The connection between Hill's nanothermodynamics and Tsallis non-extensive statistical mechanics: Extracting the thermodynamic properties of a nanosystem

Based on the entropy formulation of Tsallis, in the context of non-extensive statistical thermodynamics and the fundamental works of Hill on thermodynamics of small systems (nanothermodynamics), a connection between these two branches of thermodynamics has been made through a new theoretical approach that estimates the equilibrium probability distribution of the size of, deposited on quartz, silicon nanocrystals which are an example of the completely open statistical ensemble. This ensemble describes the behavior of small systems in which the extensive variables, such as the amount of matter in the system, fluctuate under the constraint that intensive variables of temperature, pressure and chemical potential are fixed by the surroundings. The silicon nanocrystals showed a columnar structure for film thicknesses in the range of 5-30 nm. We observed that the size distribution of silicon nanocrystals, is an overlay of q-distributions. Thermodynamic properties of the nanocrystals such as the chemical potential values at different scales and the entropy were obtained after fitting with experimental data collected in different stages of film grow. Those data were taken from literature and correspond to the experimental distributions obtained for three characteristic values of nanocrystalline film thickness, namely 5, 10 and 20 nm. The good agreement between experiment and theory signifies the validity of our model. • Theoretical connection between Hill’s nanothermodynamics and Tsallis non-extensive statistical mechanics. • Silicon nanocrystal size distributions following Tsallis statistics instead of classical Boltzmann-Gibbs distributions. • Gradual approach to the classical thermodynamic limit with increasing nanocrystal size. • Dependence of Hill’s chemical potential on system size, confirming its diminishing contribution for larger systems. • Experimental validation through LPCVD-grown silicon nanocrystals and statistical fitting of their size distributions. • New insights into the thermodynamic behavior of nanoscale systems and their non-extensive statistical properties.