Study of dimensional dependencies of thermodynamic characteristics of nanoparticles

In the article some approaches to the theoretical description of the deviations of thermodynamic characteristics, such as the heat capacity and the Debye temperature for nanoparticles are considered. The standard Debye inference for the heat capacity of massive crystalline solids was investigated for its modernization in order to take into account surface phenomena of considerable weight for nanoparticles. Unlike massive samples, not only the upper limit of possible frequencies but the lower one starts to matter for nanoparticles. Indeed, in principle, elastic waves with a wavelength greater than the size of the crystal itself cannot arise in a crystal. The equation obtained shows that the thickness of the surface layer of an atomically smooth solid is determined by one parameter — the atomic (molecular) volume of the element, which changes in accordance with the periodic law of D.I. Mendeleev. The equation in its final form, despite its simplicity, shows good agreement with the experimental data