Particles of nanometric size show low-frequency vibrational modes that can be observed by Raman spectroscopy. These modes involve the collective motion of large numbers of atoms and it is possible to calculate their frequency using elasticity theory. In this work a simple model for oblate-shaped nanoparticles is developed and compared with experimental results obtained in bismuth nanoparticles. It is found that the agreement between theory and experiment is improved in comparison to the spherical model usually employed. However for the smallest particles the elastic model is no longer valid and lattice discreteness has to be considered.
Hernández-Rosas, J., Picquart, M., Haro-Poniatowski, E., Kanehisa, M., Jouanne, M., & Morhange, J. F. (2003). Elastic vibrations of spheroidal nanometric particles. Journal of Physics Condensed Matter, 7481-7487. https://doi.org/10.1088/0953-8984/15/44/004