Specific heat of nanocrystals

The present study extends the Einstein model for heat capacity of solids to nanoclusters. In the case of small phases the contribution of surface energy to overall thermodynamic properties of the system is essential. On that physical background, the heat capacity depends on the size of cluster through its interface energy. Employing the same relation between Einstein temperature and the cluster melting point as that for the infinitely large phase, we derive a simple expression for the heat capacity, CV (n), dependence on the number of atoms in the cluster, n. We explain the experimentally observed increase of CV (n) compared to CV (∞) of an infinitely large homogeneous phase, with lowering of the Einstein temperature due to the contribution of the cluster interface energy. The heat capacity in the model presented scales at high T with the classical Dulong and Petit 3R limit and tends to zero for T → 0 as required by the third law of thermodynamics. The model reported could be applied to various systems with nanoparticles, where the knowledge of specific heat is important; for example formation of nanocomposite materials, the initial stages of formation of fogs, smog and clouds, etc. (Some figures in this article are in colour only in the electronic version)