Effect on the Phonon Density of States

     Another effect of size reduction can be seen in the lattice dynamics of nanometric particles. When the surface-to-volume ratio reaches a certain value,  the phonon spectrum broadens [9, 10]. Phonons are quasi-particles representing the vibrational modes of atoms in the lattice. On the low frequency side, the broadening is due to the contribution of surface atoms which have softer modes. The broadening toward higher frequencies is due to the lattice contraction which corresponds to increased rigidity in the system, itself the consequence of increased interatomic forces. These changes in the distribution of the phonon spectrum also affect the thermodynamic properties of the system.

    Note in particular that there is an increase in the vibrational entropy and that the specific heat deviates from a T³ dependence at low temperatures. The increase in the surface-to-volume ratio when the size decreases also has a significant effect on the melting temperature of nano-objects. This point will be dealt with in the chapter on phase transitions.

References

9. A. Kara, T.S. Rahman: Phys. Rev. Lett.81, 1453 (1998)
10. R. Meyer, S. Prakash, P. Entel: Phase Transitions,75, 51 (2002)