I think the confusion is growing here. There is NO standard definition for the word "crystallite". In different communities has different meaning and within some communities it is misused and abused (i.e. most people don't know the meaning of their "cruystallite size").

I will stick to powder diffraction as I spent the last 15 years working on the measurement of size and defects in nanostructured materials using this technique. By powder diffraction you can easily measure interatomic distances that are in the Angstrom range and the number of digits of acuracy you can get is impressive (check NIST SRMs) so there is in principle no limit to the measurement of sizes in the same range.

The whole diffraction pattern bears also information on the size of the coherently scattering domains. Those are called by some people "crystallites". If you use TEM to measure the size of the objects you see, you intrinsically measure a slightly different size. And again the measured objects are called "crystallites". people doing the synthesis of amorphous nanoclusters call them "crystallites" as well (after all we all call "crystal glass" something that is not crystalline at all!).

So I keep insisting that "crystallite" should NOT be used unless you give a definition of what you mean by it. And I also keep insisting on the fact that the size and shape of an object have noting to do with the internal (atomic) structure.

As to Graphene, the IDEAL Graphene is a 2D object. In 2D a crystal is an object that has 2D translational periodicity so again if by "crystallite" you mean a crystal of small size, this is a "crystallite". And again you can measure the coherent domain size by XRD (it will just be the in-plane one).

But beware as the size of a single object has in most cases no meaning (you are going to use several of those) so you should rather ask for a size distribution. And if you are given a "mean crystallite" size, double check (again) what is the meaning of it. Most people that will read this answer probably use Scherrer formula for estimating the "average crystallite size" for a crystalline material and probably none of them realise e.g. that the values they obtain are NOT the mean of the domain size distribution.

Graphene and silicene are not crystals. Crystal by definition is a 3D structure. So, even crystalline nanoparticles are not called nanocrystals but nanoparticles with crystalline structure. So, there are no crystals with size approaching atomic size, but there are crystalline nanoparticles.

I think the problem here is the word "crystallite", one of the most abused words in the literature. You can create a cluster of atoms (regular or irregular) of almost any size. And size is independent of the actual structure (so you can measure the size of an amorphous cluster as well). Measurement of the size is the real challenge in my opinion!

As for the definition of what's a crystal and the 3D nature of those crystals we could open an endless debate. Even a glass is a 3D structure, just non periodic. And you also have quasicrystals and modulated structures that are quasiperiodic or periodic in higher dimensions. You have also MTPs (decagonal and icosahedral particles). Plus if you consider just the periodic systems you have to exclude all layered materials and if you want to guarantee full 3D periodicity then you probably go only for ideal cases, as entropy would always like to insert some alien species (including vacancies) that break the periodicity... If you're not happy enough, well, physics tells you that even if you do things well, you always have surface relaxation (sometimes reconstruction as well) and this again can displace atoms and break the periodicity.... wild world that of crystallography!

Amorphous !

Matteo, this is not very simple as you think. Please remember that the atomic dimension are usually observed in the Angstrom range. The crystallite size approach to the atomic dimensions mean you across the smallest nano szie limits. I want to know just what will happen if it is possible...

crystallite size is defined by the thickness of a respective crystalline which has the same orientation, therefore crystallite size is determined by the calculated space between planes in the stacking crystals. (CMIIW)

if you mean 2 dimensional material (such as Graphene) which has 1 single layer atomic size, so then probably the term of crystallite is not correct.. I don't know what the right definition for that.

However, somehow i can't agree with @Bambang Soegijono, since the definition of crystallite size is fall for crystalline material only.

http://prb.aps.org/pdf/PRB/v82/i15/e155433

The smallest crystallite size is in the order of one unit cell !

I think the confusion is growing here. There is NO standard definition for the word "crystallite". In different communities has different meaning and within some communities it is misused and abused (i.e. most people don't know the meaning of their "cruystallite size").

I will stick to powder diffraction as I spent the last 15 years working on the measurement of size and defects in nanostructured materials using this technique. By powder diffraction you can easily measure interatomic distances that are in the Angstrom range and the number of digits of acuracy you can get is impressive (check NIST SRMs) so there is in principle no limit to the measurement of sizes in the same range.

The whole diffraction pattern bears also information on the size of the coherently scattering domains. Those are called by some people "crystallites". If you use TEM to measure the size of the objects you see, you intrinsically measure a slightly different size. And again the measured objects are called "crystallites". people doing the synthesis of amorphous nanoclusters call them "crystallites" as well (after all we all call "crystal glass" something that is not crystalline at all!).

So I keep insisting that "crystallite" should NOT be used unless you give a definition of what you mean by it. And I also keep insisting on the fact that the size and shape of an object have noting to do with the internal (atomic) structure.

As to Graphene, the IDEAL Graphene is a 2D object. In 2D a crystal is an object that has 2D translational periodicity so again if by "crystallite" you mean a crystal of small size, this is a "crystallite". And again you can measure the coherent domain size by XRD (it will just be the in-plane one).

But beware as the size of a single object has in most cases no meaning (you are going to use several of those) so you should rather ask for a size distribution. And if you are given a "mean crystallite" size, double check (again) what is the meaning of it. Most people that will read this answer probably use Scherrer formula for estimating the "average crystallite size" for a crystalline material and probably none of them realise e.g. that the values they obtain are NOT the mean of the domain size distribution.

Bambang, just look for Debye Scattering Formula. If you know the atomic positions then you can calculate the corresponding pattern analytically... But I still have to find domains that are monodispersed and of the size of a unit cell

Crystalline size approaching to one atomic dimension means size less than a unit cell. This size is certainly not possible.

From a materials science point of view: It is about stability of the crystal in the matrix it is found. The interfacial energy plays an important role in this.

Nucleation and growth is the mechanism which basically defines the critical size of a stable crystallite. The stability is related to the Gibbs free energy of the forming phase and the surrounding matrix.

During homogenous nucleation embryo formation is followed by growth of more stable nuclei (critical diameter for spherical nuclei). Here the gibbs free energy of the forming phase should be lower than that of the present phase so that the nature does the work and the nuclei can grow. You may refer to Porter for more information on homogeneous or heterogeneous nucleation and growth.

Phase Transformations in Metals and Alloys

http://books.google.ca/books/about/Phase_Transformations_in_Metals_and_Allo.html?id=eYR5Re5tZisC&redir_esc=y

Dear friends, i believe all of you are right!!! I believe it's a matter of which side you are approaching the issue from. Matteo is right when someone is talking about graphene an other similar compounds that are organised almost in atomic level. Dilek, Tahir and Bambang are also right when you approach the issue from a Metallurgist point of view. Crystal structure is a very confusing issue. Imagine that we are talking here about the the limits of the crystal structure at the atomic scale and at the same time is crystallinity is nowdays under question for large number of organised atoms such as in quasicrystals and complex alloys!!!!!!!!!!!!!!!!

If we used botton-up approach in the synthesis then we can achieve nanosized particle. And whenever we used crystallites its not a single molecule.

Matteo makes a good point about the definition of "crystalline." There are myriad ways of interpreting this word that varies from discipline-to-discipline.

At any rate, my colleague at Michigan Tech, Ed Laitila, observed an apparent limit on crystalline size in an (Al,Cr)3Ti alloy of approximately 2 nm. At this scale, the word "crystalline" takes on a slightly hazy meaning, as most "crystals" are, in fact, composed of a disordered "grain boundary"-like layer. Interestingly, 2 nm can be approximately the size of a critical nucleus. To a first approximation, then, the critical nucleus size *might* serve as a good first estimate/order-of-magnitude estimator of the smallest achievable crystalline size. I hope this helps answer your question.

I'm not an expert on this subject by any means, but the work I am referring to is presented here if you are interested:

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8490467

EA Laitila, DE Mikkola, "Employing X-ray scattering to characterize materials with grain sizes in the nano-regime," Powder Diffraction 23(2), 2008, p. 96-100.

Edit: This argument is along the lines of what Dr. Dilek IŞIK said above.

Patrick, it would be nice to have a look at those domains using more modern line profile analysis techniques! I agree that below the nucleation size there should be no crystals (as they would disappear according to thermodynamics.

Yes the critical point is the definition of crystal that at a certain points loses its meaning. And talking about molecules can be a bit tricky. A single buckyball is definitely a nanocrystal and is also a single molecule

No, it can never be crystallized to the size of the atom, inorder to satisfy the defination f crystalline material.

Crystallite means a small crystal. A crystal by definition is an infinite array of points in space on which atoms are placed in the form of basis. When the size of a crystallite( a small crystal) approaches to one atomic dimension, there is no crystal at all. So it is not possible that a material has a crystallite that approaches the size of an atom.

On the other hand you can imagine a primitive cell,like a simple cubic cell. It's dimensions will be at least two times the dimensions of an atom. But the primitive cell is not a crystallite. So again the crystallite having size comparable to atomic size is not possible.

Dear Matteo,

I totally agree with your opinion on the interpretation of the concepts of the "crystallite size" and "coherently scattering domain" from X-ray diffraction.