM to a "standard" to really come up with its relationship to dislocation density. (Sorry Edward, I re-posted after your comment). The formula Nagaraja has used, isolates the various parameters involved and their general relationship. I'd like to see the math for that equation. I've been working with it since 1979 starting with the group at Rutgers under the tutelage of Sigmund Weissmann et al.

Here in an example of Bragg XRD Microscopy using relative FWHM mapping for a ZnSe wafer (224) Asymmetric reflection, clearly demonstrating dislocation density patterns from the as-grown Nanostructure for the top 1.1um depth (cumulatively).

The angular spread is dimensionless; it has to be considered in radians. This will give a value which is of the order of ten thousand times smaller than what you would obtain if you don't convert to radians

See Acta Met. 1957.V.5.P.548 for high density of disloations and Phyl. Mag. 1998. V.A77. P. 1013 for low density.

Thanks Iren! Please send me PDF files if available. Anybody!

Some cool info while exploring your references on Google:

1. http://engineering.dartmouth.edu/defmech/chapter_2.htm#Plasticity limited by discrete obstacles

2. Matteo Leoni's WPPF - http://www2.fkf.mpg.de/xray/CPD_Newsletter/cpd28.pdf

Dear Ravi Ananth,

Here are the papers, these papers are cited most

And this is another one

Thanks to Irene Shul'pina and Nagaraja K.K. for these papers!

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 / log_e2)^1/2,

(If someone can post the original reference for this relationship, it would be very helpful)

Also, β²_(Sample)= β²_{(Experimental)} - β²_{(Instrumental)}

Let us take this example of GaAs (004) symmetric reflection. The experimental data is compared with the theoretical expected profile as calculated by Bruker LEPTOS software. The match and "figure of merit" should be exceptionally high in this case. In fact the "deviation" from the theoretical profile may be used to conclude the levels of stacking faults with missing smaller Ga (31) atom rows/planes or larger As (33) atom rows/planes. This would depend on which side the deviation is on, the lower angle or higher angle side of the Bragg peak.

My question then is that if FWHM is related to the average excess dislocation density, then how do we compute the volume of "stacking faults" or "twins" from the Bragg rocking curve profile?

Anyone that may entertain the idea that the "deviation" from theoretical or IDEAL Bragg condition was due to sample alignment/orientation etc. better think again after seeing this example for GaSb (004) on the same diffractometer with identical sample mounting conditions. Besides, samples rescanned on other diffractometers produced similar asymmetry in the RCP (rocking curve profile). These deviations from the theoretical profile are generally below the FHHM and can be directly attributed to stacking fault defects. I do need to find the literature references to this correlation to stacking faults and twins to the profile below the FWHM. If any of you have access to them please post links or forward to me at BraggXRDMicroscopy@gmail.com

There are more diverse example that I'll post as well regarding the "deviation".

Please feel free to join us in this following discussion and share your opinion as well:http://www.linkedin.com/groupItem?view=&gid=2683600&type=member&item=5843613667337195520&commentID=5850523044153430016&goback=%2Egde_2683600_member_5843613667337195520%2Egmr_2683600&report%2Esuccess=8ULbKyXO6NDvmoK7o030UNOYGZKrvdhBhypZ_w8EpQrrQI-BBjkmxwkEOwBjLE28YyDIxcyEO7_TA_giuRN#commentID_5850523044153430016

Ravi Ananth

examine this reference please

K. K. Nagaraja The dislocation density is a measure of the number of dislocations in a unit volume of a crystalline material i.e. the length of dislocation lines per unit volume of the crystal (m/m3) Edge dislocation Screw dislocation Dislocations distort a crystal lattice, causing elastic stress around the dislocation line, & hence strain energy. For ultimate strength, dislocations are to be eliminated.

In this video, I have discussed the nature of dislocation density and how to calculate the dislocation density from XRD using origin. In the case you want to further ask about it, please do comment on the specific video, I'll respond to it shortly. I have provided the practice as well as calculations files here. Thanks