  The validity of the linear elasticity theory is examined at the nanometer
scale by investigating the vibrational properties of silver and gold
nanoparticles whose diameters range from about 1.5 to 4 nm. Comparing the
vibration modes calculated by elasticity theory and atomistic simulation based
on the Embedded Atom Method, we first show that the anisotropy of the stiffness
tensor in elastic calculation is essential to ensure a good agreement between
elastic and atomistic models. Second, we illustrate the reduction of the number
of vibration modes due to the diminution of the number of atoms when reducing
the nanoparticles size. Finally, we exhibit a breakdown of the
frequency-spectra scaling of the vibration modes and attribute it to surface
effects. Some critical sizes under which such effects are expected, depending
on the material and the considered vibration modes are given.
