Low-2theta reflection(s) may be a good indication of regular mesoporosity. Braggs law 2dsin(Theta) = lambda is used to determine the d value, which in this case will be in nm scale. The best measurements of this kind are made using synchrotrone X-ray radiation and at relatively low energy (bigger wavelength), but even using an in-house 3-circle diffractometer the determination of regular structure with parameters in nm scale should be possible.

Dear Neha, many things have been published concerning SAXS analysis of mesoporous structures. You should check e.g. papers by B. Smarsly (just google doi10.1007/b107347) or O. Paris. Btw, SAXS stands for small-angle X-ray scattering (which should be used instead of low-angle diffraction) ;)

My interest is, in determining the effect of such Nano structure on XRD topographs from "Black Silicon" samples. These samples include etch pits with a periodicity of 20-30 microns (similar depth) on the surface. These etch pits are created to trap the incoming solar radiation on PV devices and thus obtain significantly higher efficiencies in solar cells. Here is a typical (224) reflection Bragg XRD rocking curve topograph (FWHM only) from a ZnSe wafer without etch pits: http://www.flickr.com/photos/85210325@N04/8435791663/in/set-72157632724026971

I'm yet to observe the effect of the etch pits on similar Si wafers. Waiting for beam (XRD source) time presently to repeat the observations.

What is the expected periodicity & size factor of mesoporosity in your specimen? Please describe in further details. Is your sample powder, bulk, mono-crystalline or what? Complete description will improve the potential of better advise from experts. Note that you may include an additional topic (up to 5 allowed) "up top" to get better circulation and diversity of input from a larger cross-section of RG members.

http://www.flickr.com/photos/85210325@N04/8029307446/in/set-72157632724026971

(Synchrotron based) small angle X-ray SCATTERING (SAXS) could also be of help here, depending on the expected size of the pores. The required X-ray energies depend on the nature of the sample.

The link gives you an example for a synchrotron beamline, where these measurements are possible. However, I would start with a lab based device first and continue with synchrotron methods, if the results are not sufficient.

http://photon-science.desy.de/facilities/petra_iii/beamlines/p03_minaxs/index_eng.html

X-Ray Diffraction is not the right tool to determin the porosity of a given material. A combination of X-ray absorption and X-ray refraction technique (e.g. B. R. Müller, M. P. Hentschel, K.-W. Harbich, A. Lange, J. Schors, X-ray refraction topography for non-destructive evaluation of advanced materials. The e-journal of nondestructive testing & ultrasonics 5, 1 (2000/10/15-2000/10/21, 2000).http://www.ndt.net/article/wcndt00/papers/idn257/idn257.htm) is more adapted to your problem.

Wow! Lots of awesome responses by the time I got done slowly typing mine. I like Bernd Müller's suggestion. Seems like an unique approach! I'm still studying the details.

I'd encourage you to study and master this book by Andre Guinier, to fully capitalize the advantage of XRD (WAXS, SAXS, Refraction, Absorption etc. they all run into each other at some point or the other ;)

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

http://www.flickr.com/photos/85210325@N04/10515372183/

The study by X-ray diffraction of mesoporous materials is a relatively new method from which I have no experience. I would appreciate an explanation of crystallographic methodology used by those who you have experience in this type of refinement. Porosity values ​​indicates that nanomaterials are.

Assuming your material has ordered mesoporosity (not random), then the d-spacing you get from a simple X-ray diffractometer at low angle will be the sum of the pore diameter and the wall thickness.

My advice is simple :

if you are using a lab diffractometer

1- start as low as you can for angle (0,5 ° at least)

2- count as much as you can

My suggestion! Use "good old" photographic film & transmission Laue mode to get a handle on the 2D diffractogram real quick before you get too fancy. Longer counting time (integration) should be no problem with film. You'll see any potential signal from the mesoporosity immediately including any presence of preferred orientaion. You do need to have some sense of what to expect. Study the basics of XRD 1st. A modern scanner would suffice in place of the dinosaur photo-densitometer to quantify your results. Of course, this assumes you do not have access to a modern 2D area detector to take advantage of. The Braggs had access to tools no better than those that you have. Fancy conventional analyses software will not be of much advantage at this point for you.

Here is a relevant section from Andre Guinier's book that I'd like to present:

X-ray Diffraction In Crystals, Imperfect Crystals and Amorphous Bodies by Andre Guinier. 1962 - Great book! Worth acquiring for your 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 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 sometimes ambivalent about the 0D XRD data/results.

All the rest of the suggestions are excellent as well.

http://www.flickr.com/photos/85210325@N04/10659886546/

XRD & Mesoporosity: http://www.nsrrc.org.tw/NsrrcWebSystem/UPLOADS%5CCHINESE%5CPUBLISH_YEARLY%5C2004~2005/08.pdf

Found this on Google! Here's what I'd expect!

http://www.flickr.com/photos/85210325@N04/10934831053/

Eric! "Ordered Mesoporosity" & "Random Mesoporosity"! I've been trying to visualize their effect on the 2D Diffractograms in vain.

Would "Ordered Mesoporosity" be tantamount to preferred orientation of the mesoporosity?

The original poser of the query seems to be MIA temporarily. It would be fruitful to understand the "make-up" of the sample in this question. The chemistry and morphology of the sample are important parameters to know in order to intelligently discuss the issue further.

http://www.flickr.com/photos/85210325@N04/10221987094/

Oguz! How does one determine the mesoporosity by "N2 adsorption @LN2 temperature"? Wouldn't the unknown surface area complicate this measurement? Would these measurements be absolute or relative?

BJH-?, DFT-Discrete Fourier Transform?

Aurelien! Please send me a PDF version of doi10.1007/b107347, if available and when possible. Thanx!

[email protected]

If your structure has hexagonal porous structure ("honeycomb-like", common for silica), you indeed can study the porosity using X-ray diffraction on a laboratory diffractometer. Check the works by S D Kirik, e.g. doi:10.1021/jp0482868

Ivan! Yes! Additionally, by probing the entire reciprocal space in 2D (and not integrating spatially into a 0D data point of relative intensity with a 0D point/scintillation detector), it is feasible to determine the average shape factor (pseudo-tomotopographically)! It is essentially tantamount to determining the symmetry elements of the periodicities or estimating their "preferred orientation" perhaps. I don't understand the details of how very well yet, but I intend to learn and verify experimentally. The key is in analyzing the 2D diffractogram and probing the 3D reciprocal space simultaneously.

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

Correction. Eric, is not the d-spacing but the cell parameter a0=2d100/√3.

Subsecuently, the cell parameter is the sum of the pore diameter and the wall thickness...

The combination of low angle X-ray Scattering (SAXS) and the hysteresis loop and BJH pore size distribution from the N2 ads/des measurements will indicate the porosity (whether it is ordered or disordered). From SAXS you can derive the pore diameter information. Hysteresis loop and BJH Pore size distribution will give the information of orderedness of porosity and the pore diameter both qualitatively and quantitatively.

Question is so general and easy, but answer on this type of question is not. Solution for your problem is SAXS (Small Angle X-Ray scattering) technique. Limiting parameter for using XRD laboratory setup for providing SAXS experiment is dimension of particle/pore (distance between source and detector) and type of matter which you need to research (absorption/scattering factor which depend about the chemical composition). From other side limiting is flux of X-ray which you can get from laboratory X-ray tube, and that is second limiting in the research different type of materials! May be you need some more powerful X-ray source such as Synchrotron radiation.... You have to ask much more specific your Question.

Yes Dražan! SAXS is the answer based on the periodicity of interest. "powerful X-ray source such as Synchrotron radiation" or 'more powerful/sensitive 2D real time quantitative data acquisition/analyses tools'. This is the "missing link" for the past 25 years, as I see it. Such a tool should be available to every teaching institution for real time crystallography classes. How much more interesting would the classes be? How hard is it to follow the attached video to understand, in minutes, what forward XRD images from many materials look like? Most of the data illustrated was acquired on laboratory tube type sources

Please remember this awesome Panalytical training session for: Introduction to quantitative X-ray texture analysis

Almost all physical properties of crystalline materials strongly depend on the crystal orientation. In practice, most commonly used artificial and natural solid materials are polycrystalline and show a texture, a non-random orientation distribution of the crystallites. Therefore the materials properties can only be determined if the texture of a sample is known.

X-ray diffraction is a widely used technique to determine preferred orientations from pole figures. The webinar gives a short introduction to quantitative texture analysis for the materials scientist.

Webinar details

Date: December 3, 2013

Time: 10:00 AM - 11:00 AM EST (4:00 PM - 5:00 PM CET)

Panelist information:

Hans te Nijenhuis studied Applied Physics at the Delft University of Technology in the Netherlands, with a focus on the field of physical crystallography. He obtained a PhD degree in Solid State Physics at the University of Nijmegen with a thesis on gas phase deposition of epitaxial layers. Afterwards he joined PANalytical (Almelo, the Netherlands) and is now working in the department Product Management X-ray diffraction.

http://www.linkedin.com/groupItem?view=&gid=2683600&type=member&item=5809718565762269188&qid=791f3448-4de8-465b-afcf-fbd6c8cb627a&trk=groups_most_recent-0-b-ttl&goback=%2Egde_2683600_member_5812013242498711555%2Egmr_2683600%2Egde_2683600_member_5812013242498711555%2Egmr_2683600

You can us small angle scattering and expression given by Guinier and Fournet (1955) to plot the logarithm of the X-ray scattering intensity (I (q)) against the square of the wave vector, using both Quinier’s (1963) and Porod’s laws to determine the pore size, and surface area of any sample.The Guinier region of the SAXS data (small q limit) can be analyzed by curve fitting the linear portion of the plot of ln I (q) versus q2 as q approached zero to obtain the slope of the straight line.