Surface energy, surface debye temperature and specific heat of nanocrystals

Abstract

The present study provides insight into the role of surface free energy and surface Debye temperatures in the specific heat of nanocrystals. In the case of small phases, consisted of comparable number of bulk and surface atoms, the variation of heat capacity with respect to that of infinitely large phase is significant. This effect, not accounted for in the Debye model is due to the substantial impact of interface energy of clusters. Here, in the framework of classical Gibbs thermodynamics, we introduce surface heat capacity that accounts for surface free energy contribution. Defined as a difference, between surface and bulk terms, the excess heat capacity reveals temperature gap and size limits of nanoclusters where the contribution of surface energy is essential. Considering the role of surface Debye temperatures, we evaluate the deviation of specific heat for nanoclusters having different surface atomic density and surface orientation. Being in agreement with recent experimental findings, the present model opens up a way to predict basic, size-dependent thermodynamic properties of nanocomposite systems.