Between the nano and the macro states there is a size boundary whose existence is explained within the framework of the Debye model of behaviour of phonons in crystals. If the particle size is such that a phonon with a wavelength greater than the Debye wavelength is unable to propagate, then the substance acquires different properties from the bulk properties, as only highfrequency excitations can exist within it. The particle size and temperature affect the intensity and profiles of the X-ray reflexes. On the basis of a combined examination of the Sherrer formula and the Debye-Waller factor, a method is proposed for estimating the temperature factor in the size of crystalline nanoparticles. An examination is made of the influence of temperature on the change in nanoparticle size. With account taken of the Debye-Waller factor, the possibility is shown of estimating the size of a nanoparticle on the basis of the change in energy state owing to dispersion. Grinding of the particle (increase in the coefficient of dispersion) results in a change in the effective temperature, the magnitude of which must be taken into account when assessing the parameters of nanoparticles. INTRODuCTION The development of functional nanomaterials science is based on industrial technologies for producing smallsized particles with specified, stable specific surface, activity, morphology, and structure. Modern methods for producing nanoparticles, based on mechanical, thermal, ionising, and other forms of treatment of the semiproduct, make it possible on an industrially significant scale to produce ultradisperse diamonds (UDDs), ultradisperse diamond graphite (UDDG), nanosilicates, fullerenes and nanotubes, ultradisperse powders, ultradisperse ceramics, heat-cleaved graphite, and other smallsized fillers and modifiers of polymeric, metallic, ceramic, and other matrices used in the manufacture of structural, adhesion, protective, tribotechnical, and other functional products [1-4]. Taking into account the special characteristics of small-sized particles of different composition, structure, and production technology, it is necessary to develop special methods for investigating such materials, as the methods of physicochemical analysis traditionally used in materials science do not make it possible fully to assess specific features of structure, activity, morphology, and size by virtue of design or procedural limitations of the instrument base. The most important parameters of the nanoparticles are their size and structural state, which are determined by X-ray methods. However, the use of standard methods for analysis of macrospecimens does not enable smallsized particles to be assessed. The aim of the present work was to assess the possibilities of applying X-ray methods of investigation to analyse small-sized particles, using the generality of the physical processes during the mechanical dispersion and heating of macroparticles. RESuLTS AND DISCuSSION Current ideas concerning the structure of condensed media, including nanosized materials, w...