I do not know anything exactly replying to your question, but I have in mind some studies performed indeed on nanostructures (at synchrotron) where the authors could retrieve the shape and the composition (in the verticalm direction) of semiconductor domes

you can see authors Kegel, Metzger:

Kegel, Metzger et al, Phys. Rev. Lett. 85, 1694

Kegel, Metzger et al, Phys. Rev. B 60, 2516

Kegel, Metzger et al, Phys. Rev. B 63, 035318

(later on also with Malachias, Paniago)

an interesting paper tracking the type of defects can be PRB 84 075314 (2014) + references therein (you can download it from http://www.acclab.helsinki.fi/~knordlun/pub/Ric10.pdf), via analysing the forbidden reflections.

Maybe is possible somehow to apply this kind of approach for rocking curves achieved simultaneously for a large area of the sample ?

Dear Ravi,

you might want to refer to the technique of surface X-Ray Diffraction (sXRD).

There are some basic papers:

Robinson, Tweet Rep.Prog.Phys. 55 (1992) 599-651

Robinson Phys.Rev.B 33 (1996) 3830

A. Stierle and E. Vlieg, "Surface-Sensitive X-Ray Diffraction Methods" Chapter 8 in Modern Diffraction Methods (2013m Wiley-VCH Verlag GmbH)

In a nutshell, by measuring and performing a proper analysis of the crystal rocking curves, one extracts the intensity distribution in the crystal truncation rods (CTRs), which are extremely sensitive to the vertical (perpendicular to the surface) parameters of the structure. Based on this information, one deduces the full structure of the crystal, be it crystal surface, an overlayer, thin film, etc. I am not sure, however, that each voxel on the detector delivers useful information (contrary, I am pretty sure it does not). This would probably be the case for the family of large-momentum-transfer scattering techniques, like total x-ray scattering. For the beginning you might want to look it up here:

http://www-ssrl.slac.stanford.edu/conferences/workshops/srxas2010/presentations/total_scattering_pdf_michel.pdf

and then google some more information on the Net.

Hope this answers your question to some extent

Best regards

Nikolay

Thanks Christian & Nikolay! Reflection XRD Topography mode should qualify as "total x-ray scattering". I'm still reviewing the the information you've posted and learning.

X-ray Diffraction In Crystals, Imperfect Crystals and Amorphous Bodies by Andre Guinier. 1962 - Worth acquiring for every XRD collection!

(pp. 162-163) 6.3.5. "Comparison between the Photographic and Counter Methods

It is obvious that the Geiger Counter and the ionization chamber have the advantage of precision and sensitivity. They alone permit a quantitative study of scattering. However, point by point measurements in reciprocal space are lengthy, while the photographic method gives directly a picture of the scattering in a single experiment over a large surface of reciprocal space. The resolving power of the film is excellent. Thus, sharply defined scattering regions, for example on rows or on planes of reciprocal lattice, show up very clearly on photographic film but are difficult to detect with a counter.

Let us note also that the counter is "blind". In many cases inaccuracies in the setup produce stray scattering which is easy to detect on the photographic film but which can spoil a series of experiments made with a counter.

The two methods are therefore complimentary and it would not be advisable to neglect one in favor of the other. The photographic method is admirably suited to the qualitative exploration of an unknown pattern, since one can then find totally unexpected phenomena. The counter is necessary for quantitative measurements on a pattern which is already known qualitatively."

This was printed in 1962. This has to be considered in light of the present day 2D detectors that combine the benefits of the counter & the film in one. These writings indicate some causes for the present day inertia of moving from the 0D to the modern 2D detectors. The spatial "blindness" of the 0D scintillation counter/detector is the principal reason even experienced experts using XRD are ambivalent about the 0D XRD data/results.

I put this in here just so I could find it easily next time.

[email protected]

http://www.flickr.com/photos/85210325@N04/10242907544/lightbox/

Nikolay! "I am not sure, however, that each voxel on the detector delivers useful information (contrary, I am pretty sure it does not)."

The fact that you are from the ESRF gives me pause for thought. Otherwise, I'd have argued with you in this matter vehemently and voted your response "down". BTW I disagree with you totally based on our experimental observations over the past 3+ decades. (I'll be glad to share such evidence). Meaning, our experimental observations indicate that each "PIXEL" on the detector (reciprocal space) carries the Nano structural information from a corresponding "VOXEL" on the sample surface (real space), certainly in the case of "parallel beam" optics. This is the underlying principle in XRD topography used for over a century now. Do you disagree with this contention?

The way I see it, the diffracted image is the convolution of the incident beam and the sample Nano structure. The challenge is to deconvolute the "mess" and draw meaningful inferences about the Nano structure. Let us take the instance of the incident beam conforming to the parallel beam geometry for starters.

https://www.youtube.com/watch?v=p349tGYXblk

https://www.youtube.com/watch?v=p349tGYXblk

Various options and aspects of parallel beam optics used experimentally:

1. General optics: https://www.flickr.com/photos/85210325@N04/7966430644/in/set-72157632724094863/

2. Detector plane orientaions: https://www.flickr.com/photos/85210325@N04/9311681113/in/set-72157632724094863

https://www.flickr.com/photos/85210325@N04/8040672531/in/set-72157632724094863

Nikolay! "I am not sure, however, that each voxel on the detector delivers useful information (contrary, I am pretty sure it does not)."

It would be harder to argue the counter-point to the following statement on the other hand: "I am sure that each PIXEL on the detector plane is detecting more than useful precise Nano structural information from a corresponding sample surface real space VOXEL". The reciprocal space VOXEL (theta/omega rocking curve profile) quantifyable through the XRD rocking curve methodology is also directly related to the Nano structure of the corresponding VOXEL on the sample (real space) surface. The rocking curve profile must be considered in its entirety and not just the FHHM or Bragg Peak Position. An open-minded review of the following data for ZnSe (224) asymmetric reflection rocking curve topography/microscopy (kindly provided by Panalytical for the betterment of science) will make it abundantly unequivocal. I'd be delighted to walk you through the data if needed. "A Scroll Through Reciprocal Space" :-) https://www.youtube.com/watch?v=dFCQS8oUyT0&index=40&list=PL7032E2DAF1F3941F

ZnSe (224) asymmetric - Relative Bragg Peak Position & Relative FWHM contrasted with Si (333) and GaAs (004) symmetric reflections: https://www.flickr.com/photos/85210325@N04/7805008376/in/set-72157632729045818

Details of ZnSe (224) XRD Micrographs illustrating both mono-crystalline and near polycrystalline constituents:

i. Optics: https://www.flickr.com/photos/85210325@N04/8207353860/in/set-72157632724094863

i. Relative Bragg Peak Position for each PIXEL on the detector: https://www.flickr.com/photos/85210325@N04/7896569482/in/set-72157632729045818

ii. Relative FWHM for each PIXEL on the detector: https://www.flickr.com/photos/85210325@N04/7804223452/in/set-72157632724026971

It would be hard to argue that these images of the ZnSe wafer are anything but the contrast created by the crystallographic strain field (Femtometer resolution) resulting from the imperfections in the crystal present from the time of solidification. Each perturbation at the solid-liquid interface would have been recorded, would be my guess! What are your thoughts? In this case each real space VOXEL estimated is about 1.1um deep (Cu K alpha 1 extinction depth) for the ZnSe (224) asymmetric reflection.

https://www.youtube.com/watch?v=ykSjd2ZZn64&index=4&list=PL7032E2DAF1F3941F

Stats @ 09:40hrs 6-8-14 3 contributors 5 followers

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I just increased the number of topics to 15 from 5. I also shared with followers.

Do study this RG discussion regarding the NIST 2000 SRM when convenient. It was an eye opening experience for me indeed!

Your review and feedback would be deeply appreciated.

https://www.researchgate.net/post/What_is_the_best_way_to_interpret_REAL_TIME_3D_X_Y_Omega_2Theta_reciprocal_space_relative_intensity_data_from_HRXRD_rocking_curve_analyses

Interesting behavior of Bragg profiles for a LiF crystal

https://www.flickr.com/photos/85210325@N04/34003566875/in/dateposted/