The Einstein nanocrystal

DALÍA S. BERTOLDI; ARMANDO FERNANDEZ GUILLERMET; E. N. MIRANDA

REVISTA MEXICANA DE FíSICA E

SOC MEXICANA FISICA

Lugar: México; Año: 2015 vol. 60 p. 60 - 65

1870-3542

We studythe simplest possible model of nanocrystal consisting in a simple cubic latticewith a small number of atoms (NA~ 10-103), where eachatom is linked to its nearest neighbor by a quantum harmonic potential. Someproperties (entropy, temperature, specific heat) of the nanocrystal arecalculated numerically but exactly within the framework of the microcanonicalensemble. We find that the presence of a surface in the nanocrystal modifiesthe thermostatistic properties to a greater extent than the small number ofatoms in the system. The specific heat Cv behaves similarly to the Einstein solid, with an asymptotic value for hightemperatures that differs from that of the Dulong-Petit law by a term of theorder of NA-1/3and that can be explained easily in terms of the surface. The entropy is non-additive,but this is due to the presence of the surface and we show that the additivityis recovered in the thermodynamic limit. Finally, we find that, whencalculations follow the canonical ensemble, results differ little for smallsystems (NA = 27) and are inexistentfor larger systems (NA = 1000).