I would say that your crystallites are quite small (Lorenzian shaped profile). Since their surface is comparatively big you may observe additional relaxation which disturbes the periodicity remarkably so that you perhaps also observe something which is interpreted in bulk materials as lattice strain (Gaussian shaped profile). Remarkable is the strong asymmetry of your first peaks. This might be caused by some non-stochiometry but also by some problems related to the equipment you are using. For the equipment speaks the reducing influence with increasing 2theta.  

I have looked at your XRD patterns, they are nanoparticles because of widened peaks. Not amorphous! You can calculate the average crystallite size using the Scherre formula and than compare with TEM and SEM observations.

Broad peak represent the sample is of nanosized particles

your crystallite size is finer/smaller. Based on your XRD data, it is nano particle

You can calculate the average crystallite size using the Scherre formula  0.9λ/β cosѲ where λ- wavelength of incident light, β-full width at half maximum intensity, Ѳ-diffraction angle

If you get sharp peaks that mean you have large grain size and vice verse.According to your data it seems nano sized particles. For amorphous nature , you should have one broad diffused peak.

Thank you for your answers

@ S. Anwer: I don't think that your last sentence is correct: "...you should have one diffused peak". The problem perhaps is already caused by the term "amorphous". For me  also a liquid is amorphous and often you get there no peak at all. A hump on a backgound means that there is still some near order correlation. But as far as I understood this you can also have two humps (or more). This certainly depends on the material. The typical glas peak displays the Si-O bonding but there are certainly more complicated materials having more near-order and more stable molecules. 

@R. Rahmani: From my understanding the second image describing your so-called "nonuniform" strain is at least misunderstandable. This kind of peak broadeninig appears e.g. for martensite and is the result of the loss of periodicity. The three-point bending as macroscopic technique is typically used to measure your so-called "uniform" strain. Where did you find this figure?

The broadening of the XRD peaks is suggesting presence of the nano-sized crystals.

You can use Debye-Scherrer relationship to estimate the mean crystal size.

for XRD data analysis you can use a software designed to check different possibilities for the position of peaks with 2theta or atomic distance to know other values as well.....

The software is Pcpdfwin which consist of standardized results from all over the world representing values obtained under specified conditions accepted all over  

your sample is not amorphous, but constituted of nano-particles giving rise to broadened diffraction peaks, also at relativly high angles. Your first peak is a convolution between the peaks at 27° and 31.5° 2theta, that's why the asymmetric shape. From the broadening of the diffraction peaks you can evaluate the particle size (better, the size of the coherent diffraction domains). The Scherrer method is widely applied because is quite simple, but it's not the best and has strong limitations; better results are obtained by applying the Williamson-Hall method, even though it's not yet the best. Finally the FWHM is a measure of peak broadening, but it's not the only one that can be applied. In any case to measure the broadening actually due to the examined sample, you have to use a standard to evaluate the broadening originated by you diffractometer. In this way you can subtract the instrumental contribution and evaluate the real broadening due to your sample.

I agree with Dr Gert Nolze.

I also agree with Dr. Gert Nolze

Depending on the sample preparation and nature it is difficult to differenciate between nanostructured and amorphous states. According to the shape of your diffracion peaks, you may have a mixture of amorphous and nanocrystalline phases.

Exactly, you have mostly nanostructured sample. In the case of an amorphous sample  its XRD patterns don't show peaks. Nanostructured samples always have broadened peaks in XRD patterns.

I agree with Alberto Martinelli . The low angle peak can be convoluted. 

In the case of one phase sample, additional peaks can prove distortions of  the related crystal lattice.

About the amorphous state. Its input can be seen from  background  intensity  increase in low angles region of XRD patterns. The background in your case  is increased a little. But the same result can prove a solid solution formation if some additional impurities are introduced into  the crystal lattice.  Such impurities can result the top mentioned distortions as well. 

It is a crystalline material with good match of peaks with that of the standard. Since the broadening is more, the crystallite size is obviously very small. And it is due to this broadening, the small peak at 31.5 degrees is either overlapped without noticeable change in intensity or turned out to be insignificant due to modified metastable cation distribution.

Whether the shape is Lorentzian or Gaussian or Voigt and also to find out the exact crystallite size excluding instrument broadening and strain, it needs to perform additional analysis.

I agree also with Alberto Martinelli and his remark that the knowledge and maybe (if the contribution is important) the subtraction of the instrumental contribution could be important.

I am also agree with Alberto Martinelli for that XRD peaks broadening is not related to fully amorphous material but contain an amount of nano-sized crystallites. The Debye-Scherrer method can be use for estimating the mean crystallite size. Then also the roughness/planarity of sample can introduce any instrumental aberration. In order to exclude any instrument broadening, I suggest to repeat XRD measurements by using a graphite filter in the diffractometer set-up and a standard crystalline material. Moreover a thermal treatment of sample (e.g. annealing) can be useful to remove the strain component in the peaks broadening.

This is a simple answer. If the volume of the particles is a little less than 7% of XRD you will not see this. If you are doing XRD of the sample surface you can see the peaks and if the powder is you will not see it. I did these tests many times. I have several such publications which show exactly the same results. XRD is a very good and low cost technique but materials with the content of crystalline phase  more than a few  percent.

What is the reason for peak at 2.9 degree 2 theta (powder xrd) in amorphous powder of a tartrate salt of a Active pharmaceutical ingredient?