In this paper we review some of the existing issues concerning the structural characterization of end -products obtained after extensive mechanical treatment and deformation. After recalling the basic aspects of diffraction broadening at small and wide angles, we suggest that the presence of nanostructures is testified in the diffraction patterns by the strong Cauchy or super-Cauchy character of peak profiles. Good data for this kind of experiments and analyses are currently made available at the large scale facilities for X-rays and neutrons. From the mathematical point of view the determination of crystallite or particle size distribution functions is an ill-posed problem, that is, small fluctuations of the experimental data can affect considerably the final solution. It is then necessary to start with the full control of the critical steps in data analysis corroborated with the knowledge of the thermodynamics of the systems under investigation.
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