Zhu, Y.F., Lian, J.S. and Jiang, Q. (2009) Modeling of the Melting Point, Debye Temperature, Thermal Expansion Coefficient, and the Specific Heat of Nanostructured Materials. The Journal of Physical Chemistry C, 113, 16896-16900.
https://doi.org/10.1021/jp902097f

has been cited by the following article:

• TITLE: How Good Is the Debye Model for Nanocrystals?

  AUTHORS: Enrique N. Miranda, Geraudys Mora-Barzaga

  KEYWORDS: Nanocrystals, Few-Particle Systems, Debye Model, Lattice Vibrations

  JOURNAL NAME: Journal of Modern Physics, Vol.10 No.6, May 9, 2019

  ABSTRACT: The question here is whether the Debye model is suited to evaluate the specific heat of nanocrystals. For this, the simplest possible nanocrystal is considered: a basic cubic structure made of atoms that interact through a harmonic potential. This simple model can be solved exactly. This allows the dispersion relation of the mechanical waves to be determined, so that calculating the exact specific heat turns out to be quite straightforward. Then, the same problem is solved using the Debye approximation. Our findings show that the specific heat of a nanocrystal evaluated exactly is higher than the value found in the thermodynamic limit, that is to say, the specific heat decreases as the nanocrystal size increases. In addition, it becomes clear that the Debye model is a poor approximation for calculating the specific heat of a nanocrystal. Naturally, the Einstein model yields an even worse result. The cause of the discrepancy is found in the role of the nanocrystal surface.