Statistical Thermodinamics of Schottky Defects in Metal Nanoparticles

The controversy about the size dependence of the vacancy concentration in metal nanoparticles is here reconsidered in the framework of the statistical thermodynamics. The fractional concentration of vacancies in a spherically shaped metal nanoparticle is calculated by taking into account both the core and the surface defective systems. Notwithstanding the formation energies of core and surface defects are found to increase as the particle size decreases, it is shown that the fractional concentration reaches a maximum at s mall particle sizes, provided that the formation energy of the surface vacancies in macro-crystals is sufficiently smaller than that expected in the bulk. This apparently counterintuitive conclusion, which may reconcile early opposite views, is a mere consequence of the high surface to volume ratio in nanostructures. Numerical calculations performed for copper nanoparticles are presented