I would think that the broadness of the peaks has got to do more with the size of the particles and the randomness with which they are orientated in the medium or substrate they are on. It is normally observed that some amorphous materials would display very broad X-ray peaks but the peaks become well defined as the material is annealed. During the process of annealing, smaller particles will combine, eliminating grain boundaries leading to bulk like properties of the same material.

Dear Dr. Hodaei:

This question is open yet, despite of complex it is possible gives a "picture" of answer. There is a great number of events that a priori can not be explained by a specific  "concept". Thus, some carefull is requered in the "modeling" or "generalization" of  called "nano-concepts". Sometimes, a same idea is presented with another set of words. 

By convenience, three class of nanoparticles as function of size, a nanoparticle has a size at about 0.1 to 1nm; between 1 and 10 nm the particle is the result of a growthing mechanism, particular features emerges in this scale; between 100 and 1000 nm particles can be termed sub-micrometric. In this scale, conventional features can be find. See, this separation is only functional, is not absolute or intend to polemize the central question. Then,  at sizes 1nm, due the scale effects which are based on thermodynamics concepts, the nanoparticle almost can not accomodate inner atomic defects, that leads all or major fraction of defects to migrate to surface. To minimize the great surface energy, the "nanocrystal" should be curved to attain further minimization of the surface area that gives the minor level of surface energy, but that is very very great yet. This feature is the origin of the principal characteristic of nanoparticle and its potential aplications. Also, its tendency to coalescence and under thermal treatment to exhibit a fast growthing, here is more convenient to use chemical potential. Then, a nanoparticle should be spherical by definition,  if the particle growth there is a tendency to reach the symmetry of crystal, as cubic or another, but depend on the preparation condictions. Here, again there is no intention of generate some kind of polemical idea, but only gives a sequency is a previous idea, thus a cubic nanoparticle steamming of set of original or primary nanoparticle that is spheric. In this sense, after growthing mechanism actuating, particular shapes of particles can be observed. Here, also the idea of nanostructure emerges, representing a sub-micrometric or micrometric particle that exhibitis at least one of its dimensions at nanoscale level.  From above mentioned, a "good PICTURE" of a nanoparticle is a particle with surface where atomic positions are highly distorted due defects and optimization of the superficial energy and a small nucleous almost perfect but under high level of a kind of stress. As mentioned, another pictures be possible, or a model is disponible...

X-ray diffraction is based on the Bragg's Law that is in essence a mechanistic approach and can be derived via geometric concepts, physically structured from a constructive interference phenomenon. From this, the intensity of a diffraction line is proportional the the number of atom in two-theta direction satisfying constructive interferencies. But, each line diffraction can be affected by size of crystallite and its strain. Willianson and Hall have modeled such events, again it is possible to derive W-H relation in a trivial way, since the relation or function of  Willianson-Hall that is also mechanistic being  a linear function. From this tool, both parameters size and strain can be derived or "separeted". Here, seems important the set of characteristics of a authentic or primary nanoparticle 0.1 to 1 nm above mentioned. The high level of stress/strain leads to shifiting of two-theta position of diffraction line identifyed on the XRD-pattern but also promote some broadening of diffraction line, since the diffraction line is not single, due atomic position be slight shifted from ideal positions, sometimes more high another times below of the expected. Also, if exist a very small portion of a well behavioured crystal it is possible that Bragg's Law not be satysfied, the intensity of diffraction line is almost absent.

Typically, at nanoparticles belongs to second scale of sizes 10 to 100nm a complete set of diffraction lines can be observed at XRD pattern, the intensity is below of single crystal and only slight broadening of diffraction lines can be expected. At third scale of sizes, a common or conventional pattern is expected. As a whole, only at first scale of values a absence partial or total of diffraction lines can be expected, all of them with sizes at around 10 nm should have its diffraction lines, also there is cases where a particular diffraction line set is not defined but at around of position there is a broad and diffuse "band".

Kind regards

Marcos Nobre (MAL Nobre)

Dear Nedjma Bouzidi,

thank you for your answer to my question.

Dear Dr. Volker Klemm,

thank you so much for your suggestion that really helped me find a comprehensive but simple explanation to the answer of my question.

Dear Mr. George Amolo,

thank you very much for your answer.

Dear Prof. Marcos Nobre ,

I would like to thank you so much for your deep attention to my question and your detailed answer.

regards,

Amin Hodaei

Dear Hodaei,

if you really have a material with nanosized crystals, you can try to use the Scherer's Formula in order to calculate the size of the crystallites.

As a complementary analysis, I suggest to you the EBSD (Electron backscatter Diffraction) analysis. In this sense, you can build the microstructure of your material from a Kikuchi Pattern obtained by electron diffraction in your material. By doing this, you can analyse the size of the grains, find out the different crystallographic plains, etc. Simultaneously, you can perform EDS (chemical composition) analysis on the individual grains. Both of these techniques can be found or installed in a SEM microscope.

Good Luck.

Hi Mr Amin

you can found the answer  from Scherer's  equation for calculation the crystallite size. and according to the equation more broadening mean smaller crystallite  size.   

Its all about Scherer's formula... 

Concept of physics point of view, the crystallites are mainly responsible for the diffraction / reflection of X-ray just like the reflection of mirror. In case of light and mirror, when the size of the mirror is small the intensity reflected light is low. Similarly, in X-ray physics the crystallite size is inversely proportional to the FWHM of the diffraction peak (Scherer's formula), hence small particles or crystallites generally produces broader peaks

ok

Dear Dr. B Mallick,

thank you so much for your smple but useful answer.

Completely agree with the answers before. In the crystalline domain is too small, there are less "diffracting material" available and then the intensity is less. We can say that as soon as the domain size become lower the material become more and more close to a amorphous material.

Dear Mr. Mohammed Obeid,

thank you for your provided answer.

Amin Hodaei

Hi Amin, I recommend you the book Elements of X-Ray diffraction" by B. D. Cullity, this book is a good reference.  

Dear Dr. B. Mallick you have explained peak broadening in a very much simple and short  way it is  useful to me as well thanks to you.

Welcome !  Amin and Pushpendra. Actually, I have only given the concepts and  not included the physics. Again, microstrain is playing a very vital role for the broadening the diffraction peak of small particle. Sometimes, In-Situ conditions (hot or cool, radiation effect etc) also broadened the diffraction peak depending on nature of sample. As suggested by Garcia-Sanchez, the B. D. Cullity is a nice book for the reference.

The physical properties of materials at micro and macro size materials may differ at nano size of the same materials. Therefore, XRD patterns of the materials would show rather different pattern than the usual pattern. Thus, we should search the new concept for this XRD pattern. The certain laws may not applicable at nano size because the physical properties might differ at nano size.

Dear Amin,

It is all about diffracting volume, crystallites oriented in a particular plane/direction and their constructive interference. These three factors basically contributes to the intensity. The smaller the dimension the more disordered it is and you will get crystallites randomly oriented in a diffracting volume. Hence their constructive interference results in lower intensity.

This is same as electron diffraction pattern for single crystal, poly crystal and amorphous.

Dear Dr. Cristóbal Verdugo-Escamilla,

I would like thank you very much for your answer.

Where should we put the limit in transition of crystalline state to amorphous state in a material as the domain size is decreased?

Dear Dr. Cristóbal Verdugo-Escamilla and Mohammed Obeid,

I am so grateful for your suggestions.

Dear Dr. Dattatray Gadkari,

so thankful for your answer to my question. 

Dera Dr. Subhasisa Nath,

I thank you so much for your detailed answer.

What are the limitations in transition from crystalline to amorphous state? When one can name a material "Crystalline" and when "Amorphous" from both top-down and bottom-up approaches?

Dear Amin the answer on your question is completely at these draft that i attach to you i hope to find what you search and you must know that as peak get wider the intensity must decrease due to Gaussian distribution of the peak or the statistical distribution in general. 

Dear Amin, the answer to your question is very difficult. It´s difficult to select a limit, but for me a completely amorphous material is one that does´t shows any recognisable Bragg peak.

Dear Mr. Mahmoud Soliman,

thank you so much for your explanations and also the draft you provided.

Sncerely yours,

Amin