XRD pattern of a crystalline sample arises from the diffraction of incident X-rays by atoms/ions in the respective planes of the particles, for example, in a thin film. If more particles are aligned in one plane you get intense peaks due to reflections from that plane. Therefore, the relative intensities of peaks show a correlation between particles aligned in the respective planes.

XRD pattern of a crystalline sample arises from the diffraction of incident X-rays by atoms/ions in the respective planes of the particles, for example, in a thin film. If more particles are aligned in one plane you get intense peaks due to reflections from that plane. Therefore, the relative intensities of peaks show a correlation between particles aligned in the respective planes.

The nanoparticles will always give you the broad XRD peaks because of high-angle misorientations between them. The crystallographic planes in them will also add to the broadening in case of inner boundaries existing in the particles which are mostly the twinning boundaries.

.. erm.. no, sorry Sergei. If free from defects, (single crystal) nanoparticles give broad reflections because of the small size (it is due to the Fourier Transform relationship between real and reciprocal space). Large misoriented domains in fact will give you narrow reflections. There are several contribution to the breadth (and shape!!!) of a line profile and twins are a possible one. Actually twins and stacking defects in general are the more nasty ones as they influence the lattice as well.

Unfortunately it is not easy to understand what the author of the question wants to know... whether something related to crystallographic texture or just to know how to calculate the intensity of peaks for different hkl

Matteo, we are talking about nanoparticles, aren't we? So they are always small size. I neglected to stress that you can not obtain an XRD from a single nanoparticle.

yes, i guess we are.. so misorientation is not the reason for the broad profiles! Misorientation matters only when the domains (not the particles) are so close that coherence effects between them may occur. Simple maths tells you this is quite a rare case. You just need enough particles to cover the whole orientation space to have a powder patttern.

There is no reason, but technical ones why you can't obtain a diffraction pattern from a nanoparticle. You can't obtain a powder diffraction pattern (that's because you don't have a powder), unless you play tricks (you would need to take the pattern while giving the particle all orientations in space).

In fact people doing "coherent imaging" play with the diffraction pattern of a single particle...

In my opinion different orientations of nanoparticles with respect to each other and incident X-ray or electron beam would give you the same broad peaks as those obtained from nanosized grains in a solid body made by any SPD mehod and separated from each other by high-angle boundaries.

Adding to the excellent comments above, GISAXS is a great tool to study orientational alignment even in semi-crystalline samples like block copolymers.

Sridhar, my experience with polymers, namely, UHMWPE shows that X-ray techniqies give the degree of crystallinity which is hardly reliable value. What would be the accuracy of the grazing angle scattering technique with respect to polymers, and in particular UHMWPE?

@Sergei...

Partially agree with you on this. Therefore XRD data of polymers is always complimented with crystallinity measured by DSC.

What all factors can affect the orientation change?

"Sridhar, my experience with polymers, namely, UHMWPE shows that X-ray techniqies give the degree of crystallinity which is hardly reliable value."

Probably because you were using the conventional archaic XRD techniques with a "spatially blind" 0D or "point counter" and were looking at only the "equatorial plane" XRD signal. Such methods will not clearly deconvolute the effects of strain, size, preferred orientation, etc. without machinated complex mathematical methods. All these effects are inextricably "mushed" into the conventional linear diffractogram as a result of the spatial integration of the XRD signal. 

Using modern 2D real time data acquisition techniques and instrumentation in XRD it is possible to obtain precise and reliable values for most Nano structural parameters down to femtometers.

As mentioned earlier, it is important to realize the inverse dimensional relationship in reciprocal space (XRD or Bragg space) and real (crystal) space.

UHMWPE?  ....UH?..multi-walled..poly-ethylene??

I continue to learn about Nano particle XRD signatures. Thanks for sharing :-)

https://www.flickr.com/photos/85210325@N04/14348388500/in/album-72157645018820696/

https://www.flickr.com/photos/85210325@N04/10515372183/in/album-72157645018820696/

"How XRD peaks change with different orientation of planes in nanopoarticles?

What is the relation between XRD peaks and orientation of planes?"

I'm assuming you mean the effect of "preferred orientation". If so, besides the signature "broadening" due to the Nano size of the particles, you should also see the contribution due to preferred orientation. This would mean a shift in intensity towards reciprocal spots that are involved with the "preferred orientation". But to detect this clearly you would need to use a high sensitivity 2D spatially resolved devise and capture the entire 2D XRD signal. To check this hypothesis, use some photographic film instead of the raggedy ancient "point/proportional counter" and go back to the good old "photo-densitometer" as well. These days a scanner may be used instead of the vintage photo-densitometer to digitize the photographic dental film (nearly extinct) :-)

Intuitively, I'd think that Nano size "broadening" would be accompanied by the increase/decrease in relative intensity of the (hkl)'s involved with the "preferred orientation". In other words, the variations in intensity along the diffraction "cone" (Debye-Scherrer Ring) would be affected by the presence of "preferred orientation". See examples below:

https://www.flickr.com/photos/85210325@N04/10242907544/in/album-72157645018820696/

https://www.flickr.com/photos/85210325@N04/7975835813/in/album-72157632728981912/

https://www.researchgate.net/post/Is_it_possible_to_quantify_texture_co-efficient_for_Aluminum_foil_02mm_200um_thick_using_transmission_Laue_XRD_Images